a crash-course on cooperative wireless networks

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A Crash-Course onCooperative Wireless Networks

Mischa Dohler

Senior Research Expert

CTTC, Barcelona, Spain

[email protected]

One-Day Short-Course, Melbourne, Australia 1

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– UMTS & WiMAX Capacity & Coverage Extension –

The Opportunity Driven Multiple Access (ODMA) protocol [1] in 3GPP (discontinued with R’99) as

well as the WiMAX standard facilitate relaying to enhance capacity and coverage. An extension to a

distributed deployment will be shown to further boost capacity.

Figure 1: Traditional and distributed relaying in UMTS and WiMAX.

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– WLAN Capacity & Coverage Extension –

Wireless Local Area Networks (WLANs) have sporadic hot-spot coverage in offices, cafes, train

stations, etc [2]. Traditional and distributed relaying increases capacity at WLAN cell edges and

closes coverage holes in sufficiently dense deployment areas (e.g. Orange’s UNIK service).

Figure 2: Coverage extension of high-capacity indoor WLAN towards outdoor users.

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– Sensor Networks –

Large scale sensor networks are only recently emerging with a vast gamut of applications [3].

Traditional and distributed relaying increases link reliability and - under some conditions - saves

energy and hence increases the network’s lifetime.

fire-detecting sensor

Figure 3: Distributed relaying sensor network for fire detection in forests.

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– Unmanned Aerial Vehicles –

Hybrid solutions are also foreseen, such as UAVs and sensor networks. In [4], it has been shown

that cooperative UAVs considerably increase the reliability of the transmission of sensor readings.

Transmit Sensor Cluster Receive Sensor Cluster

60 km

UAV Relay Cluster

10

00

m

Figure 4: Distributed and cooperative UAVs acting as relays, which can utilise beamforming, STCs,

multiplexing, etc., to relay sensor readings.

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– Design Dilemma –

• Above example systems have infinite design degrees of freedom, having triggered

endless white papers, conference and journal publications.

• Indeed, Google search results on ’cooperative wireless communications’ yielded:

– 1999: a handful (beginning of my personal research on this subject);

– 2008: almost one million in May 2008!

• All of these documents contain some related information; but, even if only 10% of them

are really useful to us, we would have to read and analyse 100,000 links. If we took 10

minutes for each, we would be occupied for 2 full years!

• Hence, my questions at the beginning of this tutorial:

– Is it really useful to start working in an area which seems to be so well explored?

And if so, what are the areas which still need to be explored?

– Will these systems yield decades of research but barely any commercial products?

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– Tutorial Emphasis –

• Due to the large amount of fundamental and advanced material, I had to cut down on

many important contributions and focused on novel material from 2005 − 2008.

• Also, you all have a very diverse background, making a coherent exposure difficult.

• The aim of this tutorial is thus to give you:

– a sufficient overview of the concept,

– some “feeling” for certain approaches,

– some detailed knowledge on some analysis,

– and some tools which allow extending the analysis.

• Ideally, this tutorial should inspire you and stipulate you to apply your knowledge and

enthusiasm to wireless distributed, cooperative relaying systems.

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– Tutorial Outline –

1. Preliminaries

2. Capacity Bounds

3. Hardware Realisation

4. Channel Characterisation

5. Transparent PHY Algorithms

6. Regenerative PHY Algorithms

7. MAC and Cross-Layer Design

8. System Considerations

9. The Road Ahead

10. References

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PART 1PRELIMINARIES

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– Preliminary Note –

• Due to your differing background and also due to the large degrees of freedom of

cooperative networks, a common understanding of the subject matter is pivotal.

• Such a common understanding is complicated by the fact that the same or similar

concepts are given entirely different names; or, entirely different concepts, the same

name.

• With the aim to harmonise at least some of the concepts, we will hence precede the

tutorial with some important preliminaries, i.e.:

1. useful definitions;

2. key milestones; and

3. design challenges.

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1.1 Useful Definitions

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– Structure of Definitions –

• We will give some useful definitions as per below structure:

System

Link

Node

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– System: Infrastructure –

• Infrastructure (physical or logical):

– infrastructure-based (ie available prior to deployment, eg cellular networks or WLAN),

– infrastructure-less (ie emerges after deployment or unavailable, eg ad hoc networks).

• Management of infrastructure:

– centralised (eg cellular network),

– decentralised (eg WLAN mesh network).

• Note that:

– you may have a decentralised infrastructure-based system (e.g. decentralised RRM)

– you may have a centralised infrastructure-less system (e.g. clustering)

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– System: Canonical Links –

• Four canonical information links between nodes are possible:

– point-to-point (traditional)

–

–

–

P2P P2MP MP2P MP2MP

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cttc

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– System: Information Flow [1/5] –

• From these canonical links, we can build different flows through network:

– direct link

– serial relaying

–

–

– and composites thereof

• We differentiate further between flows:

– with/without interference between flows

– with/without direct link between nodes which use relays

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• Serial Relaying:

Source

Relay#1

Destination

Relay#K

possible direct link

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• Relaying:

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• Relaying:

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• Composites Thereof:

Source

Relay#2,1

Destinationpossible direct link

Space-

Time TRx

Relay#1 Relay#2,N2

Relay#(K-1),1

Relay#(K-1),NK-1

Space-

Time TRx

Relay#K,1

Relay#K,NK

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– System: Synch versus Asynch –

• The following synchronisms can occur at PHY layer:

– Synchronous Networks, i.e. all communications can be synchronised to the precision

of carrier and phase; facilitating e.g. distributed beamforming, space-time coding, etc.

– Asynchronous Networks, i.e. communication is not synchronised which requires

attention because synchronous designs break down.

• The following synchronisms can occur at MAC layer:

– Slotted Networks, i.e. access is allowed at predefined moments and phases only;

facilitating e.g. slotted ALOHA, etc.

– Unslotted Networks, i.e. access is allowed at any moment which usually deteriorates

throughput and delay.

• Note that achieving and maintaining synchronised networks is very complex if not in

most cases prohibitive.

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– Node: Node Behaviour –

• The nodes in the network can have the following behaviour:

– egoistic (no help)

– supportive (unidirectional help)

– cooperative (mutual help)

egoistic supportive cooperative

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– Node: Relaying Methods –

• Relaying: neither information nor waveform are modified, allowing for

simple power scaling and/or phase rotations; examples are:

– Amplify and Forward (AF), i.e. amplification of analogue signal;

– Linearly-Process and Forward (LF), i.e.

– Nonlinearly-Process and Forward (nLF), i.e. relay nonlinear soft information.

• Relaying: information (bits) or waveform (samples) are modified,

requiring more complex baseband operations; examples are:

– Estimate and Forward (EF), i.e. detect and forward estimated signal;

– Compress and Forward (CF), i.e.

– Decode and Forward (DF), i.e.

– Purge and Forward (PF), i.e. eliminate interference at relay;

– Aggregate/Gather and Forward (GF), i.e. perform source coding and compression.

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– Node: Relaying Access Protocols –

• Transmission and reception in relays leads to interference/competition, which needs to

be resolved by suitable access protocols.

• The following access protocols can be used:

– Time Division Relay Access (TDRA), i.e. reception and transmission happen in

different time moments/slots;

– Frequency Division Relay Access (FDRA), i.e. reception and transmission happen in

different frequency bands;

• Note that this is not to handle multiple access problems between relays, to which

CDMA, etc., are well applicable.

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– Link: Capacity over Gaussian Channel –

• Shannon proved that one can design codes facilitating a communication rate R

bits/symbol with arbitrarily small error.

• He also showed that these codes must be infinite (very long), so as to average out the

effect of noise.

• His theory was not concerned with code construction or code complexity, nor with

decoding delay.

• The maximum data rate at which reliable communication is possible is referred to as

capacity C of the channel and is independent of the signal processing used at either

end of the channel.

• The capacity (per dimension) of a AWGN channel with signal power constraint S and

noise power N is:

C =

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– Link: Ergodic Channel –

• A stochastic process is ergodic if the time averages may be used to replace ensemble

averages; or, no sample helps meaningfully to predict values that are very far away in

time from that sample (i.e. the stochastic process is not sensitive to initial conditions).

• An ergodic channel can support a maximum error-free transmission rate with 100%

reliability, which is referred to as capacity. Generally, the concept of average is

applicable, e.g. the capacity for a SISO channel is C = Eλ

{log2

(1 + λ S

N

)}.

λ

Codeword #n

Time t

Instantaneous

Channel Power

[dB]

codeword length T ∞→Codeword #n

Time t

Codeword #m

codeword length T ∞→

Figure 5: Fading behaviour of an ergodic channel.

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– Link: Non-Ergodic Channel –

• A stochastic process is non-ergodic if it is not ergodic; or, any sample helps

meaningfully to predict values that are very far away in time from that sample (i.e. the

stochastic process is sensitive to initial conditions).

• A non-ergodic channel cannot support a maximum error-free transmission rate with

100% reliability; however, it can support any given rate R with a certain probability

Pout(R) which is referred to as rate outage probability. Generally, the concept of

outage is applicable.

λ

Codeword #n

Time t

Instantaneous

Channel Power

[dB]

codeword length T ∞→Codeword #n

Time t

Codeword #m

codeword length T ∞→

Figure 6: Fading behaviour of a non-ergodic channel.26

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– Link: Diversity/Multiplexing Trade-Off [1/3] –

• Multiplexing Capability:

– achievable rate R is proportional to log SNR;

– proportionality factor is multiplexing gain r, i.e. r = R/ log SNR.

• Diversity Gain:

– error or outage probability Pe/out(R) is proportional to SNR−d;

– exponent d is called the diversity gain.

• Diversity d - Multiplexing r Trade-Off [5]:

– d and r are related by: d = − limSNR→∞ . . .

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• Example PAM modulation over Rayleigh Channel:

– constellation minimum distance Dmin ≈ √SNR/2R;

– error probability at high SNR isa Pe(R) ≈ 12

(1 −

√D2

min

4+D2min

)≈ . . .

– from which the diversity-multiplexing tradeoff follows as dPAM = . . .

• Example QAM modulation over Rayleigh Channel:

– constellation minimum distance Dmin ≈ √SNR/2R/2;

– error probability at high SNR is the same as above;

– from which the diversity-multiplexing tradeoff follows as dQAM = . . .

aNote that 1√1+x

≈ 1 − 12x

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Spatial Multiplexing Gain r

Div

ersi

ty G

ain

d

PAM ModulationQAM Modulation

Figure 7: Diversity gain shows how fast outage / error exponent decreases with SNR; multiplexing

gain shows how fast the rate can be increased with SNR.

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– Link: Diversity/Coding/Rate Gains –

0 1 2 3 4 5 6 7 8 9 10

10−2

10−1

100

Signal−to−Noise Ratio SNR [dB]

Asy

mp

toti

c O

uta

ge

Pro

bab

ility

/ E

rro

r R

ate

Diversity Gain = 1, Rate = 1Diversity Gain = 2, Rate = 1Diversity Gain = 2, Rate = 2Diversity Gain = 2, Coding Gain = 2

increase in diversity order

increase in rate

increase in coding strength

Figure 8: Diversity (inclination), rate (right-shift) and coding (left-shift) gains can be inferred for outage

or error rates from above figure.

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1.2 Key Milestones

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– First Key Milestones –

• Early innovative contributions on supportive relaying as well as MIMO inspired the

concept of cooperative relaying and distributed MIMO.

• Surprisingly, relaying systems had already been studied for almost four decades! Early

key milestones are summarised on subsequent slides.

Supportive

Relaying

Cooperative

Relaying

1968

Meulen

1979

Cover & Gamal

2000

Dohler2002

Laneman,

Hunter

2003

Gupta,

Stefanov

2000

Laneman

1998

Sendonaris

et al

Distributed

MIMO

1996

3GPP ODMA

1998

Nix et al

MIMO1996

Foshini, Telatar

1998

Alamouti, Tarokh

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– My Pre-PhD Presentation Winter 1999/2000 –

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– Relaying Systems [1/4] –

• The method of relaying has been introduced in 1971 by van der Meulen in [6] and has also

been studied by Sato [7]. A first rigorous information theoretical analysis of the relay channel,

however, has been exposed by Cover and Gamal in [8], a more detailed description to which

can be found in his book [9].

• In these contributions, a source MT communicates with a target MT directly and via a relaying

MT. In [8] the maximum achievable communication rate has been derived in dependency of

various communication scenarios, which include the cases with and without feedback to either

source MT or relaying MT, or both. The capacity of such a relaying configuration was shown to

exceed the capacity of a simple direct link.

• It should be noted that the analysis was performed for Gaussian communication channels only;

therefore, neither the wireless fading channel has been considered, nor have the power gains

due to shorter relaying communication distances been explicitly incorporated into the analysis.

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• Only in the middle of the 90s, research in and around the Concept Group Epsilon revived the

idea of utilising relaying to boost the capacity of wireless networks, thereby leading to the

concept of ODMA [1]. The power gains due to the shorter relaying links have been the main

incentive to investigate such systems to reach MTs out of BS coverage. The emphasis of the

study was its applicability to cellular systems, as well as a suitable protocol design; no

theoretical investigations into capacity bounds, etc., have been performed.

• Interesting milestones into the above-mentioned theoretical studies have been the contributions

by Sendonaris, Erkip and Aazhang, which date back to 1998 [10]. In their study, a very simple

but effective user cooperation protocol has been suggested to boost the uplink capacity and

lower the uplink outage probability for a given rate. The designed protocol stipulates a MT to

broadcast its data frame to the BS and to a spatially adjacent MT, which then re-transmits the

frame to the BS. Such a protocol certainly yields a higher degree of diversity because the

channels from both MTs to the BS can be considered uncorrelated.

• The simple cooperative protocol has been extended by the same authors to

more sophisticated schemes, which can be found in the excellent contributions [11] and [12].

Note that in its original formulation [10], no distributed space-time coding has been considered.

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• The contributions by Laneman in 2000 [13] are a conceptual and mathematical extension to [10],

where energy-efficient multiple access protocols are suggested based on decode-and-forward

and amplify-and-forward relaying technologies. It has been shown that significant diversity and

outage gains are achieved by deploying the relaying protocols when compared to the direct link.

Note again, that no distributed space-time coding has been considered.

• The case of distributed space-time coding has been analysed by Laneman in his PhD

dissertation [14]. In his thesis, information theoretical results for distributed SISO channels with

possible feedback have been utilised to design simple communication protocols taking into

account systems with and without temporal diversity, as well as various forms of cooperation. He

has demonstrated that cooperation yields full spatial diversity, which allows drastic transmit

power savings at the same level of outage probability for a given communication rate.

• A vital asset of his thesis is also a discussion on the applicability of the suggested protocols to

cellular and ad-hoc networks. However, [14] does not incorporate an analysis of distributed

cooperative MIMO multi-stage communication systems.

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• Gupta and Kumar were the first to statistically analyse the information theoretically offered

throughput for large scale relaying networks [15]. They showed that under somewhat ideal

situations of no interference, hop-by-hop transmission and pre-defined terminal locations,

capacity per MT decreases by 1/√

M with an increasing number of MTs M in a fixed

geographic area. They also showed that if the terminal and traffic distributions are random, then

the capacity per terminal decreases even in the order of 1/√

M log M .

• The analysis in [15] has been extended by the same authors to more general communication

topologies, where the interested reader is referred to the landmark paper [16].

• Furthermore, Grossglauser and Tse have shown that mobility counteracts the decrease in

throughput for an increasing number of users in a fixed area [17]. The protocols suggested

therein benefit from the decreased power for a hop-per-hop transmission for decreasing

transmission distances. It also benefits from the location variability due to mobility, i.e. a packet

is picked up from the source MT by any passing by r-MT and only re-transmitted (and hence

delivered) when passing by the target MT.

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– MIMO Systems –

• Contributions on MIMO systems have flourished ever since the publication of the landmark

papers by Telatar [18] and Foschini & Gans [19] on capacity and Foschini [20], Alamouti [21]

and Tarokh [22, 23] on the construction of suitable space-time transceivers.

• The BLAST system introduced by Foschini in 1996 [20], a transmitter spatially multiplexes signal

streams onto different transmit antennas which are then iteratively extracted at the receiving side

using the fact that the fades from any transmit to any receive antenna are uncorrelated and of

different strength. The BLAST concept has ever since been extended to more sophisticated

systems, a good summary of which can be found in [24].

• Alamouti introduced a very appealing transmit diversity scheme by orthogonally encoding two

complex signal streams from two transmit antennas, thereby achieving a rate one space-time

block code [21].

• His work was then mathematically enhanced by the landmark paper of Tarokh [23], who

essentially exposed various important properties of space-time block codes. In [22], he also

showed how to construct suitable space-time trellis codes which were shown to yield diversity

and coding gain.

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– Distributed MIMO Systems [1/2] –

• A system utilising the advantages of both MIMO and relaying has been suggested by M. Dohler

in the winter 1999/2000 and has hence become one of the main research topics within the

Mobile Virtual Centre of Excellence (M-VCE).

• Numerous studies [25] have led to a set of patents [26], which are backed by about 20 industrial

members, such as Vodafone, Nokia, Philips, Nortel Networks, Samsung, etc.

• The studies encompassed the following (in timely order):

– downlink distributed receive diversity in cellular systems

– downlink distributed MIMO in cellular systems

– uplink distributed MIMO in cellular systems

– introduction of distributed relaying to cellular systems

– extension of the above to WLAN and hot-spot systems

– generalisation to arbitrary distributed relaying topologies

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– Distributed MIMO Systems [2/2] –

• A landmark contribution on relaying systems deploying multiple antennas at transmitting and

receiving side has been made by Gupta and Kumar [16]. The network topology exposed therein

is the most generic flat topology, i.e. any MT may communicate with any other MT.

• In [16], an information theoretic scheme for obtaining an achievable communication rate region

in a network of arbitrary size and topology has been derived. The analysis showed that

sophisticated multi-user coding schemes are required to provide the derived capacity gains.

Exposed theory is fairly intricate making the design of realistic protocols a difficult task.

• Specific distributed space-time coding schemes have also been suggested recently, e.g. by A.

Stefanov and E. Erkip [27]. In this publication, two spatially adjacent MTs cooperate to achieve

a lower frame error rate to one or more destination(s), where a quasi-static fading channel has

been assumed. Distributed space-time trellis codes have been designed which maximise the

performance for the direct link from either of the MTs to the destination and the relaying link.

• In [28], A. Ozgur et al. have shown for the first time that linear transport capacity scaling is

possible in a large network by means of cooperative hierarchies and distributed MIMO.

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1.3 Design Challenges

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– System Design –

The design of any system is a very complex interplay between business and technology.

Business CaseServices, CAPEX, OPEX, etc.

RequirmentsScenario, Channel Model, Tx Powers, etc.

Performance AnalysisCapacity, Link & System Level, Formal Verfication, etc.

Algorithmic DesignPHY, MAC, NTW, Applications, etc.

Hardware Designµ-Controller, Memory, Amplifiers, etc.

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– Example Challenges for Business Case –

Services

• identification of commercially viable services using relaying topology

• seamless integration into existing services

• facilitation of simple billing mechanisms and incentive schemes

CAPEX & OPEX

• correct estimation of short- and mid-term CAPEX

• correct estimation of mid- and long-term OPEX

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– Example Challenges for Requirements –

Channel Modelling

• measurements of channel in distributed scenarios (low Tx & Rx)

• deterministic modelling using e.g. ray tracing tools (specific environments)

• stochastic-empirical modelling, reflecting

– temporal, spectral and spatial dependency of

– pathloss (pathloss coefficient, breakpoint behaviour, etc)

– shadowing (statistics, variance)

– fading (Doppler, PDP; statistics, variance)

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– Example Challenges for Performance Analysis –

Link Capacity

• closed form Shannon capacity expressions for systems with the following properties:

– cooperative, multi-user, MIMO

– broadcast, multiple access or general relaying channel

– Rayleigh fading channel

• extension of the above to generalised fading (statistics, correlation, temporal behaviour)

• extension of the above to the case of imperfect channel state information

• max mutual information for other constraints (non-Gaussian codebooks, delay limits)

• synthesis of topology from the above insights and design guidelines

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– Example Challenges for Hardware Design –

Radio Front-End

• distributed synchronisation for cooperative communication

• saturation of amplifiers (near-far effect during cooperation)

• filter to minimise power spill-over during relaying

• low noise transparent relaying mechanisms

• efficiency and power consumption

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– Example Challenges for Algorithmic Design [1/2] –

Physical Layer

• choice of relaying, ie transperant/regenerative/hybrid [very well explored]

• degree of cooperation, ie number and choice of nodes [well explored]

• determination of suitable performance metrics (total power, complexity, etc.)

• tangible cross-layer design (coding, modulation, power control, etc.)

• codes which are robust to synchronisation, channel estimation errors, etc.

• codes which can easily trade diversity gains, coding gains, throughput and complexity

• novel interference cancellation techniques (use of temporal characteristics)

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– Example Challenges for Algorithmic Design [2/2] –

MAC Layer

• determination of suitable performance metrics (protocol overhead, etc.)

• unifying framework for distributed MACs

• tangible cross-layer design (ACM, power control, persistency factor, packet length,

routing)

• optimum access strategies (CSMA/reservation/hybrids)

• interference mitigation and avoidance protocols

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Open Issues

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– Open Issues –

There is one important thing which really deserves some attention:

• A complete and consistent set of

– terms,

– notation,

– concepts, and

– protocols,

used in the context of cooperative systems.

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PART 2CAPACITY BOUNDS

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– A Little Glimpse [16] –

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• Obtaining the capacity of a wireless system is vital in understanding the achievable

rates and their reliability.

• There are more than 100 highly complex contributions available today, which requires us

to concentrate on a very few of them.

• For this reason, we will concentrate on the following topics:

1. achievable rate region in the case of cooperation;

2. rate outage probabilities in the case of cooperation;

3. rate & outage for distributed space-time (block) coding;

4. throughput for multi-hop distributed space-time block coding;

5. capacity scaling in hierarchical MIMO cooperation structure.

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2.1 Achievable Rate Region

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– System Model –

Following [11], we would like to know what is the maximum achievable network rate for

below simple system assuming ergodic channels. From this, more general topologies can

be analysed as well as the rate outage probability obtained.

s-MT#1

s-MT#2

t-MT#0

Encoder s-MT#1

Encoder

s-MT#2

W1

Y1

Y2

W2

X1

K10

K20

K12

K21

X2

Z2

Z1

Z0 Y0

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– Mathematical Formulation –The mathematical formulation of the cooperative communication model is [11]:

Y0 = (1)

Y1 = K21 · X2 + Z1 (2)

Y2 = (3)

where

• Y0, Y1, Y2 are the received signal at the target mobile terminal (t-MT), first source MT

(s-MT#1) and second source MT (s-MT#2), respectively;

• X(1,2) is the signal transmitted by s-MT (1,2);

• Kij are the respective Rayleigh fading coefficients with variance ξ2ij and are assumed

to be frequency-flat and ergodic;

• Z0, Z1, Z2 are the respective AWGN components with total spectral density N0.

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– Transmitters & Receivers [1/2] –

• Three cases concerning channel knowledge at the Tx are considered in [11]:

– user i knows nothing about Ki0,

– user i knows knows only the phase of Ki0,

– user i knows knows amplitude and phase of Ki0.

• The user’s transmitters use the classical superposition coding (super-imposed

codebooks of large block length).

• The receivers utilise suitable decoders, such as:

– successive decoder,

– sliding-window decoder,

– backward decoder.

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– Transmitters & Receivers [2/2] –

• Without violating causality, s-MT#1 structures its information W1 such that:

– information W10 is sent at rate R10 directly to BS with fractional power P10,

– information W12 to be sent at rate R12 to the BS via #2 with fractional power P12,

– cooperative information U1 is sent directly to BS with fractional power PU1.

• The encoder then constructs signal X1 = X10 + X12 + U1 to be sent with power

P1 = P10 + P12 + PU1.

• s-MT#2 proceeds similarly as s-MT#1.

• It is imperative that power and rate allocations are such that all codebooks can be

perfectly decoded.

• For a given power constraint, it is hence the aim to determine the maximum feasible rate

in such a network.

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– Achievable Rates [1/4] –

Theorem [11]: An achievable rate region for the system given in (1)−(3) is the closure of the convex

hull of all rate pairs (R1, R2) such that R1 = R10 + R12 and R2 = R20 + R21, with

R12 < (4)

R21 < (5)

R10 < (6)

R20 < E

{C

(K2

20P20

N0

)}(7)

R10 + R20 < E

{C

(K2

10P10 + K220P20

N0

)}(8)

R10 + R20 + R12 + R21 < E

{C

(K2

10P10 + K220P20 + 2K10K20

√PU1PU2

N0

)}(9)

where C(x) = 12 log2(1 + x) is the capacity of an AWGN channel and E{·} denotes the

expectation with respect to the fading realisations Kij .

59

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Rate R2

Rat

e R

1

no cooperation

cooperation

ideal

Figure 9: Symmetric rate region for no cooperation, ideal cooperation with error-free inter-user

channel, and realistic cooperation with good inter-user channel (E{K12} = .95); N0 = 1,

P1 = P2 = 2, E{K10} = E{K20} = .63 [11].

60

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�


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Rate R2

Rat

e R

1 ideal cooperation

cooperation

no cooperation

Figure 10: Asymmetric rate region for no cooperation, ideal cooperation with error-free inter-user

channel, and realistic cooperation with medium inter-user channel (E{K12} = .71); N0 = 1,

P1 = P2 = 2, E{K10} = .95 and E{K20} = .30 [11].

61

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• Ideal cooperation is for a noiseless inter-user channel and serves as an upper bound of

cooperation. No cooperation (ignoring Y1 and Y2) yields the typical multiple access

channel. In the cooperative case, as the inter-user channel degrades, performance

approaches that of no cooperation.

• Points of interest are the

– equal rate point (R1 = R2),

– maximum rate sum point (max(R1 + R2)),

– degraded relay rate points (R1 = 0, R2 �= 0 and R1 �= 0, R2 = 0).

• [11] showed that in the design region of interest “increase in sum capacity ≈ increase in

coverage area”.

• [11] also demonstrated that repetition-based coding using CDMA spreading sequences

performs well within the rate regions.

62

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2.2 Rate Outage Probabilities

63

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– System Model [1/2] –

The characteristics of below coded cooperative scheme are [94, 95]:

• each user tries to transmit (punctured) incremental redundancy to its partner;

• overall code might be block or convolutional code or hybrid;

• no feedback is required, because decisions are based on CRC.

s-MT#1

s-MT#2

t-MT#0

own bitsCRC

Decoder

RCPC

N1 user 1 bits N2 user 2 bits

N1 user 2 bits N2 user 1 bits

Frame 1 Frame 2

Frame 1 Frame 2

punctured N1 bitsto Tx

partner'sbits

RCPC

N2 bits

N2 bits

no

yes

CRC

check

64

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�

– System Model [2/2] –The system operates as follows:

• Rate R code of each user has length N1 + N2; we define α = N1/(N1 + N2).

• N1 valid punctured code bits are transmitted to t-MT & partner.

• If partner decodes N1 successfully (CRC check), then remaining N2 parity bits are sent

by partner to t-MT; otherwise the partner’s own N2 parity bits are sent.

• 4 cases are possible, which the t-MT is either informed of or decides blindly (CRC):

#1

#2

#2's parity

#1's parity

x x

#1's parity

#2's parity

x

#1's parity

#1's parity

x

#2's parity

#2's parity

65

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– Outage Probability [1/4] –

• For an instantaneous SNR γ, the ’capacity’ of the link is given as C(γ) = log2(1 + γ)bits/s/Hz.

• The channel is in outage, if the ’capacity’ falls below a threshold R; the corresponding

outage event is C(γ) < R or γ < . . ..

• The outage probability is hence

Pout = Pr(γ < . . .) =∫ ...

...pγ(γ)d γ, (10)

where pγ(γ) denotes the pdf of the SNR.

• For a Rayleigh fading process with mean power Γ, γ is negative-exponentially

distributed as 1Γe−γ/Γ and the outage probability is hence

Pout = . . . (11)

66

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– Outage Probability [2/4] –Case 1 (Θ = 1) :

• Both partners decode correctly, which for the inter-user channel means that the capacity

offered by the channel is greater than the rate, i.e.

C12(γ12) = α log2(1 + γ12) > R

C21(γ21) = α log2(1 + γ21) > R

• The outage event for both users given the cooperative information can be written as

C10(γ10, γ20|Θ = 1) = α log2(1 + γ10) + . . . R

C20(γ10, γ20|Θ = 1) = + . . . R

Cases 2,3 & 4 (Θ = 2,3,4) :

• These cases are obtained in a similar fashion as above.67

�

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• We can calculate the outage probability for the first user and the first outage case as:

Pout,1(Θ = 1) = Pr(link12 is not in outage) AND

Pr(link21 is not in outage) AND

Pr(link10 is in outage) AND

Pr(link20 is in outage)

= . . .

68

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• Combining the 4 possible cases, the total outage probability for user 1 can hence be

calculated as [95]

Pout,1 = Pr(γ12 > 2R/α − 1) · Pr(γ21 > 2R/α − 1)

·Pr((1 + γ10)α(1 + γ20)1−α < 2R) +

Pr(γ12 < 2R/α − 1) · Pr(γ21 < 2R/α − 1)

·Pr(γ10 < 2R − 1) +

Pr(γ12 > 2R/α − 1) · Pr(γ21 < 2R/α − 1)

·Pr((1 + γ10)α(1 + γ10 + γ20)1−α < 2R) +

Pr(γ12 < 2R/α − 1) · Pr(γ21 > 2R/α − 1)

·Pr(γ10 < 2R − 1).

• Closed form expressions for the Rayleigh fading case can be found in [95].

69

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−10 −5 0 5 10 15 20 25 3010

−4

10−3

10−2

10−1

100

Mean (Uplink) SNR Γ [dB]

Out

age

Pro

babi

lity

C<

R no cooperation

coded cooperation

Figure 11: Outage versus mean uplink SNR, where inter-user channel is 10dB weaker; α = 0.7,

R = 0.5bits/s/Hz.

70

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2.3 Distributed ST(B)C

71

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• Transmitter:

– number of distributed transmit antennas: t

– transmitted space-time codeword: x ∈ Ct×1

– transmit power constraint: tr(E{xxH

}) ≤ S

• Channel:

– channel from transmitter i ∈ (1, t) to receiver j ∈ (1, r): hi,j

– fading realisations of hi,j : frequency-flat & uncorrelated

– grouping of sub-channel gains hi,j : H

• Receiver:

– received signal: y = Hx + n

– r−dimensional noise vector n has variance N per entry

• Cooperative Link:

– assumed to be error-free (!)

72

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– Exact MIMO Capacity [1/5] –

H =

⎛⎜⎜⎜⎜⎜⎝

h11 h12 · · · h1,t

h21 h22 · · · h2,t

......

. . ....

hr,1 hr,2 · · · hr,t

⎞⎟⎟⎟⎟⎟⎠

We assume first that each sub-channel realisation

hi,j is Rayleigh distributed with unit power, i.e.

E{|hi,j |2

}= 1, which will be relaxed later on.

InformationSource

Space-TimeEncoder

Space-TimeDecoder

InformationSink

s s

t

Transmit

Antennas

r

Receive

Antennas

h11

hr,t

H

MIMO

Channel

Figure 12: Multiple-Input-Multiple-Output (MIMO) transceiver model.

73

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– Exact MIMO Capacity [2/5] –Telatar proved in his landmark theorem that the MIMO capacity can be expressed as [18]

C =∫ ∞

0

log2

(1 +

λ

t

S

N

)·

m−1∑k=0

k!(k + n − m)!

[Ln−m

k (λ)]2

λn−me−λdλ (12)

where m � min{t, r}, n � max{t, r}. Furthermore, Ln−mk (λ) is the associated Laguerre

polynomial of order k and λ is an unordered eigenvalue of the Wishart matrix

W �

⎧⎨⎩HHH r < t

HHH r ≥ t(13)

The capacity in (12) can also be expressed as

C = Eλ

{m log2

(1 +

λ

t

S

N

)}(14)

with

pdfλ(λ) =1m

m−1∑k=0

k!(k + n − m)!

[Ln−m

k (λ)]2

λn−me−λ. (15)

74

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The intricate integral expression can be solved in explicit form as [100]

C =m−1∑k=0

k!(k + d)!

[k∑

l=0

A2l (k, d) C2l+d(a) + (16)

k∑l1=0

k∑l2=0,l2 �=l1

(−1)l1+l2Al1(k, d) Al2(k, d) Cl1+l2+d(a)

]

where d � n − m, Al(k, d) � [(k + d)!]/[(k − l)! (d + l)! l!] and

Cζ(a) =1

log(2)

ζ∑μ=0

ζ!(ζ − μ)!

[(−1)ζ−μ−1(1/a)ζ−μe1/aEi(−1/a) (17)

+ζ−μ∑k=1

(k − 1)!(−1/a)ζ−μ−k

]

Here, Ei(ζ) is the exponential integral function.

75

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Asymptotic capacity increases linearly with SNR and m = min{t, r}:

0 10 20 30 40 50 60 70 80 90 1000

50

100

150

200

250

300

SNR [dB]

Cap

acity

[bits

/s/H

z]

8 × 8

4 × 12

12 × 4

1 × 16

16 × 1

Monte−CarloExact − IterativeExact − Explicit

Figure 13: Capacity versus SNR for various configurations of t × r.

76

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To obtain an exact expression for the case of unequal channel gains, i.e. distributed MIMO with

channel matrix Hd, has evaded a closed solution until today; we will hence invoke an upper capacity

bound.

To this end, we remember that (12) was derived from

C = EH

{log2 det

(Ir +

HHH

t

S

N

)}. (18)

Invoking Jensen’s inequality, it is easy to show that

det(Ir +

HHH

t

S

N

)≥ det

(Ir +

HdHHd

t

S

N

), (19)

for ‖H‖2 = ‖Hd‖2, where ‖H‖ denotes the Frobenius norm of H.

This means that the distributed MIMO capacity with unequal sub-channel gains can be

upperbounded by the capacity of an equivalent MIMO system with equal sub-channel gains and a

total channel power equal to the distributed system.

77

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– Exact O-MIMO Capacity [1/9] –

Orthogonal space-time block codes (STBCs) is a signal processing scheme which orthogonalises

the MIMO channel, henceforth referred to as O-MIMO. For simplicity, we will refer to the maximum

mutual information achievable with such signal processing as O-MIMO Capacity.

We will consider distributed orthogonal STBCs of arbitrary rate R. Furthermore, the sub-channel

realisation hi,j obey Nakagami fading with fading parameter f . The sub-channels may have

different gains, thereby reflecting a possibly distributed deployment.

Distributed

Space-Time Block Encoder

Distributed

Space-Time Block Decoder

Channel

Encoder

FractionalSTBC

Space-Time

Block Decoder

Channel

Decoder

s

s

h11

hr,t

O-MIMO

Channel

FractionalSTBC

FractionalSTBC

Receiver

Receiver

Receiver

Information

Sink

Information

Source

H

Figure 14: Distributed Space-Time Block Code transceiver model.

78

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The capacity (maximum mutual information) for O-MIMO channels with fixed channel coefficients can

generally be expressed as [96]

C = R log2

(1 +

1R

‖H‖2

t

S

N

)(20)

‖H‖ denotes the Frobenius norm of H, the square of which is given as

‖H‖2 =t∑

i=1

r∑j=1

|hij |2 = tr(HHH

)(21)

where tr(·) denotes the trace operation. From (21), it is clear that

‖Ht×r‖ = ‖h1×t·r‖ (22)

where h � vectorized(H).

79

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– Exact O-MIMO Capacity [3/9] –To simplify subsequent notation, we define

u � t · r (23a)

λi � hih∗i (23b)

λ � ‖h‖2 =u∑

i=1

hih∗i =

u∑i=1

λi (23c)

γi � E {hih∗i } (23d)

With reference to definitions (23), the capacity over an ergodic flat Rayleigh fading O-MIMO channel

can be expressed as

C = Eλ

{R log2

(1 +

1R

λ

t

S

N

)}(24)

=∫ ∞

0

R log2

(1 +

1R

λ

t

S

N

)pdfλ(λ)dλ (25)

where the pdfλ(λ) of λ =∑

λi solely depends on the statistics of each sub-channel.

80

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– Exact O-MIMO Capacity [4/9] –From (23c) it is clear that the pdfλ(λ) can be obtained via a u-fold convolution in the respective pdfs

of λi, i.e.

pdfλ(λ) = pdfλ1(λ1) ∗ pdfλ2(λ2) ∗ . . . ∗ pdfλu(λu) (26)

where ∗ denotes the operation of convolution. Although analytically feasible, it has been proven

easier to use the moment generating function (MGF) to solve (26). The MGF φλ(s) of λ is defined

as

φλ(s) �∫ ∞

0

pdfλ(λ)esλ dλ (27)

the application of which is known to transform (26) into

φλ(s) =u∏

i=1

φλi(s) (28)

The pdf of λ is now obtained by performing the inverse transformation, obtained as

pdfλ(λ) =1

2πj

∫ σ+j∞

σ−j∞φλ(s)e−sλ ds (29)

Operations (27) and (29) are rarely performed since tabled, see e.g. [87].

81

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– Exact O-MIMO Capacity [5/9] –The MGF of the instantaneous power λi can be calculated from the respective statistics. For

instance, for Rayleigh with pdfλ(λ) = 1γ e−λ/γ , and Nakagami as

φλ(s) =

⎧⎨⎩ Rayleigh

(1 − γs)−f Nakagami(30)

which allow one to find closed form expressions for the capacity of channels with the above-given

statistics and possibly different channel gains γi, as shown below.

If all sub-channel gains are equal then γ1 = . . . = γu, henceforth simply denoted as γ. From (30)

and (28), the MGF of the instantaneously experienced power λ can then be expressed as

φλ(s) =1

(1 − γs)u (31)

the inverse of which yields the desired pdf [90]

pdfλ(λ) =1

Γ(u)λu−1

γue−λ/γ (32)

82

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With reference to (25) and some changes in variables, the capacity of the orthogonalised MIMO

channel can be expressed in closed form as

C =R

Γ(u)

∫ ∞

0

log2

(1 + λ

1R

γ

t

S

N

)λu−1 e−λ dλ (33)

=R

Γ(u)· Cu−1

(1R

γ

t

S

N

)(34)

where Cζ(a) is the Capacity Integral given in closed form in (35).

The procedure to find the O-MIMO capacity is hence always the same:

1. determine the MGF from the PDF of each link i;

2. multiply all MGFs of all u links;

3. determine the PDF from this resultant MGF;

4. calculate the capacity using this PDF.

83

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The capacity (maximum mutual information) for O-MIMO channels over Nakagami fading channels

with unequal sub-channel gains γi∈(1,u) and fading parameters fi∈(1,u) can be expressed as [97]

C = Ru∑

i=1

fi∑j=1

Ki,j

Γ(j)Cj−1

(1R

γi

jt

S

N

)(35)

Ki,j =

(− 1

Rγi

fitSN

)j−fi

(fi − j)!∂fi−j

∂sfi−j

⎡⎢⎢⎣

u∏i′=1,i′ �=i

1(1 − 1

Rγi′fi′ t

SN · s

)fi′

⎤⎥⎥⎦

s=

�

1R

γifit

SN

�−1

(36)

Cζ(a) =1

log(2)

ζ∑μ=0

ζ!(ζ − μ)!

[(−1)ζ−μ−1(1/a)ζ−μe1/aEi(−1/a) (37)

+ζ−μ∑k=1

(k − 1)!(−1/a)ζ−μ−k

]

where Γ(·) is the complete Gamma function and Ei(ζ) is the exponential integral function.

84

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Capacity saturates fast with f and it never exceeds the Gaussian channel:

2 4 6 8 10 12 14 16 18 202

2.5

3

3.5

Nakagami−f Fading Factor

Cap

acity

[bits

/s/H

z]

1 Tx2 Tx Alamouti3 Tx − 3/4−Rate4 Tx − 3/4−Rate3 Tx − 1/2−Rate4 Tx − 1/2−RateGaussian Channel

Figure 15: Capacity versus the Nakagami f fading factor; SNR=10dB, r = 1.

85

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Capacity of distributed STBC scheme exhibits a high stability:

γ1Fractional

STBC

FractionalSTBC

γ2

ChannelEncoder

InformationSource

Space-Time

Block Decoder

Channel

Decoder

InformationSink

(a) Distributed Alamouti scheme with unequal

sub-channel gains due to different pathloss &

shadowing.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.5

1

1.5

2

2.5

3

3.5

4

4.5

γ1

Cap

acity

[bits

/s/H

z]

1 Tx − SISO (γ1)

1 Tx − SISO (γ2=2−γ

1)

2 Tx − Alamouti (γ1 & γ

2=2−γ

1)

(b) Capacity versus the normalised power γ1

in the first link over a Nakagami fading channel;

SNR=10dB, f = 10 and γ2 = 2 − γ1.

Figure 16: Topology and performance of distributed Alamouti scheme.

86

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– Approximate MIMO Capacity [1/2] –To simplify analysis for the subsequent multi-stage topology, we use log2(1 + x) ≈ √

x and define

Λ(t, r) � Eλ

{m√

λ/t}

; this approximates the MIMO capacity as

C ≈√

γS

N· Λ(t, r) (38)

For the Rayleigh fading MIMO channel, we can obtain Λ(t, r) in explicit form as

Λ(t, r) =1√t

m−1∑k=0

k!(k + d)!

Γ3(d + k + 1)Γ(d + 32 )Γ(k − 1

2 )(k!)2Γ(d + 1)Γ(− 1

2 )× (39)

3F2(−k, d +32,32; d + 1,

32− k; 1)

where 3F2(·) is the generalised hypergeometric function with three parameters of type 1 and two

parameters of type 2. For the generic Nakagami fading MIMO channel, we have

Λ(t, r) =

√R

t

√S

N

u∑i=1

fi∑j=1

Ki,jΓ(j + 0.5)

Γ(j)

√γi

j(40)

87

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– Approximate MIMO Capacity [2/2] –

The error between exact and approximate capacity expressions does not exceed 10%:

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

SNR [dB]

Cap

acity

[bits

/s/H

z]

1 Tx, 1 Rx (exact)1 Tx, 1 Rx (approx)8 Tx, 2 Rx (exact)8 Tx, 2 Rx (approx)2 Tx, 8 Rx (exact)2 Tx, 8 Rx (approx)8 Tx, 8 Rx (exact)8 Tx, 8 Rx (approx)

Figure 17: Exact and approximate capacities versus SNR for various array configurations.

88

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– Approximate O-MIMO Capacities –

The same approach can be taken to calculate the approximate capacity for various O-MIMO

channels, some of which are summarised below as

Λ(t, r) =

⎧⎪⎪⎨⎪⎪⎩

√R√t

Γ(u+1/2)Γ(u) O-MIMO Rayleigh - Equal Channel Gains

√R√ft

Γ(fu+1/2)Γ(fu) O-MIMO Nakgami - Equal Channel Gains

√Rπ√t

∑ui=1 Ki

√γi O-MIMO Rayleigh - Unequal Channel Gains,

(41)

where Γ(x) is the Gamma function, R the rate of the STBC, t the number of transmit antennas, r

the number of receive antennas, f the Nakagami fading parameter, u = t · r, and the constants K i

are obtained as [100]

Ki =u∏

i′=1,i′ �=i

γi

γi − γi′. (42)

89

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2.4 Multi-Stage Distributed STBC

90

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�

– Choice of (practical) Topology [1/4] –

• The theoretical findings of Cover, Kumar, Gupta, Tse, Laneman, etc. are very interesting,

however, very difficult to deploy and optimise in a practical manner. Already the multiple access,

broadcast and single-hop relaying schemes over Gaussian channels, as analysed by Cover, are

fairly intricate to optimise.

• Cover [9, chapter 14.3] has established the capacity bounds for the multiple access channel

where, using sophisticated multi-user (MU) transceivers, the achievable rates for 2 users are

R1 ≤ 12

log2

(1 +

P1

N

), R2 ≤ 1

2log2

(1 +

P2

N

), R1+R2 ≤ 1

2log2

(1 +

P1 + P2

N

)

• Using orthogonal FDMA, for example, the achievable rates for 2 users are [9]

R1 =W1

2log2

(1 +

P1

NW1

), R2 =

W2

2log2

(1 +

P2

NW2

)

• The MU case (dotted line) and FDMA case (solid line) are depicted in Figure 18. Similar curves

are obtained for the broadcast channel as well as relaying channel.

91

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Loss in rate due to sub-optimum channel access scheme is small:

0 0.1 0.2 0.3 0.4 0.5 0.60

0.1

0.2

0.3

0.4

0.5

Rate of User #1

Rat

e of

Use

r #2

FDMA/TDMA CapacityCDMA/MU Capacity

C=0.5⋅ log2(1+P

2/N)

C=0.5⋅ log2(1+P

2/(P

1+N))

C=0.5⋅ log2(1+P

1/(P

2+N))

C=0.5⋅ log2(1+P

1/N)

Area, where FDMA.TDMA is inferior toCDMA/Multi−User Detection

Optimum resource sharing, where bandwidth is proportinal to

signal power.

Figure 18: Achievable rates for a multiple access channel with two users.

92

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• It can first be observed that maximum (MU) and practical (FDMA) sum rate, i.e. R1 + R2, is the

same in the point where the users in the FDMA scheme are allocated an optimum bandwidth

equal to their power, i.e. W1 = P1 and W2 = P2.

• If FDMA (or TDMA) is used, then the resource allocation scheme which maximises capacity

hence also ensures that the achieved sum-capacity is equal (or close) to the maximum

achievable capacity.

• Since only FDMA and TDMA schemes are analytically tractable for large relaying networks,

these will be the main subject of the tutorial.

• Besides the basic multiple access schemes, i.e. FDMA and TDMA, we assume a path

reservation protocol where communication from source to sink is not interfered by other links

due to a prior reserved routing path. This routing path is reserved only during the transmission

of a single packet or several packets.

• The main aim of the analysis is hence to design resource allocation rules which maximise the

throughput along a reserved path through the given topology.

93

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We will investigate the end-to-end throughput of a communication link from a source towards a sink

operating over generic ergodic and non-ergodic fading channels, where relaying and cooperation is

allowed, and each terminal is in possession of multiple antenna elements.

2nd Interference Zone Z-th Interference Zone1st Interference Zone

6th

VAA

5th

VAA

4th

VAA

(V-2)nd

VAA

(V-1)st

VAA

V-th

VAA

targ

et te

rmin

al

3rd

VAA

2nd

VAA

1st

VAA

so

urc

e t

erm

inal

1st

RelayingStage

2nd

RelayingStage

co

op

era

tion

rela

yin

g t

erm

ina

l

Figure 19: Distributed-MIMO multi-stage relaying topology with interference zones.

94

�

�

�

�

– Related Definitions –Source, Sink and Relaying Terminals:

Wireless terminals with intention to transmit information from a source towards a sink with

the possible aid of relays.

Virtual Antenna Array (VAA):

Grouping of terminals in spatial proximity which wirelessly cooperate to enhance signal

reception (diversity) and transmission (diversity, space-time coding & multiplexing).

Cooperation:

Procedure which utilises the wireless interface between terminals belonging to the same

Virtual Antenna Array to enhance signal reception.

Relaying Stage:

The wireless interface between two consecutive Virtual Antenna Arrays.

Interference Zone:

Within an interference zone, resources in terms of frame duration, frequency band and

spreading code must not be re-used.95

�

�

�

�

– General Deployment [1/3] –

Source Terminal:

• it broadcasts its data to the remaining terminals in the first VAA,

• it uses given cooperative resources in terms of power, etc.

First Relaying VAA:

• it is formed by q1 spatially adjacent terminals (including the source!),

• each terminal possesses n1,i antenna elements (first subscript relates to first VAA and 1 ≤ i ≤ q1),

• after cooperation, the data is space-time encoded (codebook has t1 =

�q1i=1 n1,i spatial dimensions),

• each terminal transmits only n1,i∈(1,q1) spatial dimensions (so that no codeword is duplicated),

• it uses relaying resources in terms of power, bandwidth, frame duration.

96

�

�

�

�


Second Relaying VAA:

• it is formed by q2 spatially adjacent terminals with n2,i antenna elements each,

• some may cooperate, hence forming Q2 clusters (everybody coop.: Q2 = 1, nobody coop.: Q2 = q2),

• j−th cluster contains r2,j receive antennas (1 ≤ j ≤ Q2 ,

�q2i=1 n2,i =

�Q2j=1 r2,j ),

• there are hence Q2 MIMO channels in the first stage (each with t1 Tx antennas and r2,j Rx antennas),

• cooperation uses given cooperative resources,

• after cooperation, the data is space-time encoded (codebook has t2 =

�q2i=1 n2,i spatial dimensions),

• each terminal transmits only n2,i∈(2,q2) spatial dimensions (so that no codeword is duplicated),

• it uses relaying resources in terms of power, bandwidth, frame duration.

97

�

�

�

�


v−th Relaying VAA:

• it is formed by qv spatially adjacent terminals with nv,i antenna elements each,

• cooperation, space-time encoding and resource utilisation is congruent to above.

V −th Relaying VAA:

• it is formed by qV adjacent terminals with nV,i antenna elements each (including the target!),

• all terminals cooperate (non-cooperative terminals have no influence on data flow),

• there is hence one MIMO channel (with tV −1 Tx antennas and

�qVi=1 nV,i Rx antennas),

Target Terminal:

• after cooperation, data is space-time decoded and passed to information sink .

98

�

�

�

�

– Aim of Capacity Analysis –Find optimum fractional resources to be assigned to each node/mobile

terminal so as to maximise the end-to-end data throughput for a specifiedcommunication scenario, where the resource considered are

frame duration, frequency band and power.

Frame Duration:

• In time-division multiple access (TDMA), each relaying stage is assigned a given frame

duration which may or may not overlap with other stage’s frames.

Frequency Band:

• In frequency-division multiple access (FDMA), each relaying stage is assigned a given

frequency band which may or may not overlap with other stage’s frequency bands.

Power/Energy:

• Each terminal in the relaying stage is assigned a given power (energy). The energy

required to deliver a packet from source to sink ought to be independent of the topology.

99

�

�

�

�

– FMDA-Based Relaying –

• α(f)v is the fractional bandwidth allocated to the v−th relaying stage operating in FDMA,

• for fairness of comparison, we have∑V −1

v=1 α(f)v = 1.

1st VAA

Orthogonal

FDMA-based

Relaying

1st Stage

t

f

t t

f

t

f

W

W#1

W#2

W#3

W#4

T

Non-Orthogonal

FDMA-based

Relaying

t

f

t t

f

t

f

W

W#1

W#2

T

Interference

2nd VAA 3rd VAA 4th VAA 5th VAA

2nd Stage 3rd Stage 4th Stage

Figure 20: Orthogonal (no interference) and non-orthogonal (interference) relaying methods.

100

�

�

�

�

– TMDA-Based Relaying –

• α(t)v is the fractional frame duration allocated to the v−th stage operating in TDMA,

• for fairness of comparison, we have∑V −1

v=1 α(t)v = 1.

Orthogonal

TDMA-based

Relaying

t

f

t t

f

t

f

W

T#

1

T#

2

T#

3

T#

4

T

Non-Orthogonal

TDMA-based

Relaying

t

f

t t

f

t

f

W

T#

1

T#2

T

1st VAA

1st Stage

2nd VAA 3rd VAA 4th VAA 5th VAA

2nd Stage 3rd Stage 4th Stage

Interference

Figure 21: Orthogonal (no interference) and non-orthogonal (interference) relaying methods.

101

�

�

�

�

– Power & Energy Allocation –

FDMA-based Relaying TDMA-based Relaying

Ev = β(Ef )v E, Tv = T, Wv = α

(f)v W Ev = β

(Et)v E, Tv = α

(t)v T, Wv = W∑V −1

v=1 β(Ef )v ≡ 1,

∑V −1v=1 α

(f)v ≡ 1

∑V −1v=1 β

(Et)v ≡ 1,

∑V −1v=1 α

(t)v ≡ 1

Sv = β(Sf )v S, Sv = Ev/Tv Sv = β

(St)v S, Sv = Ev/Tv

→ β(Sf )v = β

(Ef )v → β

(St)v = β

(Et)v /α

(Et)v∑V −1

v=1 β(Sf )v ≡ 1,

∑V −1v=1 α

(f)v ≡ 1

∑V −1v=1 α

(t)v β

(St)v ≡ 1,

∑V −1v=1 α

(t)v ≡ 1

Time T

Power S1st Stage 2nd Stage 3rd Stage

E1

E2

E3

S1, S

3

S2

T1

T2

T3

Figure 22: Relationship between power, energy and time.

102

�

�

�

�

– Equivalence between TDMA & FDMA –

FDMA-based Relaying TDMA-based Relaying

C = α(f)v · W · log2

(1 + β

(Sf )v ·S

α(f)v ·W ·N0

)C = α

(t)v · W · log2

(1 + β(St)

v ·SW ·N0

)= α

(f)v · W · log2

(1 + β

(Ef )v

α(f)v

· SN

)= α

(t)v · W · log2

(1 + β(Et)

v

α(t)v

· SN

)

C is the Shannon capacity, W is the total bandwidth, N is the total noise power captured over W ,

N0 is the noise power spectral density, αv is the fractional bandwidth/frame duration and βv is the

fractional energy allocated to the v−th stage.

Since both access schemes are equivalent, we will henceforth use:

C = αv · W · log2

(1 +

βv

αv· SN

)(43)

V−1∑v=1

βv ≡ 1 &V−1∑v=1

αv ≡ 1 (44)

103

�

�

�

�

– Ergodic: End-to-End Throughput [1/3] –

• The aim is to maximise the end-to-end data throughput for the topology shown in Figure 19

assuming an ergodic fading channel.

• Throughput is defined as the information delivered from source towards sink, which requires a

certain duration of communication T and frequency band W .

• Subsequent analysis will refer to the normalised (spectral) throughput Θ in [bits/s/Hz].

• An ergodic channel offers a normalised capacity C in [bits/s/Hz] with 100% reliability, which

allows relating capacity and throughput via Θ = C .

• Maximising the throughput Θ is hence equivalent to maximising the capacity C .

• If a certain capacity was to be provided from source to sink, all channels involved must

guarantee error-free transmission.

The end-to-end capacity C is hence dictatedby the capacity of the weakest link.

104

�

�

�

�


• Each topology has K = V − 1 distributed relaying stages.

• The v−th stage has Qv+1 MIMO channels with tv transmit antennas and rv+1,j∈(1,Qv+1)

receive antennas (for the example below: Qv+1 = 2, tv = 5, rv+1,1 = 3 and rv+1,2 = 3).

(v+1)-st Tier VAAv-th Tier VAA

nv,1

nv,2

nv,3

nv+1,1

nv+1,2

nv+1,3

MIMO #1: (nv,1

+nv,2

+nv,3

) x (nv+1,1

+nv+1,2

)

MIMO #2: (nv,1

+nv,2

+nv,3

) x (nv+1,3

)

Figure 23: Established MIMO channels from the vth to the (v + 1)st relaying VAA.

105

�

�

�

�


• At each stage, we cluster such that the capacity of all clusters (MIMO channels) is as equal as

possible.

• For the analysis, we discard all but the weakest MIMO channel because the stronger MIMO

channels will then definitely be error-free.

• (If all sub-channel gains are equal, then the weakest MIMO channel is dictated by the cluster

with the smallest number of antennas.)

• For the analysis, the v−th relaying stage is hence represented by one MIMO channel with tv

transmit and rv � minj∈(1,Qv+1){rv+1,j} receive antennas.

• The aim of the analysis is to maximise the minimum capacity C , i.e.

C = supα,β

{min

{C1(α1, β1, λ1, γ1), . . . , CK(αK , βK , λK , γK)

}}(45)

over the fractional sets α � (α1, . . . , αK) and β � (β1, . . . , βK) in dependency of the

channel statistics λ � (λ1, . . . , λK) and average channel gains γ � (γ1, . . . , γK).

106

�

�

�

�

– Ergodic: MIMO Relaying [1/4] –

• With the parameter constraints given by (44), increasing one capacity inevitably requires

decreasing the other capacities.

• The minimum is maximised if all capacities are equated and then maximised.

• The capacity of the v−th stage is given as Cv = αv · Eλv

{mv log2

(1 + λv

γv

tv

βv

αv

SN

)}.

• Using (38), the end-to-end throughput-maximising optimised fractional power and optimised

fractional bandwidth (frame duration) can be obtained as [97]

αv =

∏w �=v Eλw

{mv log2

(1 + λwρw

γw

tw

SN

)}∑K

k=1

∏w �=k Eλw

{mv log2

(1 + λwρw

γw

tw

SN

)} (46)

βv = ρv · αv (47)

with

ρv ≈ K ·∏

w �=v3√

γw · Λ2(tw, rw)∑Kk=1

∏w �=k

3√

γw · Λ2(tw, rw)(48)

107

�

�

�

�


• Similarly, the end-to-end throughput-maximising optimised fractional power with equal fractional

bandwidth (frame duration) can be obtained as [97]

αv =1K

(49)

βv =

∏w �=v γw · Λ2(tw, rw)∑K

k=1

∏w �=k γw · Λ2(tw, rw)

(50)

• For the purpose of comparison, the case of no optimisation is also considered, for which the

resource allocation strategies are

αv =1K

(51)

βv =1K

(52)

108

�

�

�

�

Inp

ut

Ch

ann

el G

ain

s

fro

m e

ach

Re

layin

g S

tag

eγ 1

, ..

., γ

Κ

Inp

ut

Num

be

r o

f A

nte

nn

a

Ele

men

ts a

t e

ach S

tage

t 1, r

1, …

, t K

, r K

Ca

lcu

late

MIM

O G

ain

s a

t ea

ch

Sta

ge

Λ1,

...,

ΛΚ

Ca

lcu

late

Au

xili

ary

Co

eff

icie

nts

ρ1,

...,

ρΚ

Ca

lcu

late

Fra

ction

al B

and

wid

ths

α1,

...,

αΚ

So

rtF

ractio

na

l R

esou

rce

s

α1<

...

< α

Κ,

β1<

...

< β

Κ

Ca

lcu

late

Fra

ction

al P

ow

ers

β1,

...,

βΚ

Ou

tpu

tF

ractio

nal B

an

dw

idth

Alloca

tio

ns

Ou

tpu

tF

ractio

na

l P

ow

er

Allo

ca

tio

ns

α1,.

..,

αΚ

−1,

αΚ

=1

− α

1−

...−

αΚ

−1

β1,.

..,

βΚ

−1,

βΚ

=1

− β

1−

...−

βΚ

−1

109

�

�

�

�


0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

1.4

SNR at First Relaying Stage [dB]

End

−to

−E

nd C

apac

ity C

[bits

/s/H

z]

Optimum End−to−End CapacityOptimised Bandwidth and Optimised PowerEqual Bandwidth and Optimised PowerEqual Bandwidth and Equal Power

t1 = 1, r

1 = 1

t2 = 1, r

2 = 1

t3 = 1, r

3 = 1

p = [0, 5, 10]

p = [0, 0, 0]

p = [0, −5, −10]

(a) Achieved end-to-end capacity of various

fractional resource allocation strategies for a 3-

stage network.

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5


End

−to

−E

nd C

apac

ity C

[bits

/s/H

z]

Optimum End−to−End CapacityOptimised Bandwidth and Optimised PowerEqual Bandwidth and Optimised PowerEqual Bandwidth and Equal Power

t1 = 1, r

1 = 2

t2 = 2, r

2 = 3

t3 = 3, r

3 = 2

p = [0, 5, 10]

p = [0, 0, 0]

p = [0, −5, −10]

(b) Achieved end-to-end capacity of various

fractional resource allocation strategies for a 3-

stage network.

Figure 24: Performance of fractional resource allocation algorithms for different 3-stage topologies;

here p � [10 log10(γ1/γ1), 10 log10(γ2/γ1), 10 log10(γ3/γ1)]

110

�

�

�

�

– Ergodic: O-MIMO with Unequal Gains [1/5] –

• If the channel attenuations within the v−th stage are different, then the fractional power βv

allocated to that stage can be distributed among the transmitting elements in an optimum

manner.

• Assuming a Rayleigh fading channel, the capacity of a space-time block encoded MIMO system

with unequal average sub-channel gains can be expressed in closed form as [99]

C = R ·t∑

i=1

r∑j=1

K(i−1)r+j · C0

(εi · γ(i−1)r+j

R

S

N

)(53)

with

K(i−1)r+j =t∏

i′=1

r∏j′=1

εi · γ(i−1)r+j

εi · γ(i−1)r+j − εi′ · γ(i′−1)r+j′

∣∣∣∣∣(i′−1)r+j′ �=(i−1)r+j

(54)

Here, εi∈(1,t) is the fractional power allocated to the i-th transmit antenna for which the

normalisation∑t

i=1 εi ≡ 1 holds.

111

�

�

�

�


• An optimum transmit power strategy allocates little or no power to the antenna(s) from which the

weakest subchannels depart; the antenna from which the strongest subchannels depart is

allocated most power.

• With this in mind, the approximate fractional power allocation εi to the i−th transmit antenna is

(possibly non-linearly) proportional to the total strength of the departing subchannels, i.e.

εi ∝

��

r�

j=1

γ(i−1)r+j

��

q

(55)

where the non-linearity coefficient q is determined numerically so as to minimise the mean-error

between optimum allocation εi and near-optimum allocation εi in a given SNR range.

• Normalising εi so that∑t

i=1 εi = 1, the power allocation can be approximated as

εi ≈(∑r

j=1 γ(i−1)r+j

)q

∑tk=1

(∑rj=1 γ(k−1)r+j

)q (56)

where q = 3 has shown to yield the smallest error for a large variety of conducted case studies.

112

�

�

�

�


Proposed allocation yields near-optimum performance for 2Tx & 1Rx:

γ1Fractional

STBC

FractionalSTBC

γ2

ChannelEncoder

InformationSource

Space-Time

Block Decoder

Channel

Decoder

InformationSink



shadowing.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 22.9

3

3.1

3.2

3.3

3.4

3.5

3.6

3.7

Relative Gain γ1 in First Sub−Channel

Cap

acity

[bits

/s/H

z]

Optimum Transmit Power DistributionNear−Optimum Transmit Power DistributionEqual Transmit Power Distribution

t = 2, r = 1γ2 = 2 − γ

1

SNR = 10dB

(b) Capacity for various power distribution al-

gorithms with deployed Alamouti scheme and

one receive antenna; SNR=10dB.


113

�

�

�

�


Proposed allocation yields near-optimum performance for 2Tx & 2Rx:

FractionalSTBC Space-Time

Block Decoder

FractionalSTBC

Receiver

Receiverγ

1

γ2

γ3

γ4

γ3

γ4

(a) (Distributed) Alamouti scheme with unequal


shadowing.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 22.5

3

3.5

4

4.5

5

5.5

6

6.5

7

Relative Gain γ1 in First Sub−Channel

Cap

acity

[bits

/s/H

z]

Optimum Transmit Power DistributionNear−Optimum Transmit Power DistributionEqual Transmit Power Distribution

t = 2, r = 2γ2 = 1.8

γ3 = 2 − γ

1, γ

4 = 0.2

SNR = 15dB

SNR = 10dB

SNR = 5dB

(b) Capacity for various power distribution al-

gorithms with deployed Alamouti scheme and

two receive antennas; SNR=5, 10, 15dB.


114

�

�

�

�


Proposed allocation yields near-optimum end-to-end throughput:

3rd TierVAA2nd Tier

VAA

1st Tier

VAA

So

urc

e M

T

4th Tier

VAA

Targ

et M

T

1.6

1.6

1.6

0.4

0.4

0.4

1.0 1.0

(a) 3-Stage distributed O-MIMO communica-

tion scenario.

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7


End

−to

−E

nd C

apac

ity C

[bits

/s/H

z]

Optimum End−to−End CapacityOptimised Bandwidth, Power & Transmit Power Distribution at each transmitting VAAOptimised Bandwidth & Power, Equal Transmit Power at each transmitting VAAEqual Bandwidth, Power & Transmit Power at each transmitting VAA

t1 = 1, r

1 =2

t2 = 2, r

2 =2

t3 = 2, r

3 = 1

p = [0, 5, 10]

p = [0, 0, 0]

p = [0, −5, −10]

(b) Capacity of various fractional resource allo-

cation strategies over O-MIMO Rayleigh chan-

nels.

Figure 27: Topology and performance of distributed Alamouti 3-stage relaying scheme.

115

�

�

�

�

– Ergodic: Frequency-Selectivity [1/2] –

• A channel appears frequency-selective if the channel delay spread exceeds the symbol duration.

• A frequency selective channel is characterised by the frequency dependent channel transfer

function H(f) over a given bandwidth W .

• In [102], it has been shown that the capacity of a frequency selective channel assuming perfect

channel state information at the receiver is given as

C = maxS(f)

∫W

EH(f)

{log2 det

(Ir +

H(f)S(f)HH(f)N

)}df (57)

where capacity maximising codewords x(f) have to be determined with a given covariance

matrix S(f) = E{x(f)xH(f)} which satisfies the power constraint∫

Wtr(S(f)

)df ≤ S.

• In [102], it is shown that the statistics of H(f) do not depend on the frequency f (Theorem 6:

“frequency selectivity does not affect the ergodic capacity of wideband MIMO channels”), which

reduces the wideband ergodic capacity (57) to the narrowband ergodic capacity given by (18).

• Therefore, developed algorithms for ergodic channels can also be applied to the wideband

system per frequency component; non-ergodic behaviour, such as outage probabilities, change.

116

�

�

�

�

– Ergodic: Frequency-Selectivity [2/2] –

6 6.5 7 7.5 8 8.5 9 9.5 101.4

1.6

1.8

2

2.2

2.4

2.6

2.8


End

−to

−E

nd C

apac

ity C

[bits

/s/H

z]

Optimum End−to−End CapacityOptimised Bandwidth and Optimised PowerQuantised Bandwidth and Optimised PowerEqual Bandwidth and Equal Power

4 sub−carriers 16 sub−carriers

32 sub−carriers

t1 = 1, r

1 = 2

t2 = 2, r

2 = 4

(a) Achieved end-to-end capacity with quan-

tised fractional bandwidth for a 2-stage relaying

network over O-MIMO Rayleigh channels.

6 6.5 7 7.5 8 8.5 9 9.5 101.4

1.6

1.8

2

2.2

2.4

2.6

2.8


End

−to

−E

nd C

apac

ity C

[bits

/s/H

z]

Optimum End−to−End CapacityOptimised Bandwidth and Optimised PowerQuantised Bandwidth (power of 2) and Optimised PowerEqual Bandwidth and Equal Power

4 sub−carriers (2 + 2)



t1 = 1, r

1 = 2

t2 = 2, r

2 = 4

(b) Achieved end-to-end capacity with quan-

tised fractional bandwidth of power of two for

a 2-stage O-MIMO relaying network.

Figure 28: Example: OFDM system with 64 sub-carriers.

117

�

�

�

�

– Non-Ergodic: Throughput [1/4] –

• The aim is to maximise the end-to-end data throughput for the topology depicted in Figure 19

assuming a non-ergodic fading channel.

• The normalised (spectral) throughput Θ measured in [bits/s/Hz] is given as [100]

Θ = Φ · (1 − Pout(Φ))

(58)

• For each dependency Pout on Φ, there exists an optimum rate Φ which maximises the

throughput Θ according to (58).

• Such rate Φ is found by differentiating (58) to arrive at

1 − Pout(Φ) = Φ · ∂

∂ΦPout(Φ) (59)

which, with respect to the closed form expressions of the outage probabilities, has proven to be

impossible to obtain in explicit form.

• To this end, the approximation of the outage probability allows the problem for non-ergodic

fading channels to be transformed into a similar problem as for ergodic channels.

118

�

�

�

�


• The outage capacity of a SIMO channel can be expressed as [100]

Pout(Φ) ≈ a ·(

2Φ − 1S/N

)b

(60)

where a = a(r) and b = b(r) and are tabled in [100]. It is easily resolved in favour of Φ as

Φ (Pout) ≈ log2

(1 + b

√Pout

a

S

N

)(61)

• Taking into account log2(1 + x) ≈ √x, the throughput in (58) can be approximated as

Θ ≈ (1 − Pout) · 2b

√Pout

a

√SN (62)

• The throughput-maximising outage probability is obtained by differentiating (62) w.r.t. Pout,

leading to

Pout ≈ 11 + 2b

. (63)

119

�

�

�

�


The outage probability is indeed approximately independent from the SNR, and hence from fractional

power and bandwidth allocation:

1 2 3 40

10

20

30

40

50

60

70

80

90

100

Number of Receive Antennas

Thr

ough

put−

Max

imis

ing

Out

age

Pro

babi

lity

[%]

Approximate Throughput−Maximising Outage Probability (independent of SNR)Exact Throughput−Maximising Outage Probability (SNR=3dB)Exact Throughput−Maximising Outage Probability (SNR=6dB)Exact Throughput−Maximising Outage Probability (SNR=9dB)

(a) Differing number of receive elements,

i.e. SIMO channel.

1 2 3 40

10

20

30

40

50

60

70

80

90

100

Number of Transmit AntennasT

hrou

ghpu

t−M

axim

isin

g O

utag

e P

roba

bilit

y [%

]

Approximate Throughput−Maximising Outage Probability (independent of SNR)Exact Throughput−Maximising Outage Probability (SNR=3dB)Exact Throughput−Maximising Outage Probability (SNR=6dB)Exact Throughput−Maximising Outage Probability (SNR=9dB)

(b) Differing number of transmit elements,

i.e. MISO channel.

Figure 29: Comparison between exact and approximate throughput-maximising outage probability.

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• [SIMO:] Combining (63), (61) and (58), and allocating a fractional bandwidth αv and a fractional

power βv to the v−th relaying stage, the throughput of that stage can be expressed as

Θv ≈ αv ·(

2b

1 + 2b

)· log2

(1 +

γv

b√

a(1 + 2b)βv

αv

S

N

)(64)

• [MISO:] Similarly, the maximum throughput for the MISO channel can be approximated as

Θv ≈ αv ·(

2b

1 + 2b

)· log2

(1 +

γv

t · b√

a(1 + 2b)βv

αv

S

N

)(65)

• [O-MIMO:] STBCs over a Rayleigh fading channel with unequal channel coefficients and an

optimum fractional transmit power εi∈(1,t) yields the following throughput

Θv ≈ αvR

(2b

1 + 2b

)log2

⎛⎝1 +

1tR

γv

b√

a(1 + 2b)1

b

√∑ti=1

∑rj=1

K(i−1)r+j

(εi·γ(i−1)r+j)b

βv

αv

S

N

⎞⎠

with K(i−1)r+j given by (54).

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– In Summary –

We developed near-optimum and sub-optimum fractional resource allocation strategies for

various multi-stage cooperative relaying networks, i.e. for

• ergodic channels

– equal sub-channel general MIMO without resource re-use

– unequal sub-channel O-MIMO without resource re-use

• non-ergodic channels

– equal sub-channel general MIMO without resource re-use

– unequal sub-channel O-MIMO without resource re-use

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2.5 Hierarchical Cooperative MIMO

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– Capacity of Large-Scale Networks [1/3] –

• After having investigated the capacity of a distributed point-to-point and distributed

multi-stage system, we now move on to large-scale systems with multiple users.

• What is the (transport) capacity Θ of below unit-area network where N randomly

placed source and destination pairs wish to randomly communicate with each other?

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• This question had been posed before, where

– Gupta & Kumar proved in [16] that with a flat topology, network capacity scales with

Θ =√

N/ log N ;

– Franceschetti et al. proved in [109] that, using percolation theory, one can do better

by building a virtual infrastructure (’highways’), leading to Θ =√

N ;

– Aeron et al. proved in [110] that, using a specific 3-phase protocol with distributed

MIMO, yields a total network throughput of Θ(N2/3);

– Ozgur et al. improved the latter specific 3-phase protocol and showed in [28] that

one can achieve Θ(N), i.e. a linear scaling!

• There is, however, no proof on the optimality of any architecture and topology doing

better than Θ =√

N/ log N .

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• According to the different protocols, the per-node-throughput hence scales as follows:

101

102

103

104

10−3

10−2

10−1

100

Number of Nodes [logarithmic]

Per

−No

de−

Th

rou

gh

pu

t [l

og

arit

hm

ic]

KumarFranceschettiAeronOzgur

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– Multi-Scale Hierarchical Cooperation [1/2] –

• Divide the area into C clusters with each containing in average M = N/C nodes.

• Initiate a three-phase communication protocol as follows:

– Phase 1 − Transmit Cooperation:

Within each cluster with source nodes, exchange required information between M

nodes; do this for all clusters in parallel in the network.

– Phase 2 − MIMO Transmission:

Set up long range M×M long-range MIMO link between each cluster containing

sources and sinks; do this sequentially in the network.

– Phase 3 − Cooperative Decoding: Within each cluster, decode information after

passing quantised observations between nodes; do this for all clusters in parallel.

• Repeat above steps by dividing each cluster C into C′ sub-clusters, given that this

iterative splitting increases capacity.

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– Multi-Scale Hierarchical Cooperation [2/2] –

• The key ideas hence are:

– use local, thus globally non-interfering, short-range communications to exchange

distributed MIMO information at source and destination;

– use global, thus potentially globally interfering and hence necessarily sequential,

long-range communications to achieve spatial multiplexing over large distances.

• The principle is depicted in below figure (taken from [28]):

PHASE 1 PHASE 2 PHASE 3

PHASE 1 PHASE 2 PHASE 3 PHASE 1 PHASE 2 PHASE 3

PHASE 1PHASE 2

PHASE 3

PHASE 1 PHASE 3PHASE 2

PHASE 3PHASE 1PHASE 2

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Open Issues

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– Open Issues –

In the field of capacity, there are endless unsolved problems. However, I believe that these

are some interesting open issues:

• Analysis of rate & outage behaviour of

– synchronisation-robust cooperative systems,

– cooperative systems with imperfections (channel, feedback, correlation, etc.),

– cooperative systems in shadowing channels.

• Using capacitive insights to

– optimise the choice (and placement) of cooperative nodes,

– optimise the cooperative communication protocol.

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PART 3HARDWARE REALISATION

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• In the end, it is the hardware which will facilitate as well as limit any implementation of

cooperative relaying schemes.

• These limitations in hardware render the implementation of some of the recently

proposed cooperative protocols infeasible.

• To understand what is really feasible, we will henceforth deal with the following topics:

1. hardware architectures for transparent relaying transceivers;

2. hardware architectures for regenerative relaying transceivers;

3. comparison between these architectures;

4. cost estimates of architectures.

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3.1 Transparent Transceivers

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– Amplify & Forward Architecture –

• Important building blocks for the AF architecture:

– frequency translator facilitating shift of df and variable gain power amplifier;

– excellent duplex filters to avoid spillage (surface/bulk acoustic wave - SAW/BAW);

– no storage of received signal, hence only (!) FDRA/FDMA protocols feasible.

f-Translator

df

Antenna

BP

F1

LNA BPFPA

Variable Gain

BP

F2

PLL VCO

Programmable Synthesizer

Rx ChainDuplex Filter

Tx Chain

f(RSSI)

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– Linearly-Process & Forward Architecture –

• Important building blocks for the LF architecture:

– frequency translator df , good duplex filters, and variable gain power amplifier;

– linear processing, such as phase rotation, etc;

– no storage of received signal, hence only (!) FDRA/FDMA protocols feasible.

f-Translator

df

Antenna

BP

F1

LNA BPFPA

Variable Gain

BP

F2

PLL VCO



Tx Chain

f(RSSI)

Linear

Operations

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– Nonlinearly-Process & Forward Architecture –

• Important building blocks for the nLF architecture:

– processing is performed at baseband because function is designed without carrier;

– realisation with I/Q is possible, as well as sampled version;

– generally no storage of received signal, hence only FDRA/FDMA protocols feasible.

BPF

fc � BB

df

Antenna

BP

F1

LNA BPFPA

Variable Gain

BP

F2

PLL VCO



Tx Chain

f(RSSI)

Non-Linear

Operations

df

PLL VCO


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– TDMA Realisation of Transparent Architectures –

• TDRA/TDMA protocols can be implemented by using below architecture; however, it is

very unlikely that such architecture would be used;

• important building blocks for the TDRA/TDMA architecture are mainly large memory and

fast data buses to store (over-)sampled signals.

IF

f

BPF

I

Q

ADC

ADC

Dig

ital

Sto

rag

e DAC

DAC

I

Q

+

f

Antenna

BP

F1

LNA BPFPA

Variable Gain

BP

F2


Tx Chain

f(RSSI)

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3.2 Regenerative Transceivers

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– Sample Processing Architectures –

• Important building blocks for the EF and CF architectures:

– f-translators to baseband, synchronisation and ADC/DAC;

– fast but not complex baseband, including memory, data buses, etc;

– processing of received signal, hence any type of protocol is feasible.

IF

f

BPF

I

Q

ADC

ADC

DAC

DAC

I

Q

+

f

Sa

mp

le-B

ase

d

Pro

ce

ssin

g

Antenna

BP

F1

LNA BPFPA

(Variable Gain )

BP

F2


Tx Chain

f(RSSI)

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– Information-Bit Processing Architectures –

• Important building blocks for the DF and PF architectures:

– f-translators to baseband, synchronisation and ADC/DAC;

– powerful baseband, including μ−controller, memory, data buses, etc;

– processing of received signal, hence any type of protocol is feasible.

IF

f

BPF

I

Q

ADC

ADC

DAC

DAC

I

Q

+

f

Info

rma

tion

-Bit

Pro

ce

ssin

g

Antenna

BP

F1

LNA BPFPA

(Variable Gain )

BP

F2


Tx Chain

f(RSSI)

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3.3 Architectural Comparisons

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– Multiple Access Schemes –

• transparent relaying schemes can only use FDRA/FDMA;

• regenerative relaying schemes can use any of these.

AF LF nLF EF CF DF PF GF

TDRA × × × � � � � �FDRA � � � � � � � �

TDMA × × × � � � � �FDMA � � � � � � � �CDMA × × × (�) (�) � � �

OFDMA × × × (�) (�) � � �MC-CDMA × × × (�) (�) � � �

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– Transceiver Complexity –

• using FMDA-like access requires very good filters to minimise spurious power spillage;

• information processing schemes are likely to be used with more sophisticated

multi-carrier wideband access schemes, which require highly linear amplifiers;

• the complexity of non-transparent schemes is generally higher, where DF, PF and GF

have highest complexity.

AF LF nLF EF CF DF PF GF

clock accuracy +++ +++ +++ +++ +++

filter design ++ ++ ++ ++ ++

power amplifier +/+++ +/+++ +++ +++ +++

complexity ++ ++ +++ +++ +++

memory ++ ++ ++ ++ ++

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3.4 Cost Estimates

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– Typical Cost of Transparent Architecture –

• The cost of the transparent architecture for the production of 1000 items at 900 MHz

can be approximately estimated as per below table.

List of Items Approximate Cost in Euros

Bandpass Filter 2

Duplex Filter 6

Low Noise Amplifier 1

Programmable Synthesizer 8

Variable Gain Amplifier 5

Printed Circuit Board 5

Other Items 2

Total 27

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– Typical Cost of Regenerative Architecture –

• The cost of the regenerative architecture for the production of 1000 items at 900 MHz

can be approximately estimated as per below table.

List of Items Approximate Cost in Euros

Transparent Architecture (minus Synthesizer) 19

Programmable Synthesizer 2 × 8

I&Q Brancher 2×5

ADCs/DACs 2×5

Signal Processing 15

Total 80

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– Cost Trends [1/2] –

• Regenerative architecture is about 3 times more expensive than the transparent one.

• Every decade in produced items diminishes the cost by approximately 10 %.

• Going from 900 MHz to 2 GHz increases the price by approximately 5 %.

• Going from 900 MHz to 5 GHz increases the price by approximately 20 %.

• All estimates usually have a 10 % error margin.

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– Cost Trends [2/2] –

100

101

102

103

104

105

106

107

108

0

20

40

60

80

100

120

140

Production Volume [logarithmic]

Ap

pro

xim

ate

Co

st [

Eu

ro]

Transparent Architecture, fc = 900MHz

Regenerative Architecture, fc = 900MHz

Regenerative Architecture, fc = 2GHz

Regenerative Architecture, fc = 5GHz

Figure 30: Transparent transceiver is significantly cheaper, whereas change in frequency has no

major impact on costs.

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Open Issues

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– Open Issues –

Since there are no relay-specific components in the transceiver, there are the usual open

problems with hardware design.

However, to improve cooperative relaying performance, the following issues are important:

• Facilitator of FDRA over closely space frequency bands, i.e. excellent duplex filters.

• Guarantor of reliable synchronisation, i.e. precise clocks.

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PART 4CHANNEL CHARACTERISATION

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• In addition to physical channel, cooperative network becomes part of the channel [30].

• The cooperative relaying channel can be decomposed into the following cases:

1. (general channel characteristics as a baseline;)

2. channel for regenerative relaying (BS-to-MT & MT-to-MT channel);

3. channel for transparent relaying (cascaded channel);

4. distributed MIMO channel behaviour.

NLOS, from BS:

same pathloss

same shadowing

different fading

NLOS, distributed:

different pathloss

different shadowing

different fading

LOS, distributed:

different pathloss

same shadowing

different fading

BS

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4.1 General Characteristics

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– General Characteristics [1/5] –

Base Station : BSMobile Station : MS

Line-of-Sight: LOSnon-LOS: nLOS

MS#1

(LOS)

BS

MS#1

(nLOS)

3. Scattering

1. Free-SpacePropagation

2. Reflection

4. Diffraction

MS#2

(LOS)

MS#2

(nLOS)

Figure 31: Channel scenario for LOS/nLOS traditional and cooperative links.

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Re

ceiv

ed

Po

we

r [d

B]

Distance [m]

-20dB/dec (Free-Space)

-n*10dB/dec (Clutter )

Shadowing Mean

Shadowing

Fading (measured)

Figure 32: Received power versus distance due to pathloss, shadowing and fading.

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Pathloss:

• Characteristics: deterministic due to free-space propagation, n = 2,

measurable > 1000 · λ

• Disadvantage: power loss which requires more Tx power with increasing distance

• Advantage: spatially limits generated interference

Shadowing:

• Characteristics: random due to obstacles, lognormal, mean absorbed in pathloss

(hence n = 2, . . . , 6), variance 2dB-18dB, measurable > 40 · λ

• Disadvantage: random power loss which requires link-budget margin

• Advantage: further limits spatially generated interference; capture effect at MAC

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(Small-Scale) Fading:

• Characteristics: random due to phasor additions, central/non-central complex Gaussian

or other, measurable at ≈ λ/2

• Disadvantage: random power loss which requires link-budget margin; often, rapid

changes in channel which needs to be catered for

• Advantage: creates temporal, spectral and spatial signatures (picked up by proper code)

Fourier Transform → useful tool for visualising fading

• channel time variation → doppler spectrum

• multipath component (MPC) delays → frequency spectrum

• spatial fading → angular spectrum

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Fading Cases:

• time domain: slow/fast fading (large/small coherence time)

• frequency domain: non-selective/selective fading (large/small coherence bandwidth)

• spatial domain: non-selective/selective fading (large/small coherence distance)

8 possible fading cases: (4 in time & frequency, spatial domain treated later)

• slow & frequency-flat

• fast & frequency-flat

• slow & frequency-selective

• fast & frequency-selective

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– Slow & Frequency-Flat Fading –

• Characteristics: no inter-pulse overlap, no amplitude change from pulse to pulse

• Disadvantage: no power gains possible, possible long fades

• Advantage: no ISI, coherent communication facilitated

s(t) Tx s(t) Tx s(t) Tx

r(t)/h(t) Rx Rx Rx

t0

1 1 1

r(t)/h(t) r(t)/h(t)

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– Fast & Frequency-Flat Fading –

• Characteristics: no inter-pulse overlap, amplitude change from pulse to pulse

• Disadvantage:

• Advantage:

Tx Tx Tx

Rx Rx Rx

t0

s(t) s(t) s(t)

r(t)/h(t)

1 1 1

r(t)/h(t) r(t)/h(t)

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– Slow & Frequency-Selective Fading –

• Characteristics: inter-pulse overlap, no amplitude change from pulse to pulse

• Disadvantage:

• Advantage:

s(t) Tx s(t) Tx s(t) Tx

r(t)/h(t) Rx Rx Rx

t0

1 1 1

r(t)/h(t) r(t)/h(t)

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– Fast & Frequency-Selective Fading –

• Characteristics: inter-pulse overlap, amplitude change from pulse to pulse

• Disadvantage:

• Advantage:

Tx Tx Tx

Rx Rx Rx

t0

s(t) s(t) s(t)

r(t)/h(t)

1 1 1

r(t)/h(t) r(t)/h(t)

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– Spatial Fading –

• Please, see subsequent section on “Distributed MIMO Behaviour”.

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– Important Channel Parameters –

• pathloss coefficient

• shadowing variance and shadowing correlation distance

• fading statistics for each multipath component (MPC) and correlation properties

• power delay profile (PDP) with RMS delay spread

Power

P

Delay τ

Instantaneous contributions

of MPCs to PDP

Instantaneous

PDP

Mean

Delay

RMS Delay

Spread

Averaged

PDP

P1

P2

P3

Tap#1

Tap#2

Tap#3

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4.2 Regenerative Relaying Channel

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– Regenerative Relaying Scenario –

• The regenerative relaying channel exhibits the following properties:

– class of distribution remains unchanged;

– mean and variance are changed;

– correlation functions also change.

BS

(fixed)

direct link

traditional

linkcooperative

link

Regenerative

Relay (mobile)

Destination

(mobile)

Figure 33: Regenerative relaying link and - as benchmark - the direct link.

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– Regenerative Relaying Channel Trends –



Shadowing Mean

Shadowing

Fading (measured)

Narrowband & Non-Cooperative Wideband & Non-Cooperative

reduced Fading

Narrowband & Cooperative

reduced Shadowing Mean

and less Aggregate Pathloss

reduced

Shadowing Variance

Wideband & Cooperative

further reduced Fading



reduced

Shadowing Variance

reduced but more

frequent Fading

Figure 34: Regenerative cooperative communication reduces pathloss, shadowing and fading.

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– General Channel Parametersa[1/2] –

Pathloss

• traditional links (high BS/AP, low MTs): n = 2 (LOS), n = 2, . . . , 4 (nLOS)

• cooperative links (low cooperating MTs): n = 2 (LOS), n = 4, . . . , 6 (nLOS)

Shadowing Variance

• traditional links (high BS/AP, low MTs): 2, . . . , 6dB (LOS), 6, . . . , 18dB (nLOS)

• cooperative links (low cooperating MTs): 0, . . . , 2dB (LOS), 2, . . . , 6dB (nLOS)

Shadowing Coherence Distance

• traditional links (high BS/AP, low MTs): >100m (LOS), tens of meters (nLOS)

• cooperative links (low cooperating MTs): 40-80m (LOS), 20-40m (nLOS)

aAll trends are (slightly) frequency dependent; these values are only indications based on [31]−[43]and [60]−[68].

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– General Channel Parameters [2/2] –

First MPC Fading Statistics (other MPCs are Rayleigh distributed)

• traditional links (high BS/AP, low MTs): Ricean K = 2, . . . , 10 (LOS), Rayleigh (nLOS)

• cooperative links (low cooperating MTs): Ricean K > 10 (LOS), Rayleigh (nLOS)

Power Delay Profile

• traditional links (high BS/AP, low MTs): negative-exponential, clustered

• cooperative links (low cooperating MTs): negative-exponential

RMS Delay Spread

• traditional links (high BS/AP, low MTs): depends on cell size, τRMS = 50ns, . . . , 4μs

• cooperative links (low cooperating MTs): τRMS = 10ns, . . . , 40ns

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– Specific Channel Models –

Cellular & Fixed Broadband (traditional link)

• Pathloss: Okumura-Hata, Walfish-Ikegami, COST231, Dual-Slope Model

• Channel Model: COST207, 3GPP A&B, Stanford University Interim Channels SUI1-6

Indoors & WLAN (traditional & cooperative link)

• Pathloss: COST231, COST259-Multiwall Model

• Channel Model: ETSI-BRAN, IEEE

(Bluetooth,) Zigbee & UWB (cooperative link)

• Pathloss: IEEE 802.15.3a CH1-CH4, IEEE 802.15.4a

• Channel Model: IEEE 802.15.3a CH1-CH4, IEEE 802.15.4a, (UWB book)

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– IEEE 802.15.3a HDR UWB Model –

• Due to unresolved disputes, this IEEE WG is discontinued!

• HDR PANs deployed in residential and office environments

• based on measurements by S. Ghassemzadeh, et al., M. Pendergrass, J. Foerster, et

al., J. Kunisch, et al., A.F. Molisch, et al., G. Shor, et al. [41]

• model distinguishes four radio environments

– LOS with a distance between TX and RX of up to 4 m (CM1)

– NLOS for a distance of up to 4 m (CM2)

– NLOS for a distance of 4−10 m (CM3)

– “heavy multipath” environments (CM4)

• pathloss model adopted from Ghassemzadeh et. al. [43]

• channel model matched to Saleh-Valenzuela model

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– IEEE 802.15.4a LDR UWB Model [1/3] –

• communication with extremely low power consumptions [36]

• development of channel models for different environments at low (100−960 MHz) and

high (3−10 GHz) frequency bands

• distance & frequency dependency has been formulised as

L(d, f) = L(d) ·L(f) =12·K0 · ηTx(f) · ηRx(f) · c2

(4πd0f0)2· (f/f0)

−2(κ+1)

(d/d0)n

• shadowing has been formulised as

PL(d) =[L(d0) − 10n log10

(d

d0

)]+ S

where the variables are subsequently described and parameterised in Table 1.

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– IEEE 802.15.4a LDR UWB Model [2/3] –

• the factor of 1/2 has been included to account for average attenuations caused by people close

to the antennas;

• K0 is a constant which has to be chosen so that at reference distance, d0, and reference

frequency, f0, the value L(d, f) is equal to the tabled parameter L(d0);

• ηTx(f) and ηRx(f) are the frequency dependent transmit and receive antenna efficiencies

and have to be provided by the system designer;

• d0 is the reference distance, which, in subsequent parameterisations, is equal to 1m;

• f0 is the reference frequency, which, in subsequent parameterisations, is equal to 5 GHz (no

frequency dependency in the lower bands has been reported so far);

• κ is the frequency decay factor;

• c ≈ 3 · 108 m/s is the speed of light;

• L(d0) is the pathloss measured at reference distance d0; and

• S is a Gaussian distributed random variable with zero mean and standard deviation σS .

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– IEEE 802.15.4a LDR UWB Model [3/3] –Table 1: IEEE 802.15.4a pathloss parameterisation for various scenarios [42].

L(d0) [dB] n κ σS [dB]

residential, LOS, high frequency −43.9 1.79 1.12 ± 0.12 2.22

residential, NLOS, high frequency −48.7 4.58 1.53 ± 0.32 3.51

office, LOS, high frequency −35.4 1.63 0.03 1.90

office, NLOS, high frequency −57.9 3.07 0.71 3.90

industrial, LOS, high frequency −56.7 1.20 -1.10 6.00

industrial, NLOS, high frequency −56.7 2.15 -1.43 6.00

outdoors, LOS, high frequency −45.6 1.76 0.12 0.83

outdoors, NLOS, high frequency −73.0 2.50 0.13 2.00

open outdoors, LOS, high frequency −49.0 1.58 0.00 3.96

indoors, NLOS, low frequency n.a. 2.40 0.00 5.90

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– Temporal Characteristics [1/4] –We assume a SISO narrowband 2D-isotropic scatterer mobile-to-mobile channel [45]−[48].

• The auto-correlation function is given as

Rhh(τ) = (66)

where f1 = v1/λ and f2 = v2/λ are Doppler shifts induced by the MTs, λ is the

wavelength, v1,2 are the velocities, τ is the time-lag, J0(x) is the zeroth-order Bessel

function of the first kind, and a = f2/f1.

• The Doppler spectrum is given as

S(f) =1

π2f1√

aK

⎡⎣1 + a

2√

a

√1 −

(f

(1 + a)f1

)2⎤⎦ , (67)

where K(x) is the complete elliptic integral of the first kind.

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– Temporal Characteristics [2/4] –

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.5

0

0.5

1

Time−Lag τ [s]

Au

to−C

orr

elat

ion

Fu

nct

ion

Rh

h(τ

)

BS−to−MT (MT @ 1 m/s)MT−to−MT (both MTs @ 1 m/s)

Figure 35: Observations: MT-to-MT channel decorrelates faster than BS-to-MT channel, which is

good for code design but bad for channel estimation purposes.

176

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• The Level Crossing Rate (LCR) is the expected number of times per second the

channel envelope |h| crosses level γ in the positive direction, and is given as

LCR(γ) =√

2π√

1 + a2 · f1 · ρ · e−ρ2, (68)

where ρ = γ/E{|h|2}.

• The Average Fade Duration (AFD) is the average duration of time the envelope

spends below level γ, and is given as

AFD =1√

2π√

1 + a2 · f1 · ρ(eρ2 − 1

). (69)

177

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−40 −30 −20 −10 0 10 200

2

4

6

8

10

12

Crossing−Level γ [dB]

Lev

el C

ross

ing

Rat

e L

CR

(γ)

[1/s

]

BS−to−MT (MT @ 1 m/s)MT−to−MT (both MTs @ 1 m/s)

Figure 36: Observations: MT-to-MT channel varies faster than BS-to-MT channel, which is good for

scheduling fairness but leads to large overhead due to frequent channel state updates.

178

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– Advanced Channel Modelling –Akki’s results have been extended to other cases, such as

• Non-Isotropic Scatterer: Akki’s model assumes isotropic scatterers, which has been

extended to non-isotropic 2D scatterers in [51].

• More General Fading Distributions: Akki’s model assumes Rayleigh fading, which

has been extended to Rician channels in [49, 50].

• 3D Scattering Environment: The 3D case has been treated in [52, 53].

• MIMO: The analysis has been extended to the MIMO case in [50] and [54]−[59].

• Correlation: The analysis has been extended in [50] to the correlated case.

• Wideband: The analysis has been extended in [53] to the wideband case.

• Measurements: Prior analysis has been corroborated and extended by means of

measurements, such as [60]−[68].

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– Non-Isotropic Relay Channel [2/3] –

−4 −3 −2 −1 0 1 2 3 40

0.2

0.4

0.6

0.8

1

1.2

1.4

Angle of Arrival/Departure (AoA/AoD)

Pro

bab

ility

Den

sity

Fu

nct

ion

(p

df)

κ = 0κ = 5κ = 10

Figure 37: Increasing κ yields larger concentration around mean; μ = 0.

180

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– Non-Isotropic Relay Channel [3/3] –

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time−Lag τ [s]

Mo

du

le o

f A

uto

−Co

rrel

atio

n F

un

ctio

n R

hh(τ

)

κ1 = 1, κ

2 = 1, μ

1 = 0, μ

2 = 0

κ1 = 1, κ

2 = 5, μ

1 = 0, μ

2 = 0

κ1 = 5, κ

2 = 5, μ

1 = 0, μ

2 = 0

κ1 = 5, κ

2 = 5, μ

1 = −π/2, μ

2 = 0

Figure 38: Increasing concentration κ yields higher correlation; non-aligned means yield lower cor-

relation; v1 = v2 = 1m/s.

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– Ricean Relay Channel [1/3] –We assume a SISO narrowband 2D-isotropic scatterer mobile-to-mobile Ricean fading

channel [49].

• The auto-correlation function is given as

Rhh(τ) =1

1 + K[J0(2πf1τ) · J0(2πaf1τ) + Q(τ)] , (70)



function of the first kind, a = f2/f1, K the Ricean fading factor, and

Q(τ) = Kej2πf3τ cos θ′ , (71)

where f3 = v3/λ, v3 =√

(v1 · cos θd − v2)2 + (v1 · sin θd)2, θd = ang(v1, v2),

θ′ = θs + θ′′, θs = ang(v1, LOS), and θ′′ = cos−1(

v21+v2

3−v22

2v1v3

).

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– Ricean Relay Channel [2/3] –

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time−Lag τ [s]

Mo

du

le o

f A

uto

−Co

rrel

atio

n F

un

ctio

n R

hh(τ

)

K = −∞ dBK = 0 dBK = 10 dB

v1 = 1 m/s

v2 = 1 m/s

Figure 39: Increasing LOS component causes increases correlation; good for channel estimation

purposes but bad for interleaver design.

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– Ricean Relay Channel [3/3] –

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time−Lag τ [s]

Mo

du

le o

f A

uto

−Co

rrel

atio

n F

un

ctio

n R

hh(τ

)

v1 = 1 m/s, v

2 = 1 m/s

v1 = 1 m/s, v

2 = 2 m/s

v1 = 1 m/s, v

2 = 2 m/s

Figure 40: Increasing speed and/or angle between Tx/Rx yields lower coherence; good for interleaver

design but bad for channel estimation purposes; K = 0dB.

184

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– Non-Isotropic Relay Channel [1/3] –We assume a SISO narrowband non-isotropic scatterer mobile-to-mobile Rayleigh fading

channel [51].

• The non-isotropic behaviour is described by means of the von Mises distribution, which

describes the pdf of AoD & AoA with mean μ and concentration κ:

pdfα(α) = exp(κ cos(α − μ))/(2πJ0(κ)). (72)

• With this, the auto-correlation function is given as

Rhh(τ) =2∏

i=1

J0

(√κ2

i − 4π2f2i τ2 + j4πκifiτ cos μi

)/J0(κi) (73)


wavelength, v1,2 are the velocities, τ is the time-lag, and J0(x) is the modified

zeroth-order Bessel function of the first kind.

185

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– MIMO Relay Channel [1/3] –We assume a 2×2 MIMO narrowband 2D-isotropic scatterer mobile-to-mobile Rayleigh

fading channel [55, 56].

• The space-time cross-correlation function is given as

Rhh(τ) =2∏

i=1

J0

(2π√

(δi/λ)2 + (fiτ)2 − 2gi(δi, τ))

(74)



function of the first kind, and

gi(δi, τ) = (δi/λ)(fiτ) cos(αi − βi), (75)

where δi is the antenna separation at Tx/Rx, αi is the angle of Tx/Rx movement, and βi

is the antenna tilt at Tx/Rx.

186

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– MIMO Relay Channel [2/3] –

00.05

0.10.15

0.20.25

0.30.35

0.40.45

0.5

0

0.1

0.2

0.3

0.4

0.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time−Lag τ [s]Spatial Seperation δ [m]

Mo

du

le o

f C

orr

elat

ion

Fu

nct

ion

R

Figure 41: Spatial and temporal domains decorrelate similarly; v1 = v2 = 1m/s; λ = 30cm;

αi = 0, βi = π/2.

187

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– MIMO Relay Channel [3/3] –

00.05

0.10.15

0.20.25

0.30.35

0.40.45

0.5

0

0.1

0.2

0.3

0.4

0.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time−Lag τ [s]Spatial Seperation δ [m]

Mo

du

le o

f C

orr

elat

ion

Fu

nct

ion

R

Figure 42: Fast terminal movements make the temporal domain to decorrelate faster; v1 = 1m/s,

v2 = 10m/s; λ = 30cm; αi = 0, βi = π/2.

188

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– Empirical Relay Channel Model [1/3] –

Measurements performed for low transmit and receive antenna heights have been

conducted in London and have lead to the following empirically fitted models [64].

• The pathloss is a function of LOS and nLOS and is given as

PLLOS = 4.62 + 20 log10(4π/λ) − 2.24ht − 4.9hr + 29.6 log10 d(76)

PLnLOS = 20 log10(4π/λ) − 2hr + 40 log10 d + C (77)

where λ is the wavelength, ht,r the transmit and receive antenna heights, d the

distance and C = 0 (buildings > 18m) and C = −4 (buildings < 12m).

• The shadowing is lognormally distributed with a std varying between 6 and 11dB.

• The auto-correlation function exhibited de-correlation between 20 and 80m, with a

mean distance of 40m.

189

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– Empirical Relay Channel Model [2/3] –The following insights have been given [64]:

• The pathloss slope changes significantly over the range of measured distances; the

slope alters to a much steeper angle as the distance from the transmitter increases.

• The pathloss increases as the transmitter height decreases and this is more evident at

short distances from the transmitter.

• The pathloss is also larger for lower receiver heights, which is again more apparent at

short distances from the transmitter.

• The pathloss does not depend on the transmitted height for nLOS scenarios.

• The ratio between LOS and nLOS decreases almost linearly in log scale from 1 to

1000m.

• The shadowing std does not depend on antenna heights nor distances between

transmitter and receiver.

190

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– Empirical Relay Channel Model [3/3] –

Figure 43: The model gives fairly good predictions with a mean error of 0.5dB [64].

191

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4.3 Transparent Relaying Channel

192

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– Transparent Relaying Scenario –

• The transparent relaying channel exhibits the following properties:

– class of distribution changes;

– mean and variance also change;

– correlation functions also change.

BS

(fixed)

direct link

traditional

linkcooperative

link

Transparent

Relay (mobile)

Destination

(mobile)

Figure 44: Transparent relaying link and - as benchmark - the direct link.

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– Transparent Relaying Channel Trends –



Shadowing Mean

Shadowing

Fading (measured)

Narrowband & Non-Cooperative Wideband & Non-Cooperative

reduced Fading

Narrowband & Cooperative



reduced

Shadowing Variance

Wideband & Cooperative



reduced

Shadowing Variance

increased and more

frequent Fading

(wrt non-cooperative case)

increased Fading

(wrt non-cooperative case)

but reduced Fading

(wrt narrow-band case)

Figure 45: Transparent cooperative communication reduces pathloss & shadowing but not fading.

194

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– Two-Hop Transparent Relay Channel [1/2] –

• Exposed results related to the transparent relay channel have been compiled

from [47, 48].

• We assume AF transparent relaying from BS → relay MT (r-MT) → target MT (t-MT).

• The received signal at the t-MT, r2, can be expressed as (omitting the time index)

r2 = A · h2 · (h1 · s + n1) + n2 (78)

where

– A is amplification factor

– h1 is channel between BS & r-MT and h2 between r-MT & t-MT

– both channels are modelled as ZMCG with power σ21 and σ2

2 , respectively

– n1,2 are the respective AWGN noise terms with equal power N

– P1 and P2 is transmission power of BS and r-MT, respectively195

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– Two-Hop Transparent Relay Channel [2/2] –

• The fixed gain relay amplification factor A has been proposed by [69]

A =

√P2

P1 · σ21 + N

, (79)

which requires only statistical knowledge of the first-hop channel.

• The variable gain relay amplification factor A has been proposed by [70]

A =

√P2

P1 · |h1|2 + N, (80)

which requires instantaneous knowledge of the first-hop channel.

• Other application-dependent factors have been proposed, but are not considered here.

196

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– Statistical Characteristics [1/3] –

• The pdf of the double-Gaussian channel envelope α = |h| = |h1 · h2| with fixed gain

A � 1 can be derived as

fα(α) =4α

σ21 · σ2

2

K0

(2

√α2

σ21 · σ2

2

), (81)

where K0(x) is the zeroth order modified Bessel function of the second kind.

• Assuming a variable gain, the pdf of the double-Gaussian channel envelope α, where

α = P2|h1|2|h1|2/(P1|h1|2 + N), can be derived as

fα(α) =4αP1

P2σ22

e−P1α2

P2σ22

[√Nα2

P2σ21σ2

2

K1

(2

√Nα2

P2σ21σ

22

)+

N

P1σ21

K0

(2

√Nα2

P2σ21σ2

2

)],

(82)

where K1(x) is the first-order modified Bessel function of the second kind.

197

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.5

1

1.5

2

2.5

3

3.5

Channel Envelope α

Pro

bab

ility

Den

sity

Fu

nct

ion

Single−Hop Rayleigh; σ2=1

Fixed−Gain 2−Hop Rayleigh; sigma12=0.5, sigma

12=0.5


12=0.1

Figure 46: Behaviour is symmetric; the weaker the product of both channels (σ21σ

22 ), the lower the

mean and hence the worse the error rate performance.

198

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.5

1

1.5

2

2.5

3

3.5

4

Channel Envelope α

Pro

bab

ility

Den

sity

Fu

nct

ion

Single−Hop Rayleigh; σ2=1


12=0.5

Variable Gain 2−Hop Rayleigh; sigma12=0.5, sigma

12=0.5

Figure 47: Variable gain improves performance by shifting the mean towards higher values of the

envelope (and hence power).

199

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• The temporal auto-correlation function of h(t) with fixed gain A � 1 is given as

Rhh(τ) = 1/2 · σ21 · σ2

2 · (83)

where f1 = v1/λ1, f2 = v1/λ2, f3 = v2/λ2 are Doppler shifts induced by MTs, λ

is the wavelength, v is the velocity, τ is the time-lag, and J0(x) is zeroth-order Bessel

function of the first kind.

• With variable gain, the temporal auto-correlation function of h(t) is approximately

Rhh(τ) ≈ ξP2πJ0(2πf1τ)(1 − J0(2πf1τ)2)4P1

2F1(1.5, 1.5, 2, J0(2πf1τ)2)r2, (84)

where r2 = σ22/2J0(2πf2τ)J0(2πf3τ), ξ = 0.4037 for unit channel variances,

noises and transmit powers, and 2F1 is the Gauss hypergeometric function.

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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

Time−Lag τ [s]

Au

to−C

orr

elat

ion

Fu

nct

ion

Rh

h(τ

)

BS−to−MT (MT @ 1 m/s)Fixed Gain MT−to−MT (both MTs @ 1 m/s)Variable Gain MT−to−MT (both MTs @ 1 m/s)

Figure 48: The 2-hop relay channel decorrelates faster than single-hop channel, which is good for

code design but bad for channel estimation purposes; variable gain decorrelates even faster.

201

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4.4 Distributed MIMO Behaviour

202

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– Spatial Fading Representation –

• MIMO channel is described by H, where hk,l is channel from k−th Tx to l−th Rx antenna

H =

⎛⎜⎜⎜⎜⎜⎝

h11 h12 · · · h1,t

h21 h22 · · · h2,t

......

. . ....

hr,1 hr,2 · · · hr,t

⎞⎟⎟⎟⎟⎟⎠

• model is useful for analysis but difficult to visualise

Distributed

Space -Time Decoder

Distributed

Space -Time Encoder

Channel

Encoder

Fractional

STC Word

Space-Time Decoder

Channel

Decoder

s

s

h11

hr,t

Distributed MIMO Channel

Fractional

STC Word

Fractional STC Word

Receiver

Receiver

Receiver

Information Sink

Information

Source

H

Figure 49: Distributed MIMO transceiver and channel.

203

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– Angular Fading Representation [1/3] –

• According to [5], using transformation

HΩ = U∗r · H · Ut

with unitary matrix U{r,t} with entries

1√{r, t}e(−j2πkl/{r,t}), {k, l} = 0, . . . , {t − 1, r − 1}

gives information over spatial domain Ω, i.e.

HΩ =

⎛⎜⎜⎜⎜⎜⎝

hΩ11 hΩ

12 · · · hΩ1,t

hΩ21 hΩ

22 · · · hΩ2,t

......

. . ....

hΩr,1 hΩ

r,2 · · · hΩr,t

⎞⎟⎟⎟⎟⎟⎠ ,

where non-zero entries of this angular matrix correspond to resolved MPCs.

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– Angular Fading Representation [2/3] –

t

Distributed Tx Antennas

r

Distributed Rx Antennas

resolved clusters in angular domain

Figure 50: Distributed MIMO channel resolved in the angular domain.

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– Angular Fading Representation [3/3] –Degree-of-Freedom (Rank):

• minimum number of non-zero rows and non-zero columns in HΩ

• depends on amount of clutter in channel & antenna separation

• determines the data multiplexing capabilities of the channel

Diversity Gain:

• number of non-zero entries in HΩ

• depends on connectivity of channel & antenna separation

• determines the reliability of the channel

Power Gain:

• strongest eigenvalue of HΩ (w.r.t. weaker eigenvalues; condition number max λi/ min λi)

• determines the beamforming capabilities

206

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– Distributed MIMO Channel Trends –

Distributed topology is submerged into rich clutter environment, resulting in:

• full-rank channel → maximum degrees-of-freedom (high data throughput)

• fully connected channel → maximum diversity gain (high reliability)

• well conditioned channel → little beamforming gain (limited range)

NLOS, from BS:

same pathloss

same shadowing

different fading

NLOS, distributed:

different pathloss

different shadowing

different fading

LOS, distributed:

different pathloss

same shadowing

different fading

BS

Figure 51: Typical (distributed) relaying pathloss, shadowing and fading behaviour.

207

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Open Issues

208

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– Open Issues –

As far as we are aware of, these are still open or only partially solved problems:

• Real-time distributed channel measurements & modelling, which capture

– shadowing correlation length for more general cooperative scenarios,

– distributed temporal shadowing behaviour,

– distributed temporal fading behaviour,

– interference pollution in cooperative bands.

• Closed-form mathematical description of AF relaying channel

– in terms of statistics and temporal behaviour,

– for different choice of amplification,

– for more general channels (Nakagami, Lognormal, composite),

– for generic number of relaying stages.

209

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PART 5TRANSPARENT PHY LAYER

210

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• Analysing the PHY layer performance of a wireless system is vital in understanding,

optimising and synthesising system parameters.

• There are several hundred highly complex contributions on transparent PHY layer

analysis and design available today, which requires us to concentrate on a very few of

them.

• For this reason, we proceed with the following topics:

1. discussion on optimum relay function;

2. performance analysis of canonical topologies;

3. space-time trellis transceiver design.

211

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5.1 Optimal Relay Function

212

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– Optimal Relay Function [1/2] –

• [71] and [72] questioned the optimality of transparent and regenerative relaying functions.

• They have derived different optimum functions for different underlying assumptions;

e.g. assuming BPSK modulation and a memoryless relay channel, the SNR-optimum f(r) is:

f(x + n1) = f(r) =

√Pr

E{tanh2(

√Psr)

} · tanh(√

Psr), (85)

where Ps and Pr are the source and relay powers, respectively.

• These results are a starter only, as they do not include the wireless fading and shadowing

channel.

Source: x Relay: f(x+n1) Destination: f(x+n1)+n2

Figure 52: Finding the optimum relaying function f(r).

213

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– Optimal Relay Function [2/2] –

−4 −3 −2 −1 0 1 2 3 4−3

−2

−1

0

1

2

3

Relay Input r

Rel

ay O

utp

ut

f(r)

Amplify & ForwardHard−DecisionSNR−Optimal Function

Figure 53: Finding the optimum SNR-maximising relaying function f(r).

214

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5.2 Performance Analysis

215

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– Performance: Topology I [1/3] –

• We will follow [46] and assume the following:

– 2-hop relay;

– single relay;

– fixed gain relay

– Rayleigh fading channels;

– no source-destination link;

• Derived results for MGF are in closed-form; however, most error rates remain in integral form.

Source

Rayleigh

Relay Rayleigh

Destination

216

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• According to [46], the end-to-end SNR at the receiver with fixed gain A and partial CSI at the

relay can be written as

γ =γ1γ2

C + γ2, (86)

where γi = Pih2i /N , Pi is the transmission power, hi is the Rayleigh fading channel, N the

noise power, C = γ1

[e1/γ1E1(1/γ1)

]−1, E1(x) is the exponential integral function and

γi = PiE{h2i }/N .

• This facilitates the MGF to be calculated, from which the performance of many coherent and

differential modulation schemes can be derived in closed form:

M(s) =1

γ1s + 1+

Cγ1seC/γ2(γ1s+1)

γ2(γ1s + 1)2E1

(C

γ2(γ1s + 1)2

). (87)

• For instance, the BER of binary DPSK is

Pb(E) =12M(1). (88)

217

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• To derive (87), one would typically go via the outage probability where we also use∫∞0

exp(−a/(4x) − bx)dx =√

a/bK1(√

ab), i.e.

Pout = P [γ < γth] =∫ ∞

0

. . . (89)

= (90)

= (91)

• By taking the derivative w.r.t. γth and using ddxK1(x) = −K0(x) − K1(x)/x and replacing

γth by γ, we obtain the pdf of γ as

pγ(γ) = (92)

• The MGF is finally found by evaluating M(s) =∫∞0

pγ(γ)e−sγdγ.

218

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– Performance: Topology II [1/3] –


– 2-hop relay with single relay;

– fixed & variable relaying gains;

– Rayleigh fading channels throughout;

– N > 1 receiver antennas at destination;

– M-PSK SER with MRC at destination.

• Closed-form results are asymptotic and only hold for high SNRs.

Source

Rayleigh

Relay

Destination

219

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• Assuming P1 = P2 and constant amplification using (79), we get for the M-PSK

Ps(E) =1π

∫ π(M−1)/M

0

(−ξ)N−1eξΓ(0, ξ) −∑N−1j=1 (j − 1)!(−ξ)N−1−j

Γ(N)(1 + 1/ξ)N1/ξdθ

≤ M − 1M

Γ(N − 1)Γ(N)

(P1

2N

)−(N+1)

, (93)

where Γ(x) is the Gamma function, Γ(·, ·) is the upper incomplete Gamma function, and

ξ = sin2 θ/(sin2(π/M)P1/N). Diversity order is hence ’only’ N + 1.

• Assuming P1 = P2 and variable amplification using (80), we get for the M-PSK

Ps(E) =1π

∫ π(M−1)/M

0

(1 +

sin2(π/M)sin2 θ

P1

N

)−2N

dθ

≤ M − 1M

(P1

2N

)−2N

, (94)

where above integral is actually solvable in closed form. Full diversity order of 2N is achieved.

220

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0 2 4 6 8 10 12 14 16 18 20

10−4

10−3

10−2

10−1

100

Source−Destination SNR [dB]

SE

R

N = 2, fixed gainN = 2, variable gainN = 3, fixed gainN = 3, variable gain

Figure 54: Upper bound to the SER of 4-PSK for different N and relay strategies.

221

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– Performance: Topology III [1/3] –


– 2-hop relay;

– K relay stations;

– variable relaying gains;


– M-PSK SER with MRC at destination.

• Exact integral and loose closed-form upper and lower SER bounds neglect noise in relays.

Source

Rayleigh

Relay #1

Destination

Relay #K

222

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• According to [74], the end-to-end SNR with MRC at the destination using a modified variable

gain, Ak =√

Pr,k/(P0|h1,k|2), which neglects noise at the relay, can be written as

γ = γ0 +K∑

k=1

γk, where γk =γ1,kγ2,k

γ1,k + γ2,k. (95)

• Again, the MGF can be calculated via the derivative of the outage; however, this leads to an

intractable integral for the SER. [74], however, proposed a tight upper and lower bound:

PL =

[(1 + γ0g)

K∏k=1

(1 + gγp,k/γσ,k

)]−1

· W (K, M), (96)

PU = 2K/g(K+1)

[γ0

K∏k=1

γp,k/γσ,k

]−1

· W (K, M), (97)

where g = sin2(π/M), γp,k = γ1,kγ2,k , γσ,k = γ1,k + γ2,k and

W (K, M) = 1/π∫ π(M−1)/M

0sin2K+2 φdφ.

223

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0 5 10 15 20 25 30

10−4

10−3

10−2

10−1

100

Source−Destination SNR [dB]

SE

R

K = 1, Lower BoundK = 1, Upper BoundK = 3, Lower BoundK = 3, Upper Bound

Figure 55: Lower and upper bounds to the SER of BPSK for different number K of relays.

224

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– Performance: Topology IV [1/3] –


– K-hop relay;

– fixed relaying gains;

– partial CSI is available;

– Rice & Nakagami fading channels;

• Derivation of optimum fixed relaying gains; derivation of fairly good upper bounds on the

end-to-end SNR.

Source

gene

ral

fadi

ng

Relay#1

Destination

Relay#(K-1)

225

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• According to [75], the end-to-end SNR with MRC at the destination using a fixed gain,

Ak =√

1/(CkN) can be written as

1γ

=1γ1

+C1

γ1γ2+ . . . +

C1 . . . CK−1

γ1 . . . γK=

1K

H, (98)

where H is the harmonic mean, i.e. H =[1/K

∑Kk=0(

∏kj=1 γj/Cj−1)−1

]−1

.

• Above SNR is intractable; however, using the fact that the harmonic mean can be upper

bounded by the geometric mean, i.e. H ≤ G = K

√∏Kk=1(

∏kj=1 γj/Cj−1), allowing γ to be

upper bounded as

γ ≤ γU = Z ·[

K∏k=1

γ(K+1−k)/Kk

](99)

where Z =[

1N

∏Kk=1 C

−(K−k)/Kk

].

226

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• The optimum gains Ak can now be derived for Nakagami-m channels as:

Ak =

√eλkλmk

k Γ(1 − mk, λk)Nk

, (100)

where λk = mk/γk.

• This allows the n−th statistical moment to be computet as:

E{γnU} = Zn

K∏k=1

⎡⎣( γk

mk

)n(K−k+1)/KK Γ

(mk + n(K−k+1)/K

K

)Γ(mk)

⎤⎦ . (101)

• Using these moments, error rates and outages can be calculated either in closed form or

approximated by a converging series of moments.

227

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– Performance: Topology V [1/2] –


– general multi-stage, multi-branch relay topology with variable relaying gains;

– derivations are applicable to any fading channel;

– MRC combining at destination.

• Noise in relays has been neglected to facilitate closed-forms. Asymptotically tight SERs are

derived using a McLaurin expansion of the channel’s pdf around zero.

Source

Relay#1

Destination

Relay#(K-1)

general fading

Relay#1 Relay#(K-1)

228

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– Performance: Topology V [2/2] –

• According to [76], the end-to-end SNR with MRC at the destination using a variable gain and

neglecting noise can be written as

γ ≈ γ1γ2

γ1 + γ2+ γ0. (102)

• The SER can be calculated as Ps(E) =∫∞0

Q (kγ) pdfγ(γ)dγ, where k depends on the

modulation scheme, Q(x) is the Marcum Q-function and pdfγ(γ) is the channel’s pdf.

• [76] has observed that Q (kγ) drops rapidly to zero for increasing γ, hence giving little

contributions to the integral. The main contribution comes from the region close to zero, in which

a McLaurin series expansion is applicable, i.e. pγ(γ) = aγt + o(γ), leading to

Ps(E) → 2taΓ(t + 3/2)√π(t + 1)

(kγ)−(t+1). (103)

• a depends on the channel; for instance, for a Rician-K channel, the SER can be bounded as

Ps(E) → 3(K + 1)2

4k2

(1γ1

+1γ2

)1γ0

. (104)

229

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5.3 Space-Time Transceiver Design

230

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– Transceiver Design: General –

• There is no time to discuss the numerous contributions which have recently emerged dealing

with the transceiver design of transparent relaying schemes; however, some are listed below.

• [77] proposes a noise reduction scheme at the transparent relay, which is only applicable to

binary modulations.

• [78] proposes a unitary precoder for the cooperative system achieving full diversity. For 4-QAM,

they arrive at a closed-form optimum precoder, greatly improving performance.

• [79] proposes a lattice-coded cooperation scheme which generalises prior non-orthogonal

amplify and forward protocols, while keeping the decoding complexity relatively low.

• [80] proposes novel STBCs based on the nonvanishing determinant criterion and is shown to

achieve the optimal diversitymultiplexing trade-off of the channel.

• [81] propose equalization methods for cooperative STBC diversity schemes over

frequency-selective fading channels.

231

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– Transceiver Design: STTC [1/4] –

• [82] and later [83] have investigated the code design requirements for transparent space-time

trellis codes (STTCs).

• By using prior analysis from [23] and [84], we wanted to derive design criteria for STTCs over

below example topology.

• We assumed n transmit and m receive antennas and arbitrary channel fading statistics.

Source

Relay

Destination

Relay

RelayRelay

232

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• Rank & Determinant Criterion (m × n ≤ 3): The average error probability of that sequence eis received if c had been sent is:

〈P (c → e)〉 ≤ E(β1,1,...,βn,m) {P (c → e|(β1,1, . . . , βn,m)} (105)

=∫

β∈Rn×m

dβ · p(β)m∏

j=1

n∏i=1

e−14

EsN0

·λi|βi,j |2 ,

where Es the symbol energy and N0 the noise spectral density; m, n the number of receive

and transmit antennas, respectively; and λi the ith eigenvalue of the distance matrix

A(c, e) = B(c, e)BH(c, e), where BH denotes the Hermitian of B. The difference matrix Bfor codewords of length l is given as [23]:

B(c, e) =

⎛⎜⎜⎜⎝

e11 − c1

1 · · · e1l − c1

l

.... . .

...

en1 − cn

1 · · · enl − cn

l

⎞⎟⎟⎟⎠ (106)

233

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• Furthermore, in (105), p(β) is the probability distribution of the n × m dimensional random

vector β = (β1,1, . . . , βn,m). For arbitrary channel realisations, this can be upper-bounded by

〈P (c → e)〉 ≤m∏

j=1

n∏i=1

[∫βi,j

p(βi,j) · e−14

EsN0

·λi|βi,j |2dβi,j

].

• Defining g(βi,j , λi) = e−14

EsN0

·λi|βi,j |2 , x = βi,j and using Schwarz’ integral inequality, it can

be shown that

〈P (c → e)〉 ≤m∏

j=1

n∏i=1

⎡⎣( 1

2π

Es

N0

) 14

·(

1λi

) 14

⎤⎦ (107)

=

(r∏

i=1

λi

)−m4

·(

2π

Es

N0

)−mr4

.

• Therefore, the minimum determinant of all codeword difference matrices needs to be maximised.

The determinant criterion hence constitutes a sufficient upper bound for channels with any pdf.

234

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0 2 4 6 8 10 12 14 16 18 2010

−2

10−1

100

SNR

FE

R

3TX, 1 t−MT, 0 r−MT, 4 States3TX, 1 t−MT, 0 r−MT, 8 States3TX, 1 t−MT, 0 r−MT, 16 States3TX, 1 t−MT, 1 r−MT, 4 States3TX, 1 t−MT, 1 r−MT, 8 States3TX, 1 t−MT, 1 r−MT, 16 States3TX, 1 t−MT, 2 r−MT, 4 States3TX, 1 t−MT, 2 r−MT, 8 States3TX, 1 t−MT, 2 r−MT, 16 States

Figure 56: FER versus SNR for STTCs over transparent relays: 3 TX, 1 t-MT, a varying number of

r-MTs and STTC states.

235

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Open Issues

236

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– Open Issues –

I believe that these are some interesting open issues:

• Analysis and optimisation of

– robust synchronisation schemes tailored to transparent architectures,

– space-time codes tailored to transparent fading channel.

• Advanced topics, such as

– utilisation of analytical insights to obtain optimum relay placements,

– capacity-approaching distributed channel and space-time code design.

237

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PART 6REGENERATIVE PHY LAYER

238

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• Analysing the PHY layer performance of a wireless system is vital in understanding,

optimising and synthesising system parameters.

• There are several hundred highly complex contributions on regenerative PHY layer

analysis and design available today, which requires us to concentrate on a very few of

them.

• For this reason, we proceed with the following topics:

1. Distributed Space-Time Block Codes;

2. Estimate and Forward Protocols;

3. Decode and Forward Protocols;

4. Asynchronous Protocols.

239

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6.1 Distributed STBCs

240

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• Transmitter:

– number of distributed transmit antennas: t

– transmitted space-time block codeword: x ∈ Ct×1

– transmit power constraint: tr(E{xxH

}) ≤ S

• Channel:

– channel from transmitter i ∈ (1, t) to receiver j ∈ (1, r): hi,j

– fading realisations of hi,j : frequency-flat & uncorrelated

– grouping of sub-channel gains hi,j : H

• Receiver:

– received signal: y = Hx + n

– r−dimensional noise vector n has variance N per entry

• Cooperative Link:

– assumed to be error-free (!)

241

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– Exact STBC Error Probabilities [1/4] –

• Following [86], we will consider distributed cooperative STBCs of arbitrary rate R.

• Furthermore, the sub-channel realisation hi,j obey Nakagami fading with fading parameter f ;

the sub-channels may have different gains, thereby reflecting a possibly distributed deployment.

• We define u � t · r, γi � E {hih∗i } and assume

∑ui=1 γi = u.

Distributed

Space-Time Block Encoder

Distributed

Space-Time Block Decoder

FractionalSTBC

Space-Time

Block DecoderError

Detector

s s

h11

hr,t

O-MIMO

Channel

FractionalSTBC

FractionalSTBC

Receiver

Receiver

Receiver

Information

Source

H

s

Figure 57: Distributed Space-Time Block Code transceiver system.

242

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Let’s define

PPSK(α, u, M) � 1(1 + α)u

[1

2√

π

Γ(u + 1/2)Γ(u + 1) 2F1

(u, 1/2; u + 1; (1 + α)−1

)(108)

+√

1 − gPSK

πF1

(1/2, u, 1/2 − u; 3/2;

1 − gPSK

1 + α, 1 − gPSK

)]

PQAM(α, u, M) � 1(1 + α)u

2q√π

Γ(u + 1/2)Γ(u + 1) 2F1

(u, 1/2; u + 1; (1 + α)−1

)(109)

− 1(1 + 2α)u

2q2

π(2u + 1)F1

(1, u, 1; u + 3/2;

1 + α

1 + 2α, 1/2

)

where Γ(x) is the complete Gamma function, 2F1(a, b; c; x) is the Gauss hypergeometric function

with 2 parameters of type 1 and 1 parameter of type 2 [87] (§9.14.1)), and F1(a, b, b′; c; x, y) is the

Appell hypergeometric function of two variables [87] (§9.180.1). Furthermore, α is a parameter, M

is the modulation order, gPSK � sin2(π/M), gQAM � 3/2/(M − 1), q � 1 − 1/√

M .

243

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• Based on the analysis of [88] & [86], the symbol error rate (SER) of M-QAM and M-PSK STBC

systems operating over a Nakagami fading channel with different sub-channel gains γ i∈(1,u)

and different fading factors fi∈(1,u) can be derived in closed form as

Ps(e) =u∑

i=1

fi∑j=1

Ki,j · PPSK/QAM

(1R

γi

fit

S

N, j, M

)(110)

where

Ki,j =1

(fi − j)!(− 1

Rγi

fitSN

)fi−j

∂fi−j

∂sfi−j

⎡⎢⎣ u∏

i′=1,

i′ �=i

1(1 − 1

Rγi′fi′ t

SN · s

)fi′

⎤⎥⎦

s=

�

1R

γifit

SN

�−1

.

• For memoryless fading channels, the bit error rate (BER) and frame error rate (FER) for frames

of D symbols are respectively well approximated by

Pb(e) ≈ Ps(e)log2(M)

and Pf (e) ≈ 1 − (1 − Ps(e)

)D(111)

244

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Error rate performance of distributed STBC scheme exhibits a high stability:

γ1Fractional

STBC

FractionalSTBC

γ2

ChannelEncoder

InformationSource

Space-Time

Block Decoder

Channel

Decoder

InformationSink



shadowing.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 210

−6

10−5

10−4

10−3

10−2

10−1

100

γ1

SE

R

1 Tx − SISO (γ1)

1 Tx − SISO (γ2=2−γ

1)

2 Tx − Alamouti (γ1 & γ

2=2−γ

1)

(b) SER versus the normalised power γ1 in the

first link for a distributed Alamouti system oper-

ating at 2 bits/s/Hz; SNR=30dB.


245

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6.2 Estimate & Forward Protocols

246

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�

– Considered Topology –

Following [86], the aim is to analyse the end-to-end error rate for the below general topology

assuming the estimate & forward protocol:

6th

VAA

5th

VAA

4th

VAA

(V-2)nd

VAA

(V-1)st

VAA

V-th

VAA

targ

et te

rmin

al

3rd

VAA

2nd

VAA

1st

VAA

so

urc

e t

erm

ina

l

1st

Relaying

Stage

2nd

Relaying

Stage

co

op

era

tion

rela

yin

g t

erm

inal

Figure 59: Distributed-MIMO multi-stage relaying topology.

247

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�

– End-to-End Error Rate [1/4] –

• We assume first no cooperation and unequal-power Rayleigh fading channels.

• To obtain the exact end-to-end BER is not trivial, as an error occurring in one node may or may

not be corrected by a parallel node.

• This creates dependencies between the error events at each stage in dependency of:

– the modulation scheme used,

– the prevailing channel statistics,

– the average channel attenuations,

– as well as the deployed STBC.

• The fairly complex interdependencies call for suitable simplifications, where we will weigh the

strength of a channel with a given error probability against the strength of the other channels.

• Subsequent explanations relate to Figure 60.

248

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3rd TierVAA2nd Tier

VAA

1st Tier

VAA

So

urc

e M

T

4th Tier

VAA

Targ

et M

T

(1,1)

(1,2)

(2,1)

(2,2)

(2,3)

(2,4)

(3,1)

(3,2)

P1,1

P1,2

P2,1

P2,2

P3,1

Figure 60: 3-stage distributed O-MIMO communication system without cooperation.

249

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• We assume that the system operates at low error rates which causes only one error event at a

time in the entire network.

• Let us assume that an error occurs in link (1,1); however, (1,2) is error free. Then the probability

that the error propagates further is related to the strengths of channels (2,1) and (2,3).

• It is intuitive and hence conjectured here that the probability that such error propagates is

proportional to the strength of the STBC branch it departs from, here (2,1) for one of two MISO

channels, and (2,2) for the other one.

• Therefore, the probability that an error which occurred in link (1,1) with probability P1,1

propagates through the O-MISO channel spanned by (2,1) and (2,3) is approximated as

P1,1 · γ2,1/(γ2,1 + γ2,3), where the strength of the erroneous channel (2,1) is normalised by

the total strength of both sub-channels.

• To capture the probability that such an error propagates until the t-MT, all possible paths in the

network have to be found and the original probability of error weighed with the ratios between

the respective path gains.

250

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• Taking the previously said into account and assuming that at high SNRs only one such error will

occur at any link, the end-to-end BER for the network depicted in Figure 60 can be expressed as

Pb,e2e(e) ≈[P1,1(e)

(γ2,1

γ2,1 + γ2,3

γ3,1

γ3,1 + γ3,2+

γ2,2

γ2,2 + γ2,4

γ3,2

γ3,1 + γ3,2

)+

P1,2(e)(

γ2,4

γ2,2 + γ2,4

γ3,2

γ3,1 + γ3,2+

γ2,3

γ2,1 + γ2,3

γ3,1

γ3,1 + γ3,2

)]+[

P2,1(e)(

γ3,1

γ3,1 + γ3,2

)+ P2,2(e)

(γ3,2

γ3,1 + γ3,2

)]+[P3,1(e)

]

• This can be simplified to

Pb,e2e(e) ≈[ξ1,1P1,1(e) + ξ1,2P1,2(e)

]+[

ξ2,1P2,1(e) + ξ2,2P2,2(e)]

+[ξ3,1P3,1(e)

]

where ξv,i is the probability that an error occurring in link (v, i) will propagate to the t-MT.

251

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�

– Clustering –

• This is easily generalised to networks of any size and any form of partial cooperation.

• To this end, remember that there are Qv∈(1,K) cooperative clusters at the vth stage, each of

which will yield an error probability of Pv∈(1,K),i∈(1,Qv).

• The end-to-end BER is hence approximated as

Pb,e2e(e) ≈K∑

v=1

Qv∑i=1

ξv,iPv,i(e) (112)

where the probabilities ξv,i are easily found from the specific network topology.

• The BERs Pv,i(e) can be found from the previously derived SERs with an appropriate number

of transmit and receive antennas per cluster, as well as prevailing channel conditions.

• The proposed approximation holds with high precision, as demonstrated by means of the

following performance graphs.

252

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– Performance –

0 5 10 15 20 25 30 35 40 45 50

10−4

10−3

10−2

10−1

100

End

−to

−E

nd B

ER

SNR [dB]

Exact (numerical)Approximate (analysis)

γ1,1

= 4, γ1,2

= 1γ2,1

= 1, γ2,2

= 4

γ1,1

= 0.1, γ1,2

= 0.05γ2,1

= 10, γ2,2

= 20

(a) Numerically obtained and derived end-to-

end BER versus the SNR in the first link for a

two-stage network without cooperation.

0 5 10 15 20 25 30 35 40 45 50

10−4

10−3

10−2

10−1

100

End

−to

−E

nd B

ER

SNR [dB]

Exact (numerical)Approximate (analysis)

γ1,1

= 1.9, γ1,2

= 0.1γ2,1

= 0.1, γ2,2

= 1.0γ2,3

= 1.0, γ2,4

= 1.9γ3.1

= 1.9, γ3,2

= 0.1

γ1,1

= 1.6, γ1,2

= 0.4γ2,1

= 0.4, γ2,2

= 1.0γ2,3

= 1.0, γ2,4

= 1.6γ3.1

= 1.6, γ3,2

= 0.4

γ1,1

= 21, γ1,2

= 22γ2,1

= 13, γ2,2

= 14γ2,3

= 15, γ2,4

= 16γ3.1

= 7, γ3,2

= 8

(b) Numerically obtained and derived end-to-

end BER versus the SNR in the first link for a

three-stage network without cooperation.

Figure 61: End-to-end BER of various 2- & 3-stage relaying topologies.

253

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– Throughput Maximisation –

• In [86], the end-to-end throughput-maximising optimised fractional power and optimised

fractional frame duration have been obtained as

α′v =

∏Kw=1,w �=v Rw · log2(Mw)∑K

k=1

∏Kw=1,w �=k Rw · log2(Mw)

(113)

β′v =

⎡⎢⎢⎢⎢⎢⎢⎣

K∑w=1

α′w

√√√√√√√√√√

Qv∑i=1

∑j∈i

ξ−1v,i K

−1v,i,jA

−1v Bv,i,j

Qw∑i=1

∑j∈i

ξ−1w,iK

−1w,i,jA

−1w Bw,i,j

⎤⎥⎥⎥⎥⎥⎥⎦

−1

(114)

where the notation j ∈ i represents the j th sub-channel belonging to the ith cluster, Further-more, Kv,i,j =

∏j′∈i,j′ �=j

γv,j

γv,j−γv,j′and

Av =

{Mv−1

Mv log2(Mv) for M-PSK2qv

log2(Mv) for M-QAMBv,i,j =

{ gPSK,v

Rv

γv,j∈i

tv

SN for M-PSK

gQAM,v

Rv

γv,j∈i

tv

SN for M-QAM

254

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6.3 Decode & Forward Protocols

255

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– Decode & Forward Methods –

• The most tractable DF methods are:

– repetition based (repeat codeword during relaying)

– channel code based (relay parity information)

– space-time code based (construct ST codeword or multiplex)

repetition

s-MT

r-MT t

channel code

s-MT

r-MT t

same data parity data

ST code

s-MT

r-MT t

ST data

Supportive Case:

256

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– Channel Coded: Topology –


– 2-hop relay;

– K relay stations;

– variable relaying gains;


– BPSK, channel coder, MRC at destination.

• Optimised power allocation at source and relays; pertinent to realistic systems.

Source

Rayleigh

Relay #1

Destination

Relay #K

257

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– Channel Coded: System Model –

• Source first broadcasts s(t) to both the destination and relays at time t.

• Upon receiving signals from the source, each relay decodes the received signal, re-encodes it

and transmits it as xr,k(t)

• The power of source and relays are constrained, where

– P is the overall power;

– α0 · P is the power allocated to the source;

– αr,k · P is the power allocated to the k−th relay;

– α0 +∑K

k=1 αr,k = 1.

• The respective fading channel powers are:

– γ0 is the average fading channel power between source and destination;

– γ1,k is average fading channel power between source and k−th relay;

– γ2,k is average fading channel power between k−th relay and source;

258

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– Channel Coded: Approximate DF Model [1/4] –

• We define:

– SNRin,1,k the input SNR at the decoder of the k−th relay;

– SNRout,1,k the output SNR of the decoder of the k−th relay;

• Relationship between these SNRs for DF is SNRout,1,k = f (SNRin,1,k).

• For convolutional codes, the above relationship can be upper-bounded at high SNR

by [90]:

SNRout,1,k ≤ SNRin,1,k · R · dfree, (115)

where R is the channel code rate and dfree its free distance.

• For other types of block and channel codes as well as tighter bounds, one can use the

theory invoked in [91].

259

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• Soft-output at the decoder k at time-sample moment i for BPSK modulation can be

modelled as

sk(i) = sk(i) (1 − nk(i)) , (116)

where sk(i) is the exact transmitted symbol.

• Furthermore, nk(i) is an equivalent noise with mean μn,k and variance σ2n,k, which

can be calculated as [92]

μn,k =1l

l∑i=1

|sk(i) − sk(i)| , (117)

σ2n,k =

1l

l∑i=1

(sk(i) − sk(i) − μn,k)2 , (118)

where l is the code sequence length.

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• The signals transmitted from the k−th relay is hence given as

xr,k(i) = βksk(i), (119)

where βk is a normalisation factor calculated from the transmit power constraint at the

relay as

β2k

((1 − μn,k)

2 + σ2n,k

)≤ αr,k · P. (120)

• After some manipulations, one can calculate the end-to-end SNR at the destination [89]:

γ ≤(

γ0 +K∑

k=1

γ1,kγ2,kαr,kRdfree

γ2,kαr,k + γ1,kαr,kRdfree + N0/P

)α0 · P

N0, (121)

where N0 is the noise power spectral density.

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• From this, we can finally calculate the optimum distributed power allocation coefficients

for source and relays:

αopt0 =

8γ20 + Rdfree

∑Kk=1 γ1,kγ2,k ± 8γ0

√γ2

0 + 14Rdfree

∑Kk=1 γ1,kγ2,k

8γ20 + 2Rdfree

∑Kk=1 γ1,kγ2,k ± 8γ0

√γ2

0 + 14Rdfree

∑Kk=1 γ1,kγ2,k

and

αoptr,k =

Rdfreeγ1,kγ2,k

8γ20 + 2Rdfree

∑Kk=1 γ1,kγ2,k ± 8γ0

√γ2

0 + 14Rdfree

∑Kk=1 γ1,kγ2,k

.

• It can be observed that the power allocation factor for k−th relaying node is

proportional to the channel and coding gain of the k-th relay link.

• The power gains w.r.t. equal power allocation for different channel configurations are

shown in the subsequent slide.

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– Channel Coded: Power Gains –

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5

4

Number of Relays K

SN

R G

ain

[d

B]

γ0=γ

1,k=γ

2,k=1

γ0=4γ

1,k=4γ

2,k=1

4γ0=γ

1,k=4γ

2,k=1

γ0=γ

1,k=4γ

2,k=1

Figure 62: Power gains can be achieved by using prior theory, where this gain will monotonically

increase as the number of relays increases.

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– Space-Time Coded: Code Design [1/4] –


– two-hop relay system with K relaying nodes;

– Rayleigh fading channel;

– relay only re-transmits if received correctly;

– MLSE detector at destination.

• Upper bound to the pairwise error probability (PEP) has been derived.

Source

Rayleigh

Relay #1

Destination

Relay #K

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• According to [103], the received sequence vector at the destination is

yd =√

P2XDIh + n, (122)

where X is the space-time code sequence, n the noise, h the channel vector from the relays to

the destination, and DI = diag(I1, . . . , IK) the relay state matrix.

• Ik = 1 with probability (1 − Pk)L if relay decoded information successfully from source and

Ik = 0 otherwise with probability 1 − (1 − Pk)L, where L is the frame length and for M-QAM

Pk ≤ 2Ng(2)bP1|h1,k|2

, (123)

where b = 3/(M − 1), g(2) = 4Y/π∫ π/2

0sin2 θdθ − 4Y 2/π

∫ π/4

0sin2 θdθ and

Y = 1 − 1/√

M . Ik is hence Bernoulli distributed.

• We will subsequently assume that all channel realisations are symmetric, i.e.

|h1,k|2 = |h1,K |2 and Pk = PK .

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• Maximum likelihood decoding is applied, where the PEP can be bounded by:

Pr(X1 → X2|I,h) = Pr(‖y −

√P2X1DIh‖2 >‖y −

√P2X2DIh‖2|I,h,X1

)

≤K∑

k=0

(1 − L · PK)k(L · PK)K−k · Ω (P2/N) (124)

where

Ω(x) =∑

I:nI=k

⎛⎝ 2k − 1

k − 1

⎞⎠

xk∏k

i=1 λIi

. (125)

Here, nI is the number of active relays (assuming that the space-time codeword is full-rank) and

λIi are the nonzero eigenvalues of sent signal matrix corresponding to state I.

• Above equation allows us to gain insights into the design criteria of the space-time code word.

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• Following [103] and assuming α to be the fractional power of the first stage, we rewrite the PEP

as

Pr(X1 → X2|I,h) ≤ SNR−KK∑

k=0

(2Lg(2)

bα|h1,K |2

)K−k

· Ω(1 − α) (126)

• The diversity gain is given as

D = limSNR→∞

− log(PEP )/ log(SNR) = K, (127)

which indicates that any full-rank MIMO code will achieve full diversity if used for the decode and

forward space-time protocol.

• The coding gain is given as

C = 1/n

√√√√ K∑k=0

(2Lg(2)

ba1|h1,K |2

)K−k

· Ω(1 − α) (128)

which indicates that − among all determinant-maximising space-time codes − special decode

and forward space-time codes need to be constructed to maximise coding gain. 267

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– Space-Time Coded: Correlation Impact [1/3] –


– two-hop relay system with K relaying nodes;

– correlated Rayleigh fading channel;

– each relay node has potentially more than one antenna;

– (Q-)OSTBCs at relays with MRC at destination.

• Upper bound to the BER with correlation has been derived.

Source

Rayleigh

Relay #1

Destination

Relay #K

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• According to [104], the BER can be Chernoff upper-bounded in the high SNR region by

BER ≤ Ne

(SNRd2

min

4M

)−M

βdeg, (129)

where Ne and dmin are the number of nearest neighbours and the minimum Euclidean

distance in the constellation diagram, M is the total number of antenna elements in the relay

stage, βdeg = det[E{vec{H}vec{H}H}]−1, H = [H(1)T , . . . ,H(K)T ]T

,

vec{H(k)} = S(k)1/2vec{Hw

(k)}, Hw(k) is spatially white and S(k) is the covariance

matrix from the k−th relaying terminal capturing correlation.

• Having 4 antennas, we can e.g. (1) take one terminal with 4 antennas or (2) two terminals with

two antennas each. The degradation coefficient can be calculated from the above [104]:

β(1)deg = (1 − 6ρ + 15ρ2 − 20ρ3 + 15ρ4 − 6ρ5 + ρ6)−1, (130)

β(2)deg = ((4α2

1 − 4α31 + α4

1)(1 − 4ρ + 6ρ2 − 4ρ3 + ρ4))−1, (131)

where ρ is the correlation coefficient and α1 is the channel gain from relay #1 (α2 = 2 − α1).

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110

0

101

102

103

104

Correlation Coefficient ρ

Deg

rati

on

Co

effi

cien

t β d

eg

4 Antennas in 1 Relaying Terminal2 Antennas in 2 Relaying Terminals with a

1=1 & a

2=1

2 Antennas in 2 Relaying Terminals with a1=0.5 & a

2=1.5

Figure 63: Correlation has bigger impact than power imbalance!

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– Distributed Multiplexing: Topology –


– two-hop relay system with K relaying nodes over Rayleigh channel;

– relays multiplex sub-stream from received full data stream;

– N receive antennas at the receiving node;

– receiving node deploys zero-forcing (ZF) or minimum mean square error (MMSE).

• Assuming no channel coding, the error rates for multiplexed streams are derived.

Source

Rayleigh

Relay #1

Destination

Relay #K

Antenna #1

Antenna #N

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– Distributed Multiplexing: System Model –

• Communication is performed in two steps:

– In the first phase, the source broadcasts a 2K−ary symbol x representing K bits,

x1, . . . , xK , with energy Es.

– In the second phase, relay k detects only xk and forwards its estimate xk to the

destination with enery Er ; all relays do this simultaneously using the same channel.

• At the destination, each multiplexed signal stream is detected by using ZF or MMSE and

then subtracted to detect the subsequent sub-stream.

• The ordering of the sub-streams and hence their order of substraction is traditionally

based on each sub-streams SNR; however, [93] propose to order according to the

log-likelihood ratio.

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– Distributed Multiplexing: Performance –

Figure 64: Spectral efficiency 4b/s/Hz, ds,r = 5m, dr,d = 100m, N=8; C-SM = cooperative spatial

multiplexing, C-DIV = cooperative diversity; all use 256-QAM between source and relay; C-SM uses

16-QAM for 2 relays and BPSK for 8 relays; C-DIV uses Alamouti STBC with 256-QAM [93].

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6.4 Asynchronous Protocols

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– Synchronisation Methods –

• Of major concern for distributed relaying networks is how to maintain synchronisation between

cooperative nodes and nodes belonging to the same relaying stage, whether cooperating or not.

• Several approaches are possible, some of which are dealt with subsequently:

– Natural Synchronisation: Assuming that terminals belonging to the same relaying hop

require the same processing time, i.e. reception, decoding, re-encoding, transmission, then

path differences leading to relative delays less than the symbol duration are acceptable.

– Extended Cyclic Prefix: As long as the cooperative scheme uses OFDM and the CP is

longer than the channel’s power delay profile plus the maximum expected asynchronism, ISI

is mitigated inherently. In addition, Cyclic Delay Diversity can be used!

– Asynchronous STC: It is also possible to design space-time coding schemes which are

robust to asynchronisms, however, mostly at the cost of a loss in spectral efficiency and/or

performance.

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– Natural Synchronisation [1/3] –

We will estimate the allowed spatial separation between relaying terminals belonging to the same

relaying stage for the best and worst case, so that natural synchronisation is still possible:

s-MT t-MTr-MT1r-MT2

Best Case (relaying in series)

r-MT1

r-MT2Worst Case (relaying in parallel)

s-MT t-MT

Δ d

d d

Figure 65: Best and worst case for natural synchronisation between terminals.

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• The time synchronisation error ought to be below sampling rate ΔT , which allows an optical

path difference of ΔT · c, where c ≈ 3 · 108m/s is the speed of light.

• Assuming equal processing time in each r-MT, the topological distribution has to obey:∣∣∣(ds→r2 + dr2→t) − (ds→r1 + dr1→t)∣∣∣ ≤ ΔT · c (132)

• For the best case, i.e. both r-MTs are on the line between s-MT and t-MT, they can be separated

by any distance because |(ds→r2 + dr2→t) − (ds→r1 + dr1→t)| = 0.

• For the worst case, i.e. one r-MT lies on the line between s-MT and t-MT and the other r-MT is

on the ellipse with the s-MT and t-MT in its foci. For simplicity, we assume that the first r-MT is

exactly in the middle between s-MT and t-MT and the second r-MT is perpendicular. For this

case, the allowed spatial separation between both r-MTs is easily obtained as:

Δd ≤√(

ΔT · c2d

+ 1)2

− 1 (133)

where d is the distance between the t-MT (s-MT) and the first r-MT.

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0 10 20 30 40 50 60 70 80 90 10010

20

30

40

50

60

70

80

90

100

Distance d between s−MT and r−MTs (r−MTs and t−MT) in [m]

Allo

wed

spa

tial s

epar

atio

n Δ

d b

etw

een

r−M

Ts

in [m

]

HiperLAN2: Ts⋅ c = 15m

UMTS: Tc⋅ c = 75m

(a) Allowed spatial separation between r-MTs

for WLAN and UMTS according to the topology

in Figure 65.

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

120

140

160

180

200

Distance d between s−MT and r−MTs (r−MTs and t−MT) in [m]

Fra

ctio

n Δ

d / d

in [%

]

HiperLAN2: Ts⋅ c = 15m

UMTS: Tc⋅ c = 75m

(b) Fraction of the allowed spatial separation

between r-MTs w.r.t. the absolute distance be-

tween s-MT and r-MT for WLAN and UMTS ac-

cording to the topology in Figure 65.

Figure 66: Study of allowed spatial separation for natural synchronisation.

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– CDD/OFDM Inherent Synchronisation [1/2] –

• Cyclic delay diversity (CDD) is the application of delay diversity (DD) to OFDM; DD has been

pioneered by A. Wittneben in 1993 and CDD by Armin Dammann and Stefan Kaiser in 2001.

• It is a transmit diversity scheme, where the same signal stream is transmitted from each

available antenna with a controlled mutual timing offset.

• This makes the channel more frequency selective and hence yields a performance gain when

detected with MLSE or MMSE equaliser.

• Furthermore, CDD has the following properties:

– The optimum delays between the transmit antennas depend on the modulation scheme (and

fading channel).

– There is no modification required to the receiving side.

– Although the deployment of MLSE and MMSE is possible without an outer channel code, this

will rarely be the case.

– A delay spread of less than the cyclic prefix length is tolerated, which makes it very attractive

for distributed deployment with loose synchronisation.

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– CDD/OFDM Inherent Synchronisation [2/2] –

Target MT

Relaying MT#2

Relaying MT#1

Modulator S/P IFFT CP

Data Bits

Modulator S/P IFFT CPδ

remove

CPFFT P/S MLSE/MMSE

Delay

Power Delay Profile

Length of

cyclic prefix (CP)

Figure 67: Cyclic delay diversity transmitter and receiver.

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– Asynchronous Space-Time Code Design [1/4] –

• Various Asynchronous space-time code designs have been proposed in recent years, most

notably [105]−[115] and also [103].

• We will concentrate on [103] according to below topology, where we assume Rayleigh channels

and orthogonal and hence loosely synchronised relay frames. This greatly facilitates

asynchronous communication.

Source

Rayleigh

Relay #1

Destination

Relay #K

Duration: T T/K T/K T/K

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• According to [103], the received sequence vector at the k−th relay is

yk =√

P1h1,ks + nr,k, (134)

where s is the source symbol sequence, nr,k the noise at the relay and h1,k the channel from

source to relay.

• It is assumed that the k−th relay performs a ’sequence-contraction’ by means of a linear

transformation tk, i.e. tkyk, where necessarily L = K .

• For subsequent analysis, a codeword vector x is defined as

x = [t1T , . . . , tKT ]T s = Ts and X = diag(x), (135)

where T is a K × K linear transformation matrix.

• From above, xk = tks and xmk is the k−th element of the xm codeword.

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• Using a maximum likelihood decoder, the PEP can be upper bounded by:

PEP = Pr(Xm → Xj) (136)

≤ NK

∏Kk=1,xmk �=xjk

(1

P1|h1,k|2+ 1

P2|h2,k|2)

∏Kk=1,xmk �=xjk

|xmk−xjk|24

. (137)

• The diversity gain is hence given as

D = limSNR→∞

− log(PEP )/ log(SNR) = minm�=j

rank(Xm − Xj), (138)

which indicates that the difference matrix xm − xj should be full-rank for any codeword x.

• The coding gain is given as

C = K

√√√√ K∏k=1

|xmk − xjk|2, (139)

which requires the minimum product distance to be maximized.

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0 5 10 15 20 25 3010

−5

10−4

10−3

10−2

10−1

100

SNR per time slot [dB]

BE

R

Asynchronous Space−Time Code, delay < slot durationSynchronous Space−Time Code, no delaySynchronous Space−Time Code, delay = 60 % of slot duration

Figure 68: BER for two relays using optimum Vandermonde matrices T for constructing x [103].

284

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Open Issues

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– Open Issues –

Again, there are endless unsolved problems. However, I believe that these are some

interesting open issues:

• Analysis and optimisation of

– robust synchronisation schemes,

– differentially modulated cooperative (space-time) schemes,

– random beamforming with sensor nodes.

• Advanced topics, such as

– design of (sub-)optimum multi-user cooperative transceivers,

– capacity-approaching distributed channel and space-time code design.

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PART 7MAC & X-Layer Design

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• The MAC layer is central to the throughput and delay of a wireless system.

• There are dozens contributions available today, which is why we only concentrate on

some basic MAC and cross-layer design issues.

• We proceed with the following topic:

1. cooperative-diversity slotted ALOHA MAC with routing protocol;

2. throughput of cooperative PHY-optimized CSMA/CA based MACs;

• These are contributions which we found very interesting but have no time to dwell on:

– Larsson: selection diversity including fading and capture effects [116];

– Dianati et al.: analytical analysis of node-cooperative ARQ scheme, which introduces

a CFC (Claim for Cooperation) into the CSMA/CA MAC structure and shows that

performance gains can thereby be achieved [119].

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– MAC is Centre of Gravity! –

The MAC decides upon:

• transmit power levels → error rates, interference behaviour

• frame lengths → throughput, interference behaviour

• scheduling timings → delay, interference behaviour

• IP packet ’buffering’ → QoS

CSMA-type MAC

(conventional)

Reservation-type MAC

(distr. & coop.)

Control Signalling

Data Traffic

synchr/hop reserv/etc. not useful

bursty data ‘regularized’ data

Hybrid

MAC

?

?

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7.1 Cooperative-DiversityALOHA MAC & Routing

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– Rational of Protocol [1/2] –

• The cooperative-diversity slotted ALOHA (CDSA) protocol has these properties [118]:

– if packet in a traditional ad hoc network gets lost along the chosen route, then a full

re-transmissions process is initiated;

– however, nodes adjacent to the troubled link may have received the packet correctly and −with a proper MAC protocol − can help relaying this packet to the destination;

– their MAC protocol is based on a modified slotted ALOHA MAC, coupled with a suitable

routing metric.

• With reference to the figure on the subsequent slide, the following can be observed:

– A wants to transmit to H and determines from the routing table that this shall happen via D;

– however, the link between A and D is in a deep fade hence corrupting reception;

– nonetheless, B, C and E have well received and decoded the packet;

– all three check the packet header and decide whether to forward the packet eventually;

– according to subsequent MAC and routing rules, only one of them chooses to forward.

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– Rational of Protocol [2/2] –

A

B

I

J

H

C

D

F

E

G

X

source destination

active

relay

active

relay

intended

receiver

Figure 69: Illustration of cooperative routing/MAC approach [118].

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– Routing Metric –

• A minimum-cost routing algorithm is considered with a route cost given by the pair (H, L),

where

– H is the number of hops towards the destinations; and

– L =∑

i 1/SNRi, where SNRi is the average SNR of the i-th hop.

• The link cost tuples are ordered such that (Hi, Li) < (Hj , Lj) if

– Hi < Hj , i.e. minimum-hop routing takes priority;

– Hi = Hj and Li < Lj , i.e. a lower link cost is chosen for the same hop count.

• The route may hence dynamically be changed by means of Routing Relays (RR), which

happens iff

– the RR overhears a packet from the transmitter and can decode it;

– the RR’s hop count towards destination is not bigger than from the transmitter;

– the RR’s link cost is also not larger than that of the transmitter.

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– MAC Protocol [1/2] –

• PRD (Packet-Reached-Destination) is populated with positive acknowledgement of final

destination;

• ACK1 is for the intended receiver (not destination) to acknowledge successful reception;

• RRF (Request-for-Relay-Forwarding) / PRD slot is populated as follows:

– if Tx receives PRD in first slot, then Tx will send second PRD to stop further transmissions;

– if Tx does not get PRD in first slot but an ACK1, then it will not transmit anything;

– if Tx receives nothing, then it will transmit RRF to get help from RR.

• One or more ACK2.i mini-slots are used for RRs to compete to relay packet, where

– if RRF does not match received packet, the RR will drop the packet;

– otherwise, it will decide whether to transmit or not and if it does then it sends ACK2.i.

Message PRD ACK1PRD/

RRFACK2.1 ACK2.k CRF

One Cooperative MAC Slot

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– MAC Protocol [2/2] –

• the CRF (Clear-to-Relay-Forwarding) mini-slot is used to select suitable RR, where

– Tx chooses RR which responded in at least one ACK2.i mini-slot with probability p;

– if there are no such mini-slots (either due to non-availability or ACK collisions), then the entire

re-transmission cycle is re-initiated.

• after having sent the ACK in at least one of the mini-slots, the RR will wait for the CRF, where

– if there is no CRF, then the RR will discard the packet;

– if CRF is present, then the RR will check whether it is the correct packet and will forward it;

• this handshaking procedure is necessary because RRs may not be able to hear their mutual

ACKs.

Message PRD ACK1PRD/

RRFACK2.1 ACK2.k CRF

One Cooperative MAC Slot

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– Performance [118] –

296

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7.2 CSMA-TypePHY/MAC Optimisation

297

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– Approach for CSMA-type MAC [1/3] –

We are interested in a general mathematical framework which quantifies:

• throughput (for bursty data)

• delay (for signalling and bursty data)

in dependency of

• node density, distribution & traffic

• transmission & interference radii

• pathloss/shadowing/fading models

which allows us to

• characterise performance of CSMA/4W-HS/SW-ARQ/etc protocols

• synthesise an optimum MAC

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Distributed

STC

Co

op

era

tio

n

So

urc

e N

od

e

Desti

nati

on

No

de

Coo

pera

tion

Coo

per

atio

n

Cooperation

Distributed

STC

STC

Sou

rce N

od

e

Destin

atio

n N

od

e

Figure 70: Multi-hop CSMA/CA scenario with two different transmit power levels (coverage areas).

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low modulation index (BPSK) high modulation index (64QAM)

→ low error rate (low prob. of loss) → high error rate (high prob. of loss)

→ long packets (high prob. of collision) → short packets (low prob. of collision)

with channel code without channel code

→ low error rate (low prob. of loss) → high error rate (high prob. of loss)

→ long packets (high prob. of collision) → short packets (low prob. of collision)

Can we capture this trade-off analytically?

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– CSMA-type PHY/MAC Optimisation [1/6] –

’1’: normalised packet length D: delay period

a: slot duration (=log2(M)/Nb) T : transmission period

p: persistency factor B: busy period

Pf : frame error probability I : idle period

D(1)

D(2)

D(1)

IT(1)

T(1)

T(2)

B(1)

B(2)

Busy Period Idle Period

a1 Sub-delayTransmission

Period

Figure 71: Time sequence of events for basic p−persistent CSMA/CA.

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The useful average end-to-end network throughput can be derived as

S = B × 1N

× U

B + I + C(140)

where

• B is the number of bits per packet;

• N is the average number of hops from source to destination;

• U is the average useful transmission time;

• B is the average busy time;

• I is the average idle time;

• C is the average cooperation time;

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• We can derive the average idle period I to be

I =a

1 − (1 − g)Mt(141)

• We can derive the average busy period B to be

B = E[D(1)] + (J − 1)E[D(2)] + J (1 + a) (142)

where the average number of busy sub-periods is given as

J =N

(1 − g)(1+1/a)(Mt−1)(143)

and

E[D(j)] =

⎧⎨⎩ d(1) j = 1

d(1 + 1/a) j = 2, 3, ...(144)

where

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d(X) =a

N − (1 − g)X(Mt−1)(145)

·∞∑

k=1

{N(1 − p)k − p

[(1 − p)k − (1 − g)k

p − g

]}

·{

(1 − p)k − p(1 − g)X

[(1 − p)k − (1 − g)k

p − g

]}Mt−1

− a(1 − g)X(Mt−1)

N − (1 − g)X(Mt−1)

∞∑k=1

[p(1 − g)k − g(1 − p)k

p − g

]Mt

• Similarly, we can derive the average useful period U to be

E[U (j)] =

⎧⎨⎩ u(1) j = 1

u(1 + 1/a) j = 2, 3, ...(146)

where

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u(X) =p · (1 − Pf )

N − (1 − g)X(Mt−1)

∞∑k=0

{(1 − p)k+1 (147)

−p(1 − g)X

[(1 − p)k+1 − (1 − g)k+1

p − g

]}Mt−2

·{(1 − g)k(1 − p)k[N(1 − g)X − 1]

+Mt

{(1 − p)k − (1 − g)X

[p(1 − p)k − g(1 − g)k

p − g

]}

·{

N(1 − p)k+1 − p

[(1 − p)k+1 − (1 − g)k+1

p − g

]}}

−Mtgp(1 − g)X(Mt−1)

N − (1 − g)X(Mt−1)

∞∑k=1

[p(1 − g)k+1 − g(1 − p)k+1

p − g

]Mt−1

·[(1 − g)k − (1 − p)k

p − g

]

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• The average cooperation time C is easily calculated as:

C =U · Nc

α, (148)

where

– U is the average useful transmission time;

– Nc is the number of cooperating links per relaying stage;

– α is the strength of the cooperative data-pipe w.r.t. the relaying pipe.

• Here, we assumed that a reservation based MAC protocol is used per cooperative stage.

• For the design and analysis of a CSMA-based MAC at the cooperative stage, please,

consult [130].

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– Performance: Transmission Range [1/6] –

no relaying (20m)

1-hop relaying (10m)

2-hop relaying (6.7m)

Figure 72: We have choice of a single hop, dual hop, triple hop, etc.

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– Performance: Transmission Range [2/6] –

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

20

Transmission Range [m]

Net

wo

rk S

pec

tral

Th

rou

gh

pu

t [b

/s/H

z]

SNR = −10dB : BPSKSNR = −10dB : QPSKSNR = −10dB : 16QAMSNR = +10dB : BPSKSNR = +10dB : QPSKSNR = +10dB : 16QAM

Figure 73: Assumptions: −30dB/dec pathloss, p = 3%, g = 0.5%, a = 0.01, B = 30 ·log2(M), one antenna per node, no cooperation (just relaying).

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– Performance: Cooperation [3/6] –

0 2 4 6 8 10 12 14 16 18 200

5

10

15

20

25

30

35

40

45

50


Net

wo

rk S

pec

tral

Th

rou

gh

pu

t [b

/s/H

z]

SNR = −10dB : BPSKSNR = −10dB : QPSKSNR = −10dB : 16QAMSNR = +10dB : BPSKSNR = +10dB : QPSKSNR = +10dB : 16QAM

Figure 74: Assumptions: −30dB/dec pathloss, p = 3%, g = 0.5%, a = 0.01, B = 30 ·log2(M), one antenna per node, three nodes cooperate, α → ∞.

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– Performance: Cooperation Pipe [4/6] –

0 2 4 6 8 10 12 14 16 18 200

5

10

15

20

25

30

35


Net

wo

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pec

tral

Th

rou

gh

pu

t [b

/s/H

z]

α = 1 : BPSKα = 1 : QPSKα = 1 : 16QAMα = 10 : BPSKα = 10 : QPSKα = 10 : 16QAM

Figure 75: Assumptions: −30dB/dec pathloss, p = 3%, g = 0.5%, a = 0.01, B = 30 ·log2(M), one antenna per node, three nodes cooperate, SNR= 10dB.

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– Performance: Channel Code [5/6] –

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5


Net

wo

rk S

pec

tral

Th

rou

gh

pu

t [b

/s/H

z]

w/out code : BPSKw/out code : QPSKw/out code : 16QAMwith code : BPSKwith code : QPSKwith code : 16QAM

Figure 76: Assumptions: −30dB/dec pathloss, p = 3%, g = 0.5%, a = 0.01, B = 30 ·log2(M), one antenna per node, no cooperation, SNR= −10dB.

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– Performance: Channel Code [6/6] –

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

20


Net

wo

rk S

pec

tral

Th

rou

gh

pu

t [b

/s/H

z]

w/out code : BPSKw/out code : QPSKw/out code : 16QAMwith code : BPSKwith code : QPSKwith code : 16QAM

Figure 77: Assumptions: −30dB/dec pathloss, p = 3%, g = 0.5%, a = 0.01, B = 30 ·log2(M), one antenna per node, no cooperation, SNR= +10dB.

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Open Issues

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– Open Issues –

The design and analysis of suitable cooperative MAC protocols is still in its infancy. I believe

that these are some interesting open issues:

• For existing MAC protocols, analysis of

– throughput & delay for finite user populations,

– throughput & delay for realistic queuing models,

– throughput & delay for cooperative systems,

• Design of optimum MAC incorporating

– x-layer optimised PHY and network layer design,

– cooperative links in an explicit way.

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PART 8SYSTEM CONSIDERATIONS

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• In the end, it will be the entire system which will facilitate/realise cooperative

communication.

• The available literature on cooperative and/or relaying systems is very unevenly spread,

i.e. there is an overabundance of information on WLAN relaying and virtually nothing on

LTE activities.

• Picking a few, we will proceed with the following topics:

1. scaling laws for large-scale systems;

2. IEEE 802.16j − WiMAX;

3. economical studies on relaying systems;

4. other multi-hop systems;

5. practical multi-hop systems.

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8.1 Scaling Laws

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– Rational behind Scalability –

• The France Telecom Group constitutes one of the biggest integrated operators worldwide.

• France Telecom’s cellular networks are composed of several million of nodes and enjoy planning

and optimization prior to roll-out.

• The number of subscribers has dramatically increased over the past years, hence requiring

cellular capacity to be augmented.

• The invoked solution consisted of introducing a hierarchical communication structure in form of

cells, where several users are connected to a base station (BS), several of these BSs are then

connected to a network controller, and the network controllers are then meshed by means of a

backbone.

• The question hence arises whether the approach taken is optimum or whether another solution

would have been more appropriate?

• We will hence try to address the issue of scalability but first defining it, then applying it to various

network laws and finally use these insights to optimise performance.

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– Definition of Scalability [1/3] –

• To attempt a more general definition than [131] and [132], we will follow [133] and first introduce

η12 =FA(N2, S2)/N2

FA(N1, S1)/N1(149)

to be the relative efficiency between two systems

– obeying the same type of architecture A;

– consisting of N1 and N2 nodes, respectively;

– tackling some problems of size S1 and S2, respectively; and

– being gauged by some ’positive’ average network-wide attribute F .

• The problem size is determined by the ’problem’ the system aims to solve and is related to the

attribute; e.g., the problem of a network to deliver a given amount of data from every node in a

cellular system, etc.

• The ’positive’ attribute could, e.g., be the total average network throughput, the inverse of the

average end-to-end delay, etc.

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• To facilitate a definition, we assume that

– The difference between the number of nodes in the two systems approaches infinity, i.e., with

N1 = N and N2 = N + Δ, we require Δ → ∞. The requirement on Δ approaching

infinity stems from the fact that the below-given ratio (150) can often only be calculated in

closed form under this assumption.

– N is sufficiently large such that the attribute F holds with sufficiently high probability. The

requirement on N being sufficiently large stems from the the fact that many network-wide

attributes, such as average throughput and delay, can only be quantified if the number of

involved nodes is sufficiently large (often even infinite).

– The problem size of the larger system does not decrease, i.e. S2 ≥ S1. This means that the

system with a larger number of nodes is not required to perform a more trivial task.

• With these assumptions, we now define an architecture A to be scalable w.r.t. attribute F if

η � limΔ→∞

FA(N + Δ, S2)/(N + Δ)FA(N, S1)/N

≥ O(1). (150)

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• The first question we pose is when a network has to be considered large. To exemplify this

problem, let us presuppose systems with and without internal conflicts [134].

• For instance, two systems without conflicts are

1. our circle of true friends, comprising a small number of elements; and

2. the soldiers of an ant colony, comprising a large number of elements.

• On the other hand, two systems with conflicts, frictions and competition are, for example,

1. a few children left on their own, comprising a small number of elements; and,

2. a state without government, comprising a large number of elements.

• As such, ’large’ is hence not about size; it is rather about managing existing and emerging

conflicts, and hence the amount of overheads needed to facilitate (fair) communication.

• This overhead is well reflected in the efficiency η, which needs to be maximised for a given

attribute F . Using different scaling laws, we will use different attributes to judge upon the

scalability of considered architectures.

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– Capacity Scaling Laws –

• By plugging the capacity expressions from Slide 125 into (150), we can judge upon the

scalability of various topologies:

– Gupta’s law [16], η = O(1/√

Δlog Δ) < O(1) (not scalable);

– Franceschetti’s law [109], η = O(1/√

Δ) < O(1) (not scalable);

– Aeron’s law [110], η = O(1/ 3√

Δ) < O(1) (not scalable);

– Ozgur’s law [28], η = O(1) = O(1) (scalable!);

• In using (150), we have assumed

– above architectures A are either flat or clustered;

– the attribute F is the average network capacity Θ;

– and, with the average network capacity being the ’problem’ to be solved in the

network, the problem size S is related to the total number of nodes in the network N

(thus certainly not decreasing with an increasing number of nodes).

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– Value Scaling Laws [1/3] –

• Mainly economically driven, various efforts in the past by e.g. Sarnoff, Reed and Metcalf

have been dedicated to establishing the value of a network in dependency of the

number of its elements N :

– Sarnoff’s Law [135] quantifies the value of a broadcast network to be proportional to

N , which stems from the fact that the N members only communicate with the BS.

– Reed’s Law [136] claims that with N members you can form communities in 2N

possible ways; the value hence scales with 2N .

– Metcalfe’s Law [137], unjustifiably blamed for many dot-com crashes, claims that N

members can have N(N − 1) connections; the value hence scales with N2.

• Since a large-scale cellular network is not truly of broadcast nature, nor do nodes form

all possible communities, nor does every node communicate with every other node,

another value scaling law is required to quantify the network’s behaviour.

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• Odlyzko and Tilly have proposed a value scaling which is proportional to N log N [138].

• Their argumentation bases on Zipf’s Law [139], an important law in biology & medicine

with discrete samples, which states that if one orders a large collection of entities by

size or popularity, the entity ranked k-th, will be in value about 1/k of the first one.

• The added value of a node to communicate with the remaining nodes is hence∑Nn=1 1/n ∝ log N (this can equally be formulated for continuous values leading to

the same result since∫ Nn=1 1/n dn ∝ log N ).

• The total value V of the network with N nodes hence scales with

V ∝ N log N. (151)

• With reference to (150) and (151), the relative efficiency can hence be calculated as

η = O(log Δ) > O(1), revealing that w.r.t. network value the architecture is scalable.

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• Odlyzko and Tilly’s law can also be used to describe the routing behaviour in multi-hop

cellular networks.

• All mobile terminals which require energy k · Emin ≤ Ek < (k + 1) · Emin to route

the information from source to the basestation/gateway are placed in zone k.

basestation or gateway

mobile node of zone 1



source mobile node

Figure 78: The value of the network with N of such zones is hence proportional to N log N .

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– Clustering: Odlyzko & Tilly’s Law [1/2] –

• Based on Odlyzko and Tilly’s value scaling law, we introduce a normalized network

value V ′, which we define as the ratio between the value given in (151) and the number

of links per unit area needed to support such connected community. This definition

hence incorporates the required links into the value of the spanned network.

• For an unclustered network, we can calculate the normalized network value V ′ as

V ′ =N log N

N log N= 1. (152)

• For a clustered network, we assume C clusters and hence M = N/C nodes per

cluster. Assuming that the value of the nodes within a cluster as well as the cluster

heads obeys Zipf’s Law, the normalized network value V ′ is

V ′ =C log C · M log M

C log C + M log M. (153)

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– Clustering: Odlyzko & Tilly’s Law [2/2] –

100

101

102

103

104

10−2

10−1

100

101

102

103

Number of Clusters [logarithmic]

No

rmal

ized

Net

wo

rk V

alu

e [l

og

arit

hm

ic]

N = 100 NodesN = 1000 NodesN = 10000 Nodes

Figure 79: Relative value of clustered network, where maximum occurs at C =√

N .

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– Clustering: Fully-Meshed Cluster-Heads [1/2] –

• We now wish to shed light onto the requirements of the architecture’s data pipes in

hierarchical cellular/WLAN systems with meshed network controllers.

• We assume that each mobile node communicates only with its respective cluster head

and all cluster heads communicate among each other using a data pipe which is

α−times stronger than the mobile node’s one.

• This leads to a 2-tier hierarchy using a 2-phase communication protocol with N total

nodes, C clusters with one cluster head and M = N/C − 1 ≈ N/C nodes per

cluster.

• The normalised throughput is hence

Θ =N

M + M · C · (C − 1)/α. (154)

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– Clustering: Fully-Meshed Cluster-Heads [2/2] –

100

101

102

103

104

10−2

10−1

100

101

102


No

rmal

ized

Net

wo

rk T

hro

ug

hp

ut

[lo

gar

ith

mic

]

nodes @ 1 kbps & cluster−heads @ 1 kbpsnodes @ 1 kbps & cluster−heads @ 100 kbps (Zigbee)nodes @ 1 kbps & cluster−heads @ 1 Mbps (Bluetooth)

Figure 80: Normalised throughput of clustered network, where maximum occurs at C =√

α.

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– Clustering: Multi-Hop Network [1/2] –

• We assume that all mobile nodes can communicate with their cluster heads over a

single hop (1-hop clusters), but that all cluster heads can only reach the base station or

gateway via multiple hops (using again α−times stronger pipes).

• The average distance from any point of the cell to the gateway can be calculated as

L = 23√

π, which allows the normalised throughput to be calculated as

Θ =3 · C · α

3 · α + C · √log C. (155)

• Comparing with a flat topology, which has a normalized throughput of

Θ′ = 3/√

log N , it can be shown that clustering improves performance if the number

of nodes N and super-nodes C relate as follows:

N > exp

[(3C

+√

log C

α

)2]

. (156)

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– Clustering: Multi-Hop Network [2/2] –

100

101

102

103

104

10−1

100

101

102

103

104


No

rmal

ized

Net

wo

rk T

hro

ug

hp

ut

[lo

gar

ith

mic

]

nodes @ 1 kbps & cluster−heads @ 1 kbpsnodes @ 1 kbps & cluster−heads @ 100 kbps (Zigbee)nodes @ 1 kbps & cluster−heads @ 1 Mbps (Bluetooth)

Figure 81: Normalised throughput of multi-hop network, where maximum occurs at C ≈ 10α.

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8.2 IEEE 802.16j − WiMAX

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– IEEE 802.x Families –

• Numerous working groups (WGs) have been created within the IEEE 802 LAN/MAN

Standards Committee family, some with overlapping goals and correlated technical

proposals [140, 141].

• IEEE 802.16 WG = Broadband Wireless Access Standards; established in 1999; aim

was to prepare formal specifications for the global deployment of broadband Wireless

Metropolitan Area Networks; official name is ”WirelessMAN”, pushes from industrial

forum lead to naming of ”WiMAX” (Worldwide Interoperability for Microwave Access).

• IEEE 802.20 WG = Mobile Broadband Wireless Access (MBWA); establishment 2002

and draft specs approved in 2006; aim to facilitate low-cost, always-on, and truly mobile

broadband wireless IP-based services; nicknamed as ”Mobile-Fi”.

• The goals of IEEE 802.20 and IEEE 802.16e are fairly similar; both are often referred to

as ”mobile WiMAX”.

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– IEEE 802.16 Letter Salad [1/2] –

• 802.16 point to multipoint broadband wireless transmission in the 10-66GHz band; only

LOS capability; single-carrier PHY.

• 802.16a was an amendment to 802.16 and delivered a point to multipoint capability in

the 2-11 GHz band; also nLOS and extension to OFDM/OFDMA.

• 802.16c was a further amendment to 802.16, delivered a system profile for the 10-66

GHz 802.16 standard.

• 802.16d was a revision project with the aim to align 802.16x with ETSI’s HIPERMAN

standard; earlier 802.16x documents were withdrawn.

• 802.16e was an amendment to .16d including mobility, better QoS, scalable OFDMA.

• 802.16f incorporates a management information base.

• 802.16g incorporates management plane procedures and services

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– IEEE 802.16 Letter Salad [2/2] –

• 802.16h incorporates improved coexistence mechanisms for license-exempt operations.

• 802.16i incorporates mobile management information base.

• 802.16j incorporates Multihop Relay Specification and will be dealt with later.

• 802.16k bridging of 802.16.

• 802.16m is an advanced air interface:

– data rates of 100 Mbit/s for mobile applications;

– data rates of 1 Gbit/s for fixed applications;

– cellular, macro and micro cell coverage;

– expected bandwidth of 20MHz or higher;

– expected completion by Sept. 2008 and approval by Dec 2008.

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– IEEE 802.16j Working Group –

• IEEE 802.16j’s Relay Task Group Leadership Team:

– Mitsuo Nohara (Chair), KDDI Corp.

– Peiying Zhu (Vice Chair), Nortel

– Mike Hart (Editor/Secretary), Fujitsu Laboratories of Europe Ltd.

– Jung Je Son (Editor/Secretary), Samsung Electronics

• This initiative is hence mainly driven by manufacturers. With the exception of a few,

operators are generally very wary of IEEE 802.x’s activities.

• IEEE 802.16’s Relay Task Group is currently developing a draft under the P802.16j

Project Authorization Request (PAR), approved by the IEEE-SA Standards Board in

March 2006.

• This PAR deals with ”Air Interface for Fixed and Mobile Broadband Wireless Access

Systems - Multihop Relay Specification.”

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– Overview of IEEE 802.16j [1/4] –

• Subsequent slides base on [142, 143] which will not be explicitly referenced again.

• The aim of [143] is to provide specifications for mobile multi-hop relay (MMR) features,

functions and interoperable relay stations to enhance coverage, throughput and system

capacity of IEEE 802.16 networks.

Coverage extension at cell edge

Penetration into inside room

Shadow of buildings

Coverage hole

Underground

Valley between buildings

Coverage extension to isolated area

M ultihop Relay

M obile Access

BS RS

RS

RS

RS

RS

RS

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• MMR-Base Station (MMR-BS):

A base station that is compliant with amendment IEEE 802.16j to IEEE Standard

802.16e.

• Relay Station (RS) types:

– fixed relay station (FRS): relay station that is permanently installed at a fixed location;

– nomadic relay station (NRS): relay station that is intended to function from a location

that is fixed for periods of time comparable to a user session;

– mobile relay station (MRS): relay station that is intended to function while in motion.

• Mobile Multihop Relay (MMR):

The system function that enables mobile stations to communicate with a base station

through intermediate relay stations.

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• In particular, [143] specifies OFDMA PHY and MAC enhancement to the IEEE 802.16

standard for licensed bands to enable the operation of relay stations.

RS TypeFixed / nom adic / m obile

M odulationOFDM A

Term inalConventional802.16 M S/SS

Backward com patibility kept

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• The proposed main features are:

– terminals that can talk with relay station: conventional .16 MS/SS only;

– modulation: OFDMA only;

– relay station type: fixed, nomadic and mobile;

– tree structure: one of the end of relayed data path should be at basestation;

– backward compatible to point-to-point mode;

– efficiently provide relay connection to mobile station via a small number of hops).

• The required working scope is hence:

– PHY: enhance normal frame structure;

– MAC: add new protocols for the relay.

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– Technical Scope of IEEE 802.16j [1/4] –

• As we have learned from previous sections of this tutorial, multi-hop enables link budget

gains, which can be exemplified by [142]:

128

130

132

134

136

138

140

142

0 0.2 0.4 0.6 0.8 1

Norm alised RS Position

Total pathloss (dB)

Direct Link Relayed Link

Relayed Link (s=1.1) Relayed Link (s=1.2)

BSRS

M S

rd

r1

r2

rd=s(r1+ r2)

rnbdBL log10

Effect of RS positioning

Propagation loss m odel:

W here: b=15.3, n=3.76

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• The scope of the IEEE 802.16j is best defined by [142]:

L

L

3

RS

RS

RS

RS

No changes to 802.16e OFDM A PM P (access) links

No changes to SS/M S

Definition of new “802.16j Relay”link air interface•Support fixed, portable, and m obile RSs•Based on OFDM A PHY•M AC to support m ulti-hop com m unication (BS -> RS and RS -> RS)•Security and M anagem ent

Definition of new RS entity:•Supports PM P links •Supports M M R links•Supports aggregation of traffic from m ultiple RSs

BS

Changes to BS:•Add support forM M R links•Add support foraggregation of trafficfrom m ultiple RSs

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• Envisaged relay station types and capabilities [142]:

Higher user throughputHigher user throughputat low SINR regionat low SINR region

Cell coverage Cell coverage extensionextensionObjectiveObjective

OnlyOnly UnicastUnicastTraffic CHTraffic CH

Both Broadcast Control CHBoth Broadcast Control CHandand UnicastUnicastTraffic CHTraffic CH

RelayingRelayingChannelsChannels

RSRSCapabilitiesCapabilities

Low CapabilityLow Capability

•Relay data traffic

only

•Control m essages

are provided

through a direct

link from BS

•RS-M S link control

by BS

High CapabilityHigh Capability

•Transm it DL

control M essages

•Provide M S w ith

Netw ork_Entry

procedure

on behalf of BS

•RS-M S link control

by RS

… … …

Centralised vs. distributed control

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• Example scenario with before-mentioned capabilities [142]:

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– Technical Challenges of IEEE 802.16j [1/2] –

• Use of advanced antenna techniques at PHY:

– MIMO, beamforming, interference nulling, etc.

• Advanced approaches at MAC/Link Layer:

– scheduling, radio resource management, power control, etc.

– centralised versus distributed control approaches, etc.

• Novel approaches for routing protocols:

– centralised versus distributed flow control;

– hierarchical or other topologies.

• QoS has to be dealt with appropriately:

– network-wide load balancing;

– congestion and flow control.

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– Technical Challenges of IEEE 802.16j [2/2] –

• Frequency planning has to be done appropriately:

– shared or separate PMP and relay link bands;

– interference mitigation in access (RS/MS) and BS/RS link;

– frequency reuse / spatial multiplexing in BS/RS link.

• Other important issues are:

– call admission and traffic shaping policies;

– transport layer protocols for multi-hop networks;

– network auto-reconfiguration under the control of BS;

– network management for portable / mobile RS;

– security considerations for portable / mobile RS.

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– 802.16j Simulations: DL Coverage [1/2] –

• The Motorola folks at IEEE 802.16j studied the downlink coverage reliability for a 2 hop

system with 6 relay stations with the below-given specs [142]:

• modelling assumptions:

– fc =2.5GHz, B = 10MHz, omni-directional antenna;

– BS-RS: LOS; RS-MS & BS-MS: nLOS; RS location: 0.6 x cell radius;

• coverage reliability:

– carrier-to-interference-and-noise-ratio (CINR) at 95% coverage;

– 95% of the users in a cell receive equal or more than the CINR value.

• interference calculations:

– single hop: no interference for intracell; from BSs in other cell for intercell.

– dual hop: no interference for intracell because of orthogonal time-slots; from one RS

in each cell for intercell.347

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– 802.16j Simulations: DL Coverage [2/2] –

• The underlying scenario and its CINR gains are as follows [142]:

1

2

5

7

6

3

4BS

RS1

RS2

RS3

RS4

RS5

RS6

(a) Scenario.

-7

-6

-5

-4

-3

-2

-1

0

1

0 500 1000 1500 2000

C ell Radius (m )

CINR (d

B) at95%

Coverage

S ingle hop 2-hop

(b) Performance Gains.

348

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– 802.16j Simulations: Efficiency & Outage [1/2] –

• The Intel folks at IEEE 802.16j studied the spectral efficiencies and link capacity outage

probabilities with the below-given specs [142]:

• assumption of a one-dimensional network from MMR-BS to MS/SS via N DF RSs

located equidistantly;

• channel includes pathloss, lognormal shadowing;

• no consideration of spatial reuse, interference, synchronization error;

• spectral efficiency denotes the maximum achievable rate per Hz;

• outage is defined as the event in which the achieved end-to-end data rate falls below the

target data rate.

M -BS RS 1 RS 2 RS 3 RS N M S/SS

349

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– 802.16j Simulations: Efficiency & Outage [2/2] –

• The spectral efficiencies and outages are as follows [142]:

0 2 4 6 8 10 120

1

2

3

4

5

6

7

Num ber of hops

Spectral efficiency (bps/Hz)

channel type = 1

path loss & shadowing only

d = 0.5 km

d = 1 km

d = 2 km

d = 3 km

Inter-term inal distance

(c) Spectral Efficiencies.

Relay gains w /o SS change

r

(d) Rate Outage Probabilities.

350

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– 802.16j Simulations: DL & UL Throughput [1/2] –

• The Samsung folks at IEEE 802.16j studied the downlink and uplink throughput gain for

2-hop fixed relays in a Manhattan-like environment with the below-given specs [142]:

• The underlying system model was as follows:

– TDD OFDMA based on IEEE Std 802.16e-2005;

– rate adaptation control scheme for both DL & UL;

– 49 BSs, housing block size of 200 m, road width of 30 m;

– frequency reuse among relays of 1 (Kr = 1) or 4 (Kr = 4).

BSX RS

351

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– 802.16j Simulations: DL & UL Throughput [2/2] –

• Env1 (high BS/RS antennas): gains of 20% in DL and 38% in UL;

Env2 (low BS/RS antennas): gains of 22% in DL and 36% in UL:

UplinkDownlink

0

10

20

30

40

50

60

Single-hop Repeater Relay (Kr=4) Relay(Kr=1)

Cell Throughput (M

bps)

Env1 Env2

0

10

20

30

40

50

60

Single-hop Repeater Relay (Kr=4) Relay(Kr=1)

Cell Throughput (M

bps)

Env1 Env2

352

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– 802.16j Simulations: RSSI & Throughput [1/3] –

• The Taiwanese academics at IEEE 802.16j studied the downlink and uplink received

signal strength and throughput in DL and UL [142]:

• 14 fixed relay stations have been deployed within the coverage of each BS, where the

baseline system is again IEEE 802.16e-2005 OFDMA.

Fixed Relay Station (FRS)

Base Station (BS)

Coverage of BS

M obile Station (M S)

BS coverage: 1 km

FRS coverage: 0.6 km (along main street)

M S speed: 30 km/hr

Handoff type: Hard Handoff

M S arrival: Poisson process

Traffic model: Full buffer m odel

353

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• Downlink improvement on average received signal quality: > 20dB;

Downlink throughput enhancement: up to 116.41%.

– Exam ple I: Sub-channels are exclusively allocated to each FRS

– Exam ple II: All sub-channels can be reused by each FRS

Received signal qualityis im proved by Relay

CDF of Received Signal Quality Cell Throughput (M bps)

354

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• Uplink average MS transmit power saved: ≈ 10dB (Example I);

Uplink throughput enhancement: up to 41.66% (Example II).

– Exam ple I: Only power control is considered

– Exam ple II: Both power and adaptive rate control are considered

M S transm it powerissaved by Relay

CDF of M S Transm it Power Cell Throughput (M bps)

355

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– 802.16j Protocol Stack –

• Above results have been considered promising and prior mentioned challenges have

been addressed, having led to [143]. An example protocol stack is shown below and all

specs can be found in [143].

R- PHY

R-MAC

MAC-CPS

MAC-CS

802.16 MR-BS Access Relay Station

PHY

MAC-CPS-liteMAC-SS

PHY

MAC-CPS

MAC-CS

802.16e MS

MAC-SS

Intermediate Relay Station

MAC-CPS-lite

R- PHY

R-MAC

R- PHY

R-MAC

R- PHY

R-MAC

Figure 82: Example multi-hop relay data protocol stack for simple relay station.

356

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8.3 Economical Studies

357

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– IEEE 802.16j Study: Motivation [1/3] –

• Numerous published documents have observed the short comings of current cellular

systems. This has been summarised in [142].

• As such, current deployments suffer from:

– limited spectrum and/or insufficient wire-line capacity;

– low SINR at cell edge;

– coverage holes due to shadowing.

• Reducing the cell size improves conditions, but:

– limited availability of wire-line infrastructure in developing markets;

– limited access to traditional cell site locations;

– prohibitive installation and operating costs (backhaul is large fraction);

– expensive redundant equipment, backhaul, backup power at cell sites for backup.

358

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• Economical coverage, capacity and QoS enhancement have been exemplified in [142]:

BS

L

L

RSL

RS

RS

RS

Fault tolerance via

m ulti-path redundancy

Load sharing am ong RSs

RS

RS

RS

RS

Flexible placem ent of cell sites

due to fewer access lim itations

Spectrally efficient architectures and

spatial frequency reuse

RS RS

Replacem ent of low rate,

unreliable links with m ultiple

high rate, reliable links

359

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• Lower CAPEX and OPEX due to:

– wireless backhaul;

– lower site acquisition costs;

– less costly antenna structure for RS;

– lower cost and complexity of RS;

– faster deployment.

• Improved return on investment (ROI):

– relay-augmented network could provide higher average revenue per user (ARPU)

through higher grades of service

– and at lower overall incremental costs.

360

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– IEEE 802.16j Study: Analysis [1/5] –

• The case of pure WiMAX and MMR-enabled WiMAX has been studied in [142]:

LO S

LOS

Legend

Relay Station Cell

M M R Base Station Cell

Base Station Cell

361

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• The following CAPEX and OPEX assumptions have been made [142]:

Administrative, backhaul, access points, and network costs

Base station

W ired backhaul provision(depending on wired backhaul traffic assum ptions)

Site acquisition & construction per cell

RS Cell

M M RConv.W iM AX

M M R-BSCell

BS Cell

<<>Current value

<<SameCurrent value

CapEx N/A>Current value

<<SameCurrent valueO pEx

Legend: > greater than

<< significantly less than

362

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• Case Scenario 1: Heavy Traffic, Urban Environment:

– capacity limited;

– traffic load is still less than capacity of MMR deployment;

– MMR-BS cell structure dimensioned for min 3.7dB SNR at cell edge;

– conventional WiMAX cell structure splits aggressively due to high traffic demand.

• Case Scenario 2: Light Traffic, Urban/Suburban/Rural Environment:

– range limited;

– traffic load based on mix of current customer demand and varying customer

densities;

– MMR-BS cell structure dimensioned for min 3.7dB SNR at cell edge;

– conventional WiMAX cell structure splits modestly due to low traffic demand.

363

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• CAPEX and Year 7 OPEX of MMR versus conventional WiMAX (Scenario 1) [142]:

0

1

2

3

4

5

6

7

8

9

10

56 33 12

Num ber of RS per M M R-BS

Relative Cost (norm

alized w.r.t. 1st bar)

M M R CapEx

M M R OpEx

Conv CapEx

Conv OpEx

364

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• CAPEX and Year 7 OPEX of MMR versus conventional WiMAX (Scenario 2) [142]:

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

56 33 12

Num ber of RS per M M R-BS

Relative Cost (norm

alized w.r.t. 1st bar)

M M R CapEx

M M R OpEx

Conv CapEx

Conv OpEx

365

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– IEEE 802.16j Study: Conclusions [142] –

• Conventional WiMAX:

– CAPEX is a significant cost relative to OPEX.

• MMR-based WiMAX:

– CAPEX grows with decreasing MMR-BS:RS ratio;

– CAPEX only slightly larger than OPEX under light load;

– CAPEX considerably less than OPEX under heavy load.

• Comparison between both:

– CAPEX and OPEX of MMR always less than conventional WiMAX;

– economic gains from capacity improvement significantly larger than those

from range extension.

366

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– KTH’s Study: Assumptions [1/2] –

Bogdan Timus aimed at addressing the following set of pertinent questions in [152]:

• Can the large scale use of fixed relays lead to a good (feasible) business case?

• Under which circumstances, i.e. should they be used in rural or urban environments, for

coverage or capacity enhancement?

• What fundamental aspect(s) makes relaying better than other techniques, e.g. direct

communication?

• How large are the gains obtained with advanced techniques as compared to traditional

relaying techniques?

• How sensitive are the results to traditional network design parameters, such as antenna

height, maximum transmission power, etc.?

367

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– KTH’s Study: Assumptions [2/2] –

• Example of empirical CAPEX and OPEX costs according to [152]:

e

e

e

368

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– KTH’s Study: Conclusions [1/2] –

The answer to the questions posed on Slide 367 can be summarised as [152]:

• Large-scale unplanned deployment of fixed relays on lamp-posts is worthy only if the

total cost of the relay is

– about 10 % of the BS cost

– and 50 − 100 % of the additional BS planning cost;

– the relay cost should hence be in the range of 3000 Euros over 10 years of operation.

• Large scale planned deployment of fixed relays brings cost savings w.r.t. cellular

systems:

– for coverage extension cases;

– relay cost is about 10 % of the BS cost;

– tight re-use of radio resources is pivotal.

369

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– KTH’s Study: Conclusions [2/2] –

• With respect to advanced cooperative techniques compared to simple relaying:

– cooperative MIMO techniques bring minor cost gains w.r.t. simple relaying;

differences are more visible if relay roll-out is planned;

– TDMA scheduling without coordination between cells does not suffice.

• Most influential system performance parameters:

– for planned roll-out, the transmission power, antenna gain and relay height are much

more important than choice of relaying technique;

– for un-planned roll-outs, there is little difference between above and below rooftop

relay deployments.

• A conclusive study entirely reflecting reality is missing; however, it is obvious that ...

A hybrid deployment with fixed relays and BSs isunlikely to bring a magnitude of cost savings!

370

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8.4 Other Multi-Hop Systems

371

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– Short-Range WLAN/Bluetooth/Zigbee –

• A huge body of research papers and standard specifications are available on

WLAN/Bluetooth/Zigbee/etc.

• They all failed to produce commercially viable multi-hop products to-date.

• This is mainly attributed to:

– scalability issues,

– long discovery times,

– large latency, etc.

• We will not go in further details as this is out of the scope of this tutorial.

372

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– Japan’s Virtual Cellular Network [1/2] –

• Adachi et al. introduced the concept of Virtual Cellular Network [155]:

– in-depth technical and performance analysis, together with entire protocol stack;

– reduced transmission power and signalling overhead in the case of cell splitting;

W ireless port

Central port

Control stationCore Network

Virtual cell

W ireless port

Central port

Control stationCore Network

Virtual cell

373

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– Japan’s Virtual Cellular Network [2/2] –

• At high load, the VCN outperforms traditional cellular systems [155]:

1E-05

1E-04

1E-03

1E-02

1E-01

1E+00

2 4 6 8 10Offered load G

Blocking probability

C =8

C =4

C =2

M ulti-hop VCN

Present cellular NW

K =20

J=4

SF=16

L=2

α =3.5

σ =6dB

374

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– 3GPP ODMA [1/3] –

• Opportunity Driven Multiple Access (ODMA) [1]:

– communications relaying protocol proposed for UMTS TDD mode;

– introduced at ETSI SMG2 ’96, proposed as UMTS standard, discontinued in R’99;

– aim was to increase range of high data rate services.

ODM ATERM INAL

H igh BitRate DataTDD

Coverage

Low BitRate DataTDD

Coverage

TDD ODM A

High Bit Rate

TDD ODM A

High Bit Rate

BorderRegion

NOcoverage

Layer 1 SynchInform ation

375

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– 3GPP ODMA [2/3] –

• A seminal (but largely forgotten) work of [153] demonstrated already in 2000 that

ODMA-type relaying decreases coverage holes (black squares):

(a) Conventional Cellular System. (b) ODMA-Based Cellular System.

376

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– 3GPP ODMA [3/3] –

• Relays neighbourhood discovery activity levels are influenced by [154]:

– number of neighbours;

– gradient to the base information of the neighbours;

– speed of the terminal; and

– battery power level.

• The lessons learned from ODMA are:

– only draft idea was proposed with many issues left for further study;

– concerns over complexity, battery life of users on standby, and signaling overhead

issues;

– routing is one of the key issues requiring more attention.

377

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– 3GPP/3GPP2 LTE [1/3] –

• The requirements on the Long Term Evolution (LTE) of 3G is tough [156]:

Metric

Peak data rate

Mobility support

Control plane latency (Transition time to active state)

User plane latency

Control plane capacity

Coverage(Cell sizes)

Spectrum flexibility

Requirement

DL: 100MbpsUL: 50Mbps(for 20MHz spectrum)

Up to 500kmph but opti-mized for low speeds from 0 to 15kmph

< 100ms (for idle to active)

< 5ms

> 200 users per cell (for 5MHz spectrum)

5 – 100km with slight degradation after 30km

1.25, 2.5, 5, 10, 15, and 20MHz

378

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– 3GPP/3GPP2 LTE [2/3] –

• LTE positions w.r.t. HSPA+ and WiMAX as follows [157]:

Com m on and Distinctive Features

M IM OBeam form ing

M IM OBeam form ing

M IM OBeam form ing

Antennaconcepts

TDD3.5-10 M Hz

OFDM (DL & UL)

QPSK-64QAMTurbo codesHARQ II

Quality-basedscheduling

W iM AX



M AC

QPSK-64QAMTurbo codes HARQ II

QPSK-64QAMTurbo codes HARQ II

Physical layer

FDD and TDD1.25-20 M Hz

FDD5 M Hz

Duplex andBandwidth

OFDM (DL)FDM A (UL)

CDM A (DL & UL)M ultiple access

LTEHSPA+

TXTX

tim efrequency

379

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– 3GPP/3GPP2 LTE [3/3] –

• LTE Phase II will start in Q4 2007 with proposals due in 2008/09.

• Research inputs are currently being requested in [157]:

– advanced antenna solutions;

– interference coordination, cancellation & avoidance;

– relaying techniques;

– simplified network operation; etc.

• Generally, operators ...

– ... do not feel entirely comfortable with relaying concepts based on mobile

relays, because QoS can only be guaranteed statistically;

– ... feel that fixed relays could be beneficial, despite the requirement of

planning and site acquisition;

– ... feel that other capacity-enhancing techniques will have a bigger impact.

380

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8.5 Practical Multi-Hop Systems

381

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– Ricochet –

• Ricochet [158] is a US company which was well ahead of its time by rolling-out a

broadband wireless network throughout major US cities more than 10 years ago.

• They simply formed a mesh network by means of relay-capable nodes attached to

lamp-posts. Technology was at its finest, including routing and MAC protocols, but the

technology just did not take of back then.

• Ricochet service is no longer available in the originally conceited form, because

Metricom, Ricochet’s parent company, went bankrupt. Aerie Networks has then bought

the Ricochet infrastructure and is attempting to restart it out in select markets (e.g.

Denver).

• Today, Ricochet has addressed some prior concerns; for instance, when consulting the

company’s website today, data security is well advertised. Ricochet has again taken up

business in a few US cities and is likely to grow over the upcoming years.

382

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– Coronis –

• Coronis’ Wavenis automatic metering solution is today the only commercially viable

multi-hop communications system [159]:

Providers

SMS /

GSM

PC/server

Wavecell

25/500mW

Wavetalk

25/500mW

Mesh

topology

Waveflow

25mW

Tree

topology

Star

topology

4km

200m

Network Installation & Configuration

Network

Management

383

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– Easy-C [1/2] –

• A German government funded project called “Enablers of Ambient Services and

Systems (EASY), Part C: Wide Area Coverage,” is currently kicking-off and addressing

the following requirements [160]:

– high spectral efficiency;

– fairness (e.g. good performance also for cell-edge users);

– low capital and operational cost per bit;

– low latency; etc.

• They aim at investigating the following techniques [160]:

– advanced multi-antenna (MIMO) techniques;

– multi-cell joint detection for interference cancellation;

– multi-cell interference coordination;

– cooperative relaying.

384

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– Easy-C [2/2] –

• A PHY-layer oriented testbed will be setup in downtown Dresden, Germany, comprising

10 sites with 30 cells, surrounded by another tier of 27 interferers [160]:

385

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Open Issues

386

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– Open Issues –

The design and deployment of entire systems facilitating relaying and cooperation are

entirely in its infancy! There are hence endless open questions, some pertinent of which are:

• Routing protocols:

– design of applicable routing protocols;

– incorporate incentive schemes into routing protocols.

• Deployment experiences:

– nobody knows until today whether a large-scale cooperative roll-out really works;

– exposure or really influential system parameters through real-world roll-outs.

387

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PART 9THE ROAD AHEAD

388

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– Only Some Thoughts –

• Capacity and algorithmic PHY layer designs are fairly well explored; despite numerous

unsolved problems, novel contributions are likely to be incremental.

• RF, MAC, routing protocols, cross-layer design and roll-outs are areas which are still in

their infancy; there is hence a lot of room for innovative contributions.

• What we may need today in these type of networks are entirely novel approaches for

system analysis, such as from physics or biology.

• A personal answer to the question posed at the beginning:

– Ripe: Technology (already available for a long time since there is no magic);

– Hype: Expectations (inflated research body on this subject).

We need commercially viable products if cooperative systems do not want to fall for

the same fate as traditional ad hoc networks, which have been researched for several

decades without any tangible product on the civil market today.

389

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– Credits –

The following people’s input (text, figures, research results) have been used with thanks

throughout this presentation:

• Dr Athanasios Gkelias, Imperial College, UK

• Dr Yonghui Li, University of Sydney, Australia

• Thomas Watteyne, France Telecom R&D, France

• Timus Bogdan, KTH, Sweden

• Roger B. Marks, Mitsuo Nohara, Jose Puthenkulam, Mike Hart, all involved in IEEE

802.16j.

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PART 10REFERENCES

391

REFERENCES REFERENCES'

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