ee401: advanced communication theory. act_diversity_2017.pdfee401: advanced communication theory...

EE401: Advanced Communication Theory

Professor A. ManikasChair of Communications and Array Processing

Imperial College London

Principles of Diversity Theory

Prof. A. Manikas (Imperial College) EE.401: Diversity Theory v.17 1 / 37

Table of Contents1 Introduction2 Generic Diversity Diagram3 Diversity Combining

Combining RulesSNRout ,div as a function of Diversity Channels/Branches

4 Diversity Techniques/SystemsClassificationExamples

5 Multipath DiversityRake Rx - Price& Green 1958Types of RAKE RxSummary of a Rake ReceiverDiversity Example: Apple imageMultipath Diversity in CDMA: CDMA Rake ReceiversOptimum Single-user Rx (employs Multipath Diversity)Optimum Multi-User ReceiverSuboptimal Linear Multi-user Receiver ArchitectureSuboptimal Multi-User (MU) Receiver: Decorrelating Rx

6 Some Comments on 3GMain Specifications


Introduction

Introduction

In general, the term "diversity system" refers to a system in whichthere are available two or more closely similar copies of some desiredsignal.

The ‘Diversity Combining’(or briefly "diversity") Concept:Diversity is defined as a general technique that utilizes two or morecopies of a signal with varying degrees of noise/interference effectsto achieve, by selection or a combination scheme, higher degree ofmessage-recovery performance than that achievable by any one of theindividual copies separately.

The concept of diversity was introduced in 1959 by Brennan[D. G. Brennan, "LinearDiversityCombiningTechniques", Proceedingsof the IRE, vol.47, no.6, pp.1075-1102, 1959]


Generic Diversity Diagram


N.B.: The terms "diversity branch " and "diversity channel" areequivalent



Equivalent Generic Diversity Diagram



If s represents the desired signal and xi denotes its i thdistorted copy,then the input (i/p) and output (o/p) may be represented as follows:

I i/p

x1 = β1sd + n1x2 = β2sd + n2....xN = βN sd + nN

⇒x1x2...xN

=

β1β2...βN

sd +n1n2...nN

︸︷︷︸

x=βsd+n

(1)

I o/p

sdiv = w1x1 + w2x2 + ...+ wN xN= wT x

= wT βsd︸︷︷︸desired

+ wT n︸︷︷︸noise

(2)

wherew =

[w1, w2, ..., wN

]TProf. A. Manikas (Imperial College) EE.401: Diversity Theory v.17 6 / 37


output SNR: The first term of Equ 2 is the desired term and thesecond term is due to the noise. The powers of these two terms are:

Pout ,desired = E{(wT βsd

)2}= Pdw

TRββw (3)

Pout ,noise = E{(wT n

)2}= wTRnnw (4)

SNRout ,div =Pout ,desiredPout ,noise

=PdwTRββw

wTRnnw=Pdσ2n

wTRββw

wTw(5)

where

cov(β) = Rββ = E{

β βT}

(6)

cov(n) = Rnn = E{n nT }(a)= σ2nIN (7)

Note: the equality (a) is valid if the noise is AWGN


Diversity Combining Combining Rules

Diversity Combining Rules

max ratio combining (MRC) or, equivalently, maximumsignal-to-noise-power ratio combining:

wMRC

= arg{maxw(SNRout ,div)

}(8)

selection combining (SC) diversity rule:

wk ={1 if SNRk > SNRi∀i0 otherwise

(9)

equal gain combining (EGC):

w1 = w2 = ... = wN (10)


Diversity Combining Combining Rules

scanning combining (SCC):

−if SNRk > threshold then{wk = 1wj = 0; ∀j 6= k

−if SNRk fall below threshold then k = k + 1−repeat

(11)

I That is, a branch (say the k-th branch) is selected that has SNR abovea predetermined threshold (SNRk >threshold) and is used until itsSNR drops below that threshold.

I Then the next branch is selected if its SNR is above the threshold, etc.


Diversity Combining SNRout,div

SNRout,div as a function of Diversity Channels/Branches


Diversity Techniques/Systems Classification

Classification of Diversity Techniques/Systems

In diversity systems, there are several known methods of obtainingtwo or more signals si , in order to be combined using one of thediversity combining rules, to obtain an improved signal.

According to the method of obtaining copies of the same signal thediversity systems and their associated techniques are classified asfollows:

I Multi-Path DiversityI Time DiversityI Frequency DiversityI Space DiversityI Polarization DiversityI Code Diversity


Diversity Techniques/Systems Examples

Examples

Multi-Path Diversity:

Time Diversity:

Frequency Diversity:



More Examples

Space Diversity (or Antenna Diversity):

1) Tx Diversity:



2) Rx Diversity:



3) Tx-Rx Diversity:

Array systems/techniques can be seen as the most sophisticated andadvanced space diversity systems/techniques.


Multipath Diversity Rake Rx

Rake Rx - Price & Green 1958

Employs the “diversity” concept which is shown in generic terms inthe figure below.



In this case the diversity branches are replaced by correlation receivers(or matched filters). This is known as multipath diversity, the overallstructure as RAKE receiver and the associated diversity branches (i.e.correlators) as RAKE fingers .Thus, in this way, a plurality of parallel correlation receivers (fingers)is used with each of them synchronised to a different path. Then theoutputs of these fingers are combined according to a diversitycombining criterion/rule (followed by a decision device).

RAKE receiver is an optimum coherent receiver for multipathchannels and it was introduced in 1958 by Price and Green[R. Price and P. E. Green, "A Communication Technique forMultipath Channels", Proceedings of IRE, pp.555-570, March 1958]



The generic structure of a RAKE receiver is below.

Hence, if one path (or more) is “lost” (because its associated pathgain coeffi cient becomes very small) the output SNR remains in anoptimum level.


Multipath Diversity Types of RAKE Rx

Types of Rake Rx

A finger is, by itself, an optimum coherent receiver (correlator ormatched filter receiver) while, according to Brennan’s original paper[Brennan 1959] there are four main diversity combining rules tocombine the outputs of the fingers.

Thus, there are four classes of RAKE receivers - based on “diversitycombining” rules:

1 RAKE with maximum-ratio combining (this is the best of these fourtypes and provides the highest output SNR - but is more complex);

2 RAKE with selection combining (RAKE-SC);

3 RAKE with equal gain combining (RAKE-EGC);

4 RAKE with scanning combining (RAKE SCC)


Multipath Diversity Summary of a Rake Receiver

Summary of a Rake Receiver

First implementation: 1950s.

RAKE receiver is a matched filter receiver for wide-band signals.

It is used to resolve paths delayed by more than Tc .

Main assumption: the channel is time invariant over the decisioninterval [0,Tcs ].

Rake-Receiver = optimum Single-user Receiver

it has a number of ‘fingers’ (One Rake-‘finger’per path)


Multipath Diversity Diversity Example: Apple Image

Diversity Example: Apple image

<TX Image– – – -

Rake’s o/p– – – —>

Images at each branch of a Rake Rx of 6 fingers


Multipath Diversity Multipath Diversity in CDMA: CDMA Rake Receivers

Multipath Diversity in CDMA

In a wireless channel, in addition to the noise, the transmitted signalis also affected by fading effects (due to multipath propagation andDoppler effects).

If the paths in a multipath channel can be separated (i.e.Tspread > Tc ) then there are two main ways to exploit the multipathpropagation channel for enhancing the performance of the receiver,using the auto-correlation properties of the PN-codes:

1 to use a correlation receiver (CORRELATION Rx) that is perfectlysynchronised to one of the paths (i.e. correct delay).

2 to employ the “diversity” concept (RAKE Rx).



Correlation RxA correlation receiver is perfectly synchronised to one of the paths(i.e. correct delay)

I This will suppress all the other received paths based on thecorrelation properties of the PN-code(with m-sequences having the best auto-correlation properties).

The figure below shows a representative example of the correlationfunction at the input and at the output of a correlator operating inthe presence of 3 paths.



The PN-signal b(t) is an m-sequence of length 31 and is synchronisedto the 3rd path which has a delay equal to 7Tc with Tc denoting thechip period.

Thus, at the o/p of the correlator only the contribution of the 3rdpath will appear (i.e. the evaluation of the correlation function at 7Tc) while the 1st and 2nd paths will be rejected as “unwanted”self-interference. Indeed:

I at point-A:

r(t) = β1b(t − 2Tc )a[n] + β2b(t − 4Tc )a[n] + β3b(t − 7Tc )a[n]

I at point-B:r(t)b(t − 7Tc )

I at point-C:(n+1)Tcs∫nTcs

r(t)b(t − 7Tc )dt =↘↘



(n+1)Tcs∫nTcs

r(t)b(t − 7Tc )dt =

'0︷︸︸︷(n+1)Tcs∫nTcs

β1b(t − 2Tc )b(t − 7Tc )a[n]dt

+

'0︷︸︸︷(n+1)Tcs∫nTcs


+

=β3NcTc a[n]︷︸︸︷(n+1)Tcs∫nTcs


= 0+ 0+ β3NcTca[n]

I However, although the correlation receiver handles the multipath problem, if the

associated path gain (i.e. β3, which changes with time) is reduced significantly (e.g.shadowing effects) this may result in the loss of the signal at the output of the correlator

(i.e. output SNR=0 or very small).



CDMA Rake Receivers

Two classes:

1 Single-user Receivers

2 Multi-user Receivers

Single user Receiver: requires no knowledge beyond the PN-sequenceand the timing of the user it wants to demodulate/receive ("desired"user)

Multi-user Receiver: not only knows the PN-sequence and the timingof every active user but also knows (or can estimate) the receivedamplitudes of all users and the noise level



Optimum Single-user Rx (employs Multipath Diversity)Optimum Single-user (SU)Receiver = RAKE RxMultipath Channel (j-th user):



BPSK-CDMA RAKE Rx (multipath-diversity)

F The delay τjk , fading coeffi ient βjk ,and φjk of the k-th path of the j-thuser is estimated ∀k using ‘scanning’correlators monitoring the pilotchannel.



BPSK-CDMA Correlation Rx (without diversity): if there is a singlepath i.e. no multipath then optimum

The delay τj2 of the 2nd path of the j-th user is estimated using a‘scanning’correlator monitoring the pilot channel.



Optimum Multi-User Receiver

Optimum Detection:A detector which employs correlators has to take into account thePN-codes (or equivalent the PN signals) of all other CDMA users inthe system in order to be optimum in the Maximum Likelihood sense,unless the PN-codes are perfectly orthogonal.

The optimum detector, however, is non-linear and computationally fartoo complex.

Optimum MU Receiver Architecture↘



Note that there is a huge gap in performance and complexity betweenthe optimum single-user and optimum multi-user receivers



Suboptimal Linear Multi-user Receiver Architecture



If T = R−1

then the Rx is known as decorrelating MU receiver

If T =(R + σ2nA−2

)−1then the Rx is known as minimum mse (mmse) MU receiver

where

R denoting the (K ×K ) cross-correlation matrix of PN-signals

A =

√P1, 0, ..., 0

0,√P2, ..., 0

..., ..., ..., ...

0, 0, ...,√PK

, (K ×K )matrixσ2n = noise power



Suboptimal Multi-User (MU) Receiver: Decorrelating Rx

T = R−1: decorrelating MU receiver

This is a typical MU receiver which is suboptimal but much simplerthan the optimum MU receiver. Also it is optimum according to thefollowing three different criteria when the received amplitudes areunknown

I least squaresI near-far resistanceI maximum-likelihood

The performance of this MU receiver is used as a comparative upperbound for the performace of different single-user receivers.



Note that:

Y = R A a+ n (12)

⇒ G = R−1Y = R−1R Aa +R−1n = Aa +R−1n (13)

wherea =

[a1[n], a2[n], ..., aK [n]

]T(14)

I e.g. Two users (K = 2) with cross-correlation ρ12 = ρ21 = ρ

⇒ R−1 =

[1, ρρ, 1

]−1=

11− ρ2

.

[1, −ρ−ρ, 1

](15)

I This implies that:

G = R−1Y ⇒[G1G2

]=

11− ρ2

.

[1, −ρ−ρ, 1

].

[Y1Y2

](16)

⇒[G1G2

]=

[ 11−ρ2

.(Y1 − ρ.Y2)1

1−ρ2.(−ρY1 + Y2)

](17)



Therefore, in this case, the decorrelating receiver, for K = 2, can beimplemented as follows:

Note: The normalisation with 11−ρ2

has been ignored (it is notnecessary since both ‘desired’and ‘noise’terms are weighted)


Some Comments on 3G Main Specifications

Some Comments on 3G: Main Specs

IS-95 UMTS

Generation 2G (USA) 3G (EU)

Type CDMA W-CDMA

Frame duration 20msec 10msec

Uplink

25MHz︷︸︸︷824− 849MHz︸︷︷︸

mod:QPSK

60MHz︷︸︸︷1920− 1980MHz︸︷︷︸

mod:balanced QPSK, i.e. QPSK2

Downlink

25MHz︷︸︸︷869− 894MHz︸︷︷︸

mod:oQPSK

60MHz︷︸︸︷2110− 2170MHz︸︷︷︸

mod:dual QPSK, i.e. QPSK1

Bss 1.23MHz 5MHz,10MHz,20MHz

Tc 813.8ns 244ns,122ns, 61ns

rc = 1Tc

1.2288Mchipssec 4.096Mchipssec (reduced to 3.084Mchipssec )

roll-off-factor 0.22;Note: Bss = 1Tc(1+roll-off-factor)=4.99712MHz'5MHz

Receiver’s type RAKE RAKE


ee401: advanced communication theory. act_diversity_2017.pdfee401: advanced communication theory...

Documents