radio planning problems and methodologies in wireless...

Politecnico di MilanoAdvanced Network Technologies Laboratory

Radio planning problems and methodologies in wireless networks. Multiple access schemes

Prof. Antonio Capone

Master program Communication Technologies, Systems and NetworksUniversidad Politécnica de ValenciaMay 14-16 2008

Antonio Capone: Wireless Networks 2

Summary

Introduction to wireless networksMain differences with wired networksRadio channelMobility management

Multiple accessPhysical channels (FDMA, TDMA, CDMA)Packet access (scheduled access, random access)

Radio resource planningCoverage planningFrequency assignmentJoint coverage and capacity planning


Wireless Networks

Is the transmission medium the only difference?

The peculiar medium characteristics have great impact on system characteristicsWireless networks allow users to move and naturally manage mobility

Wireless or wired, what is better?Wireless or wired, what is better?

wiredwire-less

Well, it depends on the situation!Well, it depends on the situation!


Network architecture

Access network

Backbone network


Wireless access networks

Wireless networks are mainly access networksBackbone networks composed of radio point-to-point links are usually not considered wireless networksWireless access networks are more challenging and have many fundamental differences with respect to wired access networksThe first main difference is that the transmission medium is broadcast


Broadcast channel

Centralized broadcast channelDistributed broadcast channel


Centralized broadcast channel

Fixed access point (cellular systems, WLAN, WMAN)

WirednetworkWirednetwork

Mobile-access pointconnection


Centralized broadcast channel

Cellular coverage: The territory coverage is obtained by Base Stations–BS (or Access Points) that provide radio access to Mobile Stations–MS within a service area called CELL

BaseStation

MobileStation

Cell


Distributed broadcast channel

Ad-hoc wireless networks (mesh networks, sensor networks)

mobile- mobile connections


Distributed broadcast channel

In multi-hop operation mobile stations can forward information

sourcedestinationrelay

relay


Wired-Wireless networks:Main differences

Shared transmission mediumMultiple access mechanismsRadio resource reuse

Centralswith

cable

Radiochannel



Radio channelVariable channel characteristicsAdvanced modulation and coding schemes


User mobilityStand-by mobilityActive session (conversation) mobility




In this course we’ll focus on the issues related to the shared wireless medium:

Multiple access (Part A)Resource planning and reuse (Part B)

But first a few comments on:

In this course we’ll focus on the issues related to the shared wireless medium:

Multiple access (Part A)Resource planning and reuse (Part B)

But first a few comments on:

Wireless channelWireless channel Mobility managementMobility management


Wireless channel

Very bad channel compared to other wired mediumsSignals propagation is subject to :

High attenuation due to distanceSupplementary attenuation due to obstaclesMultipath propagation


Wireless channel: radio spectrum

fc

=λ

m/s 103 8⋅=c

Radio waves

Wave length

Light speed

Frequency f

)2cos()( ϕπ += ftts



Higher frequencies:more bandwidthless crowded spectrumbut greater attenuation through walls

Lower frequenciesbandwidth limitedlonger antennas requiredgreater antenna separation requiredseveral sources of man-made noise


Wireless channel: antennas

Transmission and reception are achieved by means of an antennaAn antenna is an electrical conductor or system of conductors

Transmission - radiates electromagnetic energy into spaceReception - collects electromagnetic energy from space

In two-way communication, the same antenna can be used for transmission and receptionIsotropic antenna (idealized)

Radiates power equally in all directions (3D)Real antennas always have directive effects (vertically and/or horizontally)


Wireless channel: attenuation

Isotropic radiator transmitting power PT uniformly in all directions

Power density F at distance d is:

]W/m[4

22d

PF T

π=

distance d

source area



Directive characteristics of real antennas concentrate power in some directionsThis effect can be modeled using the gaing(θ) in the direction θ

The maximum gain gT is convetionally in the direction θ =0.

24/direction in distanceat power )(

dPdg

T πθθ =



The power density in the maximum gain direction is given by:

The product PT gT is called EIRP (Effective Isotropically Radiated Power) and it is the power required to reach the same power density with an isotropic radiator

]W/m[4

)( 22d

gPdF TT

π=



The received power depends on the power density at the receiver antenna and its equivalent area:

For an isotropic antenna we have:While for a directive antenna we can concentrate energy:

Where gR is the receiver antenna gainTherefore:

eR AdFP )(=

πλ4

2

=eA

eRR AgdFP )(=

2

4⎟⎠⎞

⎜⎝⎛=

dggPP RTTR π

λ


Wireless channel: free space model (Friis)

The received power is ∝ d-2

This is known as the free space propagation modelIt can be used for example with point-to-point radio links

22

44 ⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎠⎞

⎜⎝⎛=

fdcggP

dggPP RTTRTTR ππ

λ


Wireless channel: propagation impairments

Unfortunately, in real environments the propagation of electromagnetic waves is more complex that in free space:

Reflection

Shadowing


Wireless channel: propagation impairments

DiffractionWhen the surface encountered has sharp edges. Bending the wave

ScatteringWhen the wave encounters objects smaller than the wavelength (vegetation, clouds, street signs)


Wireless channel: two ray model

Just in the case of reflection with only two rays (a direct ray and a reflected one) received power is quite different wrt free spaceIt can shown that:

hR

hT

d

4

22

)(dhhggPdP RT

RTTR ≅


Wireless channel: empirical modelsMore complex scenarios can hardly be modeled with closed formulasEmpirical models are usually adopted where received power is ∝ d-η

where the η is the propagation factor which typically ranges between 2 and 5More complex empirical models (e.g. Hata) take into account several parameters including scenario (urban, rural), antenna heights, etc.

ηπλ

dggPP RTTR

14

2

⎟⎠⎞

⎜⎝⎛=


Wireless channel: empirical models

Okumura/Hata formula:

wheref frequency in MHz (from 150 to 1500 MHz)hT base station height (in m)hR mobile station height (in m) – a(hR) correlation factor depending on area shaped distance (in km)

For a 900 MHz system, hT = 30 m, a(hR) ≈ 0:

( ) [dB] loglog55.69.44)(log82.13log16.2655.69

dhhahfL

T

RTP

−++−−+=

dL P log22.3542.126 +=


Wireless channel: multipathfading

Copies of the same signal arrive from different pathsTheir combination at the receiver depends on:

Number of copies Relative shiftamplitudefrequency


Wireless channel: multipath fading

The resultingsignal can beattenuated

-2,5

-2

-1,5

-1

-0,5

0

0,5

1

1,5

2

2,5

0 5 10 15 20

s(t)s(t+T)s(t)+s(t+T)

-1,5

-1

-0,5

0

0,5

1

1,5

0 5 10 15 20

s(t)s(t+T)s(t)+s(t+T)

or amplified

T=4/5π

T= π /6


Wireless channel: shadowing

Signal can be partially absorbed or reflected by obstaclesFurther attenuation called shadowing


Mobility managementIn wireless networks, users can roam in the service area moving among cellsThis require an adaptive routing of information based on user position in the networkAll wireless networks have a set of mobility management mechanisms to track user position


Mobility management: cellular systemsIn cellular systems mobility management adopts different procedures based on user state IDLE (no active call) or ACTIVE (in conversation)

ACTIVE: dynamic call rerouting cell-by-cell (Handover)IDLE: user position tracking (Cell selection, Location Update, Paging)


Mobility management: Cell selection

Base stations transmit periodically general system information and cell identity on a broadcast channelUser terminals scan all channels to received broadcast transmissions from nearby base stationsUser terminal select autonomously the best cell, usually based on signal strength


Mobility management: Location Update

Location Area: set of cellsUser position tracking is based on location areas and not on cellsThe currently visited LA is stored in a data base

LA 1LA 2

Data Base


Mobility management: Location UpdateWhen a mobile terminal in idle state move in a different LA a Location Update procedure is startedInformation in the data base is used to route incoming call to mobile terminals

LA 2

Data Base

LA 1


Mobility management: Paging

When a call must be routed to a mobile terminal the currently visited LA is retrieved from the data baseThen the paging procedure is startedAll base stations in the LA broadcast a paging message with the ID of the called userWhen the mobile terminal replies the call is routed

Data Base

pagingpaging

reply


Mobility management: Handover

Handover is always triggered by the network based on measurements performed by the mobile terminal (received powers, quality, etc.)Handover procedures must be fast to avoid quality degradation

Δt t

Handover TH

Receiver THh



When starting a handover?

Due to signal fluctuations call may be switched back to original cell (ping-pong effect)



Hard Handover (GSM-2G)

Soft Handover (UMTS-3G)


Mobility management: Data networks (WLAN, WMAN, …)

Within the same network, mobility is managed at layer twoAmong different networks mobility is managed at layer three (using e.g. Mobile IP)

A

RAP2AP1

A


Part AMultiple access


Multiplexing and multiple access

Different information flows sharing the same physical channelOne transmitting station: multiplexingMany transmitting stations (one per flow): multiple access


Multiplexing and multiple access

AM

Node 1

AM

Node 4

AM

Node 3

AM

Node 2

Broadcast channel

MPX DMPX

Node 1 Node 2

MultipleAccess

Multiplexing


Wireless networks: Multiplexing

One transmitting station

channel 2channel 1 channel 3

Typical problem indownlink (forward link) of cellular systems (base station – mobile users)

Typical problem indownlink (forward link) of cellular systems (base station – mobile users)


Wireless networks: Multiple access

Several transmitting stations (coordination problem)

channel 1

channel 2channel 3

Typical uplink (reverse link) problem in cellular systems (from users to base station)Typical uplink (reverse link) problem in cellular systems (from users to base station)

A duplexing technique is also needed for sharing between uplink and downlink channels


Wireless networks: Frequency reuse

The radio resource is limited and can not be exclusively dedicated to a channel in a cell The same radio resource is used in different cells sufficiently far apart to not interfereCritical problem with a trade off between number and quality of channels … see later on


Multiple access

From now on “Multiple access” includes also multiplexing and duplexingMultiple access at the physical layer: A single channel is divided into subchannels using physical parameters (frequency, time, code) – static resource managementMultiple access at logical layer: packet access with logical information in the packet header and distributed coordination mechanisms – dynamic resource managementIn real systems different multiple access techniques at physical and logical layers are usually combined together


FDM/FDMA (Frequency Division Multiplexing/Multiple Access)

Available bandwidth is divided into sub-bands and assigned to different sub-channelsSimple technique used basically in all systems

fmin fmax

mod.f


TDM/TDMA (Time Division Multiplexing/Multiple Access)

Time is divided into slotsGroups of N consecutive slots are organized into framesA subchannel can use a given slot in all frames

1 2 3 4 5 1 2 3 4 53 4 5 1

frame frame

... ...

slot


TDMA: Guard time

)2(max iigT τ=


TDMA: reduced guard time

Timing Advance:If the propagation delay τ is known it can be compensated anticipating the transmission (centralized access only!)τ must be dynamically estimated and signaled back to the mobile

1) First transm.

3) Delay signaled back

2) Delay estimation 4) Subsequent transm.with reduced guard time


CDM/CDMA (Code Division Multiplexing/Multiple Access)

Symbols (bits) on the channels are multiplied by a codeIn CDM codes are orthogonal, while in CDMA they have limited correlation

0

0)()(

211

210

=⋅

=⋅

∑

∫

=ii

N

i

T

cc

tCtCC1(t)

C2(t)


CDM/CDMA (Code Division Multiplexing/Multiple Access)

+

s1

sN

s2

sN

s2

s1

C1 C1

C2C2

CN CN

∫ ∑ =⋅⎟⎠

⎞⎜⎝

⎛ −

=Tkk

N

iii sCCs

1

0


CDMA: spreading and despreading

The code “expands” the radio bandwidth of the signal

S(f)f

SM(f)f

B

nB

Spreading ofthe radio spectrum

n number of chips in the code: “spreading factor” (SF)



Different signals use the same radio band

sM1(t)

sM2(t)

+fnB



At receiver the signal is multiplied by the code (de-spreading)

fnB fBDe-spreading

fB

The interfence of the other signals is reduced by 1/n


Packet access

At logical layer multiple access can be managed in a dynamic and distributed way using multiple access protocolsFirst multiple access protocols have been designed for LANsNowadays multiple access protocols are mainly used in wireless networks (no more shared medium wired LANs)


Packet access: Classification

Scheduled accessTransmissions on the channel are sequential with no conflictsPolling schemesCentralized scheduling schemes

Random accessTransmission are partially uncoordinated and can overlap (collision)Conflicts are resolved using distributed procedures based on random retransmission delay


Packet access: Local and global queues

In the case of multiplexing (single station) we have a single queue that is managed according to a scheduling algorithmIn case of multiple access with M stations with local queues we still have the opportunity to use a single “virtual” queue at a central decision point that schedule access to the channel

...


Packet access: Local and global queues

However, to inform the scheduler of the status of the local queues and provide access grants we have to use the channel (coordination signaling)The centralized scheduling approach is quite flexible but complexIt is adopted in several wireless technologies like e.g. WiMax


Assumptions and notation

In the following we drop the assumption of global coordination and analyze distributed mechanismsLet us assume that arrival times in the M local queues are described by a Poisson process with rate λ/M (λ global rate)The system status is described by vector

Where ni is the number of packets in queue iThe system evolution is described by the process N(t)

( )Mnnn ,...,, 21=n


Polling

Polling schemes are scheduled access schemes where stations access the channel according to a cyclic orderThe polling message, or token, is the grant for access the channel The token can be distributed by a central station (roll-call polling) or passed from station to station (hub polling or token system)Let us assume that packet transmission time is T and that token passing time is h, both constantPolling schemes differentiate based on the service policy (exhaustive, gated, limited)


Exhaustive Polling

With exhaustive polling, stations when receive the token transmit all packets in the queue before releasing itLet us analyze the behavior of this systemThe probability that the channel is transmitting a packet at a random time tis give by

Tλρ =


Exhaustive Polling

The average waiting time E[W] in the queue can be calculated considering three components

Arrival in queue 8

transmission

321][ WWWWE ++=


Exhaustive Polling

E[Nc] is the average number of packets transmitted before considered packetUsing Little’s result is can be expressed as:

Therefore:

TNEW c ][1 =

][][ WENE c λ=

N

λa

T

][][1 WEWTEW ρλ ==


Exhaustive Polling

The total average waiting time is given by:

hMW

hTW

21

2)1(

2

3

2

−=

−+= ρρ

hMhTWEWE2

)1(2

)1(2

][][ −+−++= ρρρ


Exhaustive Polling

Solving by E[W] we get:

hMTWE)1(2)1(2

][ρρ

ρρ

−−

+−

=

Waiting time of a single queue (M/D/1)

Additional waiting time due to token passing time

Note that: 1max =ρ


Exhaustive Polling

The average token cycle time is given by the transmission time of all packets that arrive during a cycle plus the token passing time

[ ] [ ]

[ ]ρ

λ

−=

+=

1MhCE

MhTCECE


Gated Polling

With gated polling, stations when receive the token can transmit all packets that are in queue at the time when the token arrivesThe expression of the average waiting time is similar to previous case with an additional term This is the additional cycle the packet has to wait when it arrives when the token is already at the station

ρρ hMhM

W ==4


Gated Polling

Therefore we get:

Again

hMTWE)1(2)1(2

][ρρ

ρρ

−+

+−

=

1max =ρ


Limited Polling

With limited polling, stations when receive the token can transmit only up to k packetsThe special case of k=1 is called Round-RobinHere we have one more additional term which are the additional cycles the packet has to wait, one per each packet in the queue at the arrival moment

hWEMhMNEW c ][][

5 λ==


Limited Polling

Therefore we get:

Now we have:

h

TTh

MT

TThWE

)1(2)1(2][

+−

++

+−

=ρ

ρ

ρ

ρ

hTT+

=maxρ


Polling in real networks

There are several examples where polling is used for regulating access to a channel in wireless technologies

WiFi (Point Coordination Function – PCF or HCF – Hybrid Coordination Function)Bluetooth

The main difference with simple schemes we considered so far is that the station sequence can be dynamically changed


Polling in Bluetooth

Master

Slave 1

Slave 2

Slave 3SCO (Synchronous Connection Oriented)ACL (Asynchronous ConnectionLess)

M

S

PSB

S

S

S SS

S

P

P

SB

SB


Polling in WiFi (IEEE 802.11e)


Random access

With random access there are possible conflics on the channel (collisions)Conflicts are resolved using the channel feedback and some procedure to select a random waiting timeThe minimum channel feedback a station need to have is the information if its transmission was sccessful or notThe first and simplest random access protocol is Aloha which uses just this minimum feedback


AlohaNet

The ALOHA network was created at the University of Hawaii in 1970 under the leadership of Prof. Norman AbramsonIt was the first wireless network!


Aloha

The access mechanism is very simple:When there is a packet to be transmitted, just transmit it.If transmission fails, wait for a random time and retransmit

T T


Aloha

Let us assume the transmission starting times on channel are a Poisson process with rate λLet us consider the normalized rate G=λTThe success probability is given by the probability that there is no other transmission in a 2T interval

The normalized throughput S is therefore given by:

Gs eP 2−=

GGeS 2−=


Aloha

If transmissions are somehow synchronized (slotted Aloha) the vulnerability period reduces to T and therefore GGeS −=

Infinite population model


Aloha: Single buffer

Unfortunately, the traffic on the channel is the combination of new transmissions and retransmissions and it can increase if throughput reducesTo evaluate the dynamic behavior of Aloha let us consider an enhanced modelLet us assume we have M stations with a single transmission buffer (max 1 packet)Channel is slottedIf buffer is empty a new packet arrive and is immediately transmitted in the slot with probability αIf buffer is full, packet is retransmitted with probability β


Aloha: Single bufferThe system status is given by n(t), the number of full buffers at time tn(t) is a discrete Markov chainThe probability that in a slot there are iarrivals given n buffers are full is:

While the probability that there are i retransmission is:

inMi

inM

nia −−−⎟⎟⎠

⎞⎜⎜⎝

⎛ −= )1(),( αα

ini

in

nib −−⎟⎟⎠

⎞⎜⎜⎝

⎛= )1(),( ββ



n n+1 n+in-1 ...

a(n,i)

a(1,n)[1-b(0,n)]

a(0,n)b(1,n)

a(1,n)b(0,n)++a(0,n)[1-b(1,n)]



We can solve (numerically) the chain and get the stationary state probability πnThe throughput S is given by

),1(),0(),0(),1()(

)()]([0

nbnanbnans

nsnsESM

nn

+=

== ∑=

π



The traffic on the channel is:

and the new arrivals:

We can express n as a function of g:

And calculate

βα nnMng +−= )()(

αβα

−−

=Mgn

α)()( nMna −=

αβααα−

−−= )()( MgMga



Similarly, we can also get s(g) using stationary probabilities (the curve is very close to that of the infinite population model)We can consider points where s(g)=a(g) as equilibrium points of the processEquilibrium points can be “stable” or “unstable”


Aloha in real networks

There are several technologies where Aloha is still adopted including:

Random access signaling channel of cellular systems (like e.g. GSM)Reservation channel of WiMaxRFID


Carrier Sense Multiple Access (CSMA)

If the channel feedback is richer, more efficient random access mechanisms can be adoptedIf the propagation time is short wrt to transmission time we can sense the channel statusCSMA: like Aloha but transmit only when you sense the channel free

ττ

a=τ/T



On the channel we have cycles of Busy (at least one station sense the channel as busy) and Idle (all stations sense the channel free) periodsThe throughput S can be given by:

IBS

+=

α

where B and I are the average busy and idle periods and α is the probability that there is a success transmission in a busy period



Making the same assumptions of the aloha infinite population model we have:

)1)(1()1(

1

ZaeaeBG

I

e

aGaG

aG

++−++=

=

=

−−

−α

where Z is the time when colliding transmission partially overlap



It can be shown that:

Therefore we get:

GeaeaZ aG

aG 11

−−

+= −

−

aG

aG

eaGGeS −

−

++=

)21(


CSMA in real networks

There are several technologies that are based on variants of the CSMA protocolIncluding Ethernet

Today the most famous and widely used one is WiFi


IEEE 802.11 random access

source

destination

neighbors

RTS

DIFS

CTS

SIFS SIFS

DATA

SIFS

ACK

NAV (RTS)

NAV (CTS) Random Backoff

source

destination

neighbors

RTS

DIFS

CTS

SIFS SIFS

DATA

SIFS

ACK

NAV (RTS)

NAV (CTS) Random Backoff


IEEE 802.11 random access

Similarly to the general model we can derive a model for WiFi

))(1()231(

1

ZabebaeBG

I

e

aGaG

aG

++−+++=

=

=

−−

−α

aGaGaG

aG

GebaebGeaGGeS −−−

−

++−−−++=

)22()1)(1()21(

a = interframe spaceb = duration of RTS and CTS


Part BResource and radio planning


Summary

Introduction to radio planningCoverage planningCapacity planning (frequency assignment)Joint coverage and capacity planning (planning of CDMA systems)

References:

[1] E. Amaldi, A. Capone, F. Malucelli, C. Mannino, Optimization Problems and Models for Planning Cellular Networks, in Handbook of Optimization in Telecommunications, Ed. P.M. Pardalos and M.G.C. Resende, Kluver Academic Publishers, 2005 (available at http://www.elet.polimi.it/upload/capone)

[2] IEEE Wireless Communications Magazine, special issue on 3G/4G/WLAN/WMAN radio planning and optimization, Eds. A. Capone and J. Zhang, to appear December 2006.


Resource planning

One we divide the available spectrum into sub-channels using some multiple access technique we need to plan how sub-channels are used in the cells (these includes also data networks like wifi and wimax)This problem is strictly related to the general problem of designing the radio access part of the network (radio planning)


What is radio planning?

When we have to install a new wireless network or extend an existing one into a new area, we need to design the fixed and the radio parts of the network. This last phase is called radio planning.


What is radio planning?The basic decisions that must be taken during the radio planning phase are:

Where to install base stations (or access points, depending on the technology)How to configure base stations (antenna type, height, sectors orientation, tilt, maximum power, device capacity, etc.)

XX

XX


Radio Planning

When planning and optimizing a cellular system, a number of aspects must be considered, including

signal propagation, traffic estimation, antenna positioning, antenna configuration,interference.

Here we’ll focus on the decision problems that give rise to interesting and challenging mathematical programming models which must account for the peculiarities of the specific network technology.


Propagation prediction

One of the key elements for the radio planning is propagation prediction that allows to estimate the area covered by each base station

R

The covered area is the area where the received signal strength is above a thresholdReceived signal strength depends on emitted power and path loss


Propagation prediction (2)

Path Loss depends on several phisical effects related to the propagation of electromagnetic waves including:

DistanceFrequencyGround morfologyAtmosferic phenomenaAntenna heightsEtc.

Path loss has been modeled using many propagation models (Okumura-Hata, Cost231, Walfish-Ikegami, Bertoni, etc.) that can be grouped into three categories:

EmpiricalStatisticalDeterministic



Due to the complex propagation environment of cellular systems simple statististical models are aften adopted

Deterministic techniques (e.g. Ray tracing) are sometime used for indoor propagation

A deterministic component due to the distance is the starting point of statistical modelsPath loss:

Constants are estimated using empirical models (e.g. Okumura-Hata) or measurements

[dB] )log()( dBAdLp +=



If necessary two or three linear models are combined:

Measured Signal Strength

-120

-110

-100

-90

-80

-70

-60

-50

-4010 100 1000 10000

Meters

SS [d

Bm

]

Dual-slope prediction

1-slope prediction

Survey

Statistical dispersion of data is taken into account modeling shadow fading and multipath fading using random variables.


Traffic estimationTraffic distribution in the service area is usually hard to predict in the radio planning phase since it depends on several issues including area population, buildings, market penetration of the considered service, etc.Traffic distribution is usually provided using a discrete set of points I, test points (TP), that are considered as centroids of traffic


Antenna positioningThe selection of possible antenna sites depends on several technical (traffic density and distribution, ground morphology, etc.) and non-technical (electromagnetic pollution, local authority rules, agreements with building owners, etc.) issues.

We denote with S the set of candidate sites (CS)We can assume that the channel gain gij between TP i and CS j is provided by a propagation prediction tool


Antenna configurationRadiation diagramHorizontal (sectors) and vertical (tilt) anglesMaximum emission power (pilot channel power)HeightBase station capacityEtc.


Antenna configuration (2)

The antenna configuration affects only the signal level received at TPsFor each CS j we can define a set of possible antenna configurations KjWe can assume that the channel gain gijkbetween TP i and CS j depends also on configuration k.Based on signal quality requirement and channel gain we can evaluate if TP i can be covered by CS j with an antenna with configuration k,And define coefficients:

⎩⎨⎧

=01

ijkaif TP i can be covered by CS j with conf. k

otherwise


Summarizing

{ }

{ }

,,

otherwise 0 conf. with CSby covered is TP if 1

(TP) points test ofset ,...,1

ionsconfigurat ofset ,each for (CS) sites candidate ofset ,...,1

j

ijk

j

KkSjIi

kjia

nI

KSjmS

∈∈∈⎩⎨⎧

=

=

∈=


InterferenceMultiple access techniques are used to define communication channels on the available radio spectrum

Radio resources for wireless systems are limited and must be reused in different areas (cells)Resource reuse generates interference

TIME

FDMAFDMA

FREQUEN

CY

POW

ER

TDMATDMA

TIMEFREQUENC

Y

POW

ER

TIME

CDMACDMA

FREQUENC

Y

POW

ER


Interference (2)Interference can be tolerated (good communication quality) if the Signal-to-Interference Ratio (SIR)is high enoughSIR constraint limits the number of simultaneous communications per cells, i.e. the system capacityCapacity is another key element that must be considered during radio planningFDMA/TDMA cellular systems adopt a two phases radio planning

Coverage planningCapacity planning (frequency assignment)

CDMA cellular systems require a single phase approach

Joint coverage and capacity planning


Coverage planning


Coverage planning

The goal of the coverage planning phase is to:

Select where to install base stationsSelect antenna configurations

In order to guarantee that the signal level in all TPs is high enough to guarantee a good communication quality Note that interference is not considered in this phase


Decision variables and parameters

Decision variables:

⎩⎨⎧

= otherwise 0

CSin installed is ion configuratth station wi base a if 1 jky jk

Installation costs: jkc

Cost related to the installation of a base station in CS j with configuration k


Set covering problem (SCP)

LetVariables yjk define a subsetSuch that

{ } jjk

Kkjk

Sj Kkjkijk

Sj Kkjkjk

KkSjy

Sjy

Iiya

yc

j

j

j

∈∈∀∈

∈∀≤

∈∀≥

∑∑ ∑∑ ∑

∈

∈ ∈

∈ ∈

, 1,0

1

1

min Objective function: total network cost

Full coverage constraints

One configuration per site

Integrality constraints

SS ⊆*{ }1| == ijkjk aiP

IPSj

jk =∈U

*


Set covering problem (SCP)

SCP is NP-hardHowever several efficient algorithms has been proposed (see [3] for a survey) Even simple greedy algorithms allow to obtain high quality solutions

[3] S. Ceria, P. Nobili, and A. Sassano. Set covering problem. In M. Dell’Amico, F. Maffioli, and S. Martello, editors, Annotated Bibliographies in Combinatorial Optimization, chapter 23, pages 415–428. John Wiley and Sons, 1997.


Greedy algorithm for SCP

Step 0set S*=∅

Step 1if Pj = ∅ for all j then STOP

Otherwise find k ∈ (J-J*) such that: is maximumStep 2

S*:=S*∪{k}Pj:=Pj-Pk ∀j

Go to Step 1.

j

j

cP

Note: we don’t consider configurations here for the sake of simplicity


Greedy algorithm: Example (1)

Step 0: S*=∅

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=Π

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

11111

98857

111010101010101110000001011111110011111000001000100000100111101000010011011

CV



Step 1: k=5

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=Π

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

11111

98857

111010101010101110000001011111110011111000001000100000100111101000010011011

CV



Step 2: S*= {5}, ...

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=Π

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

11111

98857

111010101010101110000001011111110011111000001000100000100111101000010011011

CV



Step 2: … ricalculate V e Π

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=Π

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

02233

000000000000000000000000001010000001010000000000100000100010000000010001010

V



Step 1: k=1

Step 2:S*= {5,1}, ricalculate V e Π

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=Π

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

02233

000000000000000000000000001010000001010000000000100000100010000000010001010

V



… ricalculate V e Π

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=Π

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

00120

000000000000000000000000000000000001000000000000100000100000000000000000000

V



Step 1: k=2

Step 2:J*= {5,1,2}, ricalculate V e Π

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=Π

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

00120

000000000000000000000000000000000001000000000000100000100000000000000000000

V



… ricalculate V e Π

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=Π

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

00100

000000000000000000000000000000000001000000000000000000000000000000000000000

V



Step 1: k=3

Step 2:J*= {5,1,2,3}, ricalculate V e Π

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=Π

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

00100

000000000000000000000000000000000001000000000000000000000000000000000000000

V



… ricalculate V e ΠSTOP

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=Π

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

00000

000000000000000000000000000000000000000000000000000000000000000000000000000

V



In this simple example it’s easy to observe that the solution J*={5,1,2,3} is sub-optimalIn fact this solution has a lower cost:

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=Π

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

11111

98857

111010101010101110000001011111110011111000001000100000100111101000010011011

CV


Maximum coverage problem (MCP)

In practice the coverage requirement is often a “soft constraints” and the problem actually involves a tradeoff between coverage and installation costs

{ }{ } Iiz

KkSjy

Sjy

Iizya

ycz

i

jjk

Kkjk

Sj Kkijkijk

Sj Kkjkjk

Iii

j

j

j

∈∀∈∈∈∀∈

∈∀≤

∈∀≥

−

∑∑ ∑

∑ ∑∑

∈

∈ ∈

∈ ∈∈

1,0, 1,0

1

max λ Objective function: trade-off between cost and coverage

Definition of variables z

One configuration per site

Integrality constraints


Assigning test points to base stations

When a TP is covered by more than one base station:

∑∑∈ ∈Sj Kk

jkijkj

ya # of base stations covering TP i

the serving base station is not defined

We can define new assignment variables:

⎩⎨⎧

= otherwise 0 CS toassigned is TP if 1 ji

xij


Set covering with assignment (SCA)

{ }{ } SjIix

KkSjy

yax

Sjy

Iix

yc

ij

jjk

Kkjkijkij

Kkjk

Sjij

Sj Kkjkjk

j

j

j

∈∀∈∀∈∈∈∀∈

≤

∈∀≤

∈∀=

∑∑∑∑ ∑

∈

∈

∈

∈ ∈

, 1,0, 1,0

1

1

min

Coverage constraints

Definition of variables x


Capacity constraints

Obviously, without additional constraints SCA provides the same solution as SCPUsing x variables we can add constraints on cell capacity:

where di is the traffic demand associate to TP i and vjk is the capacity of a base station in CS j with configuration kOther constraints related to cell ‘shape’ can be added

SjyvxdjKk

jkjkIi

iji ∈∀≤ ∑∑∈∈


Assignment to the ‘nearest’ base station

One of these rules is the requirement of assigning a TP to the “closest” (in terms of signal strength) activated BS. One way to express this constraint for a given TP i is to consider all the pairs of BSs and configurations that would allow connection with i and sort them in decreasing order of signal strength.Let

be the ordered set of BS-configuration pairsThe constraints enforcing the assignment on the ‘nearest’ BS are:

∑+=

−≤≤≤+L

lhijkj Llxy

hll1

11 1

{ }),(),...,,(),,( 2211 LL kjkjkj


Capacity planning (frequency assignment)


Cluster model

After coverage planning, capacity planning is in charge of defining which radio resources can be used by each cellThe amount of resources (frequencies) assigned to cells determines system capacityFrequencies can be reused, but SIR (quality) constraints must be enforcedA simple ‘didactical’ model considers hexagonal cells and homogeneous trafficFrequencies are divided into K groups and assigned to a group of K cells, named cluster.The cluster is repeated in the area in a regular fashion

F1

F2F7 F3

F6F5

F4

F1

F2F7 F3

F6F5

F4F1

F2F7 F3

F6F5

F4

F1

F2F7 F3

F6F5

F4F1

F2F7 F3

F6F5

F4

F1

F2F7 F3

F6F5

F4

F1

F2F7 F3

F6F5

F4


Cluster model (2)

Only some values of K are admissible K=1,3,4,7,9,12,13, …Given the minimum value of SIR, SIRmin, we can determine K the minimum value of KReceived power:

η−⋅⋅= dGPP tr


Cluster model (2)

dr

D

d1

d2d3

d4

d5 d6

Same antennas and same power:

∑

∑

=

−

−

=

−

−

=

=⋅⋅

⋅⋅=

6

1

6

1

i i

i it

t

dd

dGPdGPSIR

η

η

η

η

Worst case d = rApproxmation di = D

η

η

η −

−

−

⎟⎠⎞

⎜⎝⎛=≅

RDrSIR 1

61

6


Cluster model (3)

SIR depends only on the reuse ratio R=D/r and not on the power and the cell radiusGeometric consideration provides:

And therefore:

3

2RK =

( )3

6 /2

min

ηSIRK =


Graph based models

Unfortunately cells are not hexagonal and traffic is not homogeneous …Other models have been proposed for practical cases (see [6] for a quite complete survey)Some popular models are based on graph coloring problems

[6] K. Aardal, S.P.M. van Hoesel, A. Koster, C. Mannino, and A. Sassano. Models and solution techniques for frequency assignment problems. 4OR, 1(4):261–317, 2003.


Graph based models (2)Compatibility graph G(V,E)

Vertices are base stationsTwo vertices are connected by an edge if the two base stations cannot reuse the same frequencies


Graph based models (3)

Any coloring of the vertices of G (i.e., assignment of colors such that adjacent vertices have different colors) is an assignment of frequencies to the network such that no mutual interfering BSs receive the same frequency. A minimum cardinality coloring of G is a minimum cardinality non-interfering frequency assignment of the network.Graph coloring problem is NP-hard and several exact algorithms and heuristics have been proposed.This simple model assumes:

One frequency per BSTwo distinct frequencies do not interfere



Generalized graph coloring models:Compatibility matrix:

Frequencies are numbered according spectrum

position

Sets Fj defines assignments of frequencies to BSs

Traffic constraints:

Compatibility constraints:

SjicC ij ∈= , }{

jjiiijji FfFfSjicff ∈∈∈≥− ,,,

SjmF jj ∈∀=

[7] W.K. Hale. Frequency assignment: Theory and applications. Proceedings of the IEEE, 68:1497–1514, 1980.



if cij=0 i and j can reuse the same frequenciesif cij=1 i and j cannot use the same frequenciesif cij=2 i and j cannot use either the same frequencies and adjacent frequencies

i jcij

Optimization objective:

Min Span(G) = number of frequencies used

MS-FAP (Minimum Span Frequency Assignment Problem)


Graph based models (6)Comments:

Graph based models do not consider SIR constrains explicitlyThe cumulative effect of interference is not accouter for

Compatible?


Interference based models

Minimum Interference Frequency Assignment Problem (MI-FAP)

Generalization of the max k-cut problem on edge-weighted graphspenalty representing the interference (cost) generated when v is assigned with f and w is assigned with g.Decision variables:

0 1

otherwise

toassigned is if

⎩⎨⎧

=vf

vfx

FgfSwvpvwfg ∈∈ ,,,


Interference based models (2)

Objective function:

0 1

otherwise

toassigned is and toassigned is if

⎩⎨⎧

=wgvf

vwfgz

wgSwv Fgf

vfvwfg xxp∑ ∑∈ ∈, ,

min

The problem can be linearized:

FgfSwvzxx vwfgwgvf ∈∈∀+≤+ , , 1



Linear MI-FAP:

∑ ∑∈ ∈Swv Fgf

vwfgvwfgzp, ,

min

FgfSwvzxx vwfgwgvf ∈∈∀+≤+ , , 1

SvvmxFf

vf ∈∀=∑∈

)(

s.t.



MI-FAP:Total interference minimizedNo control on single interference values

MI-FAP variants account for explicit SIR constraints (see [8,9])

[8] M. Fischetti, C. Lepschy, G. Minerva, G. Romanin-Jacur, and E. Toto. Frequency assignment in mobile radio systems using branch-and-cut techniques. European Journal of Operational Research, 123:241–255, 2000.

[9] A. Capone and M. Trubian. Channel assignment problem in cellular systems: A new model and tabu search algorithm. IEEE Trans. on Vehicular Technology, 48(4): 1252–1260, 1999.


Approaches to the radio planning

2nd Generation Systems 2nd Generation Systems (GSM, D(GSM, D--AMPS, ...)AMPS, ...)

two-phases approach1) Radio coverage

minimum signal level in all the service area

2) Frequency assignment

meet traffic constraintsmeet quality (SIR) constraints

3rd Generation Systems based 3rd Generation Systems based on Won W--CDMACDMA

two-phases approach not suitable because:

no frequency planning for CDMApower control determines the cell breathing effect

Planning must also consider Planning must also consider ⇒⇒ traffic demand traffic demand

distributiondistribution⇒⇒ SIR constraintsSIR constraints


Covering traffic in W-CDMA systems

Traffic generated can be considered covered (served) by the system if the QUALITY of the connection is goodQuality measure: Signal-to-Interference Ratio (SIR)

ηα ++=

inout

recdownlink II

PSFSIR

η++=

inout

recuplink II

PSFSIR


Power Control (PC) mechanism

Dynamic adjustment of the transmitted power to minimize interference

Two PC mechanisms:

Power-based PC

emission powers are adjusted so that received powers are equal to a given Ptar

SIR-based PC

emission powers are adjusted so that all SIR are equal to a given estimated SIRtar


Cell breathing effectDue to the power limitations the area actually covered by a BS depends on interference (traffic) level

When traffic (interference) increases the SIR constraint cannot be met for terminals far from the BS due to higher channel attenuationSince only terminals close to the BS can be actually served it is as if the actual cell area reducesSince this phenomenon affects coverage, traffic levels must be carefully considered during radio planning



set of candidate sites where to install BSs: S={1,…,m}

installation costs: cj, j∈Sset of test points (TPs): I={1,…,n}

traffic demand: ai, i∈Iequivalent users: ui=φ(ai)

propagation gain matrix: G=[gij], i∈I, j∈SProblem:Problem:Select a subset of candidate sites where to install BSs, and assign TPs to BSs so that quality constraints are satisfied and the total cost is minimized


Joint coverage and capacity planning (2)

Decision variables:

Basic constraints:⎩⎨⎧ ∈∈

=

⎩⎨⎧ ∈

=

otherwise 0 BS toassigned is point test if 1

otherwise 0Sjin installed is BS a if 1

SjIix

y

ij

i

{ } SjI,i,,yxSjI,iyx

Iix

jij

jij

Sjij

∈∀∈∀∈∈∀∈∀≤

∈∀≤∑∈

10

1 assignment

coherence

integrality



Objective function:

∑∑∑∈∈ ∈

−Sj

jjIi Sj

iji ycxu λmax

minimize installation costs

maximizecovered traffic

maxPgP

ij

tar ≤ power limit

We assume a power-based Power Control (received power = Ptar)

variables xij are defined only for pairs such that:



SIR constraints:

bilinear constraints which can be easily linearized:

with a value of M large enough

SjySIRPx

gPgu

Pj

Ih Sttarht

ht

tarhjh

tar ∈∀≥−∑ ∑

∈ ∈

min

total interferencesignal power

( ) Sjxgg

uSIRyMIh St

htht

hjhj ∈∀⎟⎟

⎠

⎞⎜⎜⎝

⎛−≥−+ ∑∑

∈ ∈

111 min



Solution approach:State-of-the-art ILP solvers can provide the exact solution only for very small instancesHeuristics have been proposedPromising approach based on TabuSearch

[10] E. Amaldi, A. Capone, and F. Malucelli. Planning UMTS base station location: Optimization models with power control and algorithms. IEEE Transactions on Wireless Communications, 2(5):939–952, 2003.[11] E. Amaldi, P. Belotti, A. Capone, F. Malucelli, Optimizing base station location and configuration in UMTS networks, Annals of Operations Research, vol. 143, June 2006.


Thank you!

Antonio CaponePolitecnico di MilanoAdvanced Network Technologies LaboratoryContact:Email: [email protected]: http://home.dei.polimi.it/capone (personal)

http://antlab.elet.polimi.it (laboratory)

radio planning problems and methodologies in wireless...

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