Performance of MMSE Multiuser Detection in Cellular DS CDMA Systems Using Distributed Antennas

Performance of

MM

SE Multiuser

Detecti'on

in

Cellular

DS-CDMA Systems Using Distributed Antennas

Lie-Liang Yang

School ofECS,University ofSouthampton,S017IBJ,UK

Tel: +44-23-8059 3364;Fax:+44-23-80594508 E-mail: lllyecs.soton.ac.uk; http://www-mobile.ecs.soton.ac.uk

Abstract- In this contribution we propose and investigate a high-capacity cellular direct-sequence code-division multiple-access

(DS-CDMA)wireless communications system,where numerous antennas are distributed in the area covered by the system. The bit error rate(BER) performance of the distributed antenna cellular DS-CDMA system is inves-tigated, when minimum mean-square error (MMSE) multiuser detection is employed, and when transmission pass-loss, lognormal shadowing slow fading and Nakagami-rn fast fading are considered. Our study suggests that thedistributed antenna cellularDS-CDMA system constitutes a high power-efficiency wireless system. For utilizing the same set of system parameters,it is capable ofproviding an extremely higher capacity, than the cellularDS-CDMA systemdesignedbased on theconventional cellular concepts.Furthermore, the proposed distributed antenna cellular system canbeoperated withouthavingto usepower-control.

1. INTRODUCTION

Amongradio technologies, multiple-input-multiple-output (MIMO)

systemsusing multipletransmit and/or receive antennas have attracted wide research interests in recentyears[1], [2].Inthiscontribution we

proposeand investigate a cellular DS-CDMA system using distributed antennas, where

many

antennas are distributed in the area covered by the system. Here weconsider the DS-CDMAtechnique, since it has beena typical multiple-access scheme inboth the second- and the third-generation wireless communications systems [3]. Without anydoubt, DS-CDMA technique will constitute animportant candi-date in the future generations of wireless communications systems.

In ourproposed distributed antenna cellular DS-CDMA system, the distributedantennas areconnected withanumnberof

signal processing

centers, which are referred to as base-stations (BSs), using optical fibers. Thereasonforemphasisonoptical fiber instead of wireless for implementing communications between distributedantennasand BSs ismainly for the sake of saving the highly limited wirelessresources. Notethat, we stillusethe concept ofBS, however, inthe proposed distributed antennacellular DS-CDMA system the BS isnowrather

a signal processing centerthan aconventional BS. The antennas at

the BSs of theproposed distributedantennasystemareassumed have

no priority in comparison with the other distributedantennas. ABS

or a signal processing center is mainly responsible for the signal processing of the users within the area covered by the distributed

antennasconnected with this BS.

Inthis contributionwefirst describe the distributedantennacellular DS-CDMA system. Then, the MMSE multiuser detection for the distributed antenna cellular DS-CDMA system is investigated. The

BERperformance of the cellular DS-CDMA system using distributed

antennas is evaluated, when communicating overcomposite

lognor-mal shadowing slow fading and Nakagami-nm fast fading channels associated with transmission pass-loss. Our study shows that, in the distributed antenna cellular DS-CDMA system the detection is location-aware. The distributed antennacellular DS-CDMA system constitutes ahigh

power-efficiency

wireless system. Whenusingthe

saice

setof systemparamnetersandthe

sacie nuniber

ofantennas,our

proposed distributedantennacellular DS-CDMA system iscapable of

supportinganextremely higher number ofusers,than aconventional concept-based cellular DS-CDMA system, which employs centralized

BSantennas.

II. CELLULAR DS-CDMA SYSTEMWITHDISTRIBUTED ANTENNAS

A. SystemDescription

The structure of the proposed cellular DS-CDMA system using distributed antennas canbe well-described with the aid ofFig. 1. It

is well-known that,inconventional cellular systems [4], [5] each cell is centered around a BS, which may employ a set of antennas. By contrast,in the proposed distributed antennaaided cellularconcept,

as shown inFig. l, each cell has numerous setsofantennas, which

are distributed within the area coveredby a cell and are connected

to the BS using optical fiber, as we mentioned previously. In the distributed antennacellular systems ofFig. 1, theantennas near the borders may be connected withtwo orthree BSs,sothatsoft-handoff

canbeachieved.Forexample,asshowninFig. 1, each of theantennas

within the dash-dotted boxorthe dashed circle may be connected with BS1 of Cell1, BS2of Cell2orBS3of Cell 3.

Inthe considered distributed antenna system, for the convenience ofanalysis, we assume that the cells are shaped as hexagons with the common radius of R. We assume that any a pair of

adjacent

antennas are separated by a distance of r.

Hence,

each antenna is surroundedbynumerous distributed antennas locatedat the corners of thelayered hexagons. Specifically, for the antenna miarkedas

A3

in Fig. 1, the first layer has six antennas, the second layer has 12 antennasincluding theantennalocatedatBS1, andsoon. Notethat, the

structureofFig. Iis sufficiently general for approximately modeling the distributed antenna systems having anarbitrary antenna density. Thiscanbe doneby

appropriately

changing the radius value of Rin

Fig. 1.

Indistributed antennasystemsasshown inFig. 1,we assumethat the distributed antennas only implement the functions of conveying

a signal from radio frequency (RF) to baseband orfrom baseband

to RF, in order to make the computation burden at a distributed

antenna aslowaspossible. The above assumption might be duetothe size constraint of the distributed antennas and the constraint arising fromsomesupported signal processing.Forexample,when advanced multiuser detection (MUD) isemployed,information associated with each mobile terminal (MT)and eachantennashould be sharedbyany individual processor. Inthis case, using distributed processing in the

contextof eachdistributedantennawouldrequireanextremely power-ful network forconveying the informationtimelyandefficiently,which might notbe practical in thenear future. Hence, in our distributed

antenna systemall signals received from the MTsby the distributed

antennas are conveyed to the BSs, where the processing is carried

out.

Simultaneously,

all the distributed antennas are also used for transmittingsignalsfromn the BSstothe MTs, in ordertoimuprovethe down-link transmissionquality.

of aMTareused to communicate between thisMTand its BS. Hence, the propagation channel between aMTand any of the antennas within its virtual cell can be well modeled by a composite shadowing-fading model [8],where (slow) shadowing can be described by a lognormal distribution [8],while (fast) fading by a Rician or Nakagami-m dis-tribution [9]. Specifically,inthis contribution frequency non-selective

Nakagami

fading [9] is used to model the fast

fading.

LetMTobe the referencetermninal and assume that the signal trans-mitted by the reference terminalMTois being detected. The reference terminal MTo randomly moves within the triangle area with three antennasatits corners.Forexample,MTCinFig. 1 randomlymoves

within the triangle area

S,

We assume that there are U antennas within the virtual cell ofMTo.Signals collected from these U antennas

areprocessed,inordertodetect the information transmittedbyMTo.

Consequently,

whenassuming that K user signals in additiontothat fromMToarereceivedby the uthantenna,the receivedcomplex low-passequivalent signalcanthen beexpressedas

K

ru,(t')

=

-\2h,,

bo

(t)Co (t)

+

E

.. ...hk k=1

(2)

Fig. 3. A conceptual cellular DS-CDMAsystem structure with distributed

antennas,where the distributed antennas are connected withone,two orthree base-stations(BSs) located at the centers of the cells usingopticalfiber.

In this contribution, specifically, we consider and investigate the distributedantennasystemsusing DS-CDMA signaling. Hence, when considering conventional binary phase shift keying (BPSK) baseband modulation, the transmitted DS spread spectrumsignal,sayby thekth MT,canbe expressed as

Sk

(t)

= v2Pbk

(t)Ck(t)

cos

(27rft

+

Ok)

(1) where P is the user's transmitted power,

f,

is the carrier fre-quency, while

Ok

denotes the initial phase angle associated with the carrier modulation. The data stream's waveform

bk

(t)

EZ

=

bk[]

PT

(t

-

nTP)

consists of a sequence of

mutually

independent rectangular pulses of duration I and of amplitude of

+1 or -1, where Tb is the bit duration. Finally, in (1)

Ck(t)

uiCki

yVT

(t

-jl'c)

denotes thesignature sequence waveform of the kth user, where

Ckj

assumes values of +1 or -1 with equal probability,while FbTC

(t)

is thechipwaveform,which is definedover

the interval

[0,

TP)

and has the

property

ofj0T TC.(t)dt =TP

Notethat, in this contribution we assume that each MTemploys onlya single antenna, which is sufficient for fulfillour

objectives

by focusing on the issues of the distributed antenna systems. However,

ourinvestigation canbe extendedtothe distributed antennasystems that usemultipleMT antennasaidedbysomeadvanced transmit and receive schemes [6], [7].Furthermore,we assumethat the distributed

antennacellular DS-CDMA uses nopower-control. This is because,

asshown inFig. 1,no matterwhere a MTis,it communicates witha

number ofantennaslocated within itsline-of-sight (LoS)area.The sig-nalssampled from theantennaswithin the LoSareaof the considered

MT usually fall within the cluster of strongest signal. Consequently, the consideredMTconflictsno orlightnear-farproblem.

B. PropagationChannelModeling

Indistributedantennacellular systems, for anyagiven MT, thereare anumber ofantennaswithin the LoSareaof theMT.The LoSareaofa MTis referredto asitsvirtualcell. Theantennaswithin the virtual cell

where

nU,(t)

is the complex-valued additive white Gaussian noise (AWGN)received by the uth receive antenna, which has zero-mean and a single-sided spectrum density of No per dimension, rk rep-resentsthe channel

delay

associated with

asynchronous

transmission andpropagation,which is assumedtobeuniformly distributed within

[0, Tb).

Furthermore, in (2)

hk

representsthe channelgain connecting MTk and the uth antenna. The channel gain

hk,

takes into account bothshadowing and fading, whichcanbeexpressed as

hku

=3utk5

jOk". (3)

where,withoutloss of anygenerality,the initialphaseseenin(1) and thephase duetochannel have been absorbed into

Oku,

and Okuis

as-sumedtobeuniformly distributed in

[u,

27r).

In

(3)

3urepresentsthe lognornmal shadowing factor, accounting for large scale geographical variation, while akurepresents the fastfading envelope.Weassume

that the transmission pass-loss is absorbed in the shadowing factor

k,sothat the mean-square valueofakuisunit, i.e.,Q =E [t 2

1.

Furthermnore,

we assumethat kuand

Ctku

aremutually independent and both of themarealsoindependent of

OkuP

Since the fastfading

atu

is modeledby Nakagami-rndistribution, hence,

Ct2

is Gamma distributed with theprobability density function (PDF)expressedas[9]

pa2_k

u~rY

(y)

= r

(m)

y exp

(-

rTy)

7 y>0

(4)

where F(.) is the Gamma function, and, again, m is a parameter accounting for the fading severity.In(3) k,representstheshadowing,

whichcanbe modeledaslognormal distribution [9].It canbe shown that/32, alsoobeys lognormal distribution having thePDFgiven by [9]

Pk 2(r) v exp [- (10 ) 1 r>00 (5)

where I

O/

1n10

4.3429,

and

cku

(dB)

and a

(dB)

arethe

meanand standard deviation of 10

loglo

r,respectively. Finally, since

weassumed that both the fastNakagami-a fadingand theshadowing slow fading are independent random processes, hence the PDF of

Ih

12issimply the product of (4) and (5).

Antennasinthe

virtual cell Chip-waveform

, ' ~ ~\ \ matched-filter

Sampling

V2(t)

ru(t)

'' D

-77 LIP

by

Detection

algorithms

1 iT

Co = 0X [Coo,COi,* * ,

CO(N-1)0

'N-FCk(N-1,,,,-1) Ck(N-11,_

Data output

CkU

1

Fig. 2. Receiver block diagram for thereference MT in the distributed antenna cellular DS-CDMA system.

.1)

Ck(N-1

Ck(N-lp

1.,

+l1

Ck(N-2) Ck(N2-1)

0

0 0

0 0

0 0

-Rg,

(Vkul)

C.

-Rep-.sentation

of

TheReeie Sina fhi=0

L

The receiver structure for detection of the reference signal from

MTo is shownin Fig.2.Asshown inFig.2 the received signals from the Uantennas inthe virtual cell ofMTo are first passed through a

bank of filtersmatchedtothe chip-waveformn pulse of F/TC (t).Then,

theoutputsof thematched-filtersaresampledatarateof

lIT,C

Hence,

in correspondence with each databit, a total of N samples can be

obtained fromeachantenna,whereNrepresentsthe number of chips

perbitorthespreadingfactor. Letusconsider the detection of the first

databittransmittedbyMTo.Then,the Ath sample of the uthantenna

canbeexpressedas

Yu = V2PN) I r,(t)i/-(t -A )dt (6)

where A = O,lL...IN- 1; u =

1,

2,...,U,

V/2PNlT

is a

normalization factor,and*representsthe complexconjugate.

Let

YU =

LYou,

YlU, ,Y(N-

)ut

nut = [noun.ul n(N- )u

where

RV

(Vk

) and

R&,

(vk

) arethe chip auto-correlationfunctions,

which are defined as R,(s) = T (t)i-(ts)dt and

Rp

(s) =RgI

(T

-s)for0 < s<

T,,

respectively.

Furthermore,let

y = yT yT yT T

(10) which collects all the samples from the U antennas relatedto the

detection ofthe firstbitofMTo.Then,y canbe expressedas

K

y=

(IU

X

co) hobo[0]

+

E

CkRfkHkbk (IL1)

where

n= n1 n2I ?nu (12)

isanUN-length Gaussian noisevector,whichhaszero meananda

co-variancematrix of

2uT2IuN,

XrepresentstheKroneckerproduct [10] operation,and the otherargumentsin(I 1)aregivenasfollows:

Ck

(7)

fRk

(8)

be the N-length observation vector and noise vector corresponding tothe uth antenna. Accordingto

(6),

we canknow thatthe elerment

nAtt inn is a complex Gaussian random variable with zero-mean

and avariance of(T2 = No/2Ebperdimension, where Eb = Pl'b representstheenergy perbit. Letus assumethat Ttu =ILk,,C+Vku

where Ik, > 0 and 0 < Vku < ' . Then, upon substituting the

received signal inthe form of(2) into (6) and expressing invector and matrixforms,itcanbe shown that

yul

canbeexpressedas

K

Yu ho0cobo

[0]

+

E

hkuCkuRf

(Vku)bk+

nl

(9)

k=1

wherebk

[bk

[-1]

bk

[0]]T

contains thetwodata bitstransmitted

by

the kthMTwithin

[0 '1),

while the otherargumentsin(9)aregiven

[hoi, hO2, ..,hou]T

diag {Ckl,tCk2,. ..,Cku}

diag

Rp

(Vkl),

Rf

(k2

),..**,Rf

(VkU)

[HT Hk HLUT

(13) (14)

(15)

(16)

whereHku =

hkJ2.

Letus nowdiscuss the MMSEdetectioninthe

distributedantennacellularDS-CDMAsystems.

III. LoCATION-AWARE MMSE MULTIUSER DETECTION

In this section we investigate the location-aware detection in the

distributedantennacellularDS-CDMAsystems,wherea user

signal,

sayMTo isdetectedbythe MMSEprinciplesbasedontheobservation

datasampledfrom the antennaswithin the considered user's virtual cell. The detectionis onthe basisofsymbol-by-symbol.

ForalinearMMSEassistedMUD,the receivedobservationvectory

givenin(I1),which is obtained fromthe LoSareaofMTO,is linearly

processedtoform the decisionvariable, ZO, i.e.,wehave

zo = X{wHy (17)

where }representsthe realpartofx,whilewis theweightvector,

theoptimum weightvectorofwhich in MMSEsense canbeexpressed as

w10 Ry (18)

o

o

o

o

0

0 CkO

0

CkO Ckl

Ck(lk

.-2)

Cki(1

k. -1)

Ck(ku-1) Ckt _

0 0 R,I (VkU) Rf,

(Vk

loo

to-,

10-2

10-3

10-4

l0-5 -50

m 1.5, U= 12,

EbINo

= 20dB

_30 040 80

I[m] 10 [ml

500

Fig. 3. Antennas whose signalsmaybecollected for detection ofMTO,when

MTois within the filledarea.

where fR is the autocorrelation matrix of the receivedvectory,while

7ybo

is the cross-correlation vectorbetween the receivedvectoryand

the desiredsymbolbo

[01.

Theycanbe, respectively, expressedas

Rf =E YY rybo =E

[ybo [°]]

(19)

Fig. 4. Single-user bound:BERversuscoordinates

(XI

y) performance of the distributedantennacellularDS-CDMA systemsupporting singleuserusing the specificparametersofrr = 1.5, U = 12, EbNo = 20dB, when theuser

signal experiences pass-loss,lognormal shadowingslowfading and Nakagami-7m fastfading.

Assume that all the data bitstransmittedbydifferent MTsare

indepen-dent.Then,wehave

Ry

= (IUXco)

hohot

(iU XC)

K

Ir B

[C,RQ,HkH7RTI,C;{0

21JIU

k=

(20)

cll P

(21) ;4 .n

ryb = (Iu X co)ho

where Eo represents the covariance matrix of theinterfering signals plus background noise. Finally,upon substituting (20) and (21) into

(18),weobtain

wo= (Iu o co)hoho (iu 4) +o '(Iu co)ho (22)

With the aid of the mnatrix inverselemIna [10], (22)canbesimplified as

t-1

(iu

h

(co)ho

mO=

Furthermore,the resultant MMSE is

given by

MMSE L 7yboU}

1L + ho(u co)

(Iu

c)ho

(23)

(24)

Let us now show a range of BER performance results, in order to characterize the distributedantennacellular DS-CDMAsystems.

IV. EXAMPLESOFPERFORMANCE RESULTS

In this section we provide a range of results for illustrating the

achievableperformanceof theexemplifieddistributedantennacellular DS-CDMA system using a set of specific parameters. Due to the

symmetric structureof the distributedantennasystemshowninFig.1,

it is sufficient forustoevaluate the BERperformanceofMTO,when itmoveswithin thetriangulararea shown in

Fig.31,

which shows the

'Wenotethat,forthe sake of convenience fordrawingthefigures,inFigs.4 and 5 the BERwithinthedash-dottedsquarewasevaluated. However, onlythe BERcorrespondingtothetriangularareaismeaningful.

100

lo-l

10-2

10-3 1o-4 lo-5

-50_

m7Tn: 1.5I U= 12:

EbINo

= 20dB

x[m [ml

Fig.5. MMSE:BERversuscoordinates (.r y)performanceof thedistributed

anrtennacellularDS-CDMA systemsupporting K=10000usersusingthe spe-cificparametersofm = 1.5, U = 12,

EbINo

= 20dB,whenusersignals

experiencepass-loss,lognormalshadowingslowfadigaandNakagami-Tnfast

fading.

antennas within the virtual cell ofMTO. Note that the SNR perbit ofEb1NO used in the figures of this section represents the average

SNR per bit at the MT transmitter location. Conventionally, when transmission pass-loss is not considered or ideal power-control is

assumed,the averageSNRatthe receiverisusuallyused. Duetothe transmissionpath-loss,itcanbereadilyshow that the SNRmeasured

atthe transmitter side issignificantly higherthan that measuredatthe receiver side foragivenvalue of transmittedpower.

In

Figs.

4 and 5weevaluatedthe BERperformanceofMTO, when it moved within thetriangular areaasmarked in Fig.3.Specifically,

inthecontextofFig.4using U = 12 receive antennas,we assumed

that the distributedantennacellular DS-CDMAsystemsupported only

y

A6

*10

.-1

_LOmo

5 10 15 20 25

Eb/No (dB) at the MT position

Fig. 6. Single-user bound: BER versus SNR perbit,

EbVNo,

performnance

ofthe distributed antenna cellular DS-CDMA systemsupporting single user,

when the usersignalexperiencespass-loss,lognormal shadowing slowfading

and Nakagami-m fast fading.

a)

cc

bJ

m

U=12,a=b=2, N=31

0R=500m,r=

1OOm,do=1Om,g= 1OOm

--- MMSE

1 -| Single-user bound

)10-3 1 nnnn

10o-1 0

10 15 20 25 30 35 40

Eb/No (dB) at the MT position

Fig. 7. MMSE: BER versus SNRperbit,

EbINo,

performancefor the dis-tributedantennacellular DS-CDMA systemusingMMSEdetectors,when user

signals experiencepass-loss,lognormalshadowing slow fading and

Nakagami-mfast fading(rn=2).

one user. Hence,the corresponding BERperformance represents the single-user BER bound. By contrast, Fig.5 corresponds to the dis-tributed antennacellular DS-CDMA systemsupporting K = l0000

userspercell.Fromthe results ofFigs.4and5,we canobserve that the BERperformance doesnotvary significantly,whena MT moves

within the system, provided that it is not too close to an antenna.

However,whena MTis closeto anantenna,the received powerby this

antennawill dominate the achievableBERperformance of theMTand the resultantBER is lower than thatachieved, when theMTis away from all theantennas atcertaindistances. By comparing the results of Fig.4andFig.5,itcanbe shown that the multiuser interference also

slightly

degrades the achievableBERperformance.

The results in Figs. 6 and 7 were evaluated, whenMTo is atthe

centerof the shadowedtriangleseeninFig.3.InFig.6 the single-user

BERboundversusSNR perbit of

EVNo

performancewasevaluated inthecontextof the distributedantennacellular DS-CDMA system for rM = 1,1.5, 2, 3 and oc, and for U = 3and U = 12.Explicitly, the

BERperformanceimproves,when the fastfading becomes less severe,

i.e.,when the value of the

fading

parametermincreases. Thedetection

using thesignals collected from U = 12 antennas outperforms that

from U = 3 antennas, and the gain forin = I is about5dB, while

form oc is about

3dB,

atthe BER of

10-3

By contrast,inFig.7

the achievable BERperformance of MMSE detector isdepicted. The benchmark single-userBERbound is also shown in Fig.7.Asshown

inFig. 7,whenthenumber ofuserssupportedby acell isK = l000,

weobservenoerror-floor fortheMMSEdetector. However,when the numberof users per cell is K = 5000 or K = 10000, explicit

error-floors are observed. This might bebecause, although the interfering

signalsareweak,butthenumberof interfering signals receivedbyeach antennaishigh,whichmaybe far beyond the interferencesuppression

capability of theMMSEdetector.

Furthermore, as shown in Fig. 7,for the targetBERof

10-2,

the MMSEassisted distributedantennacellular DS-CDMAsystemusinga

spreading factor of N =31 is capable of supportinguptoK= l0000

users percell with the SNR perbit of 19dB atthe transmitter site.

Supporting K =10000users per cell is far beyond the capability ofa

conventional cellularDS-CDMA concept,when itusesthe spreading

factor of N = 31 and employs 91 antennas located at the BS.

This isbecause, in thiscase,the total number of degrees-of-freedom available at a BS in the conventional cellular DS-CDMA system is about 31 x 91 = 2821. Any linear detector using this number of

degrees-of-freedom

is impossible to

distinguish

K = l0000

signals,

which have a similar power-level due to using power control. Inconclusions,inthiscontributionwehave proposed and investi-gated a distributed antenna cellular DS-CDMA wirelesssystem,where a big number of antennas are distributed in the area of a cell and are connected with the signal processing center referred to as BS. From our analysis and results, we may argue that the distributed

antennacellular DS-CDMA system consists of one of the high power-efficiency wireless systems. When using the same set of system param-eters,the distributed antenna cellular DS-CDMA system is capable of supporting anextremely higher number of users, than the conventional cellular DS-CDMA systems using centralized BS antennas.

ACKNOWLEDGMENT

The author would like to acknowledge with thanks the financial assistance from EPSRC of UK.

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