Performance of Cellular DS CDMA Systems Using Distributed Antennas

PERFORMANCE OF CELLULAR DS-CDMA SYSTEMS USING DISTRIBUTED

ANTENNAS

Lie-Liang Yang WeiFang

School ofECS,University ofSouthampton, S017 1BJ,UK School ofECS,UniversityofSouthampton, S017 1BJ,UK

ABSTRACT theconventional cellular DS-CDMAsystemsusingcentralized

BS antennas. Theproposed distributed antenna cellular DS-In thiscontributionwepropose and investigatea high-capacity CDMA system is capable of providing a platform for possibly cellular DS-CDMA wireless communications system, where integrating the conventional cellular systems into the future ad-numerous antennas are distributed in the area covered by the vanced, high-flexibility, ad-hoc and cooperative wireless net-system. The bit error rate (BER) performance of the dis- works. Furthermore, it may provide an unification platform for tributed antenna cellular DS-CDMA system is investigated, finally merging both wirelesscommunicationsandwired com-when transmission pass-loss, lognormal shadowing slow fad- munications into one, so that high-flexibility and high-quality ing andNakagami-m fastfadingareconsidered. Ourinvestiga- services are available anytime and anywhere.

tion andnumerical results suggestthat the distributed antenna

cellular DS-CDMAsystemconstitutesahighpower-efficiency 1. CELLULAR DS-CDMA SYSTEMWITHDISTRIBUTED

wireless system. For utilizing thesame set ofsystem param- ANTENNAS

eters, itis capable of providing an extremely higher capacity,

than the cellular DS-CDMAsystem builton theconventional A. SystemDescription

cellularconcepts. The novel concepts of the proposed cellular DS-CDMA system

using distributedantennas canbewell-described with the aid of I. INTRODUCTION Fig. 1. It is well-known that, in conventional cellularsystems, each cell is centered around a BS, which may employ a set

Among radio technologies, multiple-input-multiple-output of antennas. Bycontrast, in theproposed distributedantenna (MIMO)systemsusingmultipletransmit and/or receiveanten- aidedcellular systems, as shown in Fig. 1, eachcell has nu-nashave attracted wide research interestsin recent years[1]. In merous sets of antennas, whicharedistributed within the area this contributionacellular DS-CDMAsystemusingdistributed covered by a cell and are connected to the BS using optical antennas isproposed andinvestigated, whereabignumber of fiber. In the distributed antennacellular systemsofFig. 1, the antennas aredistributedintheareacoveredbythesystem. We antennas nearthe bordersmaybe connected withtwo orthree consider the DS-CDMAtechnique, since it has been atypical BSs, so that soft handoffcanbe achieved. In more details, as

multiple-access schemeinthe second and thirdgenerations of shown in Fig. 1, each of the antennas within the dash-dotted wireless communications systems [2], and withoutany doubt, box are, respectively, connected with

BS,

andBS2 of Cell 1 it will constitute an important candidate in the future gener- andCell2, while the antennas within the dashedcircle atthe ations ofwireless communications systems. In theproposed connerjointing Cells 1, 2 and 3 are all connected with BS1, distributedantennacellular DS-CDMAsystem,the distributed BS2 andBS3 of thesecells.

antennas areconnected withanumber ofsignal processingcen- In the considered distributed antenna system, for the con-ters,whicharereferredto asbase-stations (BSs), using optical venience of analysis, we assume that the cells are shaped as fibers. Note that, thereason foremphasizing opticalfible in- hexagons with the commonradius ofR. We assumethatany stead ofwireless for implementing communications between apair of adjacent antennas are separatedby a distance of r. distributed antennas and BSs ismainly for the sake ofsaving Hence, each antenna issurroundedbynumerousdistributed an-thehighlylimited wirelessresources. Additionally,westilluse tennas locatedat thecorners ofthelayered hexagons. Specif-theconceptofBS, however, it is nowrathera signalprocess- ically, forthe antenna marked as A3 in Fig. 1, the first layer ing centerthan aconventional BS. The antennas atthe BS of has six antennas, the second layerhas 12 antennas including theproposed systemareassumed have nopriority incompari- the antennalocatedat

BS,,

and so on. Notethat, the structure sonwith the other distributedantennas. The BS isresponsible ofFig. 1issufficientlygeneral forapproximatelymodelingthe for the signal processingof theuserswithin thearea, which is distributed antenna systems having an arbitrary antenna den-coveredbythe distributedantennasconnected with this BS. sity. This can be doneby appropriately changing the radius

Inthis contribution wefirst describe the distributedantenna value of R in

Fig.

1.

cellular DS-CDMAsystem. Then,theBERperformanceof the Indistributedantennasystemsasshownin

Fig. 1,

we assume

cellular DS-CDMAsystemusingdistributedantennasis inves- that the distributed antennas

only

implement

the functions of tigated,when thesimplestcorrelation detector isemployed [3]. conveying a

signal

from radio

frequency

(RF)

tobaseband or

TheBERperformance isanalyzed andevaluated, when com- from basebandtoRF,inordertomake the

computation

burden municating over compositelognormal shadowing slowfading at adistributedantenna aslowas

possible.

The above assump-and Nakagami-m fast fading channels associated with trans- tion might be due to the size constraint ofthe distributed an-mission pass-loss. Our study shows that, in the distributed tennas and the constraint arising from some supported signal antenna cellular DS-CDMA system, the detection is location processing. Forexample, when advancedmultiuser detection dependent. It issuggested that thedistributed antennacellular (MUD) is employed, information associated with each mobile DS-CDMAsystemconstitutes a high power-efficiency wireless terminal (MT) and with eachantennashould be sharedbyany system. When using the same set of system parameters, the individualprocessor. In this case, using distributed processing proposeddistributedantennacellularDS-CDMA system is ca- in thecontext of eachdistributed antennawouldrequire an ex-pable ofsupporting an extremelyhighernumber of users, than tremelypowerfulnetworkfor conveying theinformationtimely

Cell2 ber ofantennaslocated within its

line-of-sight (LoS)

area. The

r--- ~~ ~ ~~ signals sampled from the antennas within the LoS area of the consideredMTusually fall within the clusterof strongest sig-nal. Consequently,the considered MTwillconflict no or light / / ' iA CeX 1,'' \ s \ ,s' Cell3 near-far problem.

0

f -t * B. * *Propagation Channel

Modeling

In distributed antenna cellular systems, for any a

given

MT,

there are a number of antennas within the LoS area of theMT. This LoS area is referred to as a virtual cell. The antennas

within the virtual cell of aMT are usedto communicate

be-tweenthisMTand its BS. Hence,the

propagation

channel

be-tweenaMTandany of theantennaswithin its virtual cellcan

bewell modeled

by

a

composite shadowing-fading

model

[5],

where

(slow)

shadowing

canbe described

by

a

lognormal

dis-tribution

[5],

while

(fast)

fading by

aRician or

Nakagami-m

distribution [6]. Specifically, in this contribution frequency non-selective

Nakagami fading [6]

is used to model the fast

fading.

LetMTobe the referenceterminal andassumethat thesignal r 4D 40 0-1-0 0 0 transmitted by the reference terminal

MTo

is being detected. The reference terminal MTo randomly moves within the tri-angle area with three antennas at its corners. For example, Figure 1: Aconceptualcellular DS-CDMA system structure with distributed MT C in Fig 1 randomly moves within the triangle area Sa antennas,where the distributed antennas are connected withone,two or three We assumethat there are U antennas withinthe virtual cellof base-stations(BSs) locatedat the centers of the cellsusing opticalfiber. MTo. Signals collected from these Uantennas areprocessed, in ordertodetect the information transmitted byMTo. Let us now analyze the received signal by the uth antenna, which is and

efficiently,

which

might

notbe

practical

in thenearfuture.

in

the l

cell

o 0

sifally,

as

ngthat

(K +1

Hence, in our distributed antenna system all

signals

received

user

signals

cl that. from

MT0care, receiv

b

the

K th

from the MTs

by

the distributedantennas are

conveyed

tothe

anennal

th.

ereceivedcle

tsg

can

BSs, where theprocessing iscarried out. Simultaneously, all a

thedistributed antennas arealso used for transmitting signals then be

expressed

as

from the BSs to theMTs, in orderto improve the down-link K

transmissionquality.

Inthiscontribution, specifically,weconsider andinvestigate

r=t)

= Phobo(t)co(t) + E h

the distributed antenna systems using DS-CDMA signaling. xk 1

Hence,whenconsideringconventional binary phase shift key- b(t-T)C(t- T) +mtl(t) (2) ing (BPSK) baseband modulation, the transmitted DS spread

spectrumsignal,sayby thekth MT,canbeexpressedas where

nu(t)

is the

complex-valued

additive white Gaussian noise(AWGN) received by the uth receiveantenna,which has

Sk(t)

=

2Pbk(t)ck(t)

cos

(27frt

+

Ok)

(1) zero-mean anda

single-sided

spectrum

density

of

No

per

di-mension,Tk representsthechanneldelay associated with asyn-where P is the user's transmittedpower,

fJ

is the carrier fre- chronous transmission and propagation, which is assumed to quency, while

Ok

denotes the initial

phase

angle

associated be

uniformly

distributed within

[0, Tb).

Furthermore,in

(2)

hku

with the carrier modulation. The data stream's waveform represents the channel gain with respect to MTk and the uth an-bk

(t)

=

EZ

Qbk

[n]

PTb

(t

-

nTb)

consists of a sequence tenna. The channel gain

hku

takes intoaccount both shadowing

ofmutually independentrectangularpulses of duration Tb and andfading. Hence, it can be expressed as ofamplitudeof+1 or-1, whereTb is the bit duration. Finally,

in

(1)

Ck(t) =E_

ck'T,(t

-

j'T)

denotes thesignature hkj

=3ukuek

7 (3)

sequence waveform of the kth user, where Ckj assumes

val-uesof +1 or-1 withequal probability, whileFTC

(t)

is thechip where, without loss of any generality, the initial phase seen in waveform, which is definedovertheinterval

[0,

T,)

and has the (1) and the phase due to channel have been absorbed into

Oku,

property of

foT

T,(t)dt =

T,

and0kuis assumedtobeuniformly distributed in [0, 2X). In(3)

Notethat,inthis contributionwe assumethat eachMT em-

/3ku

representsthe

lognormal

shadowing factor, accountingfor ploys only a single antenna, which is sufficient for fulfill our largescalegeographical variation, while

aEkt,

represents the fast objectives by focusing on the issues of the distributed antenna fading envelope. We assume that the transmission pass-loss is systems. However, our investigation can be extended to the dis- absorbed in the shadowing factor

Qkl,

so that the mean-square tributed antenna systems that use multiple MT antennas aided value of

aEkt

is unit, i.e., Q F [ce] 1. Furthermore, we by some advanced transmit and receive schemes [4]. Fur- assume that/3k and

aEkt

are mutuallyindependentand both of thermore, we assume that thedistributedantenna cellular DS- them are also independent of

Oktl.

Antennas in the that the element

nXm

in n is a complexGaussian random

vari-virtual cell Chip-waveform S n able with zero-mean and a variance of

(72

=

No/2Eb

per

-t)

nmatched-filter

Sp dimension, where Eb PTb represents the energy per bit.

,'ri(t) \\ I Letus assume that

Tku=

lkuT, +vku, where 1ku > 0 and

T ¢ l 0 < Vku <

T,.

Then,

upon

substituting

the received

signal

r2(t) Data inthe form of

(2)

into

(6)

and

expressing

invectorand matrix

t) Detection

ott

forms,

itcanbe shown that yucanbe

expressed

as algorithms

----]_K

u

(t) Yu =

1houcbo

u

[01

+

S1

hkuCk

R

(Vku)bk

+ nu,

(9)

\~~~~* t k=1

wherebk =

[bk

[-11,

bk

[0]]T contains thetwodata bits

trans-mitted by thekthMTwithin

[0, Tb),

while the otherarguments Figure 2: Receiver block diagram for the reference MT in the distributed in (9) aregiven by

antennacellular DS-CDMA system. 1 T

Co N

[c,cO

,* *

CO(N-1).

density function (PDF) expressedas [6]

Ck(N-1ku

-1)

Ck(Nl-ku)

0 0

P12?J) 1

(mn)rmym

exp - Y >0

(4)

Ck(N1k2

Ck(Nlk ±1)

0 0

ku F (M) Q

Q~ ~~~~1

kN2 C(N)

where

F(.)

is the Gammafunction, and, again, mis aparam-

Ck1

|

Ck(N1)

0 0

C°O

eter accounting for thefading severity. In (3)

/3ku

represents Nku

=0

0 CkOl

the shadowing, which canbemodeled as lognormal distribu- ko

tion[6]. It canbe shown that

32

alsoobeyslognormal

distri-butionhaving thePDFgivenby [6] 0 0

Ck(lku-2) Ck(lku-1)

pdk1t(r)

exp 0_(og1Or

I'ku)2-

L 0 0 Ck(lku11) Cklku j

ku

of2

[7Tr

2o72

Rp(Vku) 0 1

where

10/In

I/

10 = 4.3429, and

I'ku

(dB) andor; (dB)_/ are _{R~~~~~(vk~~~~)}R

(

[)

_{R~~~~(vk~~~~~)}

RV

(Vku)

0p(V u

0

themeanand standard deviation of10

log1o

r,respectively. Fi- [

nally, sinceweassumed that both the fastNakagami-mfading

X0

RV

(V)

and the shadowing slow fading are independent random pro- where

Rg,(vk)

and R(vkt) are the chip auto-cesses, hence thePDF of

hku,

2 is simply theproduct of(4)

and

(S).

correlation

functions,

which

are defined

Ias

Rp

(s)

=

ad5. f-

T,

(t)Tt (t

-

s)dt

and

Ri(s)

=

Rp(Tc

-

s)

for

C. Representation of The ReceivedSignal 0 < s <

Tc,

respectively. The receiverstructurefor detection of the referencesignalfrom Furthermore, let

MTo

is showninFig.2. As showninFig.2the receivedsignals = T T TT 10

from the Uantennasinthevirtual cell of

MTo

arefirstpassed

[Y1,

Y2, ,Yuj (1)

through abank offilters matchedtothechip-waveform pulse which collectsall the samples from the U antennasrelatedto ofFTC

(t).

Then, theoutputsof thematched-filtersaresampled the detection ofMTo.Then,y canbeexpressedas

at a rate ofI

/Tc.

Hence,incorrespondencewith each databit, K

atotal of Nsamples canbe obtained from eachantenna,where

[0]

+ :

CkRPkHkbk

+ (

Nrepresents the number ofchipsperbitorthespreading fac-

=(Iu

co)h0b0 + tor. Let usconsider the detection of the first data bit transmitted k

by

MTo.

Then, theAthsamplewithrespecttothe uthantenna where

canbeexpressedas n=

FnT

nT

nT]T

(12)

(

2P/NT=Y~

Xf±T

rU(t)<

s(t-

ATdt

(6)

iS

an

UN-length

Gaussian noisevector,which has zero mean

AT

CC

and a covariance

matrix

of 2

2IUN,

0 represents the

Kro-neckerproduct operation, and the otherarguments in (11)are

whereA =

O0,

1...,N-1; u = 1, 2,...,U,

2P/NTb

isa givenasfollows:

normalizationfactor, and * represents the complex conjugate.

Th1

0,. ,hU~(3

Letho = [o h2.,ho](3

T

~~~~Ck

=

diag{Cki,Ck2,.

* CkU} (14)

Y=

[YOul,

Y1T,.

,

Y(N-)l>u],

(7) Rk diag

{RV,(vk1

),

RV,(vk2),.

,

RX(vi.u)}

(15)

III. LOCATION-AWAREDETECTION AND BIT ERROR RATE

In this section we investigate the location-aware detection in

the distributed antenna cellular DS-CDMA systems, where a 100 1.5 U 12 E

20dB

usersignal, sayMTO,is detected based on the observation data Tn b

UNO

sampled from the antennas within the considered user'svirtual > 10-1

-cell. Specifically,for the correlation detector, the decision vari-n

l-2

_

able for

detecting

bo

[0]

transmitted

by

MTo

using

themaximal t 10 ratio combining (MRC)principle[6] can be expressed as 4

103

_

Zo

=X{o} = X

h{ho

(Iu

X

Co)T

y

(17)

10-5

-50 whereX{Zo}represents therealpart ofZo.Upon substituting - 0

(I1) into(17), we obtain xjm] 30 20 40 [m]

U K

Zo

hou

h

l2bo[0]

+ Z hH

(Iu

X

Co)T

CkRVkHkbk

tl=1 k=1

+hH

(Iu

0

co)

n

(18) Figure

4: Single-userbound: BERversuscoordinates(x, y)performance ofthe distributedantennacellular DS-CDMA system supporting single user,

It canbe shown that the average BER ofMTo attheloca- when the_and usersignal experiences pass-loss, lognormal shadowingslowfading Nakagami-mfastfading.

tion

(x,

y)

canbe computedefficientlyusing a Gauss-Hermite quadrature integration [7],expressedas

uF/2

U n areashown in

Fig.31,

which shows the antennas within the

vir-P

fX,2

Y 1 n I Q tual cell ofMTo. Note that the SNR per bit of

Eb/No

used in

Pb : w -

_=-

7 yr

_i-=1m

+

Las

22m

sin2o the

figures

of this sectionrepresentsthe average SNR per bitat

the MTtransmitter location. Conventionally, when

transmis-0(io

i+M°u(z ))/A m dO (19) sionpass-loss is not considered or ideal power-control is as-/ i sumed, theaverageSNRatthe receiver isusuallyused. Due to the transmissionpath-loss,it can be readily show that the SNR where

w7

i and y are independent of 0, which can be found in measured at the transmitter side is significantly higher than that

[7].

measured atthe receiver sidefor a givenvalue oftransmitted

power. IV. EXAMPLES OF PERFORMANCE RESULTS

y

A4 Al2100

/ \\

// \

a

10-1 _

_

A5 A1 ___A 41IS 110-2 m_.,~2E/o2d

--I.

~~ ~ ~ ~ ~ ~ 5

-503\|A\

10-

0 0

A7

\/

_{A8 <}

_{A 9}

0/

_z

\\[ml_~~g

_{x[m] 50 0 40Y,[m]}

Figure 3: Antennaswhosesignals maybe collectedfordetection ofMTO, whenMT0is within thefilled area.

Figure 5: Correlation: BER versus coordinates (x,y) performance of In this section we provide arange of results for illustrating thedistributed antenna cellular DS-CDMA system supporting K=10000 users, thacival pefrac_{t zeacleva)eper-ormnceo -t zeexep lnc (lstlDut(}

of..the.exemplified ..distributed..

_{-an-Nakagami-m}

an- whenusersignals experience pass-loss,_{fast fading.}

lognormal

shadowing

slow

fading

and

tennacellularDS-CDMA system using a set of specific

In Figs. 4 and 5 we evaluated the BER performance of

MTO, when it moved within the triangulararea as marked in

_OR=500m,r=

a=b=2,N=31,Eb/No=20dB_{100m,do=1Om,g=1 OOm} Fig.3. Specifically, in the context ofFig. 4, we assumed that 100 1 Om'd '1Om'g' OOm

the distributed antennacellular DS-CDMA system supported 5 U=3

only one user. Hence, the corresponding BER performance ---- U=12

representsthesingle-userBERbound. By contrast,Fig.5 cor- --responds to the distributed antennacellular DS-CDMAsystem

supporting K =10000 users percell.

Fromtheresultsof Figs. 4 and5we canobserve that, indis- L 2 tributedantennacellular DS-CDMAsystems, theBERperfor- . 1

0-2

mancedoesnotchangesignificantly, whena MT moveswithin thesystem,provided that it isnot toocloseto an antenna. How-ever, whenaMTisclosetoanantenna, the receivedpower

by

thisantennawill dominate the achievableBERperformance of 100 50000 100000 150000 200000 250000 theMTand theresultantBERislower than thatachieved,when Number of Users in a cell

theMTis faraway fromall theantennas atcertain distances. Comparing the results of Fig. 4 with Fig.5, itcan be shown that, in distributed antennacellularDS-CDMA systems,

mul-tiuse

in*trfer

also degrad

the aheb

mBE

e

erf-

Figure

7: Correlation: BERversusthe number ofusers,

K,

percell for the

tisrinefrec.ls,erde

aheabeBRh efr distributedantennacellular DS-CDMA system,whenusersignals experience mance, in, however, ahighly insignificant way uponaccount- pass-loss, lognormal shadowing slow fading andNakagami-m fastfading.

ing for K= 10000 userssupportedby thesystem inFig.5. The

results ofFig.5 imply that the transmissionpath-loss has

signif-icantly mitigated the interference imposed by the MTs having BER of 10-2, the distributed antenna cellular DS-CDMA SyS-relatively high distances from the antennasconsidered. tem using a spreading factor of N = 31 is capable of

support-ing uptoK = 10000 toK = 20000 users percell. This high

number ofusers weresupported, whenemploying the simplest correlation detector. Supporting K = 10000 to K = 20000

0a=b=2,R=500m,r=

1

OOm,do=

1Om,g=lOOm userspercell is far

beyond

the

capability

ofaconventional

cel-u=3 lular DS-CDMA

system,

when ituses the

spreading

factor of

10 ---- U=12 N = 31 and employs 91 antennas located atthe BS. This is

f102

because,

in this case, the total number of

degrees

of freedom

Ulo-2

/ available at a BS inthe conventional cellular DS-CDMA

sys-L_ ' 3 \tem is about 31 x 91 = 2821, which is impossibleto handle

Lolo-3

"''i"N\\\ K = 10000 to K = 20000

signals having

asimilar level of

Lxlo-4

m=l ,l.5,2,3,wXI~ ,/' "'^'sspowerdueto

using

powercontrol.

^^o^5 Th ACKNOWLEDGMENT

E ,, I, I,

;;x

|Theauthor would liketo

acknowledge

with thanks the

financial

10 0 5 10 15 20 25 30 assistance fromEPSRC of UK.

Eb/No (dB) at the MT position

REFERENCES

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_aeor

_that

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and

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i0-3.

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