International Conference on Information and Communication TechnologyICICT 2007, 7-9 March 2007, Dhaka, Bangladesh

USER CAPACITY OF DS-CDMA CELLULAR COMMUNICATIONSYSTEMS OVER A NAKAGAMI-M DISTRIBUTED MULTI-PATH

FADING CHANNEL

'Md. Farhad Hossain, 2Md. Waliullah Khan Nomani and 3Satya Prasad MajumderDepartment of Electrical and Electronic Engineering, Bangladesh University of Engineering and

Technology, Dhaka-1000, Bangladesh.E-mail: lmfarhadhossaingeee.buet.ac.bd, 2waliullahkhangeee.buet.ac.bd

Abstract channel and Rician fading channel has been investigatedin [2, 3, 10]. Cellular DS-CDMA in a Rayleigh fading

The user capacity of the reverse link of direct channel has been analyzed in [11]. To mitigate the near-sequence code division multiple access (DS- far problem power control has also been considered inCDMA) cellular wireless mobile communication many papers [4, 5, 11]. In [11] imperfect power controlsystems over Nakagami-m distributed frequency in Rayleigh fading channel has been considered. Non-selective multi-path fading channels with respect to cellular wireless communication over a Nakagami-mboth the voice and data communications has been frequency selective multi-path fading channel for singleevaluated in this paper. Effect of perfect and carrier and multi-carrier DS-CDMA system has beenimperfect power control on the performance of the analyzed, considering perfect power control in [4, 5].

systetisobserved that the system Performance analysis and evaluation of user capacity ofsystem is considered. It DS-CDMA cellular wireless mobile communicationperformance is quite satisfactory for both the voice system over a Nakagami-m frequency selective fading

commnictio anddaachannel with perfect and imperfect power control is not

1. Introductionpublished yet which have been presented in this paper.

2. System AnalysisIn the recent years, Code Division Multiple Access 2 n Signal Modl

(CDMA) draws considerable interests of the 2.1. Transmitted Signal Modelcommunication engineers to be used as a technique for Let us assume a DS-CDMA cellular system in whichmultiple access communications. CDMA has many there are Nc interfering cells and in each cell there are Kadvantages over other multiple access techniques such as independent mobile users transmitting signals. A cellularTime Division Multiple Access (TDMA) and Frequency mobile system with six interfering cells is shown in Fig.Division Multiple Access (FDMA) [1]. 1. Transmitted signal from all the K users of a single cell

Direct sequence CDMA (DS-CDMA) is the most is given by,popular among the CDMA techniques. IMT 2000proposed cdma2000-1xRTT; cdma2000- 3xRTT; s() = E bk (t - A')cdma2000-lxEV, DV, DO; W-CDMA; TD-SCDMA k= 1and EDGE as the air interface standards for the third xak(t-rk)cos(oJCt +S) (1)generation (3G) mobile communication. For multi-usercommunication, DS-CDMA is the specified technology where, ak (t) and bk (t) are the k-th user's spreadingfor all of the above mentioned air-interfaces except for

EDGE hosestandrd i TDMA Man reserch orks signal and data signal respectively. Both are sequence ofEDGE whose standard is TDMA. Many research worksuntapidercnglrussofuainT ndT

have been done on DS-CDMA [2-5]. Multiple access unit amplitude rectangularpulses of duration Tc and Tbinterference (MAI) limits the capacity and degrades the respectively, and phase 0 or - rad with equalsystem performance. Both the standard Gaussian probability. There are Gp chips per bit and thusapproximation (SGA) and the improved Gaussianapproximation (IGA) methods are used for the statistical GP Tb /Tc is the processing gain or spreading factor.distribution of MAI [6 - 7]. The wireless channel can be cm is the common carrier frequency, Ak is the amplitudemodeled in different ways such as additive white

Gaussan nose(WGN) hanne, flt fadng chnnel of the k-th user's carrier and o7 iS the phase of the k-thand frequency selective fading channel [8-9]. The BER carrier. Delay, rk iS a random time calculated withperformance of DS-CDMA system in a Rayleigh fading

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respect to reference signal, accounting for the lack ofsynchronization among the users.

2.2. Channel Model Cei#

The low pass equivalent impulse response of a pass \ eii Ce #3band multi-path frequency selective fading channel forthe link between the k-th user transmitter and thereceiver is, L %7 a

L jO'lk 4hk (t) = aLcrlk e (t - - l'k ) (2) eiCl

Here, Ok and rTk are the phase and time delayterms introduced by the channel. These terms can be Fig. 1 Cellular mobile communication system with sixassumed to be random variables uniformly distributed FingCellsyover [0, 2 T ) and [0, Tb) respectively, where Tb is the bitperiod. L is the number of fading path and al k is the propagation. Ak is the amplitude of the received signal of

path gain component. For a Nakagami-m fading channel, user k and represents the effect of imperfect power

at/k are random variables with Nakagami-m control. For perfect power control, Ak = A for all k. n(t)1^k represents the additive white Gaussian noise (AWGN)distribution. with zero mean and two sided power spectral density

The probability density function (pdf) of the No /2.Nakagami-m distributed random variable ar1,k is given In Fig. 1, the home cell is numbered as cell #0. Asby [8, 9], the effect of the multi-user interference is additive, for

in__ 2 NC interfering cells, the received signal at the base2 Km2 I 2m-1 l,k 1ak (3) station of the home cell #0 can be represented by [9],

p (al,k ) =| a/k x e al,k >.L K (

m Q1,k )r(t) = E E AkOCal ak Clt k )l0 1 ko=I Ako oko 0 T ko

where, Q_ = ELa2 1 Multipath intensity profile (MIP)

can be taken as flat or negative exponential decaying. x bk0 (o t10ko Cos Oc + ot0koHere, in this paper a flat MIP profile is considered for NC L K 2 (

+ Y, Y, Y, A 182 ) (5)which Q kQ for all I and k. m is the Nakagami-m n= I =1 knZ= kn a1nkn aknn (l- lnknfading parameter and is given by, m = _E2 L2 l2varLak x bkn (t /nkn )Cos (co ct + lnkn ) + n (t)

[alk [l,k - where ,k = rn,k /rOk iS used to represent the loss oftheThe value of m determines the severity of the fading. m w k ' k i u th= 1 represents the Rayleigh fading, m -* o represents received signal amplitude with uniform distribution inthe conventional Gaussian scenario and m = 1/2 [0,1], Ak is the received amplitude of user k in cell #n,describes the worst-case fading condition [5]. 'k is the distance from the base station of cell #m to

2.3. Received Signal Model the k-th mobile of cell #n,I k and a00 are the fadingWhen there are no interfering cell, signal received at factors with Nakagami-m distribution respectively for

the input of the receiver consists of three components: the k-th user's signal at the l-th path of cell #n,the desired user's signal from multiple paths, the r1 k andS1nk iS the time delay and carrier phase of k-interference signals from K-i interfering users and a tinh, and ki the 1,ti day an carrierphecofek-noise signal. A conventional correlator type receiver for th user's signal at the l-th path of cell #n respectively,k-th user is shown in Fig. 2. Considering BPSK as the 1n

k = 01n k - C9Inkmodulation technique, at the receiver, the signal ' " " " i kavailable at the input of the correlator is given by,

K K Lr(t) = r (t)+ (t) kZl 1Z1 a, kAkbk (t - 7,k) 2.4. BER and SINR at the Receiver Output

k = I k = l ~~~~~~~~~~~~Letus assume that for the first user in home cell #0,xak (t - i k ) cos ±00c+ lk ) ± n (t) (4) the reference receiver can ideally lock onto the first path.

With no loss of generality, let us assumewhere, cv k corresponds to multi-path fading, Tik and that rl10 = o~lO 0=o. Then the output of the receiver

XI k are due to the lack of synchronization and multi-path in Fig. 2 after a time interval Tb is,

206

(Tb -Tb evaluate the system performance, the maximumZL,l( b- fo r(t)a, (t) cos ct dt (6) acceptable BER for voice and data communications are

Receiver Receiver taken 10-3 and 1 0-6 respectively [ 14].

Inpu;f( Outpu In Fig. 3 and 4, maximum number of simultaneouslyr (t) TZ( active user Kmax is plotted with EINo. Two sets of curvesAk cos ct ak (t) are drawn, one for BER = 10-3 and the other for BER =

akg.2CorelatortypDSCDMAreceiver.10-6. From both the plots, it is clear that a minimumFig. 2 Correlator type DS-CDMA receiver, value of EbINo is required to allow any user to get

When the power control is imperfect, the received satisfactory performance. This value lies within theamplitude Aotekhurrange from 6 to 10 dB. It is also evident that higher

amplitude Ak of the k-th user can be modeled as random nme fsmlaeul cieuesi loe onumber of simultaneously active users iS allowed forvariable with uniform distribution around the nominal voice communication compared to that of datavalue of the received amplitude level Ao. This means that communication. Comparing Fig. 3 and 4, it is clear thatthe probability density function ofAkcan be assumed as the user capacity of the system decreases with the[9], increase of the variation range of the received amplitude.

f (Ak ) = 1/2V, AO - V < AK < AO + V (7) At any condition, the correlator type receiver canwhere, V is the variation of the received amplitude from provide a satisfactory neither voice nor datathe average value Ao. communication in Rayleigh fading channel (m = 1).

Using the similar mathematical analysis as described In Fig. 5 and 6, Kmax has been plotted with thefor non-cellular case in [12], the conditional signal-to- number of the signal propagation path for imperfectinterference-noise ratio (SINR) conditioned on a1010 power control condition. From the figures, it can be

concluded that with the increase of the number ofunder imperfect power control in case of cellular system propagation path L, Kmax decreases. This occurs becausecan be determined from equation (6) and (7), and is of the increasing amount of fading for higher number ofgiven by, propagation path. For a fixed value of L, Kmax increases

zSJINR = a2 /l L1 V2 F(NCLK ,] No 1 (8) with the increase of m. It is also clear that as the number10,10 1010 3GP 3A2L 5 2Eb of interfering cell increases, the MAI of the system

To SIN is g increases which reduces the system user capacity.Then, unconditional SINR iS given byoo) 18

INR S 0INR 00,P(a ,l10) 0d10 16 L=4, GP=512, N, =6

2 ~~~~~~~~~~~~~~~~~~~~~~~~10503''NC No0[ 59 )i6 t]l <

Hence, conditional BER conditioned on a, l is X ERBBER"'l06given by, 6

BER la,1 VK 1X ) (10)|

Average (unconditional) BER is then given by, 0 1L 20- - 3000 /bNO'\dd

BER f BER la P 1,l Jdalol Fig. 3 Variation of maximum number of simultaneouslyactive allowable user with SNR per bit using L = 4, Gp

o ef( SRX1 /1 l 512 and Nc = 6 in perfect power control condition.14

( m 1M(1I L =4, GP. 512, N, 6, V/A0=1im/Ci m1VQ 1mQ)+ 12(FM+Y/1f) Qt/ I InQC mom12 m +1I m~m1010 -- m=20I

xF2 (m + 1/2, 1; m + 1; mlQC+m) (12) m 3

where, F (m 1 ,1;m is the w BER -10'21 ~~~~~~~ 2 ±1m/~~~~~~~~~~~u+m) E ~~~~~~~~6 --BR0

Hypergeometric function given in [13].

Here,c =03Gp tl+32 00i s2 Eb4 4 0 |S

0 e 10 1 20 2N 303. Results and discussion E /N dB

Fig. 4 Variation of maximum number of simultaneouslyMATLAB has been used to derive the numerical active allowable user with SNRper bit using L =4, Gp=

results. To draw all the curves, Q= 1 is assumed. To 512 andNc 6in imperfect power control condition.

207

120 __ _ __ __ _ 4. ConclusionGp = 512, V/A% = 1, Eb/No = 20dB, N=0 m = 1

100 - m=20 - The user capacity with respect to voice and data--m =30wiht an80 \\ communications over a DS-CDMA cellular wireless

mobile communication system in a Nakagami-m60 BER=10-' frequency selective multi-path fading has been

10/6 investigated in this paper. Different optimum parameters40 9 BBER= l0 G10R have been evaluated from the analysis. Both the cellular2C and the non-cellular (single cell) system in a Nakagami-

m fading channel can support both the voice________________,_____________ ,communication and the data communication. The user2 4 NumbEr; 6 10 12 capacity of the system is higher for voice

Number of Multipath, L

Fig. 5 Variation of maximum number of simultaneously communication compared to that of data communication.

active allowable user with the number of signal Referencespropagation path using Nc 0 and VIA0 1.0.

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