THE EFFECT OF MOBILE SPEED ON THE FORWARD LINK OF THE DS-CDMA CELLULAR SYSTEM

Vijitha Weerackody AT & T Bell Laboratories

600 Mountain Avenue, Murray Hill, NJ 07974.

ABSTRACT

A direct-sequences code division multiple access system has been accepted as a digital cellular standard (IS-95) in North America [l] . This digital cellular standard employs a powerful rate 1 /2, constraint length 9, convolutional code in its forward link. It is well-known that in a Rayleigh fading channel the performance of a channel code depends very heavily on the interleaving depth and the relative variations of the channel characteristics. In slow fading channels, since the input symbols to the channel decoder are highly corre- lated, the bit-error-rate at the output of the channel decoder may be unacceptably high. Interleavers of large dimensions can reduce the correlation of the input signal to the channel decoder at the expense of an intolerable delay. In this pa- per we examine the performance of the IS-95 system, at the mobile receiver. for different channel fade rates.

1. INTRODUCTION

A DS-CDMA (direct-sequence code division multiple ac- cess) system has been accepted as a digital cellular standard (IS-95) in North America [ 11. This DS-CDMA system and its advantageous are discussed in [2] and [3]. This digi- tal cellular standard employs a powerful rate t , constraint length 9, convolutional code in its forward link. It is well- known that in a Rayleigh fading channel the performance of a channel code depends very heavily on the interleaving depth and the relative variations of the channel character- istics. In slow fading channels, since the input symbols to the channel decoder are highly correlated, the bit-error-rate (BER) at the output of the channel decoder may be unac- ceptably high. Interleavers of large dimensions can reduce the correlation of the input signal to the channel decoder at the expense of an intolerable delay. Antenna diversity may also be used at the mobile receiver to improve its BER performance. Selection diversity is one of the least complex pre-detection antenna diversity schemes. In this paper we consider the performance of the IS-95 system at the mobile receiver for different fade rates and, also, demonstrate the improvements obtained from selection diversity.

This paper is organized as follows. In Section 2 we derive expressions for the signal statistics at the output of the RAKE receiver. These results are used in the computer simulations presented in Section 3. In this section we consider a RAKE receiver with pilot-aided demodulation, deinterleaver (IS-95 standard) and a soft-decision Viterbi decoder. The key focus of these simulations is to study the effect of the channel fade rate on the output BER. Finally, in Section 4 we demonstrate the effectiveness of the selection diversity scheme.

0-7803-2509-5195 US$4.00 0 1995 IEEE 147

2. THE RECEIVED SIGNAL AT T&E MOBILE

The received signal at the mobile consists of three compo- nents: the transmitted signal from its base :station, signals from adjacent cell-site base stations, and the: thermal noise signal. In this model we approximate the in1:erference aris- ing from adjacent cell-site base stations by an additive white Gaussian noise (AWGN) process [2] [4]. The interference generated by the same cell-site users is also modeled by an AWGN process. Note that since the same cel I-site users em- ploy orthogonal codes, the interference in this case is due to the energy amking from the multipaths. Analyses similar to those used in [5] are employed to examine the performance of this DS-CDMA system at the mobile recei.ver.

Denote by a; the information data bit of the k t h user at the nth time instant. At the transmitter, a; is passed through an inteideaver and a channel coder. Denote by b; the output of the channel coder for the k t h user at the nth time instant, T the duration of a data symbol, and & ( t ) a rectangular pulse of unit amplitude in tht: time interval [0, TI. Then, the channel coded signal for the k t h user is b k ( t ) = E, b ; P ~ ( t - nT). We assume that b; are inde- pendently and identically distributed random variables that take the values f l with equal probability. The k t h user signature (chip)# signal c k ( t ) may be written in a similar manner c k ( t ) = E, c:+(t -- nT,), where { c;} is the k t h user signature (chip) sequence, T, is the chip duration and 4(t) is a pulse shaping filter. In this paper, fcir ease of anal- ysis, we assume a rectangular pulse shaping filter, that is, $ ( t ) = -&PT,:(~). In the IS95 standard a; assumesfour different rates: 9600 bps, 4800 bps, 2400 bpr. and 1200 bps

[I] . In general., c k ( t ) are complex c; = :kL Ifl j - L ,

and, because of the Walsh functions used in the code se- quences [I] , they are orthogonal in the interial [O! TI, that is, 4 s,' cl( t )c:n( t )dt = 61, where 61, = I , 1 = m; and 0 otherwise. Also, in this standard, the symbol rate of b; is

= 19200 symbols/s and the chip rate & = 1.2288 x 10' chips/s. The transmitted signai s ( t ) from the base station is given by s ( t ) = { c u k A k c k ( t ) b k ( t ) } c J 2 x f G t , where K is the total number of users in the system, Jc is the carrier frequency, A k is the transmitted signal amplitude for the k t h user, crk is a factor due to voice activity. The pilot signal, which will be identified by the subscript 0, is included in the above summation. Because of the importance of the pilot signal in the receiver functions, about 20% of the total power transmitted from the base station is contained in the pilot [3]. This ensures a relatively large signal-to-noise ratio for the pilot signal at the receiver output. In the simulations presented later it is assumed that A k , k = 1 ,, 2.. .I<, are all

( Jz 4)

equal. It is well-known that the silence periods in a voice conversation increases the capacity of a DS-CDMA system. The voice activit factor c y k , k = 1 ,2 , ..A-, assumes the

spectively, to the four different rates of the speech coder: 9600 bps, 4800 bps, 2400 bps and 1200 bps. In this paper we will use the following statistic for the voice activity fac- tor: E { & } = 0.4 [2]. Note that the pilot signal does not contain message information, that is, b o ( t ) = 1 and a0 = 1.

2.1. Transmission Channel Model We assume a Rayleigh fading model for the transmission channel from the base station to the mobile terminal. Sup- pose the impulse responseof the channel, h ( t ) , is character- ized by L discrete multipaths h ( t ) = E:=;' /31(t)s(t - T L ) \

where ,8i(t) and TI are respectively, the complex amplitude and the delay of the l t h multipath component. We assume the multipath components are independent and the aver- age energy received from each one of them is equal, that is E{Pl( t )P;( t )} = 61,; 1,m =O,l , . .L- l .Sincethemo- bile radio channel IS time varying the complex amplitude of the fading process will be correlated in time. We will assume that the relative delays ri, 1 = 0, 1, ... L - 1, are indepen- dently and identically distributed and the distribution of ri is uniform in [0, T,], where Ts < T. For the IS-95 system T = 52 psec and the maximum delay spreads encountered in urban areas (Ts) are typically less than this value. Also, in order to completely resolve the multipath components at the RAKE receiver, we will assume that T, 5 I TL - r, 1 , for 1 # m.

2.2. The RAKE Receiver The received signal at the mobile terminal (baseband signal) can be written as

values, 1 , 5, 5, Y &, and these values correspond, re-

+n(t) . (1)

In the above n ( t ) is the zero-mean AWGN due to combined

Figure 1. RAKE receiver branch that corresponds to delay T,. Note that the signal path is represented by (, (n) and the pilot path

effects of thermal noise and interference due to adjacent cell-site base stations, and $ ( t ) is a carrier frequency offset introduced at the down conversion stages. This signal ~ ( t ) is despread and combined in the RAKE receiver as shown in Figure 1. The output of each branch of the RAKE receiver is added to give y(n) , which is then fed to the deinterleaver and the channel decoder. Finally, the output of the channel

by n- (n )

decoder is quantized to obtain ti: which is an estimate for the k f h user information symbol a;.

Figure 1 depicts a single branch of the RAKE receiver for User 1 (without loss of generality we will assume that the detected user corresponds to k = 1). The branch shown corresponds to the multipath whose delay is r,. The despread output of this branch at t = nT + r, is <,(n) = $ hn-,)T+r, ~ ( t ) c ; ( t - r,) d t , where the su- perscript * denotes the complex conjugation. The pilot sig- nal component which is employed in the demodulation of

nTtr,

nT+r, + En(n) is rlm(n) = : JnT+.,-- r(t)co*(t - T m ) d t . In the above A is the correlation time of the pilot sig- nal in the RAKE receiver. We have considered a corre- lation time for the pilot signal which is symmetric about [ ( n - l ) T + r,, nT + r,]. Note that, in the absence of a carrier frequency offset, increasing the correlation time of the pilot increases the signal-to-noise ratio of the detected output; however, this is no longer true in the presence of a camer frequency offset. (We have assumed the channel variations to be very small in comparison to the symbol rate.) We denote User 1 as the desired user and later in the sim- ulations set cy1 = 1, that is, the performance of this user is examined when it transmits at 9600 bps. Using (1) and

bl ( r - 7 1 2 ) 6;' by h: I I I I I

12 T + K 7 b

T i ? ' T",

Figure 2. Received signal waveforms of b l ( t ) from multipaths correspondingto T,,

above and with reference to Figure 2 we may write for the RAKE branch (of User 1) that corresponds to delay r,

(< T,), and q2 (> 7,).

where

and the function Rim is defined as &,(TI, r2, r3, r d ) = Jr: c ~ ( t - r3)ck(t - n)e '# ' ( ' )dt . In (2) CI and C2 are

defined as ri < r,, 1 E LI; TI > r,, I E CZ; and we have assumed that the variations of Pl(2) are very small in a time interval of T. In (2) we have used the no- tation /3i(n) = /31(nT). The first term on the right in (2) is the desired signal component, the next term is due to the AWGN and the rest are due to interference from multipaths whose delays, rl # r,. Suppose the car- rier frequency offset is such that d ( t ) = 2 ~ f 0 t , then we

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rm) = e ~ 2 ~ f ~ ( $ t . m ) s1nr foT TfoT '

have RlI(Tm, T + rm, rm, For the AWGN component, vm(n) , in (2), we may write E {vm(n)} = 0 ; E { lv,(n)I2} = +E { In( t ) I2} . Next, we use the central limit theorem to approximate the multi- path interference components in (2) by an AWGN process. This is a frequently used assumption in the analysis of DS- CDMA systems and the results obtained using this assump- tion are reasonably accurate [5 ] . We show in the Appendix that E{(,r(n)} = O;E { l(m~(n)12} = g f T O T ; where PTOT is the total average transmitted power. In the above we have assumed that the signature sequences are random, that is, E { c ~ c ; * } = 6 m n 6 k l . Using the above information we may write Jm ( n ) in (2) in the following simple form

where p m ( n ) is a zero-mean AWGN component. We show in the Appendix that tml,, Emlz, 11 # 1 2 , are uncorrelated. Since n( t ) is independent of tml(n)

Using a similar derivation for the pilot signal component q,(n), we havev,(n) = P m ( n ) A " e 3 2 " f o ( f + ~ m ) ~ + T f o A

em(.). where em(.) is a zero-mean AWGN component with E {lem(n)I2} = $ E {In( t ) l*} + vfTffT. Furthermore, it is shown in the Appendix that pm (n), pl ( n ) are uncorrelated for m # 1. Similarly, it can be shown that em(.), er(n) are uncorrelated for m # 1, and em(.) and p l ( n ) are uncorrelated for all m and 1. The pilot-aided demodulated and diversity combined signal at the output of the M-branch RAKE receiver is

where M contains the indices corresponding to the M-largest values ( M 5 L ) of IPm(n)12. Next, we de- termine expressions for the BER at the output of the RAKE diversity combiner. Using Appendix 4B in [6] we can obtain the following error probability for a given set of fade values

lPm(n)I2, m == 0,1, . . L - 1 , are identically and inde- pendently distributed, the probability density function of xmEM IPm(n)12, which is an order statistic, can be de- rived from the joint density function of the M largest values of l/3m(n)12 , m = 0, 1, .., L - 1. However, for general val- ues of L and M. , the desired probability density function is very complex. Therefore, we consider the special case when the number of RAKE branches is equal to the number of mul- tipaths, that is, Af = L. In this case, the desired probability density function is a x 2 - distribution with 2 M degrees of freedom andis g:iven by fp(x) = &e-5;cM-1, z 2 0. Finally, from (6) the BER at the output of the RAKE receiver for the case M == L is

Pb = lm pc(z)fp(z) d z . (8)

The average BER is determined by numerica1.ly integrating the above and the results are presented in the Eext section. Note that from (3) it can be seen that (,I ( n ) , the interference due to the multipaths, depends on the time vairiations of the fade coefficient 1 3 ~ (n ) . This effect has not becn considered in our model. However, for large number of multipaths, the dependenceof x;&,' F m l ( n ) on a particular fade coefficient is small and this assumption is incorporated into our model.

3. SIMULATIONS FOR THE IS-95 SYSTEM PARAMETERS

,LA 20 :Y) (0 y1 €c , m , 8" , Do , J m

NumbrslUS-

Figure 3. BERs for IS-95 system for different fade rates and for the following parameters: L = 3, M = 3, A = T , f~ = 0. (a) BER at the input to the Viterbi Decoder. (b) BER: at the decoder output, v = 5 km/h. (c) BER at the decoder output, v = 80 kmih. (d) BER at the decoder output - fully interleaved.

M - I - m exp [-(a' + b2)/2] M-l + 22M-1 I m ( a b ) x ( ) [ ( : ) m - ( ; ) m ] ( 6 ) m= 1 k=O

where the parameters a and b are given by

The bit error rate at the output of the RAKE receiver can be determined by averaging the conditional bit er- ror rate, P,, over the variable E,,, IPm(n)l'. Since

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In this section we present some simulation results for the DS-CDMA system analyzed above. In these simulations, at the mobile receiver, we use an M-branch RAKE receiver whose output is given by ( S ) , a deinterleaver (which is spec- ified in the standard) and a Viterbi decoder for soft-decision decoding (without channel state information) of the rate i, constraint length 9, convolutional code. The models used for Em(T) and vm(T) are given in (3). We are primarily interested in determining the variations of the output BER (for User 1) with the total number of users in the system and the fade rate of the mobile communication channel. In order to evaluate the performance of the system we adopt the following approach. We assume the total transmitted power from the base station PTOT, to be a constant inde- pendent of the number of users in the system, and the pilot signal power Ai = 0.2PTOT [3]. Hence, the total user sig- nal poweris Er=, E{cu:}E{A:} = ~ . ~ P T o T . Using the values of E{a:} = 0.4 [2] and Ak = A I , k = 2 , 3 , . . I<, it follows that A: = w. From the above it is seen

that 2 = $. Consider the following signal-to-noise ratio A2

signal. This 1s' the aveiage signal-to-noise ratio of the pilot

0

e

' " -1 0 1 2 3 L 5 5 SNR re, RAKE bFiws"" -n

Figure 4. BER for the IS-95 system for different fade rates and for the following parameters: L = 3. M = 3 , A = T , fo = 0. (a) BER at the input to the Viterbi decoder. (b) BER at the decoder output, v = 5 km/h. (c) BER at the decoder output, v = 80 k&.

signal at the output of one of the RAKE branches, due to the thermal noise (when f, = 0, A = T). Since this signal-to- noise ratio does not depend on the number of users in the system we will use S N R T as a reference in our simulation studies. In the simulation results presented next we consider a fixed value SN RT = 7 dB. Note that the AWGN compo- nent in the received signal is n ( t ) = n ~ ( t ) + n ~ ( t ) , where n r ( t ) is the noise due to the other cell-site base stations. Following [2] and [4] we assume that the ratio of the noise power due to the other cell-site base stations to the interfer- encepower from the users in the same cell-site base station is 0.6. Therefore, the noise component in the desired signal is,

from (4), = T

The corresponding term for the pilot signal is =

~~

PTOT. Also, in our simulations we assume a bit rate of 9600 bps for User 1, that is LY I = 1 . Figure 3 depicts the performance of this system for fade rates corresponding to mobile speeds of 5 km/h, 80 k m h , and the fully interleaved system. The latter case is realized using independent fade coefficients at the input to the chan- nel decoder. The results for the uncoded case are obtained from (8). It can be seen that for 20 users the BER is about

E { I n ( c ) 1 2 } E { lnT(c)12> + 0.62Tci$-l)pTOT,

E{ lnT(t)I2} I o ,6zTc (L- l A

2 x at 80 km/h, and this increases to 2.2 x lo-* at 5 km/h. The BER for the fully interleaved system is extremely small. The effect of the channel fade rate on the performance of the forward link of the IS-95 system is very clear from these results. At higher channel fade rates the correlation of the symbols at the input to the channel decoder will be less and this gives rise to lower BERs.

Next from (3) the signal-to-noise ratio (SNR) per RAKE

. In Fig- A; sin x foT E{bm(n)l2) ( T I 2 branch can be written as

ures 4 and 5 we show the' BER and the frame-error-rate (FER) performance of this system for different values of the above SNR. In these figure we assume 3 = 2. As can be

seen, for BER=1OP3 the SNR required at S km/h is about 4.9 dB and this reduces to 0.6 dB at 80 km/h. Also, to obtain a E R of the SNR required is about 3.6 dB at 5 km/h and 0.4 dB at 80 k m h .

A2

1 0 , 2 3 4 5 6 SNR w M E &"IY bnnbl

Figure 5. FER for the IS-95 system for different fade rates and for the following parameters L = 3, A4 = 3, A = T , fo = 0. (a) FER at the input to the Viterbi decoder, v = 80 km/h (b) FER at the input to the Viterbi decoder, v = 5 km/h (c) FER at the decoder output, v = 5 k m h (d) FER at the decoder output, v = 80 km/h

4. SELECTION DIVERSITY In selection diversity scheme, the signal from the antenna which has the largest signal strength is fed to the RAKE receiver section. As in the analysis carried out in the previous

Figure 6. Performance ofthe IS-95 system with selection diversity and the following parameters: L = 3 , M = 3 , A = T , f" = 0. (a) BER at the Viterbi decoder input, single antenna. (b) BER at the Viterbi decoder input, two antennas (c) BER at the Viterbi decoder output, two antennas, v = 5 km/h. (d) BER at the Viterbi decoder output, two antennas, v = 80 km/h.

sections we assume that the number of RAKE branches, ill = L , the number of multipath components. Suppose rz (n) = l,!?&,(n) I , i = 0, 1, ..I - 1, is the sum of the amplitude squares of the fade values at the ich receive

150

antenna. The probability density function of ymaI (n ) , the largest value of-y,(n), is frmaz(3:) = ~[F,,(z)]‘-~f,,(z) where f,,(3:) = & e - Z ~ M - l , 3: 2 0, is the pdf of yt ( n ) and F,, (x) is the distribution function of 7% (n ) . Then, the average BER at the output of the RAKE receiver is

pb = lm p ~ ( ~ ) f r , , ~ ( ~ ) dx. (9)

where P, is the conditional error probability given in (6). This integral is computed numerically to obtain the average BER. Figure 6 shows the average BER in the presence of two receive antennas. In this case the BERs at the input to the Viterbi decoder are determined using (8) and (9). Note that since we assumed that the channel fade rates are signifi- cantly slower than the data symbol rate, BERs at the input to the Viterbi decoder do not depend on the channel fade rates. Computer simulations are employed to obtain the BERs at the output of the Viterbi decoder for channel fade rates of 5 km/h and 80 kmh. As seen from this figure significant gains can be obtained from this simple selection diversity scheme.

ACKNOWLEDGMENT The author wishes to thank Zoran Kostic of AT&T Bell Lab- oratories for the very valuable discussions.

APPENDIX

A STATISTICS OF NOISE COMPONENTS 1.1. Determining E {Emi(n)} and E { I&i(n)12}

Since Pl(n) are zero-mean complex Gaussian random vari- ables, it follows from (3) that E { tmi(n)} = 0. Next, we make use of the following: 61: are zero-mean, independently and identically distributed binary (f 1) random variables, E { l ~ i ( n ) 1 2 } = 1, and CYk are independent of each other. Using these in (3), we have

4 “Ji 1 - L q 2 T .r”( Tc A ) + JZT - 5 + Im,

Since r, is independent of ~ t , 1 # m, and it is uniformly distributed in [O,T,], using the above and assuming that the chip duration, T, < T , we have E { l<mi(n)12} =

% (Ai + zf, E { a i } E { A i } ) . It can be shown that the total average transmitted power from the cell-site base station PTOT =: Ai + E:=’=, E { a i } E { A i } . Using this in the above we obtain

E { IFmi(n)I2} = ~ P T G T . 2Tc (A.2)

1.2. Correlationof p m ( n ) and p ~ ( n ) , m # 1. Consider the AWGN term u,(n) in (2). Since we have assumed that signature sequences are random, that is E { c ~ c ~ ’ } =: S,,, it follows that E {vr.(n)u;(n)} = 0, m # 1. Considering the next two terms in (2), since p,(n) is independent of PI(.), m # 1, we see that E {[m,~l(n)<m2i2*(n)} = 0, 11 # 12 and for all ml, m2. Also, since b; are independent, lrmLl - rmmZ I > T, and since f ( ~ ) = 0, T > T,, it can be shown that E {€ml~(n )&2i* (n ) } = 0, ml # m2. Therefore, it fol- lows that pm(n.) and p l ( n ) are uncorrelated for 1 # m.

REFERENCES [ I ] TIAIEIAIIS-95, “Mobile Station-Base Station Com-

patibility Standard for Dual-Mode Wideband Spread Spectrum Cellular System,” Telecommunication In- dustry Association, July 1993.

with <>, denoting the expectation taken over ri for a given 7,. Suppose c k ( t ) is a wide-sense stationaxy random process and denote by f ( ) the following auto- correlation function f ( t l - t 2 ) = $ E { c k ( t l ) c ; ( t z ) } .

Let us assume that E {c;cT*} = 6,,, then, it can be shown that f ( r ) = $ (1 - e) (71 < Tc;O otherwise. Next, assuming that E { c k ( t ) c ; ( t ) } = 0, k # I , we get (IR~~(T,,T i- n ,n , T,)I*), = f , Z m f 2 ( t - s ) e 3 2 n f o ( t - a ) dt ds, where we have used O(t) = 2nf0t for the camer phase offset. If we assume that the camer frequency offset is small in comparison to the chip rate (2afoTc < l) , 7~ is uniformly dis- tributed in [O,T,], T, < (T - T , ) and /TI - ~~l > T,, we can write ( IR~I(T , ,T + n, R , . , ) I 2 ) , =

$ h,% (1 - e)* (-2x + A T - 2) dx. Simi- larly, it can be shown that ( I R ~ I ( T + ~ I , T + ~ , , T ~ , ~ , ) ~ ~ ) ~ =

[2] R. Padovani, “Reverse Link Performance of IS-95 Based Cellular Systems,” IEEE Personnel Communi- cations, VoI. 1, No. 3, pp 28-34. Third Quarter, 1994.

[3] K. S. Gilhousen, I. M. Jacobs, R. IPadovani, A. J . Viterbi, I,. A. Weaver and C. E. Wh’eatley, “On the Capacity of a Cellular CDMA Systern,” ZEEE Trans. on Veh. Technol., vol. 40, No. 2, May 1991, pp 303-312.

[4] A. J. Viterbi, A. M. Viterbi, andE. Zehavi, “Other-Cell Interference in Cellular Power-Controlled CDMA,” IEEE Truns. on Commun., vol. 42, no. 4, pp. 1501- 1504, April 1994.

[5] M. Kavehrad and B. Ramamurthi, “]Direct-Sequence Spread !Spectrum with DPSK Moddation and Di- versity fix Indoor Wireless Communications,” IEEE Trans. C m r v - ” , vol. 35, pp. 224-236, Feb. 1987.

[6] J. G. Proakis, Digital Communications, McGraw-Hill, Second Edition, 1989.

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