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MC-CDMA with Quadrature Spreading for Wireless Communication Systems Slimane Ben Slimane

Radio Communication Systems Department of Signals, Sensors, and Systems Royal Institute of Technology S-100 44 Stockholm, Sweden Tel. +46 8 790 9353, Fax +46 8 790 9370, Email: [email protected]

Abstract Multi-Carrier CDMA (MC-CDMA) systems using the Orthogonal Frequency Division Division Multiple Access (OFDM) technique resolve the frequency selectivity in multipath fading channels and have good spectral properties. The addition of a spread spectrum component to the OFDM introduces a frequency diversity gain that can combat deep multipath fading situations. In this paper a MC-CDMA system operating over frequency selective, slowly fading channels is considered and its performance is studied analytically and by computer simulations. We consider the downlink of a cellular radio system where for each user a BPSK modulation and a quadrature (complex) spreading code is used. The spreading codes are arranged in a way that reduces the eect of the multipath fading channel and restores some of the orthogonality losses between users. The obtained results show considerable performance improvement compared to conventional OFDM and to MC-CDMA that uses single spreading codes. The eect of frequency osets on the system performance is also addressed in this paper. Its superior performance and low complexity receiver make MC-CDMA with quadrature spreading codes suitable for future wireless communication systems to achieve the requirements of high quality services, high speed, and low cost-receiver.

1

I. Introduction

In mobile radio communication systems, the system capacity and performance are limited by the multipath fading channel. The most common approach in dealing with this channel eect is by means of diversity and equalization where the system tries to exploits the multipath fading channel. Multi-Carrier CDMA (MC-CDMA) techniques have such capability and can be eciently used for such applications. A number of Multi-Carrier techniques based on the combination of OFDM modulation and spread spectrum have been proposed [1, 2, 3, 4]. The scheme considered in this paper and referred to as MC-CDMA is the one where each information symbol is spread in frequency with all its chips transmitted simultaneously on dierent frequencies [3, 4]. In this scheme, Orthogonal Frequency Division Multiplexing (OFDM) modulation is rst used to reduce Inter-Symbol Interference (ISI) by dividing the broad bandwidth into narrowband subcarriers and thus resolving the frequency selectivity of the channel. Orthogonal spreading codes are then used to create redundancy and increase the diversity gain of the system. Orthogonal codes are easily generated using Hadamard matrices. However, the biggest challenge is to preserve such orthogonality after the transmitted signal has gone through the channel. Orthogonality loss creates crosstalk between users and introduces Multi-User Interference (MUI). If the receiver does not take that into account, the system performance will experience an error oor that cannot be reduced by just increasing the transmitted power. Many MC-CDMA detectors have been proposed in the literature. The simplest is a conventional correlator detector where after the OFDM demodulator the receiver equalizes the phase (coherent detection) at each subcarrier followed by despreading and harddecision detection. Such a detector does not restore orthogonality between users and thus its performance is dependent on the amplitude response of the multipath fading channel. A possible improvement is to equalize both phase and amplitude of the fading channel at each subcarrier. This detector has been called Orthogonality Restoring Correlation (ORC) detector [3, 4]. It does eliminate the multi-user interference, but at the expense of a noise ampli cation. To reduce this noise ampli cation, a number of detectors have been introduced. A correlator detector with Threshold (TORC) has been studied in [5,

2

6], a TORC with iterative detection in [7] and with multi-stage detection in [8]. These detectors reduce the multi-user interference but their performance depends on the chosen threshold. The optimum receiver for MC-CDMA is based on the Maximum Likelihood Sequence Estimation (MLSE) [4]. However, its complexity increases exponentially with the number of users. As shown in [7, 9], this complexity can be reduced if the transmitted signals of all users are grouped in smaller blocks. All detectors that have been proposed and studied consider single spreading codes. Complex spreading codes are usually used to combat intentional jamming by forcing the jammer to split its power between the quadrature components of the carrier signal [10]. For MC-CDMA systems, quadrature spreading can be used to reduce the eects of multipath fading and reduce interference from other users. In this paper a MC-CDMA system that uses quadrature spreading codes is investigated. With quadrature spreading codes a diversity gain can be obtained and the interference from other users can be reduced. The system performance over frequency selective, slowly fading channels is evaluated for two simple detectors. A correlator detector with phase equalization only and a correlator detector with zero forcing equalization (phase and amplitude equalization). The obtained results show that quadrature spreading codes is an ecient way to reduce the eect of multipath fading channels in MC-CDMA systems and improve their performance. This paper is organized as follows: In section II brief descriptions of the system model and the channel model are given, followed by the receiver model and performance analysis. In section IV, the impact of frequency errors on the system performance is investigated. Simulation results are presented in section V and compared with the analytical results. Section VI gives conclusions and some discussions. II. System Model

A. Transmitter Model

We consider a MC-CDMA for the downlink of a cellular radio system where the signals of the dierent users are transmitted synchronously through the multipath fading channel. The transmitter block diagram of the system which consists of Nu users is shown in

3

Figure 1. The modulation process is the same for all users where the input data is rst modulated in baseband using BPSK, multiplied by the spreading sequence of the user, and then modulated using an OFDM modulator. The signals from all users are then combined and transmitted. The system uses orthogonal Walsh-Hadamard spreading codes. Each user code is arranged in a quadrature format as shown in Figure 1, where the code on the quadrature side is just the reverse of that of the in-phase side. The choice of such an arrangement will become clear in the following. The MC-CDMA transmitted signal can be written as follows:

o n x(t) = Re xl (t)ej fct ; 2

(1)

where fc is the carrier frequency and xl (t) is the equivalent lowpass of x(t),

xl (t) = with

s

NX ?1 m=0

m

smej  Tb t; 2

(k ? 1)T  t ? Tb  kT;

NX u? sm = 2ETb (cm;n + jcN ? ?m;n)an; m = 0; 1;


; N ? 1; n 1

1

=0

(2)

(3)

is the transmitted signal at subcarrier m, cm;n are elements of a Walsh-Hadamard orthogonal code of length N (assumed the same as the total number of subcarriers), with jcm;nj = p1 ; N an = 1, with equal probability, is the information bit from user n during the OFDM block kT , and Eb is the energy per bit. Tb is the eective block duration, and T ? Tb = Tg is a guard time interval inserted between consecutive OFDM blocks to minimize the eect of the delay spread of the channel. B. Channel Model

The mobile radio channel can be represented at the baseband by the lowpass equivalent complex impulse response function [11]

(t) =

PX ?1 i=0

iej i (t ? i );

(4)

4

where i ej i and i are the weight coecient and the relative time delay for the ith path, respectively. P represents the number of resolvable paths. The amplitudes i are assumed mutually uncorrelated Rayleigh distributed with probability density function (pdf) fi (x) = 2px e?x2 =pi ; x  0; i P P ? where pi = E [i ] and i pi = 1. The phases i are mutually independent random variables uniformly distributed over the interval [0; 2). In the expression of (t) we have assumed a slowly varying fading channel with a Doppler frequency very small compared to the subcarrier width, 1=Tb. 2

1 =0

III. Receiver Model

The received signal, which consists of the sum of all signal paths plus the additive white Gaussian noise having a two sided power spectral density N =2, is rst down-converted to baseband using a local oscillator (fl = fc) giving 0

r(t) =

PX ?1 i=0

iej

(

i +) x (t

l

? i) + z(t);

where  is the phase of the local oscillator and z(t) is a complex Gaussian process. The signal r(t) is then passed through the OFDM demodulator. For a guard interval larger that the maximum delay spread of the channel, the received sample at the mth subcarrier is free of Inter-Symbol Interference (ISI) (or Inter-Chip Interference (ICI)) and is given by Z Tb m r(t)e?j  Tb tdt rm = p1 Tb q = hm ejm Tb sm + zm ; (5) 2

0

where sm is as de ned in (3), zm is a complex Gaussian random variable with zero mean, and

hm ejm =

PX ?1 i=0

ie?j

mi =Tb ? i ?)

(2

(6)

is the multiplicative channel coecient of subcarrier m. From (4), it is observed that the amplitude hm is Rayleigh distributed with probability density function (pdf)

fh(x) = 2xe?x2 ; x  0;

(7)

5

with E [hm ] = 1 and the phase m is uniformly distributed with pdf p(x) = 21 ; 0  x < 2: We further assume independent Rayleigh fading in each subcarrier. Let us consider the N samples at the output of the OFDM demodulator. Eq. (5) can be written in a matrix form as follows: s r = E2e HCa + z; with Ee = TTb Eb; (8) where r = [r ; r ;


; rN ? ]T is the received vector, H = diagfh ej0 ; h ej1 ;


; hN ? ejN ?1 g, is a diagonal matrix, 2

0

1

1

0

1

2 N ? ;


c ;N ? + jcN ? ;N ? 66 c ; + jc . ... ... .. C = 664 cN ? ; + jc ;


cN ? ;N ? + jc ;N ? 00

10

10

0

1

00

1

1

1

0

1

1

3 77 77 ; 5

(9)

1

is an N  N square matrix of the quadrature spreading codes, a is the data information bit vector from all users, and z is a vector of complex Gaussian random variables with zero mean and variance N =2. 0

A. The MC-CDMA Detector

Consider the following two elements of the received vector r in (8), s Nu? X rm = hm ejm E2e (cm;k + jcN ? ?m;k ) ak + zm; k s Nu? X j (cN ? ?m;k + jcm;k ) ak + zN ? ?m ; rN ? ?m = hN ? ?m e N ?1?m E2e k As these elements carry the same information we can combine them before despreading the signal. In the following we consider two combing techniques: Equal Gain Combining (EGC) and Maximal Ratio Combining (MRC). 1

1

=0

1

1

1

1

1

=0

A.1 Equal Gain Combining With equal gain combining the receiver equalizes the phase angle of each element and then combines each pair as follows:

o o n n vm = Re rm e?jm + Im rN ? ?m e?jN ?1?m 1

6

q NX u? = m Ee cm;k ak + zm0 ; 1

h0

(10)

k=0

o o n n vN ? ?m = Im rme?jm + Re rN ? ?m e?jN ?1?m q NX u? cN ? ?m;k ak + zN0 ? ?m ; = h0m Ee 1

1

1

1

k=0

(11)

1

where zm0 is a Gaussian random variable with zero mean and variance N and h0m = hm +phN ? ?m ; m = 0; 1;


; N=2 ? 1; 2 having as pdf 0

1

 p  fh0 (x) = 2xe? x2 +  2x ? 1 e?x2 erf(x); 2

(12)

x  0;

2

with erf(
) representing the error function. De ning a vector v = [v ; v ;


; vN ? ]T , (10) and (11) can be rewritten in a matrix form, 0

1

1

q

v = EeH0C0a + z0;

(13)

where H0 = diagfh0 ; h0 ;


; h0N= ? ; h0N= ? ;


; h0 ; h0 g, and 0

1

2

1

2

1

1

0

2 66 c .;


c ;N. ? .. C0 = 664 .. . . . cN ? ;


cN ? ;N ? 00

10

0

1

1

3 77 77 5

(14)

1

is the N  N square matrix whose columns are the single spreading codes. Notice that after combining the fading coecient of subcarrier m becomes the same as that of subcarrier N ? 1 ? m. This feature is very suitable for systems using Hadamard codes since half of the multi-user interference will be automatically cancelled. A.2 Maximal Ratio Combining With maximal ratio combining the two elements vm and vN ? ?m of the vector v are obtained as: 1

o o n n vm = Re rm hm e?jm + Im rN ? ?mhN ?m? e?jN ?1?m q NX u?  h0m Ee cm;k ak + zm0 ; 1

1

k=0

1

7

o o n n vN ? ?m = Im rmhm e?jm + Re rN ? ?mhN ? ?m e?jN ?1?m q NX u?  h0m Ee cN ? ?m;k ak + zN0 ? ?m ; 1

1

1

1

1

k=0

1

where zm0 is Gaussian with variance N and the multiplicative factor h0m is now given by 0

q h0m = hm + hN ? ?m; m = 0; 1;


; N=2 ? 1; 2

with its pdf given by

2

1

(15)

fh0 (x) = 2x e?x2 ; x  0: 3

Once the vector v is obtained, the receiver equalizes the channel (Zero Forcing Equalizer (ZFE)) by multiplying vm by the inverse of the new channel coecient h0m, or

q

y = EeH0? H0C0a + H0? z0: 1

1

The information bit for user n is then extracted by despreading the vector y with the code cn = [c ;n; c ;n;


; cN ? ;n] followed by a hard-decision detector 0

1

1

a^n = sgn fcn
yg : A simpli ed block diagram of the MC-CDMA receiver is shown in Figure 2. For the detection of MC-CDMA signals with quadrature spreading codes, the new channel coecient prior to the equalizer is the sum of two fading amplitudes. In this case the noise enhancement after equalization is reduced as compared to the case when single spreading codes are used. As shown in Figure 3, by using quadrature spreading the probability of having a noise enhancement (P (hm < 1)) is reduced from 63% to 31% for the EGC case and only 27% for the MRC case. This noise enhancement can be further reduced if a Minimum Mean Square Error (MMSE) equalizer is used [11]. That is, multiplying vm by h0m ; h0m + z0 =a where z0 is the variance of the noise and a is the variance of the transmitted data. In the following, the average bit error probability for bit an of user n, 0  n  Nu ? 1; is evaluated for the ZFE case. Both MRC and EGC will be considered. 2

2

2

2

2

8

B. Performance Analysis

Consider the detection of the information bit of user n during a given OFDM block interval kT . Assuming a zero forcing equalizer, the despreaded signal can be written as

q

cn
y = an Ee +

N=X 2?1 cn;izi0 + cn;N ?1?izN0 ?1?j : h0i i=0

The decision is then made based on the sign of the above expression. A wrong decision is made if this sign is dierent from that of an . The conditional bit error probability of the system for a given Channel State Information (CSI) vector, h0 = (h0 ; h0 ;


; h0N= ? ), can be written as 0

1

2

1

0v u Ee BBu 1 N 0 P (errorjh ) = 2 erfc @u t 4N PN= ? i 2 =0

0

1

1

h0i 2

1 CC A;

(16)

where erfc(
) is the complementary error function. The elements of h0 are as given in (12) for EGC or as in (15) for MRC. De ning a new random variable h0min as

  h0min = min h0 ; h0 ;


; h0N= ? ; 0

1

2

1

we can write the following inequality

0 1? h0min  @N=X? 1 A  h0 : min N=2 h0i i 2

2

1

1

2

=0

2

(17)

The above inequality can be used to derive two bounds (upper and lower) on the average bit error probability of the system. The lower limit in (17) is obtained only when all h0i 's have the same value. Under uncorrelated fading, the probability of such an event occurring is very close to zero for large values of N . The corresponding bound (upper bound) is then expected to be loose and is given here for illustration only. Using (17) we can write PL  Pb  PU ; where

PL =

Z 0

11

+

2 erfc

s

! E e Nx 4N fh0min (x)dx; 2

0

(18)

9

s ! E e PU = (19) f 0 (x)dx: erfc x 2 2N hmin The function fh0min (
) is the pdf of the random variable h0min and is given by [12] f 0 (x) = N [1 ? F 0 (x)]N= ? f 0 (x); (20) Z

11

+

2

0

0

hmin

2

h

2

where fh0 (
) is the pdf of h0 and

Fh0 (x) =

Zx 0

1

h

fh0 (t)dt

is its distribution function. After some simpli cations the two bounds can be written as a function of a single integral

q PL = ? N NEe0 IN q PU = ? NEe0 I ; 1 2

(21)

2

1 2

2

where

Z 1 2 h iN p 1 e?x iEe= N0 e? x2 + xe?x2 erf(x) 2 dx Ii = p 2 if equal gain combining is used or Z 1 2 iN h e?x iEe= N0 e?x2 + x e?x2 2 dx Ii = p1 2 if maximal ratio combining is used. +

2

4

0

+

4

2

0

IV. Effects of Frequency Errors on the Performance

In MC-CDMA systems using OFDM modulation, frequency asynchronism destroys the orthogonality between subcarriers and therefore introduces ICI and MUI into the system. In this section we consider the eects of frequency errors on the performance of MC-CDMA systems over additive white Gaussian noise and multipath fading channels. Let us assume a local oscillator frequency given by

fl = f c + fD ; where fD is a constant frequency oset with jfD Tbj  1.

10

The received sample at the mth subcarrier, given in (5), becomes

q rm = ej fD Tb  sinc(fD Tb)hm ejm Tb sm NX ? q Tbsiej fD Tb  sinc(fD Tb) 1 +1i?m hieji + zm ; + (

+ )

1

(

(22)

+ )

fD Tb

i=0

i6=m

where  is the phase of the local oscillator and sinc(x) = sin(x)=(x). We notice that due to the frequency oset, each transmitted symbol is rotated by an angle of fD T + . The above expression also shows that all symbols within a block are attenuated and interfere with each other. For a constant frequency oset, the phase rotation is the same for all symbols and can be estimated. After phase equalization the received vector becomes s r = sinc (fD Tb) E2e FHCa + z; where F is an N  N square matrix representing the eect of the frequency oset and is given by

F = [fij ] ;

(23)

where

fij = f TfD+Tjb ? i ej j ?i : (24) D b The matrices H and C are as previously de ned. The vector v is then constructed following the same procedure as described in section 3. With equal gain combining or maximal ratio combining, the vector v takes the following form: q 0 0 (25) v = sinc (fD Tb ) Ee F C a + z0; (

where C0, a, z0 are as de ned in (13), and

)

h i

F0 = fij0 with 0

fij

(26)

# " f T h sin(  ?  ) h cos(  ?  ) D b N ? ? j N ? ? j i j j i = p ? f T ?j?i+N ?1 2 fD" Tb + j ? i D b # h sin(  ?  ) h cos(  ?  ) f T j j N ? ? i N ? ? j N ? ? j N ? ? i D b + p f T +j+i?N +1 + fD Tb ? j + i 2 D b 1

1

1

1

1

1

11

for the equal gain combining case and " # h cos(  ?  ) f T h h sin(  ?  ) 0 j j i D b i N ? ? j N ? ? j i fij = q ? f T ?j?i+N ?1 D b hi + hN ? ?i fD Tb + j ? i # " h cos(  ?  ) f T H h sin(  ?  ) N ? ? j N ? ? j N ? ? i D b N ? ? i j j N ? ? i + +q fD Tb ? j + i hi + hN ? ?i fD Tb + j + i ? N + 1 1

2

2

1

1

2

1

2

1

1

1

1

1

for the maximal ratio combining case. It is observed from the expression of fij0 that when there is no fading (AWGN only) the elements of the matrix F0 reduces to

8 > < 1; j = j ( f 0 D Tb ) fij = => (fD Tb) ? (j ? i) :  0; i = 6 j; fD Tb  1. 2

2

2

(27)

The matrix F0 then becomes an identity matrix and all interference due to a frequency oset is cancelled except for the amplitude attenuation. This shows that the arrangement of the spreading codes proposed in this paper can also help reduce the eect of frequency errors. However, its performance will still depend on the multipath fading channel. Under multipath fading conditions there will be phase variations between subcarriers. As a result, some of the interference will remain. V. Numerical Results

In this section, we consider a MC-CDMA system with a total of Nu = N = 64 (assumed equal to the total number of the OFDM subcarriers) users. The spreading codes for the dierent users are arranged as described in the previous sections. We will present simulation results for the system performance in a frequency selective fading channel. The channel is modeled as at fading on each subcarrier. We also assume perfect frequency interleaving. The performance is evaluated for a full system and is compared to that of a regular OFDM and also to a MC-CDMA system with single spreading codes. Figure 4 gives simulation results for the bit error probability of user n as a function of Eb =N when a zero forcing equalizer is used after combining. It is observed that with maximal ratio combining the system performance is about 0.5 dB better than that with equal gain combining. Compared to regular OFDM, considerable performance improvement is obtained with any of the two combining techniques. These results are con rmed using the 0

12

lower bound of (18), which gives a good indication about the asymptotic behavior of the system performance at high SNR. When only phase equalization is used, code orthogonality is partially restored and half of the interference from other users is canceled. The bit error probability experiences an error oor which is in this case about 3:5 10? as shown in Figure 4. Figure 5 illustrates the performance of the MC-CDMA system for the two spreading codes. It is clearly observed that the use of quadrature spreading codes outperforms the single spreading codes. This low bit error probability is obtained without increasing the complexity of the system and gives the possibility to use higher level modulation schemes (M -level PAM) compensating for any reduction in eciency. We notice from Figure 5 that with single spreading codes the system performance is always worse than that of a regular OFDM scheme. This is due to the noise enhancement caused by the channel coecients. This statement can be easily veri ed by computing a lower bound using (18). That is, 3

Pb  PL =

Z

0

11

+

2 erfc

s

! E b Nx N fhmin (x)dx; 2

0

(28)

where

fhmin (x) = N [1 ? Fh(x)]N ? fh(x) = 2Nxe?Nx2 ; x  0; 1

(29)

with fh(x) as given in (7). Carrying out the integration in (28), the lower bound reduces to

2

v

3

u u 1 4 PL = 2 1 ? t 1 +EbE=N=N 5 ; b 0

0

(30)

which is the bit error rate of the regular OFDM scheme. Figure 6 shows the bit error probability of the MC-CDMA system for two equalization techniques. It can be seen that for most SNRs, the performance of the ZFE is about 1 dB away from that of the optimum MMSE equalizer. Therefore, by using quadrature spreading codes one can safely use a ZFE at the receiver and avoids all the additional complexity of the MMSE equalizer.

13

A. Eects of Frequency Errors

We start this investigation by considering an additive white Gaussian noise channel. The bit error probability of the MC-CDMA system is shown in Figure 7 as function of the product fD Tb and for a SNR of 7 dB. It is observed that over such channel quadrature spreading codes outperform single spreading codes. This shows (see also (27)) that the chosen arrangement of the spreading codes can also reduce the sensitivity of the system to frequency errors. For a multipath fading channel, the system performance depends on the phase distribution of the fading coecient at dierent subcarriers. The bit error probability is shown in Figure 8 for the two combining techniques. A worst case situation has been assumed where the phases of the subcarriers are identically independent and uniformly distributed. A similar tendency in performance is observed for the two combining techniques. VI. Conclusions

A Multi-Carrier CDMA system that uses quadrature spreading codes has been considered in this paper. The in-phase and quadrature components of the spreading code for each user were arranged in a way that helped restore some of the orthogonality losses between codes caused by the multipath fading channel. This consisted of using one Hadamard code on the in-phase side and the reverse of the same code on the quadrature side. The system performance in frequency selective fading channels has been examined analytically and by computer simulations. The obtained results showed that a MC-CDMA system with quadrature spreading codes performs considerably better than a MC-CDMA system with single spreading codes. This performance improvement is obtained without the need for complicated receiver structures. With a zero forcing equalizer the obtained performance is only 1 dB away from that obtained with the optimum MMSE equalizer. The eects of frequency errors on the system performance have also been addressed in this paper and investigated. For an additive white Gaussian noise channel, the use of quadrature spreading codes reduces the sensitivity of the system to frequency errors. For a more severe channel, the system performance is dependent on the phase variations between subcarrier signals.

14

References

[1] L. Vanderdorpe: Multitone spread spectrum multiple access communications system in a multipath Rician fading channel. \IEEE Trans. Veh. Techn." Vol. 44, May 1995, p. 327-337. [2] E. A. Sourour, M. Nakagawa: Performance of orthogonal multicarrier CDMA in a multipath fading channel. \IEEE Trans. Commun." Vol. COM-44, March 1996, p. 356-367. [3] N. Yee, J.-P. Linnartz, G. Fetteweis: Multi-carrier CDMA in indoor wireless networks. \IEICE Trans. Commun." Vol. E77-B, July 1994, p. 900-904. [4] K. Fazel: Performance of CDMA/OFDM for mobile communication systems. Proc. ICUPC '93, 1993, p. 975-979. [5] T. Mueller, K. Brueninghaus, H. Rohling: Performance of coherent OFDM-CDMA for Broadband mobile communications. \Wireless Personal Communications 2." 1996, p. 295-305. [6] N. Yee, J.-P. Linnartz: Controlled equalization of multi-carrier CDMA in an indoor Rician fading channel. Proc. VTC '94, Stockholm, Sweden, May 1994, p. 1665-1669. [7] K. Fazel, S. Kaiser, M. Schnell: A exible and high performance mobile communications system based on orthogonal multi-carrier SSMA. \Wireless Personal Communications 2." 1995, p. 121-144. [8] D. N. Kalofonos, J. G. Proakis: Performance of the multi-stage detector for a MCCDMA system in a Rayleigh fading channel. Proc. Globecom '96, London, UK, November 1996, p. 1784-88. [9] S. Kaiser: OFDM-CDMA versus DS-CDMA: Performance evaluation for fading channels. Proc. ICC '95, Dallas, USA, Juner 1995, p. 1722-26. [10] R. L. Peterson, R. E. Ziemer, D. E. Borth: Introduction to Spread Spectrum Communications. Printice Hall, NJ, 1995. [11] J. G. Proakis: Digital Communications. Third Edition, McGraw Hill, New York, 1995. [12] A. Papoulis: Probability, Random Variables, and Stochastic Processes, Second Edition, McGraw-Hill, New York, 1984.

15

List of Figure Captions Fig. 1 - Transmitter block diagram of the MC-CDMA system that uses quadrature

spreading codes. Fig. 2 - Simpli ed receiver block diagram for user n. Fig. 3 - Cumulative distribution density function of the fading amplitude aecting the MC-CDMA signal for the two cases of spreading codes. Fig. 4 - Performance of MC-CDMA with quadrature spreading over frequency-selective, slowly fading channels. Full interleaving, perfect CSI, and Nu = N = 64. Fig. 5 - Performance comparison between MC-CDMA with quadrature spreading codes and MC-CDMA with single spreading codes. Full interleaving, perfect CSI, and Nu = N = 64. Fig. 6 - Performance comparison between MC-CDMA detection with zero forcing equalizer and MC-CDMA detection with MMSE equalizer over a frequency-selective, slowly fading channel. Fig. 7 - Eects of frequency errors on the performance of MC-CDMA over an additive white Gaussian noise channel for the two spreading codes and a SNR=7 dB. Fig. 8 - Eects of frequency errors on the performance of MC-CDMA detection with ZFE over a frequency selective, slowly fading channel for a SNR=11 dB.

16

user 0

input data

BPSK

a0

c0,0+jcN-1,0

e

jw 0 t

c1,0+jcN-2,0

e

jw1 t

multiplex

cN-2,0+jc1,0

e

jw N-2 t

cN-1,0+jc0,0

e

jw N-1 t

input data

user 1

input data

user Nu-1

xl (t)

17

cos (wl t) r(t)

local oscillator

OFDM demodulator (FFT)

combining & equalization

sin (wl t)

channel estimation

despreading & detection

a^n

18

Cumulative Distribution Function (CDF) of the Fading Amplitude 1 0.9 0.8 0.7 CDF of h_m CDF of h_m´, EGC CDF of h_m´, MRC

CDF

0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.5

1

1.5 Threshold

2

2.5

3

3.5

19

Performance of MC−CDMA, Nu=64 −1

10

−2

Bit Error Probability

10

lower bounds

−3

10

−4

10

regular OFDM phase equalization EGC & ZFE MRC & ZFE

−5

10

2

4

6

8

10 12 Eb/No, dB

14

16

18

20

20

Performance of MC−CDMA, Nu=64

0

10

−1

Bit Error Probability

10

−2

10

−3

10

regular OFDM single spreading quadrature spreading

−4

10

phase equalization zero forcing equalizer

−5

10

2

4

6

8

10 12 Eb/No, dB

14

16

18

20

21

Performance of MC−CDMA, Nu=64 −1

10

−2

Bit Error Probability

10

−3

10

−4

10

EGC & ZFE MRC & ZFE EGC & MMSE MRC & MMSE

−5

10

2

4

6

8

10 Eb/No, dB

12

14

16

18

22

Additive White Gaussian Noise Channel

0

10

−1

10 Bit Error Probability

single spreading quadrature spreading −2

10

−3

10

−4

10

−2

10

−1

10 F_DT

0

10

23

Effect of Frequency Errors, SNR = 11.0 dB

0

10

EGC MRC

−1

Bit Error Probability

10

−2

10

−3

10

−4

10

−2

10

−1

10 F_DT

0

10

24

Slimane Ben Slimane received the B. Eng. degree from l'Universite du Quebec a trois-

Rivieres, Quebec, Canada in 1985, the M. Eng. and the Ph.D. degrees from Concordia University, Montreal, Canada, in 1988 and 1993, respectively. From 1993-1995, he worked as a research associate in the Department of Electrical and Computer Engineering of Concordia University. In 1995, he joined the Radio Communication Systems group, Department of Signals, Sensors, and Systems, Royal Institute of Technology (KTH), Stockholm, Swedem, where he is currently an assistant professor. His research interest is in the area of mobile and personal communications with special emphasis on digital modulation, error control coding, and multiple access.