Abstract

This paper examines the performance of a multicarrier CDMA system over multipath fading channel. Due to the dispersive nature of the mobile communications channels, Multi-Carrier Code Division Multiple Access (MC-CDMA) signals will be affected by Inter Channel Interference (ICI),

Inter Symbol Interference (ISI) and Multiple Access Interference (MAI), due to the loss of subcarrier orthogonality. To solve the ISI problem, a cyclic extension was introduced to the transmitted symbols, known as guard time, but its introduction results into loss of spectral efficiency. In this context, we consider the use of a Frequency-Time minimum mean square error Equalizer (FTE) to compensate for the corresponding loss in performance, and compare the resulting MC-CDMA systems with the use of guard time. The effect of system parameters such as output Signal-to Noise Ratio (SNR), number of sub-carriers, delay spread, is investigated by simulation, from which we show that MC-CDMA/FTE provides better performance than guard time technique.

Keywords: Guard time, MMSE equalizer, Multi-carrier CDMA, Multipath fading channels.

Introduction

As the radio frequency spectrum is a scarce resource, future wireless radio networks need to make efficient use of the frequency spectrum by providing high capacity in terms of number of users allowed in the system. As a consequence, modulation and multiple access techniques designed specifically for wireless channels, such as MCCDMA, play an important role in achieving this goal. Due to their special signal structure, MC-CDMA signals will not experience significant linear distortion in fading channels where the symbol duration is much larger than the delay spread, which is a measure of the length of the impulse response of the channel. When the multipath time spread is a significant fraction of the symbol duration, MC-CDMA signals will be affected by ISI as well as ICI, as the orthogonality between the transmitted sub carriers is lost.

Thus, the use of a guard time interval longer than the delay spread of the channel has been suggested, but the introduction of the Guard time results into disadvantage of the receiver using only a fraction of the received energy [1]. As an alternative to the use of the guard time, different MC-CDMA receiver structures that rely on the use of antenna diversity and equalising techniques have been proposed [2]-[4]. In this context the approach proposed in this paper as an alternative to the use of the guard time technique, is a FTE already described in [5]. Let us note that in [5] the average output Signal-to-Interference and Noise Ratio (SINR) at the MMSE equalizer output over all users are used as the figure of the merit for investigating the impact of guard time length on FTE. Our work is based on [5] and deals with the computation of the Bit Error Rate (BER) by varying the MC-CDMA system parameters such as guard time length, input SNR, number of sub-carriers and compare it to the MC-CDMA/ FTE BER. We restrict our study to the case where the transmission system is over a slow fading channel with Additive White Gaussian Noise (AWGN).

The organisation of the paper is as follows. In section II, the MC-CDMA system model over multipath fading is presented, and the transmitter model is discussed. In section III, the discrete-time frequency-selective fading channel is considered. Section IV reviews, FTE design and channels parameters. Section V provides simulation and computational results. Section VI concludes the paper.

System Model

A model of Multi-Carrier CDMA (MC-CDMA) transmission over dispersive channel, for the kth user is shown in Figure1.

With MC-CDMA [5]-[6], each data symbol is simultaneously transmitted on Q Binary Phase Shift-Keying (BPSK) narrowband subcarriers, each separated by q/[T.sub.s] Hz ([T.sub.s] is the subcarrier symbol duration), where q is an integer. Each of the Q sub-carrier waveforms is modulated (multiplied) by a spreading code of length Q chips. A baseband equivalent synchronous MC-CDMA system diagram is shown in Figure1, where the available bandwidth is divided into Q sub-bands that are equally spaced by 1/[T.sub.s]. In MC-CDMA modulation, the number of subcarriers, Q, equals to the length of the spreading sequence and each data symbol is transmitted in parallel using multiple chips over all Q subcarriers. We assume K active users in the system. The transmitted base band signal for the ith user can be written as

[x.sup.i](t) = [square root of [E.sup.i]] [[infinity].summation over (n=-[infinity]) [S.sup.i.sub.n] [Q-1.summation over q=0] [C.sup.i.sub.q] [[phi].sub.q] (t - n[T.sub.c]). (1)

where [S.sup.i.sub.n] is the nth transmitted symbol from the ith user, [C.sup.i] = [[[c.sup.i.sub.0] [c.sup.i.sub.1 ... [c.sup.i.sub.Q-1]].sup.T] is the user spreading sequence, [E.sup.i] is the transmitted energy on each sub carrier and [[phi].sub.q](t) represents the chip waveform at the qth (q=0, 1, ..., Q-1) sub carrier and is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where [T.sub.g] is the guard time

Channel Model

A discrete-time frequency-selective fading channel is considered [7]. The channel impulse response consists of M resolved (echo) paths and each path is characterised by a random (complex) amplitude [[alpha].sub.m](t)

h([tau],t) = [M.summation over (m=1)] [[alpha].sub.m] (t) [delta]([tau] - [[tau].sub.m]), (3)

where [[tau].sub.m] is a multiple of 1/BW (BW is the signal Band-Width, equal to Q/[T.sub.s] for the MC-CDMA system).

In this section, we exclusively consider a two-path slow fading model ([[alpha].sub.m](t) are constants), where the delay of the first path is [[tau].sub.0] [less than or equal to] [T.sub.g], and that of the second one is [[tau].sub.1], with [T.sub.g] < [[tau].sub.1] < [T.sub.s], following [5]-[8]-[9]. Thus, the channel impulse response for the ith user can be expressed as

[H.sup.i](t) = [[alpha].sup.i.sub.0] [delta](t - [[tau].sup.i.sub.0]) + [[alpha].sup.i.sub.1] [delta] (t - [[tau].sup.i.sub.1]). (4)

[ILLUSTRATION OMITTED]

The signal at the receiver front-end input in the presence of AWGN noise N(t) (with zero mean and double sided variance [N.sub.o]/2 is

r(t) = [k.summation over (i=1)] ([square root of [E.sup.i]] [[infinity].summation over (n=-[infijnity])] [S.sup.i.sub.n] [Q-1.summation over (q=0)] [C.sup.i.sub.q][[phi].sub.q](t - n[T.sub.c])) * [h.sup.i](t) + N(t). (5)

The received signal is first stripped of its cyclic extension and then passed through a bank of chip matched filters, as shown in Figure 1, where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

is the chip matched filter for the pth sub channel, followed by chip rate (1/[T.sub.c]) sampling. Collecting the samples within the nth transmitted data symbol duration yields a Q length received vector

[y.sub.n] = [[[y.sub.n,0], ..., [y.sub.n,Q-1]].sup.T]. (7)

The operations of multicarrier modulation and demodulation in Figure1 can be efficiently implemented

using the FFT [5]. The output of the pth chip-matched filter can be explicitly written as

[y.sub.p] = [[integral].sup.nTc+Ts.sub.nTc] r(t)[??](t - n[T.sub.c])dt. (8)

[FIGURE 1 OMITTED]

After some algebraic manipulations, (7) becomes

[y.sub.n,p] = [K.summation over (i)] [Q-1.summation over (q=0)] ([C.sup.i.sub.q][S.sup.i.sub.n][v.sup.i.sub.p,q,0] + [C.sup.i.sub.q][S.sup.i.sub.n-1][v.sup.i.sub.p,q,1]) + N(t), (10)

where:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (11)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

[[beta].sup.i.sub.1] = [[tau].sup.i.sub.1] - [T.sub.g] / [T.sub.s] is defined as the effective excess delay, and m, as the number of the considered paths.

In the case of two paths, (m=0, 1) the matrix form is as

[y.sub.n] = [V.sub.0]C[S.sub.n] + [V.sub.1] C[S.sub.n-1] + [N.sub.n], (13)

where;

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)

[S.sub.n] = [[[S.sup.1.sub.n] ... [S.sup.K.sub.n]].sup.T.sub.Kx1], (16)

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)

For the first path, m=0

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

For the second path, m=1

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

For M paths [y.sub.n] can be expressed as [5]

[y.sub.n] = [M.summation over (m=0)] [V.sub.m]C[S.sub.n-m] + [N.sub.n]. (20)

The second term in equation (18) represents the ICI for a user of interest while the presence of [V.sup.i.sub.p,1], reflects the combined ISI and MAI, due to the loss of sub carrier orthogonality.

It is necessary to indicate that when the cyclic prefix exceeds the maximum delay spread, ISI is eliminated and sub carrier orthogonality holds. Hence, (13) reduces to

[y.sub.n] = [V.sub.0] C[S.sub.n] + [N.sub.n], (21)

with

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (22)

where the structure of [V.sup.i.sub.p,0] reflects pure scaling due to the channel.

Fte Design and Channels Parameters

In this section, we investigate the MC-CDMA system performance gauged by the bit error rate (BER) through analysis and simulation.

The BER is computed under the following assumptions: Orthogonal spreading sequences of length (Q=4, 8, and 32) at three active users. The cyclic prefix length is normalized by [T.sub.s] and varied from zero to the maximum value 0.5[T.sub.s]. Two-path channel model is used. The first path delay is assumed to be uniformly distributed in [0, [T.sub.g]] and the second uniformly distributed in ([T.sub.g], [T.sub.s]]; this allows us to consider both insufficient and sufficient prefix cases as the (chosen) cyclic prefix length is changed from zero to 0.5Ts. The path amplitudes and delays can be found in Table 1. Two different Up Link channels scenarios have been used. In both cases, the amplitudes of the first and the second paths were set to 1.0 resulting to very high interference conditions. A frequency-Time MMSE equalizer (see figure2) proposed in [5] is used to assess the performance of MC-CDMA over slow fading scenarios. From (13), it follows that

[y.sub.n] = [P.sub.0][S.sub.n] + [P.sub.1][S.sub.n-1] + [N.sub.n], (23)

where

[P.sub.0] = [V.sub.0]C = [[[p.sub.0,1] ... [p.sub.0,i] ... [p.sub.0,K]].sub.QxK], (24)

[P.sub.1] = [V.sub.1]C = [[[p.sub.1,1] ... [p.sub.1,i] ... [P.sub.1,K]].sub.QxK]. (25)

The structure of the joint MMSE detector, which minimize the mean square error between the transmitted symbol [S.sup.k.sub.n] and its estimate [[??].sup.k.sub.n], is determined by solving

[W.sub.k] = arg min E([[parallel][[??].sup.k.sub.n] - [S.sup.k.sub.n][parallel].sup.2]), (26)

where

[[??].sup.k.sub.n] = [W.sup.H.sub.k][Y.sub.n], (27)

and the (2[M.bar] + 1) Q-dimension vector [Y.sub.n] is

[Y.sub.n] = [[[y.sup.T.sub.n - [M.bar]] ... [y.sup.T.sub.n] ... [y.sup.T.sub.n+[M.bar]]].sup.T]. (28)

The optimal equalizer coefficients can be expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (30)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (31)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (32)

[FIGURE 2 OMITTED]

Simulation and Computational Results

In the following, we investigate the MC-CDMA performance potential by assuming that ideal channel information is available.

Figure 3 illustrates the BER of MC-CDMA system versus prefix length (guard time interval) for three users, with Q=8, 16, and 32. All users have identical transmitting power for an input SNR equal to 10dB. As prefix length increases, the BER of MC-CDMA system decreases, especially when the number of subcarriers increases.

Figure 4 considers two different Up-link channel scenarios with "channel 2" representing bad channel with 32 = Q , for single and three users. We observe that the performance of MC-CDMA system is affected when the worst channel conditions are used, due to the presence of the longer delay path in channel 2 compared to channel 1. Moreover, larger number of users induces severe MAI.

As pointed out in [10], the price paid for using cyclic prefix is a 10%-25% spectral efficiency loss. Furthermore, the delay spread of some wireless channel shows time-variations, thereby complicating the choice of an appropriate prefix length. In the following we consider a FTE considered in [5].

The uplink simulation scenarios consist of an MC- CDMA system with both single and three users with Q=32. The parameter settings of the channels used in the uplink computer simulation scenarios are depicted in table I. Here, the performance of MC-CDMA/ FTE in an uplink scenario is compared to the MC-CDMA with and without cyclic prefix operating in similar channel conditions. MC-CDMA operating over AWGN channel is also depicted (Figure 5). It can be seen that the MC-CDMA/FTE out-performs MC-CDMA with cyclic prefix. It is shown that by employing a FTE, performance degradation due to the frequency equalizer with insufficient cyclic prefix can be restored, therefore cyclic prefix /guard time can be abandoned.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Conclusion

We have presented and analysed a FTE receiver structure for MC-CDMA systems. MC-CDMA/FTE and MC-CDMA system deploying the well-known guard time technique were simulated and compared in terms of BER.

Numerical results show that system performance degradation due to insufficient guard time can be recovered with FTE; i.e, full spectral efficiency can be achieved at the price of additional complexity.

Reference

[1] Demosthenes Ikonomou, Luc Vandendorpe.: "A fractionally spaced Decision Feedback Joint Detection Proposal for Multi Carrier CDMA". European Transactions On Telecommunications and related technology, AEEI, Milano, Vol.10, no 4, July/August 1999, pp.407-416.

[2] P. Jung, K. Kammerlander, F. Berens, J. Plechinger.: "On Multicarrier CDMA Mobile Radio systems with Joint detection and coherent receiver antenna diversity" . Proceedings of the ICUPC, pages 61-65, 1996

[3] P. Jung, F. Berens, J. Plechinger.: Joint detection for multicarrier CDMA mobile radio systems--Part I: system model. Proceedings of the ISSSTA, pages 991-995, 1996.

[4] P. Jung, F. Berens, J. Plechinger.: "Joint detection for multicarrier CDMA mobile radio systems- Part II: Detection techniques". Proceedings of the ISSSTA, pages 996-1000, 1996.

[5] Chenyang Li, Sumit Roy.: "Performance of Frequency--Time MMSE Equalizer for MC-CDMA over Multipath Fading channel". Wireless Personal Communications, 18(2), pp 179-192 , August 2001.

[6] Nathan Yee, Jean--Paul Linnartz.: "Multicarrier Code Division Multiple Access (MC-CDMA): A New Spreading Technique For Communication Over Multipath Channels". Final report 1993-1994 for MICRO project 93-10. Industrial Sponsor: Teknekron Communication Systems.

[7] Essam A. sourour, Masao Nakagawa.: "Performance of Orthogonal Multi-Carrier CDMA in a Multipath Fading Channel". IEEE Transaction in communications. Vol.44, No.3, March 1996.

[8] E. Viterbo, K. Fazel.: "How to combat longs echoes in OFDM transmission schemes: Sub-channel equalization or more powerful channel coding". In GLOBECOMM 95', Pp.2069-2074.

[9] L. Vandendorpe, O. Van De Wiel.: "Performance analysis of linear MIMO equalizers for multitone DS/SS systems in multipath channels". Wireless Personnel Communications, vol.2, pp.145-165, 1995.

[10] W.Y. Zou, Y. Wu.: COFDM: "An overview". IEEE Trans. Broadcasting, vol.41, pp.1-8, Mar.1995.

F. Bouasria *, A. Djebbari *, M. Bouziani *, J. M. Rouvaen ** and Abdelmalik Taleb Ahmed ***

* Telecommunications and Digital Signal Processing Laboratory University Djillali Liabes of Sidi Bel Abbes 22000, Algeria E-mails: d_b_fatibou@yahoo.fr, djebbari@univ-sba.dz, mbouziani@univ-sba.dz

** I.E.M.N. Dept. O.A.E, (U.M.R. 8520, C.N.R.S.) ENSIMEV Universite de Valenciennes et du Hainaut Cambresis le Mont Houy 59313. France E-mail : Jean-Michel.Rouvaen@univ-valenciennes.fr,

*** laboratoire LAMIH UMR C.N.R.S 8530, Universite de Valenciennes et du Hainaut Cambresis le Mont Houy 59313. France E-mail: abdelmalik.taleb-ahmed@univ-valenciennes.fr

Table 1: Channels Parameters of Up Link Scenarios

                                             Channels 1

                                      User 1     User 2     User 3

1st path amplitude:                   1.0        1.0        1.0

2nd path amplitude:                   1.0        1.0        1.0

Delays of 1st path: ([[tau].sub.0])   0.25 Ts    0.125Ts    0.083 Ts

Delay of 2nd path: ([[tau].sub.1])    1Ts        0.6Ts      0.5Ts

                                                 Channel 2

                                      User 1     User 2     User 3
1st path amplitude:                   1.0        1.0        1.0

2nd path amplitude:                   1.0        1.0        1.0

Delays of 1st path: ([[tau].sub.0])   0.25 Ts    0.125Ts    0.083 Ts

Delay of 2nd path: ([[tau].sub.1])    0.925Ts    0.725Ts    0.65Ts