Performance of multicode DS-CDMA using
frequency domain equalisation in frequency
selective fading channel
F. Adachi, T. Sao and T. Itagaki
For the reception of multicode direct sequence (DS)-CDMA signals,
the MMSE frequency domain equalisation is applied instead of RAKE
combining. The achievable BER performance in a frequency selective
Rayleigh fading channel is evaluated by computer simulation. It isshown by computer simulation that the DS-CDMA with MMSE
frequency domain equalisation outperforms the DS-CDMA withRAKE combining and shows only slight performance degradationcompared to the MC-CDMA with minimum mean square error
combining (MMSEC).

Introduction: In direct sequence code division multiple access(DS-CDMA), one way to achieve high-speed data transmission is touse orthogonal multicode multiplexing [1]. However, frequency
selective multipath fading encountered in a broadband wirelesscommunication system severely degrades the bit error rate (BER)
performance of multicode DS-CDMA. An effective technique toimprove the BER performance is a RAKE receiver. However, as thespreading chip rate becomes higher, the frequency selectivity of themultipath channel becomes more severe due to the increasing numberof resolvable propagation paths. This causes a number of problems.
The intercode interference (ICI) becomes stronger and the accurate
channel estimation necessary for RAKE combining becomes moredifficult. The RAKE receiver complexity increases due to the increasing number of RAKE fingers required.
Recently, much attention has been paid to multicarrier CDMA(MC-CDMA) [2], in which the frequency domain spreading is used.
The frequency selective fading distorts the MC-CDMA signals anddestroys the orthogonality property of the spreading codes. Before
despreading of the received MC-CDMA signal, frequency domain
equalisation is applied for partial restoration of code orthogonality.
The most effective frequency equalisation and despreading is theminimum mean square error combining (MMSEC) [3]. The frequency
domain equalisation has also been attracting much attention recently forthe single carrier wireless transmission systems [4].
In this Letter, we apply the concept of frequency domain equalisation
to multicode DS-CDMA signal reception. First, a signal transmission
system model of DS-CDMA with frequency domain equalisation basedon minimum mean square error (MMSE) is presented and then, theachievable BER performance in a frequency selective Rayleigh fading
channel is evaluated by computer simulation. The performance comparison is presented for the DS-CDMA with MMSE frequency domain
equalisation and with RAKE combining (i.e. time domain equalisation)and the MC-CDMA with MMSEC.

received signal back to a DS-CDMA signal in the time domain.
The introduction of DFT and IDFT requires the insertion of a guardinterval (GI) at the transmitter side as in MC-CDMA. The transmission system model of a multicode DS-CDMA system transmitting C
data in parallel is shown in Fig. 1. Each data is spread using the time
domain orthogonal spreading code with chip length Tc. Without lossof generality, we consider the time interval of one multicode DSCDMA symbol, i.e. 0  t < T with T ¼ Ts þ Tg, where Ts and Tg are,respectively, the effective symbol length and GI, as introduced in MCCDMA. Throughout this Letter, discrete-time representation of themulticode DS-CDMA signal is used.
Let xn be the nth data-modulated symbol with jxnj ¼ 1. During
0  t  T, {xn; n ¼ 0  C  1} are transmitted in parallel using theorthogonal spreading codes {cn(i); n ¼ 0  C  1, i ¼ 0  SF  1}with jcn(i)j ¼ 1. After summing up (i.e. code multiplexing) the C
parallel spread chip sequences, long scramble code {cscr(i);i ¼ . . . , 1, 0, 1, . . . } with jcscr(i)j ¼ 1 is multiplied in order to transform the multicode DS-CDMA signal into noise-like signal. The
resultant multicode DS-CDMA signal may be expressed using theequivalent lowpass representation assðiÞ ¼C1P pﬃﬃﬃﬃﬃﬃ

2Pxn cn ðiÞcscr ðiÞð1Þn¼0for i ¼ 0  SF  1, where P represents the transmit power per datasymbol. After insertion of the Ng-sample GI, where Ng ¼ Tg=Tc, theresultant multicode DC-CDMA signal {s̃(i); i ¼ Ng  SF  1} istransmitted over a multipath channel, where s̃(i) ¼ s(imod SF ).

Fig. 2 Comparison of DS-CDMA with MMSE-FE and with RAKE
combining
Eb=N0 ¼ 0.5Es=N0 for QPSK data modulation. C=SF ¼ 1

The received multicode DS-CDMA signal, which is perturbed by theadditive white Gaussian noise (AWGN), is sampled at the chip rate toobtain {r̃(i); i ¼ Ng  SF  1}. Ideal sampling timing is assumed. The
Ng-sample GI is removed and SF-point DFT is applied to decompose
the received DS-CDMA signal into the SF-carrier components:


SF1
P
j2pkið2Þ
rk ¼
r~ ðiÞexpSFi¼0
for k ¼ 0  SF  1. Let xk denote the propagation channel gain at the kthcarrier frequency. The MMSEC weight derived for MC-CDMA [3] canbe applied to our case. The MMSE frequency domain equalisation
weight for rk is given byFig. 1 Multicode DS-CDMA transmission modelwk ¼
MMSE frequency domain equalisation: The use of frequency domain
equalisation avoids ICI, and the complexity and the channel estimation problems of RAKE combining. The frequency domain equalisation is implemented by first applying the discrete Fourier transform(DFT) to the received multicode DS-CDMA signal, then weighting
the resulting frequency domain components based on MMSE criterion, and finally applying inverse DFT (IDFT) to transform thexkjxk j2 þ ½C=SFð1 þ Tg =Ts Þ1 ðEs =N0 Þ1ð3Þ

where Es=N0 represents the average received signal energy per data
symbol-to-AWGN power spectrum density ratio and ()* denotes
complex conjugate. The factor of (1 þ Tg=Ts) reflects the power penalty
due to GI insertion. After MMSE frequency domain equalisation, IDFT
is carried out to obtain the multicode DS-CDMA signal in the time
domain:ELECTRONICS LETTERS 23rd January 2003 Vol. 39 No. 2s^ ðiÞ ¼ SF 1

SF1Pk¼0wk rk exp

j2pkiSF

ð4Þ

for i ¼ 0  SF  1. Finally, multicode despreading is carried out toobtainx^ n ¼

SF1Ps^ ðiÞfcn ðiÞcscr ðiÞgð5Þ

i¼0The soft values {x̂n; n ¼ 0  C  1} are parallel-to-serial converted fordata demodulation.
Computer simulation: The spreading factor of SF ¼ 64 and the guardinterval of GI ¼ 8Tc (i.e. Tg=Ts ¼ 1=8) are assumed. Quadrature phaseshift keying (QPSK) data modulation is used. The spreading codesand scramble code used are Walsh codes of 64 chips and M-sequenceof 4095 chips. Channel is a very slow frequency selective Rayleighfading channel with uniform power delay profile having L independent paths; the time delay of the lth path is assumed to be tl ¼ lTc,l ¼ 0  L  1. For performance comparison, DS-CDMA with RAKE
combining and MC-CDMA with MMSEC, both using the same
spreading factor, are considered. Channel estimation for frequency
domain equalisation and RAKE combining is assumed to be ideal. Itshould be noted that for DS-CDMA with RAKE combining, no guardinterval is necessary; hence, its transmission data rate is 9=8 times
faster than that of DS-CDMA and MC-CDMA, both with frequency
domain equalisation, for the same spreading bandwidth. Fig. 2
compares the simulated average BER performances of multicode
DS-CDMA with MMSE frequency domain equalisation (MMSEFE) and with RAKE combining for C ¼ 64, i.e. C=SF ¼ 1. RAKE
combining exhibits large error floors when L > 1 due to strong ICI
produced by asynchronism of propagation paths. Conversely, the useof frequency domain equalisation produces no error floor and significantly improves the average BER performance compared to theRAKE combining case. Fig. 3 compares the simulated average BER
performances of DS-CDMA with MMSE-FE and MC-CDMA withMMSEC for C ¼ 64. DS-CDMA with MMSE-FE shows only slightdegradation in the BER performance compared to MC-CDMA.
Conclusion: We applied the MMSE frequency domain equalisation tothe reception of multicode DS-CDMA signals. It was shown bycomputer simulation that the DS-CDMA with MMSE frequency
domain equalisation outperforms DS-CDMA with RAKE combining
and provides a BER performance only slightly degraded fromMC-CDMA.

Fig. 3 Comparison of DS-CDMA with MMSE-FE and MC-CDMA withMMSECC=SF ¼ 1# IEE 2003
Electronics Letters Online No: 20030160
DOI: 10.1049/el:20030160

16 October 2002

F. Adachi, T. Sao and T. Itagaki (Department of ElectricalEngineering, Graduate School of Engineering, Tohoku University,
05 Aza-Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan)
E-mail: adachi@ecei.tohoku.ac.jp
References
1234ADACHI, F., OHNO, K., HIGASHI, A., and OKUMURA, Y.: ‘Coherent multicode
DS-CDMA mobile radio access’, IEICE Trans. Commun., 1996, E79-13,pp. 1316–1325
HARA, S., and PRASAD, R.: ‘Overview of multicarrier CDMA’, IEEECommun. Mag., 1997, 35, pp. 126–144
CHOULY, A., BRAJAL, A., and JOURDAN, S.: ‘Orthgonal multicarrier
techniques applied to direct sequence spread spectrum CDMA system’.
Proc. IEEE GLOBECOM’93, Houston, TX, USA, November 1993,
pp. 1723–1728
FALCONER, D., et al.: ‘Frequency domain equalization for single-carrier
broadband wireless systems’, IEEE Commun. Mag., 2002, 40, pp. 58–66

ELECTRONICS LETTERS

23rd January 2003

Vol. 39 No. 2