Improved Performance of MMSE Multiuser Receivers for Asynchronous CDMA: Preliminary Results Paolo Banelli, Saverio Cacopardi, Luca Rugini D.I.E.I. – University of Perugia – Italy – email: {banelli, cacopardi, rugini}@diei.unipg.it Abstract – The Minimum Mean Square Error (MMSE) multi- user detector has received great attention in the last years as the optimum linear solution for reducing the Multiple Access Inter- ference (MAI) in DS-CDMA systems. In asynchronous frequency selective channels the covariance matrix estimation errors may introduce BER performance degradation. Aim of this paper is to outline such degradation and to improve the MMSE receiver per- formance by convenient covariance matrix estimations. Two dif- ferent approaches are introduced. Simulation results are shown in order to validate the effectiveness of the proposed techniques. Keywords – DS-CDMA, Multiuser Detection, MMSE, Spectral Decomposition, Multiple Access Interference. I. INTRODUCTION The presence of MAI in DS-CDMA systems makes attract- ing the use of multiuser receivers. The MAI can be exploited to improve the performance by using banks of symbol matched filters as proposed in [1]. Such multiuser detectors are charac- terised by very cumbersome front-ends, because the number of matched filters (or RAKEs in multipath channels) depends on the active users number. An alternative architecture, that uses only a single chip matched filter and a sampler at the chip rate, is not only characterised by a greater flexibility, but it also al- lows channel estimation by blind techniques. The main benefit of the blind methods is the bandwidth saving due to the absence of training sequences, and it becomes significant in time- varying channels. Since the blind multiuser detection algo- rithms are characterised by a very high computational complex- ity, great attention is dedicated to the class of linear receivers. It is well known that the linear MMSE receiver can be obtained multiplying the inverse of the covariance matrix by the desired user total channel (comprehensive of multipath and spreading) [2]. The estimation errors of the covariance matrix of the signal received through the frequency selective fading channels may introduce BER performance degradation. This problem wors- ens for time varying channels, because the estimate can be done by averaging on few bits. Moreover, the estimation errors are amplified by the inverse operation, particularly at high SNR, producing bit error rates remarkably higher than those obtained in the ideal situation. This paper proposes to reduce such errors by two ap- proaches. Both of them rely on the spectral decomposition of the covariance matrix that is also used for the multiuser channel estimation. The first one is based on perturbing the estimated eigenvalues leading to a CMOE type receiver [3], while the other one is based on a successive re-estimation of the covari- ance matrix by exploiting the estimated channels of all users. II. SYSTEM MODEL The multiple-input multiple-output (MIMO) baseband chan- nel model introduced in [4] is herein summarised. The transmit- ted signal of the kth user, in a DS-CDMA system with K users, is expressed by (1) 1 0 () () ( ) I k k k k k i x t A b is t iT τ − = = − − ∑ (1) where T is the symbol duration, k A and () k s t are the amplitude and the spreading waveform of the kth user respectively, k τ is the kth user relative delay ( 0 k T τ ≤ < ), I is the number of transmitted symbols, and () k b i is the ith symbol of the kth user. It is assumed that () k b i belongs to a set of indipendent equiprobable { } 1 – random variables. The spreading waveform () k s t can be expressed by (2) 1 0 1 () ()( ) 0 N c k k j s t c j t jT t T N ψ − = = − ≤ < ∑ (2) where N is the processing gain, / c T T N = is the chip dura- tion, () t ψ is the normalised rectangular chip waveform of dura- tion c T and () k c j is the { } 1 – jth value of the kth user binary code sequence. We suppose to deal with slowly time varying channels such that they can be considered constant during the transmission of P symbols ( ) P I ≤ . The kth user channel is denoted by (3) , , 1 () ( ) Q k qk qk q g t t α δ τ = = − ∑ (3) where Q is the number of paths, , qk τ and , qk α are respectively the delay and the complex amplitude of the qth path, 1, 2 1, 2, max q q k q k q k τ τ ∆ = − is the maximum delay spread, () t δ is the Dirac function. When the channels are supposed to be constant, the received signal component of the kth user is , , 1 () () () ( ) Q k k k qk k qk q y t x t g t x t α τ = = ∗ = − ∑ . (4) The total received signal is the superposition of the K signals () k y t and a complex zero-mean white Gaussian noise () vt with power spectral density 2 σ . The received signal () rt , ex- pressed by (5), is first filtered by a chip-matched filter and then sampled at the chip rate 1/ c T , obtaining (6) 1 () () () () () K k k rt y t vt yt vt = = + = + ∑ . (5)