The multiuser detection of space coded, Multi Input Multi Output (MIMO), Code Division Multiple Access (CDMA) signals in the downlink direction with channel estimation error is investigated. The main challenge in the system is dealing with the errors in estimating the channel coefficients at the receiving antennas. The performance of the decorrelating detector (DD) under different channel estimation errors, timing errors, and impulsive noise is investigated. A new Robust decorrelating detector (RDD) is proposed which compensates the channel estimation errors by modifying the channel matrix in the system. RDD also deals with the timing errors by the modification of the spreading matrix, and finally, it passes the impulsive components of the additive noise through a robust non-linearity to reduce the impulsive effects. The results show that the performance of the RDD is superior to that of the DD.

Abstract-The leaky least-mean-square (LLMS) algorithm was first proposed to mitigate the drifting problem of the leastmean-square (LMS) algorithm. Though the LLMS algorithm solves this problem, its performance is similar to that of the LMS algorithm. In this paper, we propose an improved version of the LLMS algorithm that brings better performance to the LLMS algorithm and similarly solves the problem of drifting in the LMS algorithm. This better performance is achieved at a negligible increase in the computational complexity. The performance of the proposed algorithm is compared to that of the conventional LLMS algorithm in a system identification and a noise cancellation settings in additive white and correlated, Gaussian and impulsive, noise environments. IndexTerms-Leaky least-mean-square, system identification, noise cancellation. I. INTRODUCTIONThe least-mean-square (LMS) algorithm [1] is one of the most famous adaptive filtering algorithms because of its simplicity and ease of analysis. This has made most researchers to improve the LMS algorithm and also to find solutions to some of its drawbacks. Some of these improved algorithms include: the normalized least-mean-square (NLMS) [2], variable step-size least-mean-square (VSSLMS) [3], etc. These improved algorithms generally improve the performance of the LMS algorithm in terms of convergence rate and mean-square-error (mse) value.One of the main drawbacks of the LMS algorithm is the drifting problem as analyzed in [4]. This is a situation where the LMS algorithm generates unbounded parameter estimates for a bounded input sequence. This may drive the LMS weight update to diverge as a result of inadequate input sequence [4]. The drifting problem has been shown in [5]-[7] in details.The leaky least-mean-square (LLMS) algorithm is one of the improved LMS-based algorithms that use a leakage factor to control the weight update of the LMS algorithm [5], [6]. This leakage factor solves the problem of drifting in the LMS algorithm by bounding the parameter estimate. It also improves the tracking capability of the algorithm, convergence and stability of the LMS algorithm.One of the main drawbacks of the LLMS algorithm is its low convergence rate compared to the other improved LMSbased algorithms. In this paper, we propose a new algorithm that improves the convergence rate of the LLMS algorithm. This is achieved by employing the sum of exponentials of the error as the cost function; this cost function is a generalized of the stochastic gradient algorithm as proposed by Boukis et al. [8]. A leakage factor is added to the sum of exponential cost function which makes the proposed algorithm a combination of the generalized of the mixednorm stochastic gradient algorithm with a leaky factor. This paper is organized as follows. In Section II, a review of the LLMS is introduced. In Section III, the proposed algorithm is introduced. In Section IV, experimental results are presented and discussed. Finally, the conclusions are drawn. II. LEAKY LEAST MEAN SQUARE ALGORITHMIn sy...

A large class of physical phenomenon observed in practical wireless systems exhibits non-Gaussian behavior. The performance of many multiuser detectors can degrade substantially in the presence of such impulsive ambient noise. In this paper, multiuser detection of space coded MIMO and code division multiple access (CDMA) signals under impulsive noise with diversity reception are investigated. We analyze and derive the probability of bit error (P b ) performance of a successive interference cancelation (SIC) system under impulsive noise and maximal ratio combining. We use Middleton's class A model for the noise distribution. Furthermore, we employ post detection SIC as the robust multiuser detection technique for combating the impulsive noise at specific noise parameters in a CDMA setting. The performance of the system under power imbalance is also shown. Novel analytical derivations for both combining techniques are presented, and simulations were performed, which confirm the theoretical results.where c n is the channel coefficient between the transmit antenna and pth receive antenna, a k is the amplitude of the kth user from the transmit antenna, s k Á s k t mT s p is the spreading code of the kth user, T s is the symbol interval, n,p is the time delay between the transmit antenna and pth receive antenna, b k,m .t / is BPSK modulated data, M is the frame size, and n.t / is the noise term; the channel coefficients are independent zero-mean complex Gaussian variables with unit variance. The discrete time model for the matched filter signal at the pth receive antenna is and signal processing, he has offered a broad range of courses ranging from circuits, electronics, and signals and systems. His research interests include multicarrier modulation techniques, OFDM, multi-input multi-output (MIMO) communications, wireless communications, and signal processing of digital communications.

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