Adaptive Fuzzy Neural Filtering for Decision Feedback Equalization and Multi-Antenna Systems

1.1 Background In ordinary channel equalizer and multi-antenna system, many types of detecting methods have been proposed to compensate the distorted signals or recover the original symbols of the desired user [1]-[3]. For channel equalization, transversal equalizers (TEs) and decision feedback equalizers (DFEs) are commonly used as a detector to compensate the distorted signals [2]. It is well-known that a DFE performs significantly better than a TE of equivalent complexity [2]. As to a multi-user-multi-antenna system, adaptive beamforming (BF) detectors have provided practical methods to recover the symbols of the desired user [3]. Many classical optimization algorithms, such as minimum mean-squared error (MMSE) [1][4], minimum bit-error rate (MBER) [5]-[9], adaptive MMSE/MBER training methods [6], [10]-[12] and the bagging (BAG) adaptive training method [13], are proposed to adjust the parameters of the above mentioned classical detectors (i.e., TE, DFE and BF). Due to the optimal nonlinear classification characteristics in the observed space, Bayesian decision theory derived from maximum likelihood detection [15] has been extensively exploited to design the so-called Bayesian TE (BTE) [14]-[15], Bayesian DFE (BDFE) [16]-[17] and Bayesian BF (BBF) [18]-[19]. The bit-error rate (BER) or symbol-error rate (SER) results of Bayesian-based detectors are often referred to as the optimal solutions, and are extremely superior to those of MMSE, MBER, adaptive MMSE (such as least mean square algorithm [1]), adaptive MBER (such as linear-MBER algorithm [6]) or BAG-optimized detector. The BTE, BDFE and BBF can be realized by the radial basis functions (RBFs) [14], [17], [19]-[23]. Classically, the RBF TE, RBF DFE or RBF BF is trained with a clustering algorithm, such as kmeans [14], [17], [24] and rival penalized competitive learning (RPCL) [25]-[31]. These clustering techniques can help RBF detectors find the center vectors (also called center units or centers) associated with radial Gaussian functions.