Minimum Error-rate Filtering Algorithm

Filtering has been an enabling receiver technology and has attracted ever-increasingattention in various state-of-the-art communicaiton systems, and has applied to various areas,including channel equalization, multi-user detection, beamforming, MIMO(multiple-input andmultiple-output) receiver. Traditionally, filtering has been developed based on the Wiener orminimum mean square error(MMSE) approach, the corresponding adaptive iteration is calledas least mean square(LMS) algorithm, and the corresponding closed-form solution is called asMMSE algorithm. The famous LMS algorithm with its low computational complexity readilymeets the fast real-time computational constraint of high-speed communication, has beenwidely used in various communication systems. However, it is the system’s bit error rate, notthe mean square error, that really matters. It has been recognized that minimising the MSEiteration does not necessarily produce the minimum BER performance when no channelcoding is applied, the novel filtering based on minimum-BER has opened up a whole newchapter in the optimisation receiver of communication systems. This article continues thistheme, the author conducts the research of minimum error rate filtering for channelequalization and MIMO receiver, builds BER objective functions, and carries out a globaloptimization looking for a corresponding adaptive MER filtering algorithm or a closed-formsolution, in contrast to the LMS or MMSE algorithm.The contribution of this article includes the following areas: First, the article reviewedadaptive minimum bit-error rate equalization and adaptive minimum symbol-error rateequalization algorithms, advantages and disadvantages of them are analysed. Second, in thispaper we present a new approach for minimum symbol-error rate equalization, which is calledas normalized AMSER(NAMSER) algorithm, it differs from the existing AMSERequalization, it does not need channel parameters and has a simpler calculation, moreover anormalization factor is introduced and can help to speed up convergence, more attractively ithas a uniform iterative formulation for different source modulation schemes; Third, the articlereviewed minimum error-rate linear MIMO reveiver algorithm, it is the first closed-formalgorithm up to the author’s knowledge, the solutions are presented in the two-input casefirstly, and then extended to the arbitrary-input case using cascaded receivers of a MMSE group receiver and a MER receiver; Fourth, in this paper we present a new implicitclosed-form solution for minimum symbol-error rate MIMO receiver, we argue thatminimizing the upper bound of BER is equivalent to minimizing BER, and then we derive animplicit closed-form solution using convex programming constraints.