Adaptive equalization of a nonlinear channel by means of Gaussian radial basis functions

Abstract

This paper proposes a preset adaptive equalizer which effectively equalizes the distortion caused by channel nonlinearities. This equalizer closely approximates an optimal equalizer by using the Gaussian radial basis function (RBF) expansion. The RBF expansion consists of a nonlinear transformation using the distribution of a number of vectors, called centers, and a linear combination of the signals after transformation. The behavior of the RBF expansion largely depends on the choice of the centers used in the nonlinear transformation and on their variances. It is first shown that the received signal vectors and their variances can be estimated from the one-to-one correspondence of the transmitted signal vectors and received signal vectors. It is next shown that when the estimated received signal vector and its variance are used as the center and variance for the nonlinear transformation of RBF expansion, the capabilities of the RBF expansion are sufficiently manifested. Moreover, the one-to-one correspondence of the transmitted signal vectors and received signal vectors allows effective setting of the optimum values of parameters for the linear combiner used in the RBF expansion. We show by computer simulation that the proposed equalizer can achieve the same capabilities as an optimum equalizer with a smaller amount of test data and will have a smaller bit error rate than conventional adaptive equalizers. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(6): 42–53, 1997