Wavelet packet-based subband adaptive equalization

This paper proposes adaptive algorithms for channel equalization in the wavelet packet transform domain. Adaptation to highly correlated time-varying channels is achieved by the use of the orthogonal tree-structured time-varying filter bank associated to this transform. The filter bank structure, that is, the type of decomposition, is obtained, for a fixed number of bands, as the one that leads to a quasi-optimum convergence rate of the adaptive filters in the different subbands. Then, we propose an NLMS-type adaptive strategy for two possible implementations, a block algorithm, BWPKNLMS, and a non-block approach, WPKNLMS. A theoretical analysis of both schemes is also provided: we obtain the mean squared error after the adaptive algorithm has converged and we find the expression for the optimal solution, to finally show that faster convergence is achieved. Experimental results for the learning curves show the efficiency of the proposed schemes and illustrate the previously presented theoretical results. (C) 2001 Elsevier Science B.V. All rights reserved.