Subband adaptive algorithms for high-order transversal filters

Abstract

Adaptive filters have been employed in wide range of applications where signal characteristics are not available, or are time-varying, such as acoustic echo cancellation and adaptive noise cancellation. Despite their widespread use, performance of the adaptive filters is degraded in some applications by two major factors, namely, (i) coloring of the input signal, and (ii) long impulse response of the unknown system. The classical least-mean-square (LMS) algorithm is computationally efficient but its convergence speed deteriorates as the eigenvalue spread of the input autocorrelation matrix increases due to the coloring of the input signal. The convergence problem worsens when the order of the adaptive filter is increased in order to model the unknown system with sufficient accuracy. In contrast, recursive least-squares (RLS) algorithm is adequate in dealing with colored excitation with large spectral dynamic range. Nevertheless, high computational complexity renders the algorithm not applicable in real-time for the case of high-order adaptive filter. Those problems have motivated various approaches of employing subband and multirate techniques in designing computationally efficient adaptive algorithms with improved convergence performance against high eigenvalue disparity. Conventional subband adaptive filters (SAFs) decompose the input signal and desired response into multiple contiguous spectral bands, decimate the subband signals, process each subband with separate adaptive subfilters, and finally interpolate and recombine the resulting subband signals to obtain a filtered output. Intuitively, faster convergence is possible because the spectral dynamic range is greatly reduced in each subband. Furthermore, the computational burden can be reduced by decimating both the order and adaptation rate of the subfilters. Yet, detailed analysis shows that the convergence ATTENTION: The Singapore Copyright Act applies to the use of this document. Nanyang Technological University Library viii rate of the conventional SAF is limited by aliasing and band-edge effects, in spite of a number of modifications that have been proposed, such as, introducing adaptive cross-filters or spectral gaps between adjacent subfilters, as well as oversampled scheme. This thesis describes, analyzes, and generalizes a new class of SAFs, called the normalized SAF (NSAF), whereby the adaptive filter is no longer separated into subfilters. Instead, subband signals, which are normalized by their respective subband input variance, are used to adapt the fullband tap weights of a modeling filter. The