Adaptive filtering techniques are receiving increasing attention due to the explosive interest in communications and biomedical applications, among other areas. Although the theory of adaptive filters has been widely studied over the last four decades, new challenges in efficiency and performance call for novel structures and new algorithmic forms. These challenges are motivated, for example, by the desire to meet the ever increasing demands on higher transmission rates over wireless and wireline communications, which in turn require more sophisticated equalization and echo cancellation techniques; two primary areas of application for adaptive filtering.
The main contribution of this work is the development of fast fixed-order and order-recursive adaptive filtering algorithms for applications that involve a large number of taps. This is addressed in two ways.
First, by relying on block processing techniques, an embedding framework for the derivation of frequency-domain adaptive filters is developed in Chapter 2. As a result, the arguments move beyond the existing derivations that are limited to the case of DFTs and show that other efficient signal transformations can be applied to frequency-domain structures.
The dissertation continues by addressing the issue of efficiency in fast recursive least-squares (RLS) algorithms by using orthonormal filter models (to be introduced in Chapter 3), in contrast to the usual finite impulse response (FIR) representations. It has been generally believed in the literature that efficient RLS algorithms are only possible for tapped-delay line structures, since these induce the needed shift-structure in the input data. This dissertation overcomes this difficulty and shows that efficient RLS schemes can be derived for certain general structures, other than tapped-delay line models. In so doing the resulting adaptive algorithms offer enhanced modeling capabilities at considerably lower computational cost, yet maintaining the inherent fast convergence of RLS algorithms. These results appear in Chapters 4 and 5 for both fixed-order and order-recursive (lattice) algorithms.
Acknowledgment This work was supported in part by the National Science Foundation under grants CCR-9732376, ECS-9820765, by UC CoRe Project CR 98-19, and by the ARO grant DAAH04-96-1-0176-P00005. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation and the other sponsors.