Efficient Matrix Computations in Adaptive Filtering with Orthonormal Basis Functions

Adaptive filtering is a topic of immense practical value with applications in a wide range of areas in signal processing and communications. This talk focuses on the class of least-squares adaptive filters and examines two typical implementations: one is based on a tapped-delay line realization while the other employs orthonormal basis functions such as a Laguerre network. While extensive prior works in the literature have shown that fast least-squares schemes are possible for tapped-delay-line (Toeplitz) structures, little is said about efficient implementations for orthonormal networks. In this talk, we show that efficient orthonormal networks are possible. We do so by exploiting more general forms of matrix structure that arise in the context of fast least-squares solutions for orthonormal networks, in both cases of fixed-order and order-recursive algorithms. In particular, we develop a theory that accomodates such general filter structures, and we use it to devise exact fast least-squares algorithms. We also comment on some algorithmic issues that are relevant for the development of reliable filters, especially in quantized environments. Simulation results are used to illustrate some ill-conditioning difficulties as well as the performance of the proposed filters.