Krylov and predictive sequential least-squares methods for dimensionality reduction in adaptive signal processing and system identification

Abstract

Rapid time variation of the environment, a large number of parameters which need to be adjusted, and the presence of a reduced subset of the parameters that are relevant at any point in time create significant challenges for adaptive signal-processing algorithms in underwater acoustic applications. In applications such as underwater acoustic communications, the environment is represented by the ‘‘taps’’ of the time-varying impulse response. The instability of estimation algorithms or inability to track rapid channel fluctuations are among the problems that are encountered. An approach to addressing these challenges is to dynamically select a subspace in which the adjustment of taps takes place. Here, two algorithms for doing this are presented. The first is based upon using subspace basis vectors, which form a Krylov subspace with respect to the channel input correlation matrix and the channel input/output correlation vector. This method does not use a prediction residual error to select the basis vectors. A second algorithm is a new variant of the matching pursuit algorithm. In this case, ‘‘important’’ taps of the channel impulse response are selected to minimize a forward prediction residual error. The properties and performance of these two algorithms are presented and compared using simulation and field data.