Advances in nonstationary adaptive signal processing

The wide applications of adaptive filtering have necessitated a great deal of theoretical research in order to supply engineers with efficient adaptation algorithms, conditions of stability of the adaptive filter, optimal values of the parameters, ... etc. Therefore, many papers have appeared. However, most of these papers are restricted to the case of stationary adaptive filtering. The analysis of the nonstationary case has not yet received sufficient care and it is far from being complete. This paper has two main goals. The first one is to provide a tutorial review of the theoretical results that have been achieved in the context of nonstationary adaptive filtering and to highlight some open issues. The second goal is to provide new results concerning the tracking properties of the sign-sign algorithm, an adaptive filtering algorithm that has received a great deal of interest in the area of high speed data communications.