A TIME-DOMAIN FEEDBACK ANALYSIS OF FILTERED-ERROR ADAPTIVE GRADIENT ALGORITHMS

This paper provides a time-domain feedback analysis of gradient-based adaptive schemes, A key emphasis is on the robustness performance of t he adaptive filters in the presence of disturbances and modeling uncer tainties (along the lines of H-infinity-theory and robust filtering), The analysis is carried out in a purely deterministic framework and as sumes no prior statistical information or independence conditions. It is shown that an intrinsic feedback structure can be associated with t he varied adaptive schemes, The feedback structure is motivated,ia ene rgy arguments and is shown to consist of two major blocks: a time-vari ant lossless (i.e., energy preserving) feedforward path and a time-var iant feedback path, The configuration is further shown to lend itself to analysis via a so-called small gain theorem, thus leading to stabil ity and robustness conditions that require the contractivity of certai n operators, Choices for the step-size parameter in order to guarantee faster rates of convergence are also derived, and simulation results are included to demonstrate the theoretical findings. In addition, the time-domain analysis provided in this paper is shown to extend the so -called transfer function approach to a general time-variant scenario without any approximations.