A unified approach to mean-square analysis of adaptive filters

Adaptive filters are systems that respond to variations in their environment by adapting their internal structure in order to meet certain performance specifications. Such systems are widely used in communications, signal processing, and control. Many adaptive algorithms have been suggested in literature. To choose one for a given application, the designer must evaluate its performance in terms of its transient behavior and steady-state response.  It is common to study different adaptive filters separately due to the differences that exist in their update equations. These differences in turn call for distinct assumptions and analysis methods, which obscures commonalities that might exist among them.

In this talk, we present a unified approach to the analysis of adaptive filters that employ general data or error nonlinearities. The approach is based on energy conservation arguments to derive closed form expressions for the transient and steady-state performance and conditions for stability. In addition to deriving earlier results in a unified manner, the approach also leads to new stability and performance results without imposing restrictions on the color or statistics of the input sequence.