On the application of a unified adaptive filter theory in the performance prediction of adaptive filter algorithms

Employing a recently introduced unified adaptive filter theory, we show how the performance of a large number of important adaptive filter algorithms can be predicted within a unified way. This approach is based on energy conservation arguments and does not need to assume the specific models for the regressors. This general performance analysis can be used to evaluate the mean square and tracking performance of the least mean square (LMS) algorithm, its normalized version (NLMS), the family of affine projection algorithms (APA), the recursive least squares (RLS), the data-reusing LMS (DR-LMS), its normalized version (NDR-LMS), and the transform domain adaptive filters (TDAF). Also, we establish the general expressions for the excess mean square in the stationary and nonstationary environments for all these adaptive algorithms. Finally, we demonstrate through simulations that these results are useful in predicting the adaptive filter performance.