Analysis of Deficient-Length Partitioned-Block Frequency-Domain Adaptive Filters

Abstract

This paper studies the convergence behavior of the partitioned-block frequency-domain adaptive filters (PBFDAF) for under-modeling scenarios. We focus on a family of the overlap-save PBFDAF algorithms with 50% overlap, including both of the constrained and unconstrained versions. The stochastic analysis of the constrained and unconstrained algorithms is carried out individually due to their convergence differences. For each algorithm, the frequency-domain error vector and the update equations are transformed into the time-domain counterparts, so we can analyze their convergence behavior completely in the time domain. We present the mean and mean-square convergence behavior of the augmented weight-error vector, and we obtain the closed-form expressions for the learning curve and the steady-state solutions. Based on the solution of the steady-state weight-error vector, we analyze if each version of the PBFDAF algorithm converges to the true solution and the Wiener solution. The theoretical model gains new insights into the convergence behavior of the deficient-length PBFDAF algorithms. The computer simulations support the theoretical model very well.