Analysis of the partitioned frequency-domain block LMS (PFBLMS) algorithm

In this paper, we present a new analysis of the partitioned frequency-domai n block least-mean-square (PFBLMS) algorithm. We analyze the matrices that control the convergence rates of the various forms of the PEBLMS algorithm and evaluate their eigenvalues for both white and colored input processes. Because of the complexity of the problem, the detailed analyses are only gi ven for the case where the filter input is a first-order autoregressive pro cess (AR-1). However, the results are then generalized to arbitrary process es in a heuristic way by looking into a set of numerical examples. An inter esting finding (that is consistent with earlier publications) is that the u nconstrained PFBLMS algorithm suffers from slow modes of convergence, which the FBLMS algorithm does not. Fortunately, however, these modes are not pr esent in the constrained PFBLMS algorithm. A simplified version of the cons trained PFBLMS algorithm, which is known as the schedule-constrained PFBLMS algorithm, is also discussed, and the reason for its similar behavior to t hat of its fully constrained version is explained.