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

In this paper, we present a new analysis of the partitioned frequency-domain 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 given for the case where the filter input is a first-order autoregressive process (AR-1). However, the results are then generalized to arbitrary processes in a heuristic way by looking into a set of numerical examples. An interesting finding (that is consistent with earlier publications) is that the unconstrained PFBLMS algorithm suffers from slow modes of convergence, which the FBLMS algorithm does not. Fortunately, however, these modes are not present in the constrained PFBLMS algorithm. A simplified version of the constrained PFBLMS algorithm, which is known as the schedule-constrained PFBLMS algorithm, is also discussed, and the reason for its similar behavior to that of its fully constrained version is explained.