Analysis of the frequency-domain block LMS algorithm

In this paper, we present a new analysis of the frequency-domain block leas t-mean-square (FBLMS) algorithm. An earlier analysis uses a mapping of the frequency-domain information to the time-domain before proceeding with the analysis of the algorithm. We present a direct analysis of the FBLMS algori thm in the frequency domain. As compared with the previous analysis, the ne w analysis is easier to follow. It is also more rigorous than the previous works and gives a better insight to the effect of various processing compon ents in the algorithm structure on its convergence behavior. In particular, we show how the transformation of input samples to the frequency domain, c ombined with the effect of the involved windowing matrices, and step-normal ization affect the convergence behavior of both constrained and unconstrain ed versions of the FBLMS algorithm. We also report a procedure for derivati on of misadjustment equations of various versions of the FBLMS algorithm.