Analysis of the frequency-domain block LMS algorithm

Abstract

In this paper, we present a new rigorous analysis of the FBLMS algorithm. We derive the equations which control the expected convergence of the FBLMS algorithm and then go on to analyze the eigenvalues of the matrix which controls the convergence behaviour of the FBLMS algorithm. Using Gerschgorin's theorem, we then show that all the eigenvalues of the normalized constrained and unconstrained FBLMS algorithms tend asymptotically towards the same value.