On the Convergence of the Frequency-Domain LMS Adaptive Filter using LMS-DFT

This paper presents an analysis of the convergence of the frequency-domain LMS adaptive filter when the DFT is computed using the LMS steepest descent algorithm. In this case, the frequency-domain adaptive filter is implemented with a cascade of two sections, each updated using the LMS algorithm. Since the structure contains two adaptive algorithms updating in parallel, an analysis of the overall system convergence needs to consider the effect of the two adaptive algorithms on each other, in addition to their individual convergence. Analysis was done based on the expected mean-square coefficient error for each of the two LMS adaptive algorithms, with some simplifying approximations for the second algorithm, to describe the convergence behavior of the overall system. Simulations were used to verify the results