On the convergence and MSE of Chen's LMS adaptive algorithm

Abstract

The recently proposed Chen's LMS algorithm [1] costs only half multiplications that of the conventional direct-form LMS algorithm (DLMS). Despite of the merit, the algorithm lacked rigorous theoretical analysis. This work intends to characterize its properties and conditions for mean and mean-square convergences. Closed-form MSE are derived, which is slightly larger than that of DLMS algorithm. It is shown, under the condition that the LMS step size mu is very small and an extra compensation step size alpha is properly chosen, Chen's algorithm has comparable performance to that of the DLMS algorithm. For the algorithm to converge, a tighter bound for alpha than before is also derived. The derived properties and conditions are verified by simulations.