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

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 μ is very small and an extra compensation step size α is properly chosen, Chen’s algorithm has comparable performance to that of the DLMS algorithm. For the algorithm to converge, a tighter bound for α than before is also derived. The derived properties and conditions are verified by simulations.