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

The previously proposed Chen's (see IEEE Trans. Circuits Syst.-II: Analog and Digital Signal Processing, vol.43, p.372-8, May 1996) LMS algorithm costs only half the multiplications of the conventional direct-form LMS algorithm (DLMS). Despite of this merit, the algorithm lacked a rigorous theoretical analysis. This article characterizes its properties and conditions for mean and mean-square convergences. The closed-form MSE is derived, which is slightly larger than that of the DLMS algorithm. It is shown, under the condition that the LMS step size /spl mu/ is very small and an extra compensation step size /spl alpha/ is properly chosen, that Chen's algorithm has a comparable performance to that of the DLMS algorithm. For the algorithm to converge, a tighter bound than before is also derived. The derived properties and conditions are verified by simulations.