NSLMS: A proportional weight algorithm for sparse adaptive filters

In this paper we discuss a proportional weight algo-rithm that is similar to LMS. The distinction is that the new algorithm (called normalized sparse LMS, or NSLMS) has a time-varying vector stepsize, whose co-efficients are proportional to the magnitudes of the current values of the tap estimates. We show that when the system to be identified is sparse, NSLMS converges faster than LMS (to the same asymptotic MMSE for both algorithms). We also discuss the effect of the initialization on the performance of NSLMS.