Comparative tracking performance of the LMS and RLS algorithms for chirped narrowband signal recovery

Abstract

This paper studies the comparative tracking performance of the recursive least squares (RLS) and least mean square (LMS) algorithms for time-varying inputs, specifically for linearly chirped narrowband input signals in additive white Gaussian noise. It is shown that the structural differences in the implementation of the LMS and RLS weight updates produce regions where the LMS performance exceeds that of the RLS and other regions where the converse occurs. These regions are shown to be a function of the signal bandwidth and signal-to-noise ratio (SNR). LMS is shown to place a notch in the signal band of the mean lag filter, thus reducing the lag error and improving the tracking performance. For the chirped signal, it is shown that this produces smaller tracking error for small SNR. For high SNR, there is a region of signal bandwidth for which RLS will provide lower error than LMS, but even for these high SNR inputs, LMS always provides superior performance for very narrowband signals.