On the design of LMS-based channel estimators using the Doppler spread parameter

An analysis of the optimization of the LMS (Least Mean Square) algorithm for the estimation of time-varying and frequency-selective communication channels is here presented. In contrast to previous works on this subject, in which the step-size optimization is rooted on the assumption of specific channel models, this analysis is much more generic in respect to the modelling of both the Doppler and delay spreadings. Besides, it addresses not only the steady-state performance of channel estimators, but also their transient behaviors. Several useful approximate expressions for designing LMS-based channel estimators are herein derived and validated by comparisons with simulation and with a previous work on this kind of analysis. These expressions are remarkably suitable for practical application, since they depend on a few parameters of the communication system. With regard to the channel variability, the knowledge of the Doppler spread parameter is shown to be enough to optimize the performance of a LMS channel estimator using the analysis here presented.