Analytical performance of the LMS algorithm on the estimation of wide sense stationary channels

The performance of the least mean square (LMS) algorithm on the estimation of time-varying channels is analytically evaluated, using the estimation error correlation matrix, the mean-square weight error (MSWE) and the mean-square estimation error (MSE) as parameters. Expressions for those parameters are obtained from a set of hypotheses usually adopted in the communication systems context. The channel is modeled as a wide sense stationary (WSS) discrete time stochastic field with known autocorrelation. The expressions for the steady-state MSWE and MSE are particularized for the class of WSS channel models, and an original analysis of the optimum LMS step-size parameter for usual channel models is addressed. For the sake of comparison with other works, the analytical step-size optimization for random-walk models is also considered. Several estimates of MSWE curves obtained by computer simulation are compared with analytical results for validation purposes. A very good agreement between simulated and analytical results for both the MSWE expressions and the optimum value of the LMS step-size parameter is shown.