Analytical Performance of the LMS Algorithm on the Estimation of Wide Sense Stationary Channels

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 specialized 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.