LMS and RLS tracking analysis for WSSUS channels

The tracking performance of the least mean square (LMS) and the exponentially weighted recursive least squares (RLS) algorithm for the identification of linear time-varying communication channels is studied. The concept of wide-sense stationary uncorrelated scattering (WSSUS) serves as a stochastic model for the time evolution of the channel´s impulse response. This description is of practical relevance for the mobile radio channel. Based on an approximate analysis of the adaptive algorithms as coefficient filters, closed-form expressions are obtained for the mean-squared identification error in terms of the channel´s scattering function and the LMS step size or RLS weighting factor. The analytical results show good agreement with experiments and thus make it possible to match the design parameters of the recursive identification schemes to the a priori knowledge of the physical channel. Further simulation experiments show that both the RLS and the LMS tracking performance degrades significantly when the adaptive filter order is insufficient to model the true channel.<>