Mean-squared error analysis of the binormalized data-reusing LMS algorithm using a discrete-angular-distribution model for the input signal

Providing a quantitative mean-squared-error analysis of adaptation algorithms is of great importance for determining their usefulness and for comparison with other algorithms. However, when the algorithm reutilizes previous data, such analysis becomes very involved as the independence assumption cannot be used. In this paper, a thorough mean-squared-error analysis of the binormalized data-reusing LMS algorithm is carried out. The analysis is based on a simplified model for the input-signal vector, assuming independence between the continuous radial probability distribution and the discrete angular probability distribution. Throughout the analysis only parallel and orthogonal input-signal vectors are used in order to obtain a closed-form formula for the excess mean-squared error. The formula agrees closely with simulation results even when the input-signal vector is a delay line. Furthermore, the analysis can be readily extended to other algorithms with expected similar accuracy.