On the Properties of the System Mismatch Covariance Matrix in the LMS Adaptive Algorithm

The system mismatch covariance matrix is of major interest in some of the optimization approaches of the least-mean-square type adaptive algorithms. Some examples are the ones based on the Kalman filtering theory, or the variable step-size algorithms based on the minimization of the mean square system mismatch. All of them require information about this specific matrix. The usual assumption is to approximate this matrix with a scaled unity one. This paper analyzes the validity conditions of this assumption. Simulation results support the theoretical findings.