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

Ahstract-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.