LMS coupled adaptive prediction and system identification: astatistical model and transient mean analysis

The LMS algorithm has been successfully used in many system identification problems. However, when the input data covariance matrix is ill-conditioned, the algorithm converges slowly. To overcome the slow convergence, an adaptive structure is studied, which incorporates an LMS adaptive predictor (prewhitener) prior to the LMS algorithm for system identification (canceler). Since the prewhitener is also adaptive, the input to the LMS canceler is nonstationary, even when the input is stationary. Because of the coupling and the nonstationarity of LMS canceler input, analysis of the performance of the two adaptations is extremely difficult. A simple theoretical model of the coupled adaptations is presented and analyzed. First and second moment analysis indicates that the adaptive predictor significantly speeds up the LMS canceler as compared to a system without prewhitening and enlarges the stability domain of the canceler (larger allowable μ). Monte-Carlo simulations are presented which are in good agreement with the predictions of the mathematical model