LMS COUPLED ADAPTIVE PREDICTION AND SYSTEM-IDENTIFICATION - A STATISTICAL-MODEL AND TRANSIENT MEAN ANALYSIS

The LMS algorithm has been successfully used in many system identifica tion problems. However, when the input data covariance matrix is ill-c onditioned, the algorithm converges slowly. To overcome the slow conve rgence, an adaptive structure is studied here, which incorporates an L MS adaptive predictor (prewhitener) prior to the LMS algorithm for sys tem identification (canceler). Since the prewhitener is also adaptive, the input to the LMS canceler is nonstationary, even when the input i s stationary. Because of the coupling and the nonstationarity of LMS c anceler input, analysis of the performance of the two adaptations is e xtremely difficult. A simple theoretical model of the coupled adaptati ons is presented and analyzed. First and second moment analysis indica tes that the adaptive predictor significantly speeds up the LMS cancel er as compared to a system without prewhitening and enlarges the stabi lity domain of the canceler (larger allowable mu). Monte-Carlo simulat ions are presented which are in good agreement with the predictions of the mathematical model.