Noise cancellation with improved residuals

An effective adaptive scheme for noise cancellation when the signal to be recovered has known autocorrelation is presented. Two algorithms that exploit a special form of prior information are investigated. In this approach the desired signal is removed from the output feedback by linear prediction: the prior information used is the desired signal´s autocorrelation. Knowing this, one can find a filter that whitens the desired signal. Screening the error feedback through this filter removes most of the desired signal energy, reducing its interference with the coefficient update. This is the basis for the first algorithm discussed, namely, the least-mean-square algorithm with augmented predictor (LMS-AP) proposed by Orgren et al. (1986). In many applications the whitening filter may not be strictly positive real (SPR). In such cases a different algorithm is needed; one which is assuredly convergent regardless of the satisfaction of the SPR condition. A modified LMS algorithm with augmented predictor (MLMS-AP) which provides such an alternative is proposed