A performance bound for a cascade LMS predictor

We study the performance of an FIR cascade structure for adaptive linear prediction, in which each FIR filter stage is independently adapted using an LMS algorithm. The performance bound is derived for the cascade LMS predictor under some assumptions. We discover that it is possible for this bound to be better than that of the linear predictive coding (LPC) technique using the block-based Levinson-Durbin algorithm if the cascade LMS predictor is well selected. We show some examples of this bound for synthetic and real audio signals in which a cascade LMS predictor outperforms the LPC technique using the Levinson-Durbin algorithm.