Adaptive filter performance with nonlinearities in the correlation multiplier

Abstract

It is well known that the correlation multiplier used to form the update signal in adaptive transversal filters need not be a true multiplier. By using an approximate multiplier such as a sign-bit-only multiplier, implementation can be made less costly. In this paper we derive expressions for the convergence rate and misalignment noise of adaptive transversal filters with arbitrary correlation-multiplier non-linearities. The analysis shows any such nonlinearities to always harm performance and quantifies the penalty suffered. Sign-bit-only multiplication suffers a significant penalty, and power-of-two multiplication is suggested as a better alternative. Its performance is almost equal to that of a true multiplier, and in a digital implementation, at least, it is only slightly more difficult to realize than a sign-bit-only multiplier. The theory is developed in a way emphasizing physical understanding and has been verified to be in good agreement with simulation.