Adaptive filter performance with nonlinearities in the correlation multiplier

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.