A set-membership NLMS algorithm with time-varying error bound

Set membership adaptive filtering is known for a number of attractive features, including reduction of computational complexity due to less frequent coefficient updates. This paper addresses the problem of choosing the error bound to be used in SM adaptation algorithms. This choice has often been based on the experience of the designer, and affects directly not only algorithm performance, but also its computational complexity. We propose a time-varying error bound for a set-membership normalized least mean squares (SM-NLMS) algorithm that yields near constant average coefficient updating rate during both transient and steady state. The expressions given herein not only offer a method to calculate the error bound automatically, but also describes the behavior of a conventional SM-NLMS algorithm. The results were obtained for the particular application of linear time-invariant channel estimation, but certainly provide insightful hints to other scenarios