L∞-norm based partial-update adaptive filtering algorithm for echo cancellation

We provide a framework for developing a low-complexity adaptive filtering algorithm by incorporating the concept of partial-updating into the technique of finding the gradient vector in the hyperplane based on the L_∞-norm criterion. The resulting algorithm is referred to as the partial-update normalized sign LMS (PU-NSLMS) algorithm. A specific case of the PU-NSLMS algorithm, called the M-Max PU-NSLMS algorithm, based on the concept of having a minimum Euclidean length of the coefficient-update vector, is considered. It is shown that this algorithm is computationally less complex compared to the partial-update normalized least-mean squares (PU-NLMS) algorithm. Results concerning the mean-square analysis of the M-Max PU-NSLMS algorithm are given. The performance of this algorithm is compared with that of the PU-NLMS algorithm in the case of network echo cancellation. It is shown that the convergence rate of the proposed algorithm is comparable to that of the PU-NLMS algorithm, but with a reduced complexity, making it a good choice for applications requiring a long filter tap, especially for real-time implementations.