Averaging sign algorithms for adaptive filtering

This paper is motivated by the recent developments on iterate averaging of recursive stochastic approximation algorithms and asymptotic analysis of sign-error algorithms for adaptive filtering. We develop averaging algorithms for adaptive filtering. The proposed algorithms are based on constructions of a sequence of estimates using large step sizes followed by iterate averaging and averaging on both iterates and observations. We demonstrate that the performance of the algorithms are improved via the use of averaging. The proof is based on establishing asymptotic normality of a suitably scaled sequence of the estimation errors. The asymptotic covariance is calculated and shown to be the smallest possible leading to asymptotic efficiency. We also propose and investigate the variants of the algorithm including sign-regressor procedures and constant-step algorithms. As applications, we demonstrate how averaging algorithms can be used for blind multiuser detection in DS/CDMA systems.