| Motivated by recent developments in averaging methods of recursive stochastic approximation algorithms, this dissertation develops two-stage procedures for adaptive filtering algorithms. The premise of adaptive filtering is that given sequences of reference and output signals, one adaptively adjusts a parameter process so that the weighted signals best approximate the reference signals in an appropriate sense. By best approximation, it is meant that a cost function is minimized. The focus is on asymptotic analysis of two-stage algorithms, which construct a sequence of estimates recursively using large step sizes (larger than O( 1n ), the choice of usual adaptive stochastic approximation algorithms) followed by iterate averaging. Following the resurgent interest in efficient adaptive signal processing algorithms for interference suppression in wireless CDMA (Code Division Multiple Access) communication networks, this work addresses the asymptotic properties of adaptive filtering algorithms using sign operators. First, we aim to improve the efficiency of sign-regressor procedures, which are known to have reduced complexity compared with the classical Least Mean Square algorithms and better performance compared with the sign-error procedures. Discrete-time algorithms that include both iterate and observation averaging are suggested. Under the assumption of stationary, bounded, and correlated &phis;-mixing type signals, we show that such algorithms converge to the minimizer with probability one and the convergence rate is optimal. Next, we examine continuous-time adaptive filtering algorithms. The use of continuous-time algorithms stems from the needs of treating problems with high sampling rates. Under the assumption of uniform mixing signals, we prove the convergence of an iterate-averaging sign-regressor algorithm and derive its asymptotic normality. Representation of the asymptotic covariance is also derived. The stability of the algorithm is obtained via the use of Liapunov function method. In addition, we demonstrate that the use of iterate averaging improves the asymptotic efficiency. As a by-product, we also examine continuous-time sign-error adaptive filtering algorithms. Due to non-smoothness, such algorithms are more difficult to analyze and the conditions posed are stronger. |
