Robust Reduced-Rank Adaptive Processing Based on Parallel Subgradient Projection and Krylov Subspace Techniques

Abstract: In this paper, we propose a novel reduced-rank adaptive filtering algorithm by blending the idea of the Krylov subspace methods with the set-theoretic adaptive filtering framework. Unlike the existing Krylov-subspace-based reduced-rank methods, the proposed algorithm tracks the optimal point in the sense of minimizing the \sinq{true} mean square error (MSE) in the Krylov subspace, even when the estimated statistics become erroneous (e.g., due to sudden changes of environments). Therefore, compared with those existing methods, the proposed algorithm is more suited to adaptive filtering applications. The algorithm is analyzed based on a modified version of the adaptive projected subgradient method (APSM). Numerical examples demonstrate that the proposed algorithm enjoys better tracking performance than the existing methods for the interference suppression problem in code-division multiple-access (CDMA) systems as well as for simple system identification problems.