Krylov-proportionate NLMS algorithm based on multistage Wiener filter representation

This paper proposes a fast converging adaptive filtering algorithm named Krylov-proportionate normalized least mean-square (KPNLMS) by extending the proportionate normalized least mean square (PNLMS) algorithm. PNLMS is known to exhibit faster convergence than the standard NLMS algorithm for sparse unknown systems. The proposed algorithm attains similar effects for non-sparse unknown systems by constructing, based on the multistage Wiener filter (MWF) representation, an orthonormal basis with which the unknown system has a sparse structure. The proposed algorithm can be analyzed by the adaptive parallel variable-metric projection framework. Numerical studies for non-sparse unknown systems are presented, comparing KPNLMS and the MWF-based reduced-rank method.