Nearest Kronecker Product Decomposition Based Normalized Least Mean Square Algorithm

Recently, nearest Kronecker product (NKP) decomposition based Wiener filter and Recursive Least Squares (RLS) have been proposed and was found to be a good candidate for system identification and echo cancellation and was shown to offer better tracking performance along with lower computational complexity, especially for identification of low-rank systems. In this paper, we derive the Least Mean Square (LMS) versions of adaptive algorithms which take advantage of NKP decomposition, namely NKP-LMS and NKP Normalized LMS (NKP-NLMS) algorithms. We compare the convergence and tracking performance along with computational complexity between standard NLMS, standard RLS, NKP based RLS (RLS-NKP), the standard Affine Projection Algorithm (APA) and NKP-NLMS algorithm, to evaluate the efficacy of NKP-NLMS algorithm in the context of system identification. Simulation results show that NKP-NLMS can be a good candidate for system identification, especially for sparse/low rank systems.