Sparsity-aware Adaptive Filtering Algorithms and Application to System Identification

Abstract

In this thesis, low-complexity adaptive filtering algorithms that exploit the sparsity of signals and systems are derived and investigated. Specifically, sparsity-aware normalized least-mean square and affine projection algorithms are developed based on the l1-norm incorporated to their cost function, which we term zero-attracting NLMS (ZA-NLMS) and zero-attracting APA (ZA-APA). These algorithms are analyzed and applied to the identification of sparse systems. To further improve the filtering performance, the reweighted ZA-NLMS (RZA-NLMS) and reweighted ZA-APA (RZA-APA) are also proposed, which employs reweighted step sizes of the zero attractor for different taps, inducing the attractor to selectively promote zero taps rather than uniformly promote zeros on all the taps. We also develop zero forcing techniques to further improve their performance when the system has a significantly degree of sparsity, i.e., a very small number of non-zero coefficients. Simulation results show that the proposed algorithms outperform the standard NLMS and APA algorithms in both convergence rate and steady-state performance for sparse systems.