Performance Analysis of PRLS-based Time-Varying Sparse System Identification

Sparse adaptive filter algorithms governed by zero-attracting (ZA) or proportionate updating (PU) mechanisms have been widely employed for sparse system identification. Least mean squares (LMS)-type sparse algorithms have been extensively investigated with good understanding of their performance. In contrast, the performance of sparse recursive least squares (RLS) algorithms is much less studied. This paper presents a theoretical performance analysis of the proportionate RLS (PRLS) algorithm under time-varying sparse systems. Based on reasonable assumptions, expressions for steady-state excess mean square error (EMSE) are derived, gaining insights into the proper selection of step size for the PRLS algorithm. Both simulation and experimental results corroborate our theoretical analyses.