Performance Analysis of $l_0$ Norm Constrained Recursive Least Squares Algorithm

Performance analysis of l0 norm constrained Recursive least Squares (RLS) algorithm is attempted in this paper. Though the performance pretty attractive compared to its various alternatives, no thorough study of theoretical analysis has been performed. Like the popular l0 Least Mean Squares (LMS) algorithm, in l0 RLS, a l0 norm penalty is added to provide zero tap attractions on the instantaneous filter taps. A thorough theoretical performance analysis has been conducted in this paper with white Gaussian input data under assumptions suitable for many practical scenarios. An expression for steady state MSD is derived and analyzed for variations of different sets of predefined variables. Also a Taylor series expansion based approximate linear evolution of the instantaneous MSD has been performed. Finally numerical simulations are carried out to corroborate the theoretical analysis and are shown to match well for a wide range of parameters. Index Terms Adaptive filters, sparsity, l0 norm, Recursive Least Squares (RLS) algorithm, mean square deviation, performance analysis.