  Performance analysis of $l_0$ 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 $l_0$ Least Mean Squares (LMS) algorithm,
in $l_0$ RLS, a $l_0$ 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.
