Transient Performance Analysis of the $\ell _1$-RLS

The recursive least-squares algorithm with <inline-formula><tex-math notation="LaTeX">$\ell _1$</tex-math></inline-formula>-norm regularization (<inline-formula><tex-math notation="LaTeX">$\ell _1$</tex-math></inline-formula>-RLS) exhibits excellent performance in terms of convergence rate and steady-state error in identification of sparse systems. Nevertheless few works have studied its stochastic behavior, in particular its transient performance. In this letter, we derive analytical models of the transient behavior of the <inline-formula><tex-math notation="LaTeX">$\ell _1$</tex-math></inline-formula>-RLS in the mean and mean-square error sense. Simulation results illustrate the accuracy of these models.

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