  The recursive least-squares algorithm with $\ell_1$-norm regularization
($\ell_1$-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
$\ell_1$-RLS in the mean and mean-square sense. Simulation results illustrate
the accuracy of these models.
