Convergence analysis of clipped input adaptive filters applied to system identification

One of the efficient solutions for the identification of long finite-impulse response systems is the three-level clipped input LMS/RLS (CLMS/CRLS) adaptive filter. In this paper, we first derive the convergence behavior of the CLMS and CRLS algorithms for both time-invariant and time-varying system identification. In addition, we employ results arising from this analysis to derive the optimal step-size and forgetting factor for CLMS and CRLS. We show that these optimal step-size and forgetting factor allow the algorithms to achieve a low steady-state misalignment.