A Switching-Based Variable Step-Size PNLMS Adaptive Filter for Sparse System Identification

The standard proportionate normalized least mean square (PNLMS) adaptive algorithm suffers from convergence performance limitation due to a constant step-size during the convergence period. In this paper, a switching-based variable step-size PNLMS is proposed to improve the convergence performance in sparse system identification. To adjust the step-size, the convergence performance of PNLMS is first analysed in the statistical sense and by exploiting the analysis, a switching-based method is then proposed, which brings about a fast convergence towards the desired steady-state mean-square weight deviation. The step-size reduces during the convergence period in a few steps, while in the case of abrupt change in the system impulse response, the step-size increases to its initial value. A sub-band version of the proposed adaptive algorithm is further proposed for highly correlated input signals. Simulation results confirm the superiority of the proposed full-band and sub-band algorithms in terms of convergence performance compared to some competing adaptive algorithms.