Proportionate Minimum Error Entropy Algorithm for Sparse System Identification

Sparse system identification has received a great deal of attention due to its broad applicability. The proportionate normalized least mean square (PNLMS) algorithm, as a popular tool, achieves excellent performance for sparse system identification. In previous studies, most of the cost functions used in proportionate-type sparse adaptive algorithms are based on the mean square error (MSE) criterion, which is optimal only when the measurement noise is Gaussian. However, this condition does not hold in most real-world environments. In this work, we use the minimum error entropy (MEE) criterion, an alternative to the conventional MSE criterion, to develop the proportionate minimum error entropy (PMEE) algorithm for sparse system identification, which may achieve much better performance than the MSE based methods especially in heavy-tailed non-Gaussian situations. Moreover, we analyze the convergence of the proposed algorithm and derive a sufficient condition that ensures the mean square convergence. Simulation results confirm the excellent performance of the new algorithm.