A Delayless Sub-band PNLMS Adaptive Filter for Sparse Channel Identification

In sparse system identification applications such as acoustic and underwater communication, the convergence performance of conventional normalized least-mean-square (NLMS) adaptive filter is degraded due to the sparse nature of the unknown channels and the high correlation of input signals. To overcome the above issues, we propose a delayless sub-band proportionate NLMS adaptive filter with weight update process being made a function of the inverse of the approximated sub-band input correlation matrix and the estimated sub-band mean-squared error. The approximation of matrix inverse is estimated recursively using a modified matrix inversion lemma. Simulation results verify the improved performance of the proposed algorithm compared to sub-band NLMS, sub-band proportionate NLMS (PNLMS), and sparsity-aware normalized sub-band adaptive filter (NSAF) algorithms having the same sub-band structure.