Bias-Compensated PNLMS Algorithm With Multi-Segment Function for Noisy Input

To address the estimation bias caused by ignoring input noise in existing adaptive filtering algorithms, a new proportionate-type algorithm is proposed in this paper. First, a bias-compensation term is derived based on an unbiased criterion when constructing the cost function of the algorithm to achieve unbiased estimation. Next, this bias-compensation term is integrated into the mu-law PNLMS (MPNLMS) algorithm to design the bias-compensated PNLMS combined with the multi-segment function (BC-MS-PNLMS) algorithm. Simulation results for echo paths and underwater channels demonstrate that the BC-MS-PNLMS algorithm outperforms other sparse-type algorithms in sparse experimental environments.