A modified NLMS algorithm for adaptive noise cancellation

Adaptive noise cancellation (ANC) is used widely to reduce noise from a noisy speech sound. However the least-mean-square (LMS) algorithm and its variants, such as the normalized (N)LMS, the modified (M)-LMS and the constrained stability (CS)-LMS algorithms do not perform well in ANC since the desired speech signal has a bad effect on the convergence rate and steady state misadjustment of these algorithms. Thus, we propose a new adaptive algorithm that further relaxes the constraint in the CS-LMS algorithm. The new algorithm attempts to minimize the estimation error of the a posteriori error and the estimation is obtained using the concept of Taylor´s expansion. The analysis and simulation results show that the proposed new algorithm outperforms the NLMS and CS-LMS algorithms.