Optimal Regularization Parameter of the Multichannel Filtered- $x$ Affine Projection Algorithm

We discuss the optimal regularization parameter of the Filtered- Affine Projection (FX-AP) algorithm suitable for feedforward active noise control. While the original FX-AP algorithm always provides a biased estimate of the minimum-mean-square solution, we show that the optimal regularized FX-AP algorithm is capable to eliminate the bias of the asymptotic solution and thus that the regularization parameter can optimize both the convergence speed and the residual MSE of the algorithm. We derive some expressions for the optimal regularization parameter, and we discuss some heuristic estimations of the optimal regularization parameter in practical conditions.