Generalized Hyperbolic Tangent Based Random Fourier Conjugate Gradient Filter for Nonlinear Active Noise Control

The filtered-x least mean square (FxLMS) algorithm has been proposed for an active noise control (ANC) system. However, due to the used mean square error (MSE) criterion, FxLMS suffers from performance degeneration for non-Gaussian noises, dramatically. To address this issue, a novel robust generalized hyperbolic tangent (GHT) criterion is first constructed in this paper. Then, the random Fourier features (RFF) method and the conjugate gradient (CG) method are used to address the nonlinearity existing in ANC and solve the quadratic optimization problem induced by the GHT criterion, respectively. Finally, a novel robust random Fourier conjugate gradient filtered-x generalized hyperbolic tangent (RFCGFxGHT) algorithm is proposed for ANC. The theoretical analyses regarding the convergence and computational complexity of RFCGFxGHT are also derived. Simulation experiments on nonlinear ANC systems corrupted by the synthetic logistic chaotic and $\alpha$-stable noises, as well as real-world functional magnetic resonance imaging (fMRI) and server room noises, are conducted to confirm the effectiveness, robustness, and desirable nonlinear learning ability of the proposed algorithm.