Less complex solutions for active noise control of impulsive noise

All adaptive algorithms suffer stability issues when employed for the impulsive noise control under the domain of active noise control (ANC) systems. There is a dire need of investigations to overcome this limitation for the impulsive noise, a robust adaptive algorithm is proposed in literature. In the first part of paper, this robust adaptive algorithm is tested for the first time under ANC environment for impulsive noise cancellation and thus, a new ANC algorithm named filtered-x least cosine hyperbolic (FxLCH) algorithm is presented. Simulations are carried out to validate the improved performance of proposed FxLCH algorithm where the impulsive noise realizations are generated by symmetric α-stable distributions. Moreover, the proposed solutions perform better than the standard filtered-x least mean square (FxLMS) algorithm including its variants, and it shows better stability and converges faster than its competitors. Robustness of the algorithm is a constraint in the presence of high impulsive noise. To overcome this problem and to enhance the robustness of proposed FxLCH algorithm, two modifications are suggested. First proposed modification clips the reference and error signals (CFxLCH algorithm), while the second modification integrates already reported normalized step size with FxLCH (MFxLCH) algorithm. The performance of suggested MFxLCH algorithm is validated by extensive simulations. The results exhibited that MFxLCH algorithm acts as a trade-off between FxLMS and filtered-x recursive least square (FxRLS) family algorithms. It has shown better convergence speed than that of FxLMS family algorithms and can approach steady state error as of FxRLS family with almost same computational complexity as of FxLMS family algorithms.