Filtered-X Least Mean Fourth (FXLMF) and Leaky FXLMF adaptive algorithms

Adaptive filtering algorithms promise an improvement of the active noise control (ANC) problem encountered in many scenarios. Just to name a few, the Filtered-X Least Mean Square (FXLMS) algorithm, the Leaky FXLMS (LFXLMS) algorithm, and other modified LMS-based algorithms have been developed and utilized to combat the ANC problem. All of these algorithms enjoy great performance when the signal-to-noise ratio (SNR) is high. On the other hand, when the SNR is low, which is a known trend in ANC scenarios, the performance of these algorithms is not attractive. The performance of the Least Mean Fourth (LMF) algorithm has never been tested on any ANC scenario under low or high SNR. Therefore, in this work, reflecting the development in the LMS family on the LMF, we are proposing two new adaptive filtering algorithms, which are the Filtered-X Least Mean Fourth (FXLMF) algorithm and the Leakage-based variant (LFXLMF) of the FXLMF algorithm. The main target of this work is to derive the FXLMF and LFXLMF adaptive algorithms, study their convergence behaviors, examine their tracking and transient conduct, and analyze their performance for different noise environments. Moreover, a convex combination filter utilizing the proposed algorithm and algorithm robustness test is carried out. Finally, several simulation results are obtained to validate the theoretical findings and show the effectiveness of the proposed algorithms over other adaptive algorithms.