Variable leakage FXLMS algorithms for nonlinear active control applications

When linear adaptive algorithms are used in active control applications, they do not consider the system nonlinearities in the update equations. On the other hand, such an application class is inherently nonlinear due to the nature of the system components. So, in such an environment a nonlinear adaptive algorithm, including information about the system nonlinearities, would be the most indicated for performance. However, this requires the knowledge of the model of the nonlinearities, which is mostly unavailable. In this paper, we propose the use of the linear FXLMS algorithm with variable leakage as a way for overcoming the need of a prior knowledge of the system nonlinearities. Thus, we show that: (i) the performance of the linear leaky FXLMS algorithm versions with variable leakage can approximate to that of the nonlinear ones; (ii) the knowledge about the system nonlinearities is no longer needed. Therefore, the proposed algorithm represents an interesting alternative for practical implementation in the presence of saturation-type nonlinearities. We confirm the conjectures made through numerical examples.