Filtered-X NLMS algorithm with compensation of memoryless nonlinearities for Active Noise Control

In this paper we consider the problem of deriving an efficient adaptation algorithm when the secondary path of a single-channel feed-forward Active Noise Control (ANC) system contains a memoryless nonlinearity affecting the output of the controller. In order to avoid complex nonlinear adaptation strategies, the solution proposed consists in the design of a predistorter that linearizes the input-output relationship of the memoryless nonlinearity. The linearization technique exploits the histograms and the cumulative density functions of the input and output signals. Then, we show how the linear NLMS adaptation algorithm can be suitably modified and applied in the framework of a feed-forward delay-compensated scheme. Theoretical considerations are developed to show that the algorithm is in general affected by a bias that depends on the deviations of the linearized model from the ideal linear input-output characteristic. The results of the reported experiments confirm, in agreement with the theoretical analysis, that the accurate design of the predistorter can reduce the bias so that useful results can be obtained.