Nlfxlms and thf-nlfxlms algorithms for wiener-hammerstein nonlinear active noise control

Filtered-X least mean square (FXLMS) control algorithm is a conventional algorithm employed to cancel the noise in linear environment. However, in practical applications nonlinearities may present. These nonlinearities are usually associated with the secondary path components, such as amplifiers and loudspeakers. Block oriented method is used to represent the linear and nonlinear components in the secondary path.Usually, linear components are represented by finite impulse response (FIR) filters and nonlinear component with saturation nonlinearity scaled error function (SEF). Nonlinear FXLMS (NLFXLMS) control algorithm based on SEF has been previously developed to cancel the noise in environment with external factors that can cause nonlinearity. The major drawback of using SEF based NLFXLMS (SEF-NLFXLMS) is that the degree of nonlinearity must be known in advance for good control performance. In recent works, it was shown that the SEF can be approximated using tangential hyperbolic function (THF) for Hammerstein and Wiener NLFXLMS algorithms, such that the degree of nonlinearity can be estimated using modelling approach. The THF-NLFXLMS method is extended here for Wiener-Hammerstein model. Using this method, the need for the knowledge of the degree of nonlinearity in advance can be avoided. The proposed algorithm models the Wiener-Hammerstein linear and nonlinear components in the secondary path and applies the estimated degree of nonlinearity of the nonlinear secondary path in the control algorithm design.In previous works, SEF-NLFXLMS and THF-NLFXLMS algorithms for Hammerstein and Wiener structures were developed where the acoustic path is assumed to be a unit gain. However, this assumption may lead to inaccurate secondary path model. In this work, the modelling of acoustic path using FIR filters is incorporated for both algorithms for Wiener-Hammerstein structure. The development of these algorithms becomes the first and second objectives of this research. It is hypothesised that incorporating the acoustic path model would improve the modelling of the secondary path and subsequently improves the level of noise cancellation. The proposed SEF-NLFXLMS and THF-NLFXLMS algorithms are compared with the conventional FXLMS and 2nd order Volterra FXLMS algorithms (which is determined to be of comparable computational complexity with the THF-LFXLMS). The simulation results show that the Wiener-Hammerstein THF-NLFXLMS has close performance with the SEF-NLFXLMS. It outperforms the FXLMS by 2.5dB and 4dB and 2nd order Volterra FXLMS by 3.5dB and 4.5dB for low and medium degrees of nonlinearity, respectively. In addition, Wiener-Hammerstein THF-NLFXLMS shows better performance compared to Wiener THF-NLFXLMS algorithm