Adaptive acoustic echo cancellation in the presence of multiple nonlinearities

A Hammerstein-Wiener system consists of a linear time invariant subsystem sandwiched between two memoryless nonlinear blocks as is the case of an acoustic system with a nonlinear loudspeaker and a nonlinear microphone. We propose to model the memoryless nonlinear blocks of the Hammerstein-Wiener system using a linear combination of nonlinear basis functions, and concentrate on the task of parameter estimation for the nonlinear blocks. An adaptive algorithm is proposed using a pseudo magnitude squared coherence (PMSC) function-based criterion. The proposed method carries out nonlinearity identification without knowing the linear block in the Hammerstein-Wiener system. This is particularly useful for nonlinear acoustic echo cancellation (NAEC) applications, where dealing with the linear and nonlinear blocks together can be computationally challenging due to the long room impulse response. Numerical examples are provided to illustrate the performance of the proposed method.