Abstract

The nonlinearity of amplifier and/or loudspeaker gives rise to nonlinear echo in acoustic systems, which degrades seriously the performance of speech and audio communications. Many acoustic echo cancellation (AEC) schemes have been proposed by researchers to cancel the disturbing echo. In this thesis, two approaches for nonlinear echo cancellation, namely, the 2 nd order Volterra filter-based canceller and the sigmoid-transform-based (STB) canceller, are developed. Volterra filter (VF) plays a critical role in modeling a nonlinear acoustic system where the nonlinear distortion is mainly caused by a loudspeaker. However, the large number of coefficients and the high computational complexity always make the VF difficult to be used in practice. By analyzing a general 2 nd order VF model and a cascade model consisting of a 2 nd order VF and a transversal filter, this thesis proposes a simplified 2 nd order VF structure with relatively low computational complexity for the echo canceller, which is shown to be more efficient in acoustic echo cancellation applications. A theoretically justification is also provided to show the feasibility of such a simplification. Moreover, a normalized least mean square (NLMS) algorithm for kernel-separated 2 nd order VF is derived to accelerate the convergence speed of the coefficients of the nonlinear filter. This algorithm uses a new range of the step size or called convergence factor to ensure the stability of the adaptive filter. The outstanding performance of the proposed AEC is verified by computer simulations For solving the nonlinear distortion caused mainly by an amplifier, a simple yet efficient nonlinear echo cancellation scheme is proposed by using an adaptable sigmoid function in conjunction with a conventional transversal adaptive filter. The new scheme uses the least mean square (LMS) algorithm to update the sigmoid function and the recursive least square (RLS) algorithm to determine the weight vector of the transversal filter. The proposed acoustic echo canceller is proved to be convergent under some reasonable assumptions. Extensive computer simulations show that the proposed AEC has a very satisfactory echo cancellation performance for saturation-type nonlinear distortion