| IntroductionIn the applications of multimedia communication, real-time speech transmission and hand-free telephone conference, echo cancellation is essential to improve the speech quality. In recent years, the emphasis of the echo cancellation research has changed from hybrid echo to acoustic echo. The way of the echo cancellation is acoustic echo canceller (AEC), instead of echo control. A typical AEC is defined as the coefficients of the AEC filter are used to model the room impulse responses between the microphone and the loudspeaker. If a far-end speech is sent into near-end room, an echo replica speech is generated by the AEC filter, and subtracted from the microphone signal. If the filter coefficients are the same as those of the room impulse responses, the echo will be canceled perfectly and there remains only the near-end signal, which includes a near-end speech and a background noise in the return path.There are some difficulties in traditional echo cancellation methods as followed: (1) Because there is reverberation in the room, the impulse response of signal is very long. It ranges form several hundreds to few thousands of taps for AEC. (2) The extension of speech signal eigenvalue is extensive. Then it is difficult to ensure the convergence for the common adaptive algorithm. (3) The echo path is timevarying, which requires the good track performance. Traditional adaptive algorithms can't directly resolve many echo cancellation questions. LMS algorithm is simple and easy to be implemented, but it has slow convergence speed. And very high order filter will lead to error cumulation. Convergence properties of RLS algorithm are quite good, but its computational complexity is prodigious. In this paper, an adaptive method, which operates in subband signal with conjugate gradient algorithm for acoustic echo cancellation is proposed. Instead of using a very long filter, a subband structure using frequency division technology is presented. With the reduction of the sampling rate of subband signal, the length of filter is also lowered. So this proposed technique allows computational savings as well as better convergence behavior.1. Conjugate Gradient AlgorithmIn recent years, many adaptive filtering algorithms based on the conjugate gradient (CG) method of optimization have been reported. In these works several modifications have been proposed to improve the performance of the CG algorithm for various applications. The CG method can be applied to adaptive transversal filters. The objective is the solving of where is the correlation matrix of the input data vector , and is the cross-correlation vector between the input data and the desired response . Many adaptive filtering applications require the weight coefficients to be updated at each incoming data sample. Although, with previously developed CG algorithms, this can be done at the expense of running several iterations per sample. The proposed modifications allow the algorithm to run just one iteration per sample but still maintain performance comparable with RLS or LMS-Newton. One of the main difficulties of the RLS and LMS-Newton algorithms is the necessity to estimate . If the estimated loses the property of positive definiteness, that will cause the algorithm to diverge. This does not happen with the CG method since there is no need to compute the inverse of .The CG algorithm has many advantages such as the quick convergence speed and the simple computation. In CG algorithm, the correlation matrix of the input data vector can be obtained just by per iteration per sample. So we can improve Capon spectral estimate method by using the modified recursive calculation of inverse correlation matrix , which is developed in this paper. The simulation results show that the new method has the better performance than the general Capon spectral estimate method.2. Subband Adaptive Filter With the improvement of the multirate signal processing techniques, the application of multirate filer banks in echo cancellation is investigated. B...
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