Subband Affine Projection Algorithm for Acoustic Echo Cancellation System
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Research Article Subband Affine Projection Algorithm for Acoustic Echo Cancellation System Hun Choi and Hyeon-Deok Bae Department of Electronic Engineering, Chungbuk National University, 12 Gaeshin-Dong, Heungduk-Gu, Cheongju 361-763, South Korea Received 30 December 2005; Revised 14 April 2006; Accepted 18 May 2006 Recommended by Yuan-Pei Lin We present a new subband affine projection (SAP) algorithm for the adaptive acoustic echo cancellation with long echo path delay. Generally, the acoustic echo canceller suffers from the long echo path and large computational complexity. To solve this problem, the proposed algorithm combines merits of the affine projection (AP) algorithm and the subband filtering. Convergence speed of the proposed algorithm is improved by the signal-decorrelating property of the orthogonal subband filtering and the weight updating with the prewhitened input signal of the AP algorithm. Moreover, in the proposed algorithms, as applying the polyphase decomposition, the noble identity, and the critical decimation to subband the adaptive filter, the sufficiently decomposed SAP updates the weights of adaptive subfilters without a matrix inversion. Therefore, computational complexity of the proposed method is considerably reduced. In the SAP, the derived weight updating formula for the subband adaptive filter has a simple form as ever compared with the normalized least-mean-square (NLMS) algorithm. The efficiency of the proposed algorithm for the colored signal and speech signal was evaluated experimentally. Copyright © 2007 H. Choi and H.-D. Bae. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Adaptive filtering is essential for acoustic echo cancellation. Among the adaptive algorithms, least-mean-square (LMS) is the most popular algorithm for its simplicity and stability. However, when the input signal is highly correlated and the long-length adaptive filter is needed, the convergence speed of the LMS adaptive filter can be deteriorated seriously [1, 2]. To overcome this problem, the affine projection (AP) algorithm was proposed [3–11]. The improved performance of the AP algorithm is characterized by an updating-projection scheme of an adaptive filter on a P-dimensional data-related subspace. Since the input signal is prewhitened by this projection on an affine subspace, the convergence rate of the AP adaptive filter is improved. However, a large computational complexity is a major drawback for its implementation, because P-ordered AP adaptive filter is based on the data matrix that consists of the last P + 1 input vectors and it requires matrix inversion in weight updating. The orthogonal subband filtering (OSF) is an alternative method that can whiten the input signal [12–15]. The OSF can be considered a kind of projection operation. It is
similar in the view of decorrelating property to the affine projection scheme. Therefore,
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