Wavelet-Based MPNLMS Adaptive Algorithm for Network Echo Cancellation
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Research Article Wavelet-Based MPNLMS Adaptive Algorithm for Network Echo Cancellation Hongyang Deng1 and Miloˇs Doroslovaˇcki2 1 Freescale
Semiconductor, 7700 W. Parmer Lane, Austin, TX 78729, USA of Electrical and Computer Engineering, The George Washington University, 801 22nd Street, N.W. Washington, DC 20052, USA
2 Department
Received 30 June 2006; Revised 23 December 2006; Accepted 24 January 2007 Recommended by Patrick A. Naylor The μ-law proportionate normalized least mean square (MPNLMS) algorithm has been proposed recently to solve the slow convergence problem of the proportionate normalized least mean square (PNLMS) algorithm after its initial fast converging period. But for the color input, it may become slow in the case of the big eigenvalue spread of the input signal’s autocorrelation matrix. In this paper, we use the wavelet transform to whiten the input signal. Due to the good time-frequency localization property of the wavelet transform, a sparse impulse response in the time domain is also sparse in the wavelet domain. By applying the MPNLMS technique in the wavelet domain, fast convergence for the color input is observed. Furthermore, we show that some nonsparse impulse responses may become sparse in the wavelet domain. This motivates the usage of the wavelet-based MPNLMS algorithm. Advantages of this approach are documented. Copyright © 2007 H. Deng and M. Doroslovaˇcki. 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.
1.
INTRODUCTION
With the development of packet-switching networks and wireless networks, the introduced delay of the echo path increases dramatically, thus entailing a longer adaptive filter. It is well known that long adaptive filter will cause two problems: slow convergence and high computational complexity. Therefore, we need to design new algorithms to speed up the convergence with reasonable computational burden. Network echo path is sparse in nature. Although the number of coefficients of its impulse response is big, only a small portion has significant values (active coefficients). Others are just zero or unnoticeably small (inactive coefficients). Several algorithms have been proposed to take advantage of the sparseness of the impulse response to achieve faster convergence, lower computational complexity, or both. One of the most popular algorithms is the proportionate normalized least mean square (PNLMS) algorithm [1, 2]. The main idea is assigning different step-size parameters to different coefficients based on their previously estimated magnitudes. The bigger the magnitude, the bigger step-size parameter will be assigned. For a sparse impulse response, most of the coefficients are zero, so most of the update emphasis
concentrates on the big coefficients, thus increasing the convergence speed. The PNLMS algorithm, as demonstrated by several simulations, has very fast initial convergence for sparse impulse response
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