Adaptive sparse system identification using wavelets

This paper proposes the use of wavelets for the identification of an unknown sparse system whose impulse response (IR) is rich in spectral content. The superior time localization property of wavelets allows for the identification and subsequent adaptation of only the nonzero IR regions, resulting in lower complexity and faster convergence speed. An added advantage of using wavelets is their ability to partially decorrelate the input, thereby further increasing convergence speed. Good time localization of nonzero IR regions requires high temporal resolution while good decorrelation of the input requires high spectral resolution. To this end we also propose the use of biorthogonal wavelets which fulfil both of these two requirements to provide additional gain in performance. The paper begins with the development of the wavelet-basis (WB) algorithm for sparse system identification. The WB algorithm uses the wavelet decomposition at a single scale to identify the nonzero IR regions and subsequently determines the wavelet coefficients of the unknown sparse system at other scale levels that require adaptation as well. A special implementation of the WB algorithm, the successive-selection wavelet-basis (SSWB), is then introduced to further improve performance when certain a priori knowledge of the sparse IR is available. The superior performance of the proposed methods is corroborated through simulations.

[1]  Milos Doroslovacki,et al.  On-line identification of echo-path impulse responses by Haar-wavelet-based adaptive filter , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[2]  Delores M. Etter,et al.  Analysis of an adaptive technique for modeling sparse systems , 1989, IEEE Trans. Acoust. Speech Signal Process..

[3]  Delores M. Etter,et al.  System modeling using an adaptive delay filter , 1987 .

[4]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[5]  D. Etter,et al.  An adaptive technique for multiple echo cancelation in telephone networks , 1987, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[6]  Delores M. Etter,et al.  Multiple short-length adaptive filters for time-varying echo cancellations , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[7]  Neil J. Bershad,et al.  On the probability density function of the LMS adaptive filter weights , 1989, IEEE Trans. Acoust. Speech Signal Process..

[8]  Delores M. Etter,et al.  An adaptive multiple echo canceller for slowly time-varying echo paths , 1990, IEEE Trans. Commun..

[9]  M. Hatori,et al.  A TAP selection algorithm for adaptive filters , 1986, ICASSP '86. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[10]  Shannon D. Blunt,et al.  Enhanced adaptive sparse algorithms using the Haar wavelet , 2002, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).

[11]  John Homer,et al.  Detection guided NLMS estimation of sparsely parametrized channels , 2000 .

[12]  Shannon D. Blunt,et al.  Novel sparse adaptive algorithm in the Haar transform domain , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[13]  Truong Q. Nguyen,et al.  Wavelets and filter banks , 1996 .

[14]  Srinath Hosur,et al.  Wavelet transform domain adaptive FIR filtering , 1997, IEEE Trans. Signal Process..

[15]  T. Moon,et al.  Mathematical Methods and Algorithms for Signal Processing , 1999 .

[16]  Donald L. Duttweiler,et al.  Proportionate normalized least-mean-squares adaptation in echo cancelers , 2000, IEEE Trans. Speech Audio Process..

[17]  Simon Haykin,et al.  Adaptive filter theory (2nd ed.) , 1991 .

[18]  Iven M. Y. Mareels,et al.  LMS estimation via structural detection , 1998, IEEE Trans. Signal Process..