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Set-Membership Proportionate Affine Projection Algorithms

EURASIP Journal on Audio, Speech, and Music Processing volume 2007, Article number: 034242 (2007) Cite this article

Abstract

Proportionate adaptive filters can improve the convergence speed for the identification of sparse systems as compared to their conventional counterparts. In this paper, the idea of proportionate adaptation is combined with the framework of set-membership filtering (SMF) in an attempt to derive novel computationally efficient algorithms. The resulting algorithms attain an attractive faster converge for both situations of sparse and dispersive channels while decreasing the average computational complexity due to the data discerning feature of the SMF approach. In addition, we propose a rule that allows us to automatically adjust the number of past data pairs employed in the update. This leads to a set-membership proportionate affine projection algorithm (SM-PAPA) having a variable data-reuse factor allowing a significant reduction in the overall complexity when compared with a fixed data-reuse factor. Reduced-complexity implementations of the proposed algorithms are also considered that reduce the dimensions of the matrix inversions involved in the update. Simulations show good results in terms of reduced number of updates, speed of convergence, and final mean-squared error.

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References

  1. 1.

    Martin RK, Sethares WA, Williamson RC, Johnson CR Jr.: Exploiting sparsity in adaptive filters. IEEE Transactions on Signal Processing 2002,50(8):1883-1894. 10.1109/TSP.2002.800414

    Article  Google Scholar 

  2. 2.

    Duttweiler DL: Proportionate normalized least-mean-squares adaptation in echo cancelers. IEEE Transactions on Speech and Audio Processing 2000,8(5):508-518. 10.1109/89.861368

    Article  Google Scholar 

  3. 3.

    Gay SL: An efficient, fast converging adaptive filter for network echo cancellation. Proceedings of the 32nd Asilomar Conference on Signals, Systems & Computers, November 1998, Pacific Grove, Calif, USA 1: 394-398.

    Google Scholar 

  4. 4.

    Benesty J, Gay SL: An improved PNLMS algorithm. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '02), May 2002, Orlando, Fla, USA 2: 1881-1884.

    Google Scholar 

  5. 5.

    Rao BD, Song B: Adaptive filtering algorithms for promoting sparsity. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '03), April 2003, Hong Kong 6: 361-364.

    Google Scholar 

  6. 6.

    Khong AWH, Benesty J, Naylor PA: An improved proportionate multi-delay block adaptive filter for packet-switched network echo cancellation. Proceedings of the 13th European Signal Processing Conference (EUSIPCO '05), September 2005, Antalya, Turkey

    Google Scholar 

  7. 7.

    Doğançay K, Naylor P: Recent advances in partial update and sparse adaptive filters. Proceedings of the 13th European Signal Processing Conference (EUSIPCO '05), September 2005, Antalya, Turkey

    Google Scholar 

  8. 8.

    Deshpande A, Grant SL: A new multi-algorithm approach to sparse system adaptation. Proceedings of the 13th European Signal Processing Conference (EUSIPCO '05), September 2005, Antalya, Turkey

    Google Scholar 

  9. 9.

    Werner S, Apolinário JA Jr., Diniz PSR, Laakso TI: A set-membership approach to normalized proportionate adaptation algorithms. Proceedings of the 13th European Signal Processing Conference (EUSIPCO '05), September 2005, Antalya, Turkey

    Google Scholar 

  10. 10.

    Deng H, Doroslovăcki M: Proportionate adaptive algorithms for network echo cancellation. IEEE Transactions on Signal Processing 2006,54(5):1794-1803.

    Article  Google Scholar 

  11. 11.

    Tanrıkulu O, Doğançay K: Selective-partial-update normalized least-mean-square algorithm for network echo cancellation. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '02), May 2002, Orlando, Fla, USA 2: 1889-1892.

    Google Scholar 

  12. 12.

    Kivinen J, Warmuth MK: Exponentiated gradient versus gradient descent for linear predictors. Information and Computation 1997,132(1):1-63. 10.1006/inco.1996.2612

    MathSciNet  Article  MATH  Google Scholar 

  13. 13.

    Benesty J, Gänsler T, Morgan D, Sondhi M, Gay S (Eds): Advances in Network and Acoustic Echo Cancellation. Springer, Boston, Mass, USA; 2001.

    Google Scholar 

  14. 14.

    Hoshuyama O, Goubran RA, Sugiyama A: A generalized proportionate variable step-size algorithm for fast changing acoustic environments. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '04), May 2004, Montreal, Quebec, Canada 4: 161-164.

    Google Scholar 

  15. 15.

    Gollamudi S, Nagaraj S, Kapoor S, Huang Y-F: Set-membership filtering and a set-membership normalized LMS algorithm with an adaptive step size. IEEE Signal Processing Letters 1998,5(5):111-114. 10.1109/97.668945

    Article  Google Scholar 

  16. 16.

    Diniz PSR, Werner S: Set-membership binormalized data-reusing LMS algorithms. IEEE Transactions on Signal Processing 2003,51(1):124-134.

    MathSciNet  Google Scholar 

  17. 17.

    Werner S, Diniz PSR: Set-membership affine projection algorithm. IEEE Signal Processing Letters 2001,8(8):231-235. 10.1109/97.935739

    Article  Google Scholar 

  18. 18.

    Gollamudi S, Kapoor S, Nagaraj S, Huang Y-F: Set-membership adaptive equalization and an updator-shared implementation for multiple channel communications systems. IEEE Transactions on Signal Processing 1998,46(9):2372-2385. 10.1109/78.709523

    Article  Google Scholar 

  19. 19.

    Malipatil AV, Huang Y-F, Andra S, Bennett K: Kernelized set-membership approach to nonlinear adaptive filtering. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '05), March 2005, Philadelphia, Pa, USA 4: 149-152.

    Google Scholar 

  20. 20.

    Fogel E, Huang Y-F: On the value of information in system identification—bounded noise case. Automatica 1982,18(2):229-238. 10.1016/0005-1098(82)90110-8

    MathSciNet  Article  MATH  Google Scholar 

  21. 21.

    Dasgupta S, Huang Y-F: Asymptotically convergent modified recursive least-squares with data-dependent updating and forgetting factor for systems with bounded noise. IEEE Transactions on Information Theory 1987,33(3):383-392. 10.1109/TIT.1987.1057307

    Article  MATH  Google Scholar 

  22. 22.

    Deller JR Jr., Nayeri M, Liu MS: Unifying the Landmark developments in optimal bounding ellipsoid identification. International Journal of Adaptive Control and Signal Processing 1994,8(1):43-60. 10.1002/acs.4480080105

    MathSciNet  Article  MATH  Google Scholar 

  23. 23.

    Joachim D, Deller JR Jr.: Multiweight optimization in optimal bounding ellipsoid algorithms. IEEE Transactions on Signal Processing 2006,54(2):679-690.

    Article  Google Scholar 

  24. 24.

    Gollamudi S, Nagaraj S, Huang Y-F: Blind equalization with a deterministic constant modulus cost-a set-membership filtering approach. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '00), June 2000, Istanbul, Turkey 5: 2765-2768.

    Google Scholar 

  25. 25.

    Diniz PSR, Werner S: Set-membership binormalized data-reusing algorithms. Proceedings of the IFAC Symposium on System Identification (SYSID '00), June 2000, Santa Barbara, Calif, USA 3: 869-874.

    Google Scholar 

  26. 26.

    Werner S, de Campos MLR, Diniz PSR: Partial-update NLMS algorithms with data-selective updating. IEEE Transactions on Signal Processing 2004,52(4):938-949. 10.1109/TSP.2004.823483

    MathSciNet  Article  Google Scholar 

  27. 27.

    Werner S, Apolinário JA Jr., de Campos MLR, Diniz PSR: Low-complexity constrained affine-projection algorithms. IEEE Transactions on Signal Processing 2005,53(12):4545-4555.

    MathSciNet  Article  Google Scholar 

  28. 28.

    Nagaraj S, Gollamudi S, Kapoor S, Huang Y-F: BEACON: an adaptive set-membership filtering technique with sparse updates. IEEE Transactions on Signal Processing 1999,47(11):2928-2941. 10.1109/78.796429

    Article  Google Scholar 

  29. 29.

    Werner S, Diniz PSR, Moreira JEW: Set-membership affine projection algorithm with variable data-reuse factor. Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS '06), May 2006, Island of Kos, Greece 261-264.

    Google Scholar 

  30. 30.

    Rupp M: A family of adaptive filter algorithms with decorrelating properties. IEEE Transactions on Signal Processing 1998,46(3):771-775. 10.1109/78.661344

    Article  Google Scholar 

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Author information

Affiliations

  1. Signal Processing Laboratory, Helsinki University of Technology, Otakaari 5A, Espoo, 02150, Finland

    Stefan Werner

  2. Department of Electrical Engineering, Instituto Militar de Engenharia, Rio de Janeiro, 2229-270, Brazil

    José A Apolinário Jr.

  3. Signal Processing Laboratory, COPPE/Poli/Universidade Federal do Rio de Janeiro, Rio de Janeiro, 21945-970, Brazil

    Paulo S R Diniz

Authors
  1. Stefan Werner
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  2. José A Apolinário Jr.
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  3. Paulo S R Diniz
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Corresponding author

Correspondence to Stefan Werner.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Werner, S., Apolinário, J.A. & Diniz, P.S.R. Set-Membership Proportionate Affine Projection Algorithms. J AUDIO SPEECH MUSIC PROC. 2007, 034242 (2007). https://doi.org/10.1155/2007/34242

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Keywords

  • Acoustics
  • Convergence Speed
  • Adaptive Filter
  • Matrix Inversion
  • Projection Algorithm