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Blind Deconvolution in Nonminimum Phase Systems Using Cascade Structure


We introduce a novel cascade demixing structure for multichannel blind deconvolution in nonminimum phase systems. To simplify the learning process, we decompose the demixing model into a causal finite impulse response (FIR) filter and an anticausal scalar FIR filter. A permutable cascade structure is constructed by two subfilters. After discussing geometrical structure of FIR filter manifold, we develop the natural gradient algorithms for both FIR subfilters. Furthermore, we derive the stability conditions of algorithms using the permutable characteristic of the cascade structure. Finally, computer simulations are provided to show good learning performance of the proposed method.


  1. 1.

    Amari S: Natural gradient works efficiently in learning. Neural Computation 1998,10(2):251–276. 10.1162/089976698300017746

    Article  Google Scholar 

  2. 2.

    Bell AJ, Sejnowski TJ: An information-maximization approach to blind separation and blind deconvolution. Neural Computation 1995,7(6):1129–1159. 10.1162/neco.1995.7.6.1129

    Article  Google Scholar 

  3. 3.

    Cardoso J-F, Laheld B: Equivariant adaptive source separation. IEEE Transactions on Signal Processing 1996,44(12):3017–3030. 10.1109/78.553476

    Article  Google Scholar 

  4. 4.

    Comon P: Independent component analysis: a new concept? Signal Processing 1994,36(3):287–314. 10.1016/0165-1684(94)90029-9

    Article  Google Scholar 

  5. 5.

    Amari S, Douglas S, Cichocki A, Yang H: Novel on-line algorithms for blind deconvolution using natural gradient approach. Proceedings of the 11th IFAC Symposium on System Identification (SYSID '97), July 1997, Kitakyushu, Japan 1057–1062.

    Google Scholar 

  6. 6.

    Bellini S: Bussgang techniques for blind equalization. Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '86), December 1986, Houston, Tex, USA 1634–1640.

    Google Scholar 

  7. 7.

    Benveniste A, Goursat M, Ruget G: Robust identification of a nonminimum phase system: blind adjustment of a linear equalizer in data communications. IEEE Transactions on Automatic Control 1980,25(3):385–399. 10.1109/TAC.1980.1102343

    MathSciNet  Article  Google Scholar 

  8. 8.

    Godard DN: Self-recovering equalization and carrier tracking in two-dimensional data communication systems. IEEE Transactions on Communications Systems 1980,28(11):1867–1875. 10.1109/TCOM.1980.1094608

    Article  Google Scholar 

  9. 9.

    Hua Y: Fast maximum likelihood for blind identification of multiple FIR channels. IEEE Transactions on Signal Processing 1996,44(3):661–672. 10.1109/78.489039

    Article  Google Scholar 

  10. 10.

    Shalvi O, Weinstein E: New criteria for blind deconvolution of nonminimum phase systems (channels). IEEE Transactions on Information Theory 1990,36(2):312–321. 10.1109/18.52478

    Article  Google Scholar 

  11. 11.

    Tong L, Xu G, Kailath T: Blind identification and equalization based on second-order statistics: a time domain approach. IEEE Transactions on Information Theory 1994,40(2):340–349. 10.1109/18.312157

    Article  Google Scholar 

  12. 12.

    Tugnait JK: Channel estimation and equalization using high-order statistics. In Signal Processing Advances in Wireless and Mobile Communications. Volume 1. Edited by: Giannakis GB, Hua Y, Stoica P, Tong L. Prentice-Hall, Upper Saddle River, NJ, USA; 2000:1–40.

    Google Scholar 

  13. 13.

    Tugnait JK, Huang B: Multistep linear predictors-based blind identification and equalization of multiple-input multiple-output channels. IEEE Transactions on Signal Processing 2000,48(1):26–38. 10.1109/78.815476

    Article  Google Scholar 

  14. 14.

    Li Y, Cichocki A, Zhang L: Blind source estimation of FIR channels for binary sources: a grouping decision approach. Signal Processing 2004,84(12):2245–2263. 10.1016/j.sigpro.2004.07.020

    Article  Google Scholar 

  15. 15.

    Amari S, Cichocki A, Yang HH: A new learning algorithm for blind signal separation. In Advances in Neural Information Processing Systems. Vol. 8 (NIPS '95). Edited by: Touretzky DS, Mozer MC, Hasselmo ME. MIT Press, Cambridge, Mass, USA; 1996:757–763.

    Google Scholar 

  16. 16.

    Douglas SC: Simplified plant estimation for multichannel active noise control. Proceedings of 18th International Congress on Acoustics (ICA '04), April 2004, Kyoto, Japan

    Google Scholar 

  17. 17.

    Labat J, Macchi O, Laot C: Adaptive decision feedback equalization: can you skip the training period? IEEE Transactions on Communications 1998,46(7):921–930. 10.1109/26.701319

    Article  Google Scholar 

  18. 18.

    Zhang L-Q, Cichocki A, Amari S: Multichannel blind deconvolution of nonminimum phase systems using information backpropagation. Proceedings of the 6th International Conference on Neural Information Processing (ICONIP '99), November 1999, Perth, Australia 210–216.

    Google Scholar 

  19. 19.

    Waheed K, Salam FM: Cascaded structures for blind source recovery. Proceedings of the 45th IEEE International Midwest Symposium on Circuits and Systems (MSCAS '02), August 2002, Tulsa, Okla, USA 3: 656–659.

    Google Scholar 

  20. 20.

    Zhang L-Q, Cichocki A, Amari S: Multichannel blind deconvolution of nonminimum-phase systems using filter decomposition. IEEE Transactions on Signal Processing 2004,52(5):1430–1442. 10.1109/TSP.2004.826185

    MathSciNet  Article  Google Scholar 

  21. 21.

    Hyvärinen A, Karhunen J, Oja E: Independent Component Analysis. John Wiley & Sons, New York, NY, USA; 2001.

    Google Scholar 

  22. 22.

    Haykin S: Unsupervised Adaptive Filtering, Volume 2: Blind Deconvolution. John Wiley & Sons, New York, NY, USA; 2000.

    Google Scholar 

  23. 23.

    Nandi AK, Anfinsen SN: Blind equalization with recursive filter structures. Signal Processing 2000,80(10):2151–2167. 10.1016/S0165-1684(00)00074-8

    Article  Google Scholar 

  24. 24.

    Amari S, Douglas SC, Cichocki A, Yang HH: Multichannel blind deconvolution and equalization using the natural gradient. Proceedings of the 1st IEEE Signal Processing Workshop on Signal Processing Advances in Wireless Communications (SPAWC '97), April 1997, Paris, France 101–104.

    Google Scholar 

  25. 25.

    Pham DT: Mutual information approach to blind separation of stationary sources. IEEE Transactions on Information Theory 2002,48(7):1935–1946. 10.1109/TIT.2002.1013134

    MathSciNet  Article  Google Scholar 

  26. 26.

    Amari S, Chen T-P, Cichocki A: Stability analysis of learning algorithms for blind source separation. Neural Networks 1997,10(8):1345–1351. 10.1016/S0893-6080(97)00039-7

    Article  Google Scholar 

  27. 27.

    Zhang L-Q, Cichocki A, Amari S: Geometrical structures of FIR manifold and multichannel blind deconvolution. The Journal of VLSI Signal Processing 2002,31(1):31–44. 10.1023/A:1014441120905

    Article  Google Scholar 

  28. 28.

    Inouye Y, Ohno S: Adaptive algorithms for implementing the single-stage criterion for multichannel blind deconvolution. Proceedings of the 5th International Conference on Neural Information Processing (ICONIP '98), October 1998, Kitakyushu, Japan 733–736.

    Google Scholar 

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Correspondence to Bin Xia.

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Xia, B., Zhang, L. Blind Deconvolution in Nonminimum Phase Systems Using Cascade Structure. EURASIP J. Adv. Signal Process. 2007, 048432 (2006).

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  • Manifold
  • Computer Simulation
  • Learning Process
  • Deconvolution
  • Quantum Information