Abstract
This paper reviews the basic identifiability conditions and identification methods for blind system identification. This review focuses on the exploitation of the second-order statistics of the system output. The blind methods vary significantly according to the categories of the systems: i.e., single-input, single-output (SISO) systems, single-input, multiple-output (SIMO) systems, or multiple-input, multiple-output (MIMO) systems. For SISO systems, the blind methods require white input and minimum phase frequency response. For SIMO systems, the blind methods can generally yield the exact identification up to a scalar using a finite set of data. For MIMO systems, the blind identifiability conditions and the blind methods are much more involved.
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K. Abed-Meraim, W. Qiu and Y. Hua, Blind system identification,Proc. IEEE, vol.85, no. 8, pp. 1310–1322, August 1997.
S.-I. Amari, and A. Cichocki, Adaptive blind signal processing—neural network approaches,Proc. IEEE, vol. 86, no. 10, pp. 2026–2048, October 1998.
A. Belouchrani, K. Abed-Meraim, J.-F. Cardoso, and E. Moulines, A blind source separation technique using second-order statistics,IEEE Trans. Signal Process., vol.45, no. 2, pp. 434–443, February 1997.
J. A. Cadzow, Blind deconvolution via cumulant extrema,IEEE Signal Process. Magazine, vol. 13, no. 3, pp. 24–42, May 1996.
J.-F. Cardoso, Blind signal separation: Statistical principles,Proc. IEEE, vol. 86, no. 10, pp. 2009–2025, October 1998.
A. Gorokhov, and P. Loubaton, Subspace-based techniques for blind separation of convolutive mixtures with temporally correlated sources,IEEE Trans. Circuits and Systems-I, vol. 44, no. 9, pp. 813–820, September 1997.
E. J. Hannan, and M. Deistler,The Statistical Theory of Linear Systems, John Wiley, New York, 1988.
Y. Hua, Fast maximum likelihood for blind identification of multiple FIR channels,IEEE Trans. Signal Process., vol. 44, no. 3, pp. 661–672, March 1996.
Y. Hua, and K. Abed-Meraim, Techniques of eigenvalues estimation and association,Digital Signal Processing, Academic Press, San Diego, CA, vol. 7, no. 4, pp. 253–259, October 1997.
Y. Hua, S. An and Y. Xiang, Blind identification and equalization of FIR MIMO channels by BIDS,IEEE International Conference on Acoustic, Speech, and Signal Processing, Salt Lake City, UT, May 2001.
Y. Hua, S. An, and Y. Xiang, Blind identification and equalization of FIR MIMO channels driven by colored signals,IEEE Trans. Signal Process., submitted September 2000.
Y. Hua, and T. K. Sarkar, Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise,IEEE Trans. Acoust., Speech, Signal Process., vol.38, no. 5, pp. 814–824, May 1990.
Y. Hua and J. Tugnaif, Blind identifiability of FIR-MIMO systems with colored input using second order statistics,IEEE Signal Process. Lett., vol. 7, no. 7, pp. 348–350, December 2000.
Y. Hua, Y. Xiang, and K. Abed-Meraim, Blind identification of colored signals distorted by FIR channels,Proc. of IEEE ICASSP'2000, Istanbul, Turkey, June 2000.
Y. Hua, X. Xiang, T. Chen, K. Abed-Meraim, and Y. Miao, A new look at the power method for fast subspace tracking,Digital Signal Processing, vol. 9, no. 4, pp. 297–314, Academic Press, October 1999.
T. Kailath,Linear Systems, Prentice-Hall, Englewood Cliffs, NJ, 1980.
R. Liu and L. Tong, eds., Special issue on blind identification,Proc. IEEE, October 1998.
T. Ma, Z. Ding, and S. F. Yau, A two stage algorithm for MIMO blind deconvolution of colored input signals,IEEE Trans. Signal Process., vol. 48, no. 4, April 2000.
E. Moulines, P. Duhamel, J. Cardoso, and S. Mayrargue, Subspace methods for blind identification of multichannel FIR filters,IEEE Trans. Signal Process., vol. 43, no. 2, pp. 516–525, February 1995.
W. Qiu, Y. Hua, and K. Abed-Meraim, A subspace method for the computation of the GCD of polynomials,Automatica, vol. 33, no. 4, pp. 741–743, April 1997.
L. Tong, R.-W. Liu, V. C. Soon, and Y.-F. Huang, Indeterminacy and identifiability of blind identification,IEEE Trans. Circuits and Systems, vol. 38, no. 5, pp. 499–509, May 1991.
L. Tong and S. Perreau, Multichannel blind identification: from subspace to maximum likelihood methods,Proc. IEEE, vol. 86, no. 10, pp. 1951–1968, October 1998.
J. Tugnait and B. Huang, On a whitening approach to partial channel estimation and blind equalization of FIR/IIR multiple-input multiple-output channels,IEEE Trans. Signal Process., vol. 48, no. 3, March 2000.
B. D. Van Veen, and K. M. Buckley, Beamforming: a versatile approach to spatial filtering,IEEE Signal Process. Magazine, vol. 5, pp. 4–24, April 1988.
Y. Xiang, K. Abed-Meraim, and Y. Hua, Adaptive blind source separation by second order statistics and natural gradient,IEEE ICASSP'99, Phoenix, AZ, March 1999.
G. Xu, H. Liu, L. Tong, and T. Kailath, A least-square approach to blind channel identification,IEEE Trans. Signal Process., vol. 43, no. 12, pp. 2982–2993, December 1995.
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Hua, Y. Blind methods of system identification. Circuits Systems and Signal Process 21, 91–108 (2002). https://doi.org/10.1007/BF01211654
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DOI: https://doi.org/10.1007/BF01211654