Conditions on Blind Source Separability of Linear FIR-MIMO Systems with Binary Inputs

Authors: Jiashan Tang

Abstract:

In this note, we investigate the blind source separability of linear FIR-MIMO systems. The concept of semi-reversibility of a system is presented. It is shown that for a semi-reversible system, if the input signals belong to a binary alphabet, then the source data can be blindly separated. One sufficient condition for a system to be semi-reversible is obtained. It is also shown that the proposed criteria is weaker than that in the literature which requires that the channel matrix is irreducible/invertible or reversible.

Keywords: Blind source separable, FIR-MIMO system, Binary input, Bezout equality.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331433

References:

[1] J. Herault, C. Jutten, and B. Ans, Detection de grandeurs primitives dans un message composite par une architecture de calcul neuromimetique en apprentissage non supervise. in Porc. GRETSI, Nice, France, 1985, 1017-1020.
[2] J. M. Mendel, Tutorial on higher-order statistics (spectra) in Signal Processing and System Theorey: Theoretical Results and some Applications, Proceedings of the IEEE, Mar 1991, 79:277-305
[3] K. Abed-Meraim, W. Qiu and Y. Hua, Blind system identification. Proceeding of the IEEE, 1997, 85(8):1310-1322.
[4] L. Tong, G. Xu, and T. Kailath, New approach to blind identification and equalization of multipath channels. in Proc. 25th Asilomar Conf. Pacific. Grove, CA, 1991, 856-860.
[5] W. Gardner, A new method of channel identification. IEEE Trans. Commun. 1991, 39: 813-817.
[6] Z. Ding and Y. Li, Blind equalization and identification. Marcel Dekker, Inc. New York, 2001
[7] Y. Inouye, and R. W. Liu, A sysmtem-thoretic foundation for blind equalization of an FIR MIMO channel system. IEEE Trans. Circults and Systems. 2002, 49(4): 425-436
[8] R. W. Liu, Y. Inouye, and H. Luo, system-theoretic foundation for blind signal separation of MIMO-FIR convolutive mixtures - a review. Proc. 2nd Int. Workshop on Independent Component Analysis and Signal Separation, Helsinki, Finland, pp. 205-210, 2000.
[9] A. J. van der Veen, S. Talwar, and A. Paulraj, Blind identification of FIR channels carrying multiple finite alphabet signals. IEEE ICASSP-95, 1995, 1213-1216
[10] Z. Y. Zhang, and E. W. Bai, Direct blind sequence detection of SIMO channels with common zeros. Acta Electronica Sinica, 2005, 33(4): 671- 675