Tensor-based techniques for the blind separation of DS-CDMA signals

In this paper we present new deterministic tensor-based techniques for the blind separation of a mixture of DS-CDMA signals received by an antenna array. First, we show that the blind receiver follows from a simultaneous matrix decomposition. We present a new, relaxed, bound on the number of users that can be allowed at the same time. We further derive two algorithms that jointly exploit the CDMA structure and the constant modulus property of the transmitted signals.

[1]  Eric Moulines,et al.  A blind source separation technique using second-order statistics , 1997, IEEE Trans. Signal Process..

[2]  Joos Vandewalle,et al.  Computation of the Canonical Decomposition by Means of a Simultaneous Generalized Schur Decomposition , 2005, SIAM J. Matrix Anal. Appl..

[3]  Nikos D. Sidiropoulos,et al.  Parallel factor analysis in sensor array processing , 2000, IEEE Trans. Signal Process..

[4]  Josef A. Nossek,et al.  Simultaneous Schur decomposition of several matrices to achieve automatic pairing in multidimensional harmonic retrieval problems , 1996, 1996 8th European Signal Processing Conference (EUSIPCO 1996).

[5]  J. Cardoso,et al.  Blind beamforming for non-gaussian signals , 1993 .

[6]  J. Kruskal Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics , 1977 .

[7]  Rasmus Bro,et al.  Multi-way Analysis with Applications in the Chemical Sciences , 2004 .

[8]  Dinh-Tuan Pham,et al.  Blind separation of instantaneous mixtures of nonstationary sources , 2001, IEEE Trans. Signal Process..

[9]  J. Chang,et al.  Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition , 1970 .

[10]  Arie Yeredor,et al.  Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separation , 2002, IEEE Trans. Signal Process..

[11]  N. Sidiropoulos,et al.  On the uniqueness of multilinear decomposition of N‐way arrays , 2000 .

[12]  Arogyaswami Paulraj,et al.  An analytical constant modulus algorithm , 1996, IEEE Trans. Signal Process..

[13]  Lieven De Lathauwer,et al.  A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization , 2006, SIAM J. Matrix Anal. Appl..

[14]  Richard A. Harshman,et al.  Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multi-model factor analysis , 1970 .

[15]  Gene H. Golub,et al.  Matrix computations , 1983 .

[16]  Joos Vandewalle,et al.  A Multilinear Singular Value Decomposition , 2000, SIAM J. Matrix Anal. Appl..

[17]  Nikos D. Sidiropoulos,et al.  Blind PARAFAC receivers for DS-CDMA systems , 2000, IEEE Trans. Signal Process..

[18]  Jean-Francois Cardoso,et al.  Super-symmetric decomposition of the fourth-order cumulant tensor. Blind identification of more sources than sensors , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[19]  A. V. D. Veen Algebraic methods for deterministic blind beamforming , 1998, Proc. IEEE.

[20]  Nikos D. Sidiropoulos,et al.  Khatri-Rao space-time codes , 2002, IEEE Trans. Signal Process..

[21]  Harold Gulliksen,et al.  Contributions to mathematical psychology , 1964 .

[22]  S. Leurgans,et al.  A Decomposition for Three-Way Arrays , 1993, SIAM J. Matrix Anal. Appl..

[23]  Nikos D. Sidiropoulos,et al.  Kruskal's permutation lemma and the identification of CANDECOMP/PARAFAC and bilinear models with constant modulus constraints , 2004, IEEE Transactions on Signal Processing.

[24]  Alle-Jan van der Veen Statistical performance analysis of the algebraic constant modulus algorithm , 2002, IEEE Trans. Signal Process..

[25]  H. Law Research methods for multimode data analysis , 1984 .

[26]  R. Cattell “Parallel proportional profiles” and other principles for determining the choice of factors by rotation , 1944 .