Blind beamforming for non-gaussian signals

The paper considers an application of blind identification to beamforming. The key point is to use estimates of directional vectors rather than resort to their hypothesised value. By using estimates of the directional vectors obtained via blind identification, i.e. without knowing the array manifold, beamforming is made robust with respect to array deformations, distortion of the wave front, pointing errors etc., so that neither array calibration nor physical modelling is necessary. Rather suprisingly, ‘blind beamformers’ may outperform ‘informed beamformers’ in a plausible range of parameters, even when the array is perfectly known to the informed beamformer. The key assumption on which blind identification relies is the statistical independence of the sources, which is exploited using fourth-order cumulants. A computationally efficient technique is presented for the blind estimation of directional vectors, based on joint diagonalisation of fourth-order cumulant matrices; its implementation is described, and its performance is investigated by numerical experiments.

[1]  D. Godard,et al.  Self-Recovering Equalization and Carrier Tracking in Two-Dimensional Data Communication Systems , 1980, IEEE Trans. Commun..

[2]  D. Donoho.  ON MINIMUM ENTROPY DECONVOLUTION , 1981 .

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

[4]  Jutten,et al.  1 - Une solution neuromimétique au problème de séparation de sources , 1988 .

[5]  B.D. Van Veen,et al.  Beamforming: a versatile approach to spatial filtering , 1988, IEEE ASSP Magazine.

[6]  Jean-Francois Cardoso,et al.  Source separation using higher order moments , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[7]  J. Mendel,et al.  Cumulant based identification of multichannel moving-average models , 1989 .

[8]  Lang Tong,et al.  BLIND ESTIMATION OF CORRELATED SOURCE SIGNALS , 1990, 1990 Conference Record Twenty-Fourth Asilomar Conference on Signals, Systems and Computers, 1990..

[9]  R. Liu,et al.  An extended fourth order blind identification algorithm in spatially correlated noise , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[10]  Lang Tong,et al.  Indeterminacy and identifiability of blind identification , 1991 .

[11]  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.

[12]  Benjamin Friedlander,et al.  Direction finding algorithms based on high-order statistics , 1991, IEEE Trans. Signal Process..

[13]  Dinh Tuan Pham,et al.  Separation of a mixture of independent sources through a maximum likelihood approach , 1992 .

[14]  P. Comon.  Independent Component Analysis , 1992 .

[15]  R. Liu,et al.  A new eigenstructure-based parameter estimation of multichannel moving average processes , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[16]  J. Cardoso,et al.  Fourth-order cumulant structure forcing: application to blind array processing , 1992, [1992] IEEE Sixth SP Workshop on Statistical Signal and Array Processing.

[17]  Jean-Francois Cardoso,et al.  ITERATIVE TECHNIQUES FOR BLIND SOURCE SEPARATION USING ONLY FOURTH-ORDER CUMULANTS , 1992 .

[18]  Ehud Weinstein,et al.  New criteria for blind deconvolution of nonminimum phase systems (channels) , 1990, IEEE Trans. Inf. Theory.

[19]  Y. Bar-Ness,et al.  Bootstrap: a fast blind adaptive signal separator , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[20]  Georgios B. Giannakis,et al.  Modeling of non-Gaussian array data using cumulants: DOA estimation of more sources with less sensors , 1993, Signal Process..

[21]  Sylvie Mayrargue,et al.  Spatial equalization of a radio-mobile channel without beamforming using the constant modulus algorithm (CMA) , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[22]  Lang Tong,et al.  Waveform-preserving blind estimation of multiple independent sources , 1993, IEEE Trans. Signal Process..

[23]  P. Loubaton,et al.  Blind deconvolution of multivariate signals: A deflation approach , 1993, Proceedings of ICC '93 - IEEE International Conference on Communications.

[24]  Eric Moreau,et al.  New self-adaptative algorithms for source separation based on contrast functions , 1993, [1993 Proceedings] IEEE Signal Processing Workshop on Higher-Order Statistics.