This paper considers an application of blind identification to beamforming. The key point is to use estimates of directional vectors rather than resorting to their hypothesized value. By using estimates of the directional vectors obtained via blind identification i.e. without knowing the arrray 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 modeling are necessary. Rather surprisingly, `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 blind identification relies on is the statistical independence of the sources, which we exploit using fourth-order cumulants. A computationally efficient technique is presented for the blind estimation of directional vectors, based on joint diagonalization of 4th-order cumulant matrices

Blind signal separation (BSS) and independent component analysis (ICA) are emerging techniques of array processing and data analysis, aiming at recovering unobserved signals or `sources' from observed mixtures (typically, the output of an array of sensors), exploiting only the assumption of mutual independence between the signals. The weakness of the assumptions makes it a powerful approach but requires to venture beyond familiar second order statistics. The objective of this paper is to review some of the approaches that have been recently developed to address this exciting problem, to show how they stem from basic principles and how they relate to each other.

Acoustic signals recorded simultaneously in a reverberant environment can be described as sums of differently convolved sources. The task of source separation is to identify the multiple channels and possibly to invert those in order to obtain estimates of the underlying sources. We tackle the problem by explicitly exploiting the nonstationarity of the acoustic sources. Changing cross-correlations at multiple times give a sufficient set of constraints for the unknown channels. A least squares optimization allows us to estimate a forward model, identifying thus the multi-path channel. In the same manner we can find an FIR backward model, which generates well separated model sources. Furthermore, for more than three channels we have sufficient conditions to estimate underlying additive sensor noise powers. We show good performance in real room environments and demonstrate the algorithm's utility for automatic speech recognition.

A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and matrix algorithms for use in multichannel /multipath problems. Using abstract algebra/group theoretic concepts, information theoretic principles, and the Bussgang property, methods of single channel filtering and source separation of multipath mixtures are merged into a general FIR matrix framework. Techniques developed for equalization may be applied to source separation and vice versa. Potential applications of these results lie in neural networks with feed-forward memory connections, wideband array processing, and in problems with a multi-input, multi-output network having channels between each source and sensor, such as source separation. Particular applications of FIR polynomial matrix alg...

This paper links the direct-sequence code-division multiple access (DS-CDMA) multiuser separation-equalization-detection problem to the parallel factor (PARAFAC) model, which is an analysis tool rooted in psychometrics and chemometrics. Exploiting this link, it derives a deterministic blind PARAFAC DS-CDMA receiver with performance close to nonblind minimum mean-squared error (MMSE). The proposed PARAFAC receiver capitalizes on code, spatial, and temporal diversity-combining, thereby supporting small sample sizes, more users than sensors, and/or less spreading than users. Interestingly, PARAFAC does not require knowledge of spreading codes, the specifics of multipath (interchip interference), DOA-calibration information, finite alphabet/constant modulus, or statistical independence/whiteness to recover the information-bearing signals. Instead, PARAFAC relies on a fundamental result regarding the uniqueness of low-rank three-way array decomposition due to Kruskal (and generalized herein to the complex-valued case) that guarantees identifiability of all relevant signals and propagation parameters. These and other issues are also demonstrated in pertinent simulation experiments.

"Blind source separation" is an array processing problem without a priori information (no array manifold). This model can be identified resorting to 4th-order cumulants only via the concept of 4th-order signal subspace (FOSS) which is defined as a matrix space. This idea leads to a "Blind MUSIC" approach where identification is achieved by looking for the (approximate) intersections between the FOSS and the manifold of 1D projection matrices. Pratical implementations of these ideas are discussed and illustrated with computer simulations.

. This paper presents a family of adaptive algorithms for the blind separation of independent signals. Source separation consists in recovering a set of independent signals from some linear mixtures of them, the coefficients of the mixtures being unknown. In the noiseless case, the `hardness' of the blind source separation problem does not depend on the mixing matrix (see the companion paper [1]). It is then reasonable to expect adaptive algorithms to exhibit convergence and stability properties that would also be independent of the mixing matrix. We show that this desirable uniform performance feature is simply achieved by considering `serial updating' of the separating matrix. Next, generalizing from the gradient of a standard cumulant-based contrast function, we present a family of adaptive algorithms called `PFS', based on the idea of serial updating. The stability condition and the theoretical asymptotic separation levels are given in closed form and, as expected, depend only on ...

Blind identification of spatial mixtures allows an array of sensors to implement source separation when the array manifold is unknown. A family of 4th-order cumulant-based criteria for blind source separation is introduced. These criteria involve a set of cumulant matrices, whose joint diagonalization is equivalent to criterion optimization. An efficient algorithm is described to this effect. Simulations on both real and synthetic signals show that source separation is achieved even at small sample size. 1 Introduction The problem of blind separation of sources is a typical HOS issue, since it amounts to identifying a linear system whose only output is observed. While much attention has been paid to the identification of convolutional mixtures, blind source separation concerns itself only with `spatial' mixtures. It is naturally targeted to narrow band array processing. Consider an array of m sensors receiving signals from n narrow band sources. The array output denoted x(t) is a m ...

Tensors appear more and more often in signal processing problems, and especially spatial processing, which typically involves multichannel modeling. Even if it is not always obvious that tensor algebra is the best framework to address a problem, there are cases where no choice is left. Blind identification of multichannel non monic MA models is given as an illustrating example of this claim.

In blind array processing, the array manifold is unknown but, under the signal independence assumption, the signal parameters can be estimated by resorting to higher-order information. We consider the 4th-order cumulant tensor and show that sample cumulant enhancement based on rank and symmetry properties yields cumulant estimates with the exact theoretical structure. Any identification procedure based on enhanced cumulants is then equivalent to cumulant matching, bypassing the need for initialization and optimization. 1. INTRODUCTION This paper deals with a linear data model where a m- dimensional complex vector x(t) is assumed to be the superposition of n linear components, possibly corrupted by additive noise. An observation can then be written as: x(t) = X p=1;n sp(t) ap +N(t) (1) where each sp(t) is a complex stationary scalar process, each ap is a deterministic m21 vector, and the m21 vector N(t) represents additive noise. This is the standard model in narrow band array p...