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This paper introduces a tensor framework to solve the problem of nonunitary joint block diagonalization (JBD) of a set of real or complex valued matrices. We show that JBD can be seen as a particular case of the block-component-decomposition (BCD) of a third-order tensor. The resulting tensor model fitting problem does not require the block-diagonalizer to be a square matrix: the over- and underdetermined cases can be handled. To compute the tensor decomposition, we build an efficient nonlinear conjugate gradient (NCG) algorithm. In the over- and exactly determined cases, we show that exact JBD can be computed by a closed-form solution based on eigenvalue analysis. In approximate JBD problems, this solution can be used to efficiently initialize any iterative JBD algorithm such as NCG. Finally, we illustrate the performance of our technique in the context of independent subspace analysis (ISA) based on second-order statistics (SOS). [ABSTRACT FROM PUBLISHER]

In this paper, a novel algorithm to blindly separate an instantaneous linear underdetermined mixture of nonstationary sources is proposed. It means that the number of sources exceeds the number of channels of the available data. The separation is based on the working assumption that the sources are piecewise stationary with a different variance in each block. It proceeds in two steps: 1) estimating the mixing matrix, and 2) computing the optimum beamformer in each block to maximize the signal-to-interference ratio of each separated signal with respect to the remaining signals. Estimating the mixing matrix is accomplished through a specialized tensor decomposition of the set of sample covariance matrices of the received mixture in each block. It utilizes optimum weighting, which allows statistically efficient (CRB attaining) estimation provided that the data obey the assumed Gaussian piecewise stationary model. In simulations, performance of the algorithm is successfully tested on blind separation of 16 speech signals from nine linear instantaneous mixtures of these signals. [ABSTRACT FROM AUTHOR]

Multidimensional vector cross-product has not been studied from the perspective of signal processing so far to the best of our knowledge and hence no effort has been made to develop any generalized algorithm for its hardware implementation. In this paper firstly, we identify the application domain of cross-product in signal processing and then introduce a novel recursive algorithm for generalized nD cross-product computation considering three dimensional (3D) cross-product as the fundamental operation. Subsequently a generalized scheme for architecture implementation for nD cross-product is proposed based on this algorithm. Secondly, we show that if 4D cross-product is used as the fundamental operation for formulating nD cross-product problem, then exploiting the inherent mathematical symmetry of 4D cross-product it is possible to reduce the total hardware cost of nD cross-product significantly at the architecture level (symmetry-based approach). Mathematical models for hardware complexity and operational delay have been formulated both for the generalized and symmetry-based approaches. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of source separation in the case when the observations result from a multiple-input multiple-output convolutive mixing system. In a blind framework, higher order contrast functions have been proved to be efficient for extracting sources. Inspired by a semiblind approach, we propose new contrast functions for blind signal separation that make use of reference signals. The main advantage of this approach consists in the quadratic form of these criteria: the extraction of one source hence reduces to a simple optimization task for which fast and efficient algorithms are available. The separation of the other sources from the mixture is then carried out by an iterative deflation method. Furthermore, these contrasts are shown to be valid for both independent identically distributed (i.i.d.) and non-i.i.d. source signals. The performance offered by these criteria is investigated through simulations: they appear as very appealing tools compared with some classical contrast functions. [ABSTRACT FROM AUTHOR]

In this paper, we develop a maximum-likelihood (ML) spatio--temporal blind source separation (BSS) algorithm, where the temporal dependencies are explained by assuming that each source is an autoregressive (AR) process and the distribution of the associated independent identically distributed (i.i.d.) innovations process is described using a mixture of Gaussians. Unlike most ML methods, the proposed algorithm takes into account both spatial and temporal information, optimization is performed using the expectation-maximization (EM) method, the source model is adapted to maximize the likelihood, and the update equations have a simple, analytical form. The proposed method, which we refer to as autoregressive mixture of Gaussians (AR-MOG), outperforms nine other methods for artificial mixtures of real audio. We also show results for using AR-MOG to extract the fetal cardiac signal from real magnetocardiographic (MCG) data. [ABSTRACT FROM AUTHOR]

Blind inversion of a linear and instantaneous mixture of source signals is a problem often encountered in many signal processing applications. Efficient fastICA (EFICA) offers an asymptotically optimal solution to this problem when all of the sources obey a generalized Gaussian distribution, at most one of them is Gaussian, and each is independent and identically distributed (i.i.d.) in time. Likewise, weights-adjusted second-order blind identification (WASOBI) is asymptotically optimal when all the sources are Gaussian and can be modeled as autoregressive (AR) processes with distinct spectra. Nevertheless, real-life mixtures are likely to, contain both Gaussian AR and non-Gaussian i.i.d. sources, rendering WASOBI and EFICA severely suboptimal. In this paper, we propose a novel scheme for combining the strengths of EFICA and WASOBI in order to deal with such hybrid mixtures. Simulations show that our approach outperforms competing algorithms designed for separating similar mixtures. [ABSTRACT FROM AUTHOR]

We consider the design and analysis of quantizers for equal gain transmission (EGT) systems with finite rate feedback-based communication in flat-fading multiple input single output (MISO) systems. EGT is a beamforming technique that maximizes the MISO channel capacity when there is an equal power-per-antenna constraint at the transmitter, and requires the feedback of t - 1 phase angles, when there are t antennas at the transmitter. In this paper, we contrast two popular approaches for quantizing the phase angles: vector quantization (VQ) and scalar quantization (SQ). On the VQ side, using the capacity loss with respect to EGT with perfect channel information at transmitter as performance metric, we develop a criterion for designing the beamforming codebook for quantized EGT (Q-EGT). We also propose an iterative algorithm based on the well-known generalized Lloyd algorithm, for computing the beamforming vector codebook. On the analytical side, we study the performance of Q-EGT and derive closed-form expressions for the performance in terms of capacity loss and outage probability in the case of i.i.d. Rayleigh flat-fading channels. On the SQ side, assuming uniform scalar quantization and i.i.d. Rayleigh flat-fading channels, we derive the high-resolution performance of quantized EGT and contrast the performance with that of VQ. We find that although both VQ and SQ achieve the same rate of convergence (to the capacity with perfect feedback) as the number of feedback bits B increases, there exists a fixed gap between the two. [ABSTRACT FROM AUTHOR]

While a pair of N \times N matrices can almost always be exactly and simultaneously diagonalized by a generalized eigendecomposition, no exact solution exists in the case of a set with more than two matrices. This problem, termed approximate joint diagonalization (AJD), is instrumental in blind signal processing. When the set of matrices to be jointly diagonalized includes at least N linearly independent matrices, we propose a suboptimal but closed-form solution for AJD in the direct least-squares sense. The corresponding non-iterative algorithm is given the acronym \DIEM (DIagonalization using Equivalent Matrices). Extensive numerical simulations show that \DIEM is both fast and accurate compared to the state-of-the-art iterative AJD algorithms. [ABSTRACT FROM PUBLISHER]

Blind identification of underdetermined mixtures can be addressed efficiently by using the second ChAracteristic Function (CAF) of the observations. Our contribution is twofold. First, we propose the use of a Levenberg-Marquardt algorithm, herein called LEMACAF, as an alternative to an Alternating Least Squares algorithm known as ALESCAF, which has been used recently in the case of real mixtures of real sources. Second, we extend the CAF approach to the case of complex sources for which the previous algorithms are not suitable. We show that the complex case involves an appropriate tensor stowage, which is linked to a particular tensor decomposition. An extension of the LEMACAF algorithm, called LEMACAF\BBC then proposed to blindly estimate the mixing matrix by exploiting this tensor decomposition. In our simulation results, we first provide performance comparisons between third- and fourth-order versions of ALESCAF and LEMACAF in various situations involving BPSK sources. Then, a performance study of LEMACAF\BBC is carried out considering 4-QAM sources. These results show that the proposed algorithm provides satisfying estimations especially in the case of a large underdeterminacy level. [ABSTRACT FROM AUTHOR]