Blind MIMO paraunitary equalizer (original) (raw)
Related papers
On the Relationships between Blind Equalization and Blind Source Separation – Part I: Foundations
Journal of Communication and Information Systems, 2007
The objective of this two-part work is to present and discuss the relationships between the problems of blind equalization and blind source separation. Both tasks appear, at first sight, to be essentially distinct, since equalization theory was developed mainly under single-input / single-output (SISO) and single-input/ multiple-output (SIMO) models, whereas the very idea of source separation strongly suggests the need for considering models with multiple inputs and multiple outputs (MIMO). However, in this second part, equivalences between the Benveniste-Goursat-Ruget theorem and the approach to blind source separation based on maximum-likelihood, between the Shalvi-Weinstein techniques and the separation methods that employ kurtosis and, finally, between the Bussgang algorithms and the ICA tools built from concepts such as negentropy and nonlinear principal component analysis are indicated. Finally, some connections previously unexplored in the literature are presented that are derived from ideas such as that of temporality and that of considering the parallels existing between a two-stage (magnitude and phase) equalization procedure and the classical pair PCA / ICA.
On the Relationships between Blind Equalization and Blind Source Separation - Part II: Relationships
2007
The objective of this two-part work is to present and discuss the relationships between the problems of blind equalization and blind source separation. Both tasks appear, at first sight, to be essentially distinct, since equalization theory was developed mainly under single-input / single-output (SISO) and single-input/ multiple-output (SIMO) models, whereas the very idea of source separation strongly suggests the need for considering models with multiple inputs and multiple outputs (MIMO). However, in this second part, equivalences between the Benveniste-Goursat-Ruget theorem and the approach to blind source separation based on maximum-likelihood, between the Shalvi-Weinstein techniques and the separation methods that employ kurtosis and, finally, between the Bussgang algorithms and the ICA tools built from concepts such as negentropy and nonlinear principal component analysis are indicated. Finally, some connections previously unexplored in the literature are presented that are derived from ideas such as that of temporality and that of considering the parallels existing between a two-stage (magnitude and phase) equalization procedure and the classical pair PCA / ICA.
BLIND MIMO PARA-UNITARY EQUALIZATION
2004
LABORATOIRE I3S: Les Algorithmes / Euclide B -2000 route des Lucioles -B.P. 121 -06903 Sophia-Antipolis Cedex, France -Tél. (33) 492 942 701 -Télécopie : (33) 492 942 898 http://www.i3s.unice.fr/I3S/FR/
IEEE Transactions on Signal Processing, 1999
The algorithms of blind separation of sources, in the general case and for instantaneous mixtures, are based on high-order statistics; most of them use the fourth-order statistics. For an instantaneous mixture of only two sources, we proposed in an algorithm of blind separation of sources. The separation was achieved by minimizing the cross-cumulant (2x2) of the two output signals. The minimization of that cross-cumulant was achieved using a gradient algorithm. In this paper, we derive a new cost function which is more general than the first one, also based on the cross-cumulant (2x2) of the output signals. This new algorithm deals with Multiple Inputs and Multiple Outputs (MIMO) and uses a Levenberg-Marquardt method for the minimization of the cost function. The actual algorithm is very fast; the criterion convergence is attained in less than 50 iterations. In addition, it yields good results even in the case of about 300 signal samples. Good experimental results were obtained even with five stationary signals.
Blind paraunitary equalization
Signal Processing, 2009
In this paper a blind MIMO space-time equalizer is described, dedicated to convolutive mixtures when observations have been pre-whitened. Filters preserving space-time whiteness are paraunitary; a parameterization of such filters is proposed. Theoretical developments then lead to a numerical algorithm that sweeps all pairs of delayed outputs. This algorithm involves the solution of a polynomial system, whose coefficients depend on the output cumulants. Simulations and performance of the numerical algorithm are reported.
A General Theory of Closed-Form Estimators for Blind Source Separation
We present a general theory for the closed-form parametric estimation of the unitary mixing matrix after prewhitening in the blind separation of two source signals from two noiseless instantaneous linear mixtures. The proposed methodology is based on the algebraic formalism of bicomplex numbers and is able to treat both real and complex valued mixtures indiscriminately. Existing analytic methods are found as particular cases of the exposed unifying formulation. Simulations in a variety of separation scenarios --- even beyond the noiseless two-signal case --- compare, assess and validate the methods studied.
Multichannel Blind Separation of Sources Algorithm For Instantaneous Mixture
The algorithms of blind separation of sources, in the general case and for instantaneous mixtures, are based on high-order statistics; most of them use the fourth-order statistics. For an instantaneous mixture of only two sources, we proposed in an algorithm of blind separation of sources. The separation was achieved by minimizing the cross-cumulant (2x2) of the two output signals. The minimization of that cross-cumulant was achieved using a gradient algorithm. In this paper, we derive a new cost function which is more general than the first one, also based on the cross-cumulant (2x2) of the output signals. This new algorithm deals with Multiple Inputs and Multiple Outputs (MIMO) and uses a Levenberg-Marquardt method for the minimization of the cost function. The actual algorithm is very fast; the criterion convergence is attained in less than 50 iterations. In addition, it yields good results even in the case of about 300 signal samples. Good experimental results were obtained even with five stationary signals.
1998
A new algorithm for the instantaneous mixture of the blind separation of sources problem is derived. This algorithm deals with multi-input multi-output (MIMO) channels. The cost function proposed in this paper can be considered as an extension of that previously proposed by us for only two sources and two sensors. The cost function is based on the cross-cumulant 2×2 and it is minimized using the Levenberg-Marquardt method. Generally, algorithm convergence is attained in less than 50 iterations and the experimental results are satisfactory even with five stationary sources and two non-stationary sources
A Maximum Likelihood Approach to Nonlinear Convolutive Blind Source Separation
Independent Component Analysis and Blind Signal Separation, 2006
A novel learning algorithm for blind source separation of postnonlinear convolutive mixtures with non-stationary sources is proposed in this paper. The proposed mixture model characterizes both convolutive mixture and post-nonlinear distortions of the sources. A novel iterative technique based on Maximum Likelihood (ML) approach is developed where the Expectation-Maximization (EM) algorithm is generalized to estimate the parameters in the proposed model. The post-nonlinear distortion is estimated by using a set of polynomials. The sufficient statistics associated with the source signals are estimated in the E-step while in the M-step, the parameters are optimized by using these statistics. In general, the nonlinear maximization in the M-step is difficult to be formulated in a closed form. However, the use of polynomial as the nonlinearity estimator facilitates the M-step tractable and can be solved via linear equations.
A well-known fact in blind deconvolution is that if the unknown source signal is white (temporally) and the unknown channel filter is minimum phase, it is possible to determine the inverse filter (equalizer) by evaluating simply the power spectral density (PSD) of the received signal. For blind source separation, however, a similar special case, equivalent to the situation in blind deconvolution, is not reported. In this paper, we identify the special conditions for which the solution of the blind source separation problem can be identified using only second order statistics of the observed mixtures. In this special case, the equivalent of minimum phase channel turns out to be a symmetric mixing matrix, and the equivalent of temporally white input signal translates to uncorrelated source signals. A fast-converging and robust on-line blind source separation algorithm using a recently introduced principal components analysis (PCA) algorithm named SIPEX-G is also presented and its performance is evaluated in simulations of source separation.