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The time-frequency (TF) representations are used to introduce new methods for the underdetermined blind source separation (UBSS) of TF-nondisjoint nonstationary sources. The advantages of the new separation algorithms include a weaker assumption on the source 'sparseness' and an explicit treatment of the overlapping points using subspace projection, which has improved the performance.

The problem of estimating parameters of multicomponent polynomial-phase signals is addressed when impinging on a multisensor array. It is demonstrated that the use of a multisensor array allows the exploitation of spatial information and leads to the consideration of multiple filters with different observation equations.

The problem of joint direction of arrival and Doppler frequency estimation using an array in partially known additive noise is addressed. A specular reflection model with a radar cross-section fluctuating from one pulse repetition interval to another is considered.

Research was conducted to examine an efficient blind beamformer dedicated to the problem of interference mitigation in direct sequence spread spectrum (DSSS) communication systems by means of a two sensor array. The receiver is implemented in two different structures. One contains the blind beamformer followed by the spread spectrum demodulator. The other has a reversed cascading order where the spread spectrum demodulators are applied at both sensors. The performance of each structure is described based on the achieved signal-to-interference and noise ratio and the computational cost.

A new carrier tracking approach with guaranteed global convergence is presented based on the statistical independence of the real and imaginary parts of the emitted signal. Numerical simulations revealed satisfactory features and performance of the proposed approach. These characteristics allow the new technique to be applied in QAM modems for digital cable TV broadcasting requiring higher level modulation schemes.

A blind identification technique for temporally correlated sources based on a joint diagonalization of several covariance matrices is proposed. The technique capitalizes on the time coherence of the source signals. It allows the separation of Gaussian sources and is more robust due to its use of several covariances. Numerical experiments have proven the benefit of capitalizing on several covariance matrices in complex contexts.

We propose a new blind minimum mean square error (MMSE) equalization algorithm of noisy multichannel finite impulse response (FIR) systems, that relies only on second-order statistics. The proposed algorithm offers two important advantages: a low computational complexity and a relative robustness against channel order overestimation errors. Exploiting the fact that the columns of the equalizer matrix filter belong both to the signal subspace and to the kernel of truncated data covariance matrix, the proposed algorithm achieves blindly a direct estimation of the zero-delay MMSE equalizer parameters. We develop a two-step procedure to further improve the performance gain and control the equalization delay. An efficient fast adaptive implementation of our equalizer, based on the projection approximation and the shift invariance property of temporal data covariance matrix, is proposed for reducing the computational complexity from to , where is the number of emitted signals, the data vector length, and the dimension of the signal subspace. We then derive a statistical performance analysis to compare the equalization performance with that of the optimal MMSE equalizer. Finally, simulation results are provided to illustrate the effectiveness of the proposed blind equalization algorithm.

We examine the problem of blind separation of nonstationary sources in the underdetermined case, where there are more sources than sensors. Since time-frequency (TF) signal processing provides effective tools for dealing with nonstationary signals, we propose a new separation method that is based on time-frequency distributions (TFDs). The underlying assumption is that the original sources are disjoint in the time-frequency (TF) domain. The successful method recovers the sources by performing the following four main procedures. First, the spatial time-frequency distribution (STFD) matrices are computed from the observed mixtures. Next, the auto-source TF points are separated from cross-source TF points thanks to the special structure of these mixture STFD matrices. Then, the vectors that correspond to the selected auto-source points are clustered into different classes according to the spatial directions which differ among different sources; each class, now containing the auto-source points of only one source, gives an estimation of the TFD of this source. Finally, the source waveforms are recovered from their TFD estimates using TF synthesis. Simulated experiments indicate the success of the proposed algorithm in different scenarios. We also contribute with two other modified versions of the algorithm to better deal with auto-source point selection.

A method for solving blind source separation problems was developed based on a joint diagonalization of a combined set of spatial time-frequency (t-f) distribution (STFD) resulting from t-f distribution to a vector signal. The structure of the STFD resembled the data spatial correlation matrix commonly used in array signal processing. The technique permitted the separation of Gaussian sources with the same spectral forms but with different t-f localization features.

This paper considers the blind separation of nonstationary sources in the underdetermined case, when there are more sources than sensors. A general framework for this problem is to work on sources that are sparse in some signal representation do- main. Recently, two methods have been proposed with respect to the time-frequency (TF) domain. The first uses quadratic time-frequency distributions (TFDs) and a clustering approach, and the second uses a linear TFD. Both of these methods assume that the sources are disjoint in the TF domain; i.e., there is, at most, one source present at a point in the TF domain. In this paper, we relax this assumption by allowing the sources to be TF-nondisjoint to a certain extent. In particular, the number of sources present at a point is strictly less than the number of sensors. The separation can still be achieved due to subspace projection that allows us to identify the sources present and to estimate their corresponding TFD values. In particular, we propose two subspace-based algorithms for TF-nondisjoint sources: one uses quadratic TFDs and the other a linear TFD. Another contribution of this paper is a new estimation procedure for the mixing matrix. Finally, then numerical performance of the proposed methods are provided highlighting their performance gain compared to existing ones. [ABSTRACT FROM AUTHOR]