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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.

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]