Distribution Of Sample Covariance Matrix Research Articles

Nonnegative block-sparse Bayesian learning algorithm for EEG brain source localization

Localizing electrical sources on the cortex surface from scalp recorded electroencephalogram (EEG) is challenging, due to ill-posed problem, noises/artifacts contamination, etc. Applying sparse Bayesian learning (SBL) in this field can automatically give sparse solution to ill-posed problem, while most of the SBL-based algorithms require precise or estimated version of noise statistics information. As EEG signals are more likely to stem from locally synchronized neural masses, modeling source block-sparsity on the cortex surface would bring benefits. In this paper, we develop an EEG brain source localization algorithm in SBL framework, with innovative modeling at sensor level as well as source level. For sensor-level modeling, the distribution of sample covariance matrix of multi-electrode measurements is considered, to circumvent the requirement of noise covariance matrix information. The innovation of source-level modeling is that, with block-sparsity prior used, the block-sparse signal reconstruction problem is transformed to an atom-sparse one, in which variance parameters of brain regions are to be estimated. As these parameters are nonnegative, their priors are modeled by nonnegative Gaussian, which was neglected by previous studies, and ultimately a nonnegative block-SBL (NNBSBL) algorithm is proposed in expectation–maximization (EM) approach. Simulations demonstrate that the proposed NNBSBL algorithm has excellent performance in variations of source number, source locations, homoscedastic/heteroscedastic noises, signal-to-noise ratio (SNR), and number of samples, compared to benchmark and state-of-the-art algorithms. The performance of the proposed algorithm is also evaluated through real P300 EEG data, which is proved consistent with the conclusions of P300 source locations in literature.

Information divergence‐based low probability of intercept waveform detection for multi‐antenna intercept receivers

Based on the asymptotic spectral distribution of sample covariance matrix, a new low probability of interception (LPI) signal detection method for multi-antenna intercept receiver is proposed via reforming the noise sequence into a Wishart matrix. The authors deduce the asymptotic cumulative distribution function (CDF) of eigenvalues of sample covariance matrix. Also a numerical Kullback–Leibler divergence of the empirical spectral CDF based on test samples from the deduced asymptotic CDF is established, which is treated as the test statistic. By comparing with other signal detection methods, simulation results show the new LPI signal detection method is superior and robust.

A robust reduced-rank monopulse algorithm based on variable-loaded MWF with spatial blocking broadening and automatic rank selection

For antenna array with large number of elements, the multistage Wiener filter (MWF) is an efficient method to perform reduced-rank beamforming. Similar to the generalized sidelobe canceller (GSC), MWF is also sensitive to direction of arrival (DOA) mismatch of the signal of interest (SOI). This condition limits the application of MWF to monopulse beamforming, in which the actual DOA of SOI may mismatch the assumed direction (i.e. the pattern look direction) due to target movement and platform disturbance. In this paper, we develop a variable-loaded multistage Wiener filter with spatial blocking broadening and automatic rank selection (VLSRS-MWF) to perform robust reduced-rank monopulse beamforming. Firstly, a null-broadened spatial blocking matrix which can be used for both the sum and difference beams is developed instead of the derivative constraints and the eigenvector constraints based blocking matrices. Secondly, a l2-norm regularization method is incorporated with MWF to further improve the output signal to noise ratio and to restrict the pattern sidelobe level. Then a Ritz value criterion with deterministic threshold for selecting the rank of the reduced-rank subspace is developed utilizing the eigenvalue distribution of sample covariance matrix and the Ritz value criterion. Simulation results show that the proposed VLSRS-MWF based monopulse algorithm can maintain good robustness and high angle estimation accuracy in presence of DOA mismatch.