Exploitation of source nonstationarity in underdetermined blind source separation with advanced clustering techniques

The problem of blind source separation (BSS) is investigated. Following the assumption that the time-frequency (TF) distributions of the input sources do not overlap, quadratic TF representation is used to exploit the sparsity of the statistically nonstationary sources. However, separation performance is shown to be limited by the selection of a certain threshold in classifying the eigenvectors of the TF matrices drawn from the observation mixtures. Two methods are, therefore, proposed based on recently introduced advanced clustering techniques, namely Gap statistics and self-splitting competitive learning (SSCL), to mitigate the problem of eigenvector classification. The novel integration of these two approaches successfully overcomes the problem of artificial sources induced by insufficient knowledge of the threshold and enables automatic determination of the number of active sources over the observation. The separation performance is thereby greatly improved. Practical consequences of violating the TF orthogonality assumption in the current approach are also studied, which motivates the proposal of a new solution robust to violation of orthogonality. In this new method, the TF plane is partitioned into appropriate blocks and source separation is thereby carried out in a block-by-block manner. Numerical experiments with linear chirp signals and Gaussian minimum shift keying (GMSK) signals are included which support the improved performance of the proposed approaches

One-stage blind source separation via a sparse autoencoder framework

Blind source separation (BSS) is the process of recovering individual source transmissions from a received mixture of co-channel signals without a priori knowledge of the channel mixing matrix or transmitted source signals. The received co-channel composite signal is considered to be captured across an antenna array or sensor network and is assumed to contain sparse transmissions, as users are active and inactive aperiodically over time. An unsupervised machine learning approach using an artificial feedforward neural network sparse autoencoder with one hidden layer is formulated for blindly recovering the channel matrix and source activity of co-channel transmissions. The BSS sparse autoencoder provides one-stage learning using the receive signal data only, which solves for the channel matrix and signal sources simultaneously. The recovered co-channel source signals are produced at the encoded output of the sparse autoencoder hidden layer. A complex-valued soft-threshold operator is used as the activation function at the hidden layer to preserve the ordered pairs of real and imaginary components. Once the weights of the sparse autoencoder are learned, the latent signals are recovered at the hidden layer without requiring any additional optimization steps. The generalization performance on future received data demonstrates the ability to recover signal transmissions on untrained data and outperform the two-stage BSS process

A modified underdetermined blind source separation algorithm using competitive learning

The problem of underdetermined blind source separation is addressed. An advanced classification method based upon competitive learning is proposed for automatically determining the number of active sources over the observation. Its introduction in underdetermined blind source separation successfully overcomes the drawback of an existing method, in which the goal of separating more sources than the number of available mixtures is achieved by exploiting the sparsity of the non-stationary sources in the time-frequency domain. Simulation studies are presented to support the proposed approach

Sub-Nyquist optical pulse sampling for photonic blind source separation

We propose and experimentally demonstrate an optical pulse sampling method for photonic blind source separation. The photonic system processes and separates wideband signals based on the statistical information of the mixed signals, and thus the sampling frequency can be orders of magnitude lower than the bandwidth of the signals. The ultra-fast optical pulses collect samples of the signals at very low sampling rates, and each sample is short enough to maintain the statistical properties of the signals. The low sampling frequency reduces the workloads of the analog to digital conversion and digital signal processing systems. In the meantime, the short pulse sampling maintains the accuracy of the sampled signals, so the statistical properties of the under-sampled signals are the same as the statistical properties of the original signals. The linear power range measurement shows that the sampling system with ultra-narrow optical pulse achieves a 30dB power dynamic range

Sub-Nyquist optical pulse sampling for photonic blind source separation

We propose and experimentally demonstrate an optical pulse sampling method for photonic blind source separation. The photonic system processes and separates wideband signals based on the statistical information of the mixed signals, and thus the sampling frequency can be orders of magnitude lower than the bandwidth of the signals. The ultra-fast optical pulses collect samples of the signals at very low sampling rates, and each sample is short enough to maintain the statistical properties of the signals. The low sampling frequency reduces the workloads of the analog to digital conversion and digital signal processing systems. In the meantime, the short pulse sampling maintains the accuracy of the sampled signals, so the statistical properties of the under-sampled signals are the same as the statistical properties of the original signals. The linear power range measurement shows that the sampling system with ultra-narrow optical pulse achieves a 30dB power dynamic range

Array processing based on time-frequency analysis and higher-order statistics

Ph.DDOCTOR OF PHILOSOPH

A unified approach to sparse signal processing

A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common potential benefits of significant reduction in sampling rate and processing manipulations through sparse signal processing are revealed. The key application domains of sparse signal processing are sampling, coding, spectral estimation, array processing, compo-nent analysis, and multipath channel estimation. In terms of the sampling process and reconstruction algorithms, linkages are made with random sampling, compressed sensing and rate of innovation. The redundancy introduced by channel coding i

Spatial Parameter Identification for MIMO Systems in the Presence of Non-Gaussian Interference

Reliable identification of spatial parameters for multiple-input multiple-output (MIMO) systems, such as the number of transmit antennas (NTA) and the direction of arrival (DOA), is a prerequisite for MIMO signal separation and detection. Most existing parameter estimation methods for MIMO systems only consider a single parameter in Gaussian noise. This paper develops a reliable identification scheme based on generalized multi-antenna time-frequency distribution (GMTFD) for MIMO systems with non-Gaussian interference and Gaussian noise. First, a new generalized correlation matrix is introduced to construct a generalized MTFD matrix. Then, the covariance matrix based on time-frequency distribution (CM-TF) is characterized by using the diagonal entries from the auto-source signal components and the non-diagonal entries from the cross-source signal components in the generalized MTFD matrix. Finally, by making use of the CM-TF, the Gerschgorin disk criterion is modified to estimate NTA, and the multiple signal classification (MUSIC) is exploited to estimate DOA for MIMO system. Simulation results indicate that the proposed scheme based on GMTFD has good robustness to non-Gaussian interference without prior information and that it can achieve high estimation accuracy and resolution at low and medium signal-to-noise ratios (SNRs)