Wideband DOA Estimation via Sparse Bayesian Learning over a Khatri-Rao Dictionary

This paper deals with the wideband direction-of-arrival (DOA) estimation by exploiting the multiple measurement vectors (MMV) based sparse Bayesian learning (SBL) framework. First, the array covariance matrices at different frequency bins are focused to the reference frequency by the conventional focusing technique and then transformed into the vector form. Then a matrix called the Khatri-Rao dictionary is constructed by using the Khatri-Rao product and the multiple focused array covariance vectors are set as the new observations. DOA estimation is to find the sparsest representations of the new observations over the Khatri-Rao dictionary via SBL. The performance of the proposed method is compared with other well-known focusing based wideband algorithms and the Cramer-Rao lower bound (CRLB). The results show that it achieves higher resolution and accuracy and can reach the CRLB under relative demanding conditions. Moreover, the method imposes no restriction on the pattern of signal power spectral density and due to the increased number of rows of the dictionary, it can resolve more sources than sensors

Successive Linear Approximation VBI for Joint Sparse Signal Recovery and Dynamic Grid Parameters Estimation

For many practical applications in wireless communications, we need to recover a structured sparse signal from a linear observation model with dynamic grid parameters in the sensing matrix. Conventional expectation maximization (EM)-based compressed sensing (CS) methods, such as turbo compressed sensing (Turbo-CS) and turbo variational Bayesian inference (Turbo-VBI), have double-loop iterations, where the inner loop (E-step) obtains a Bayesian estimation of sparse signals and the outer loop (M-step) obtains a point estimation of dynamic grid parameters. This leads to a slow convergence rate. Furthermore, each iteration of the E-step involves a complicated matrix inverse in general. To overcome these drawbacks, we first propose a successive linear approximation VBI (SLA-VBI) algorithm that can provide Bayesian estimation of both sparse signals and dynamic grid parameters. Besides, we simplify the matrix inverse operation based on the majorization-minimization (MM) algorithmic framework. In addition, we extend our proposed algorithm from an independent sparse prior to more complicated structured sparse priors, which can exploit structured sparsity in specific applications to further enhance the performance. Finally, we apply our proposed algorithm to solve two practical application problems in wireless communications and verify that the proposed algorithm can achieve faster convergence, lower complexity, and better performance compared to the state-of-the-art EM-based methods.Comment: 13 pages, 17 figures, submitted to IEEE Transactions on Wireless Communication

Underwater Source Localization based on Modal Propagation and Acoustic Signal Processing

Acoustic localization plays a pivotal role in underwater vehicle systems and marine mammal detection. Previous efforts adopt synchronized arrays of sensors to extract some features like direction of arrival (DOA) or time of flight (TOF) from the received signal. However, installing and synchronizing several hydrophones over a large area is costly and challenging. To tackle this problem, we use a single-hydrophone localization system which relies on acoustic signal processing methods rather than multiple hydrophones. This system takes modal dispersion into consideration and estimates the distance between sound source and receiver (range) based on dispersion curves. It is shown that the larger the range is, the more separable the modes are. To make the modes more distinguishable, a non-linear signal processing technique, called warping, is utilized. Propagation model of low-frequency signals, such as dolphin sound, is well-studied in shallow water environment (depth D\u3c200 m), and it was demonstrated that at large ranges (range r\u3e1 km), modal dispersion is utterly visible at time frequency (TF) domain. We used Peker is model for the aforementioned situation to localize both synthetic and real underwater acoustic signals. The accuracy of the localization system is examined with various sounds, including impulsive signal, sounds with known Fourier transform, and signals with estimated source phase. Experimental results show that the warping technique can considerably lessen the localization error, especially when prior knowledge about the source signal and waveguide are available

Large Eddy Simulation Of Surface Pressure Fluctuations Generated By Elevated Gusts

Wind gusts cause substantial damage to wind turbines. If these damaging winds could be detected prior to their interaction with the turbine, the turbine rotor can be decoupled from the generator and gearing system to prevent damage during the gust event. This would significantly reduce wind turbine repair costs. Wind gusts can also create unsafe conditions for aircraft landing. A ground based detection system that monitored elevated wind gusts can provide new information for pilots to use when determining whether or not it is safe to land. In addition, the ability to monitor elevated gust events would provide a new probe to study features in the atmospheric boundary layer. Previous research indicates that elevated velocity events, such as gusts, may trigger pressure fluctuations on the ground. If that is true, it should be possible to monitor elevated wind gusts by measuring these pressure fluctuations. The goal of this project is to develop a ground based detector that monitors the behavior of pressure fluctuations on the ground for indicators that a gust event may be taking place at higher altitudes. In order to recognize these indicators from the pressure measurements on the ground, cross-correlation analysis between the time evolution of the frequency structures corresponding to elevated wind gusts and the pressure on the ground below were investigated. The data for these analysis was generated using a large eddy simulation. This numerical approach was chosen because the nature of the cross-correlation analysis demanded full field wind velocities and pressures at several altitudes. Collecting this data outdoors would be impractical. Correlation coefficients between 0.75 - 0.90 were found. These high correlations indicate that the two signals are causally related. Several comfeatures of the pressures caused by elevated gusts were identified. These features were used to develop a tracking program that monitors fast moving high amplitude pressure fluctuations and to design a ground based pressure sensing array. The array design and tracking software was used to identify several new gust events within the simulated atmosphere. In total, eight gust events have been identified. These events show that the group velocities of the pressure fluctuations measured on the ground increase with the altitude location of the corresponding wind gust source. The methods, tracking software, and array design are ready to be used for experimental research outdoors

Computational Methods for Underdetermined Convolutive Speech Localization and Separation via Model-based Sparse Component Analysis

In this paper, the problem of speech source localization and separation from recordings of convolutive underdetermined mixtures is studied. The problem is cast as recovering the spatio-spectral speech information embedded in a microphone array compressed measurements of the acoustic field. A model-based sparse component analysis framework is formulated for sparse reconstruction of the speech spectra in a reverberant acoustic resulting in joint localization and separation of the individual sources. We compare and contrast the computational approaches to model-based sparse recovery exploiting spatial sparsity as well as spectral structures underlying spectrographic representation of speech signals. In this context, we explore identification of the sparsity structures at the auditory and acoustic representation spaces. The auditory structures are formulated upon the principles of structural grouping based on proximity, autoregressive correlation and harmonicity of the spectral coefficients and they are incorporated for sparse reconstruction. The acoustic structures are formulated upon the image model of multipath propagation and they are exploited to characterize the compressive measurement matrix associated with microphone array recordings. Three approaches to sparse recovery relying on combinatorial optimization, convex relaxation and Bayesian methods are studied and evaluated based on thorough experiments. The sparse Bayesian learning method is shown to yield better perceptual quality while the interference suppression is also achieved using the combinatorial approach with the advantage of offering the most efficient computational cost. Furthermore, it is demonstrated that an average autoregressive model can be learned for speech localization and exploiting the proximity structure in the form of block sparse coefficients enables accurate localization. Throughout the extensive empirical evaluation, we confirm that a large and random placement of the microphones enables significant improvement in source localization and separation performance

Towards joint communication and sensing (Chapter 4)

Localization of user equipment (UE) in mobile communication networks has been supported from the early stages of 3rd generation partnership project (3GPP). With 5th Generation (5G) and its target use cases, localization is increasingly gaining importance. Integrated sensing and localization in 6th Generation (6G) networks promise the introduction of more efficient networks and compelling applications to be developed

Structured Sub-Nyquist Sampling with Applications in Compressive Toeplitz Covariance Estimation, Super-Resolution and Phase Retrieval

Sub-Nyquist sampling has received a huge amount of interest in the past decade. In classical compressed sensing theory, if the measurement procedure satisfies a particular condition known as Restricted Isometry Property (RIP), we can achieve stable recovery of signals of low-dimensional intrinsic structures with an order-wise optimal sample size. Such low-dimensional structures include sparse and low rank for both vector and matrix cases. The main drawback of conventional compressed sensing theory is that random measurements are required to ensure the RIP property. However, in many applications such as imaging and array signal processing, applying independent random measurements may not be practical as the systems are deterministic. Moreover, random measurements based compressed sensing always exploits convex programs for signal recovery even in the noiseless case, and solving those programs is computationally intensive if the ambient dimension is large, especially in the matrix case. The main contribution of this dissertation is that we propose a deterministic sub-Nyquist sampling framework for compressing the structured signal and come up with computationally efficient algorithms. Besides widely studied sparse and low-rank structures, we particularly focus on the cases that the signals of interest are stationary or the measurements are of Fourier type. The key difference between our work from classical compressed sensing theory is that we explicitly exploit the second-order statistics of the signals, and study the equivalent quadratic measurement model in the correlation domain. The essential observation made in this dissertation is that a difference/sum coarray structure will arise from the quadratic model if the measurements are of Fourier type. With these observations, we are able to achieve a better compression rate for covariance estimation, identify more sources in array signal processing or recover the signals of larger sparsity. In this dissertation, we will first study the problem of Toeplitz covariance estimation. In particular, we will show how to achieve an order-wise optimal compression rate using the idea of sparse arrays in both general and low-rank cases. Then, an analysis framework of super-resolution with positivity constraint is established. We will present fundamental robustness guarantees, efficient algorithms and applications in practices. Next, we will study the problem of phase-retrieval for which we successfully apply the sparse array ideas by fully exploiting the quadratic measurement model. We achieve near-optimal sample complexity for both sparse and general cases with practical Fourier measurements and provide efficient and deterministic recovery algorithms. In the end, we will further elaborate on the essential role of non-negative constraint in underdetermined inverse problems. In particular, we will analyze the nonlinear co-array interpolation problem and develop a universal upper bound of the interpolation error. Bilinear problem with non-negative constraint will be considered next and the exact characterization of the ambiguous solutions will be established for the first time in literature. At last, we will show how to apply the nested array idea to solve real problems such as Kriging. Using spatial correlation information, we are able to have a stable estimate of the field of interest with fewer sensors than classic methodologies. Extensive numerical experiments are implemented to demonstrate our theoretical claims