Statistical Nested Sensor Array Signal Processing

Source number detection and direction-of-arrival (DOA) estimation are two major applications of sensor arrays. Both applications are often confined to the use of uniform linear arrays (ULAs), which is expensive and difficult to yield wide aperture. Besides, a ULA with N scalar sensors can resolve at most N − 1 sources. On the other hand, a systematic approach was recently proposed to achieve O(N 2 ) degrees of freedom (DOFs) using O(N) sensors based on a nested array, which is obtained by combining two or more ULAs with successively increased spacing. This dissertation will focus on a fundamental study of statistical signal processing of nested arrays. Five important topics are discussed, extending the existing nested-array strategies to more practical scenarios. Novel signal models and algorithms are proposed. First, based on the linear nested array, we consider the problem for wideband Gaussian sources. To employ the nested array to the wideband case, we propose effective strategies to apply nested-array processing to each frequency component, and combine all the spectral information of various frequencies to conduct the detection and estimation. We then consider the practical scenario with distributed sources, which considers the spreading phenomenon of sources. Next, we investigate the self-calibration problem for perturbed nested arrays, for which existing works require certain modeling assumptions, for example, an exactly known array geometry, including the sensor gain and phase. We propose corresponding robust algorithms to estimate both the model errors and the DOAs. The partial Toeplitz structure of the covariance matrix is employed to estimate the gain errors, and the sparse total least squares is used to deal with the phase error issue. We further propose a new class of nested vector-sensor arrays which is capable of significantly increasing the DOFs. This is not a simple extension of the nested scalar-sensor array. Both the signal model and the signal processing strategies are developed in the multidimensional sense. Based on the analytical results, we consider two main applications: electromagnetic (EM) vector sensors and acoustic vector sensors. Last but not least, in order to make full use of the available limited valuable data, we propose a novel strategy, which is inspired by the jackknifing resampling method. Exploiting numerous iterations of subsets of the whole data set, this strategy greatly improves the results of the existing source number detection and DOA estimation methods

Maximizing the Number of Spatial Nulls with Minimum Sensors

In this paper, we attempt to unify two array processing frameworks viz, Acoustic Vector Sensor (AVS) and two level nested array to enhance the Degrees of Freedom (DoF) significantly beyond the limit that is attained by a Uniform Linear Hydrophone Array (ULA) with specified number of sensors. The major focus is to design a line array architecture which provides high resolution unambiguous bearing estimation with increased number of spatial nulls to mitigate the multiple interferences in a deep ocean scenario. AVS can provide more information about the propagating acoustic field intensity vector by simultaneously measuring the acoustic pressure along with tri-axial particle velocity components. In this work, we have developed Nested AVS array (NAVS) ocean data model to demonstrate the performance enhancement. Conventional and MVDR spatial filters are used as the response function to evaluate the performance of the proposed architecture. Simulation results show significant improvement in performance viz, increase of DoF, and localization of more number of acoustic sources and high resolution bearing estimation with reduced side lobe level

AERO & VISTA: Demonstrating HF Radio Interferometry with Vector Sensors

AERO (Auroral Emission Radio Observer) and VISTA (Vector Interferometry Space Technology using AERO) are recently selected NASA HTIDeS CubeSat missions for terrestrial auroral science and radio interferometric technology demonstration. The AERO and VISTA CubeSats both host vector sensing antenna systems providing advanced electromagnetic capabilities. Together, they will provide the first in-space demonstration of interferometric imaging, beamforming, and nulling using electromagnetic vector sensors at low frequencies (100 kHz –15 MHz). A key goal of the joint missions’ technology demonstration is to validate theoretical sensor performance modeling indicating that interferometric arrays composed of vector sensors will be able to maintain sensitivity even in the presence of terrestrial interference. If validated in flight, this capability would relax the requirement that space-based low frequency interferometers be placed far from the Earth (e.g. lunar orbit), and the closer communications range will significantly increase the data volume returned from space-based radio telescope systems. The two-spacecraft AERO+VISTA mission will address the auroral science goals of AERO (Erickson et al. 2018, SSC18) while adding three additional technology demonstration goals enabled by the second CubeSat, VISTA

Statistical Performance Analysis of Sparse Linear Arrays

Direction-of-arrival (DOA) estimation remains an important topic in array signal processing. With uniform linear arrays (ULAs), traditional subspace-based methods can resolve only up to M-1 sources using M sensors. On the other hand, by exploiting their so-called difference coarray model, sparse linear arrays, such as co-prime and nested arrays, can resolve up to O(M^2) sources using only O(M) sensors. Various new sparse linear array geometries were proposed and many direction-finding algorithms were developed based on sparse linear arrays. However, the statistical performance of such arrays has not been analytically conducted. In this dissertation, we (i) study the asymptotic performance of the MUtiple SIgnal Classification (MUSIC) algorithm utilizing sparse linear arrays, (ii) derive and analyze performance bounds for sparse linear arrays, and (iii) investigate the robustness of sparse linear arrays in the presence of array imperfections. Based on our analytical results, we also propose robust direction-finding algorithms for use when data are missing. We begin by analyzing the performance of two commonly used coarray-based MUSIC direction estimators. Because the coarray model is used, classical derivations no longer apply. By using an alternative eigenvector perturbation analysis approach, we derive a closed-form expression of the asymptotic mean-squared error (MSE) of both estimators. Our expression is computationally efficient compared with the alternative of Monte Carlo simulations. Using this expression, we show that when the source number exceeds the sensor number, the MSE remains strictly positive as the signal-to-noise ratio (SNR) approaches infinity. This finding theoretically explains the unusual saturation behavior of coarray-based MUSIC estimators that had been observed in previous studies. We next derive and analyze the Cramér-Rao bound (CRB) for general sparse linear arrays under the assumption that the sources are uncorrelated. We show that, unlike the classical stochastic CRB, our CRB is applicable even if there are more sources than the number of sensors. We also show that, in such a case, this CRB remains strictly positive definite as the SNR approaches infinity. This unusual behavior imposes a strict lower bound on the variance of unbiased DOA estimators in the underdetermined case. We establish the connection between our CRB and the classical stochastic CRB and show that they are asymptotically equal when the sources are uncorrelated and the SNR is sufficiently high. We investigate the behavior of our CRB for co-prime and nested arrays with a large number of sensors, characterizing the trade-off between the number of spatial samples and the number of temporal samples. Our analytical results on the CRB will benefit future research on optimal sparse array designs. We further analyze the performance of sparse linear arrays by considering sensor location errors. We first introduce the deterministic error model. Based on this model, we derive a closed-form expression of the asymptotic MSE of a commonly used coarray-based MUSIC estimator, the spatial-smoothing based MUSIC (SS-MUSIC). We show that deterministic sensor location errors introduce a constant estimation bias that cannot be mitigated by only increasing the SNR. Our analytical expression also provides a sensitivity measure against sensor location errors for sparse linear arrays. We next extend our derivations to the stochastic error model and analyze the Gaussian case. We also derive the CRB for joint estimation of DOA parameters and deterministic sensor location errors. We show that this CRB is applicable even if there are more sources than the number of sensors. Lastly, we develop robust DOA estimators for cases with missing data. By exploiting the difference coarray structure, we introduce three algorithms to construct an augmented covariance matrix with enhanced degrees of freedom. By applying MUSIC to this augmented covariance matrix, we are able to resolve more sources than sensors. Our method utilizes information from all snapshots and shows improved estimation performance over traditional DOA estimators