Spatial Sparsity-based Theory And Methods Of Array Signal Processing

The requirement of direction-of-arrival (DOA) estimation in demanding scenarios oflow signal-to-noise ratio (SNR), much limited snapshots and spatially adjacent targetshave emerged in various areas, partially due to the widespread applications of the lowprobability of intercept (LPI) techniques and the increase of the electromagneticemitters. The state-of-the-art array processing theory and technique dominated by thesubspace-based methods can hardly meet the requirement. Recently, the sparserepresentation algorithms have been introduced into this area to make use of the priorinformation of the spatial sparsity of the incident signals, and the correspondingmethods have witnessed a significant enhancement in adaptation to theabove-mentioned demanding scenarios. Unfortunately, the DOA estimation precision ofthem is constrained by the shortcomings of the sparse reconstruction algorithms andmay be not satisfyingly enough.In this dissertation, a spatial sparsity-based array signal processing framework isestablished after analyzing the relations and distinctions between the array signalprocessing and the sparse reconstruction problems. This framework grounds on aprecise spatial reconstruction of the signal characters and aims at high-precision DOAestimation. The relevance vector machine (RVM) is then introduced for theimplementation of the framework, and a method named RVM-DOA is proposed fornarrowband signals. Theoretical analyses are also carried out to reveal the properties ofthe method in convergence and separable signal number. RVM-DOA makes good useof the spatial sparsity of the incident signals and achieves precise signal recovery byevading the interaction of different signals, which is then exploited to obtainhigh-precision narrowband DOA estimates. It is demonstrated empirically thatRVM-DOA owns much enhanced superresolution and adaptation to low SNR andlimited snapshots, and surpasses the existing sparsity-inducing methods in DOAestimation precision, and it also performs well in separating correlated signals.After that, two methods of CV-RVM (Covariance Vector-exploited RVM) and SFRVM-DOA (Spatial Filtering-based RVM-DOA) are proposed to improve thecomputational efficiency of RVM-DOA at low SNR and its DOA estimation precisionof correlated signals, respectively. By exploiting the first-and second-order statistics ofthe covariance vector estimation errors, CV-RVM realizes DOA estimation of bothindependent and correlated narrowband signals by reconstructing those vectors, whichcontains the directional information of the incident signals and their SNR is higher thanthat of the raw array output vectors when sufficient snapshots have been collected.CV-RVM gains much improved computational efficiency than RVM-DOA at theexpense of adaptation to much limited snapshots, and it also owns better performance at low SNR and for spatially adjacent signals. Moreover, CV-RVM is able to separatemore signals than the sensor number in well-designed arrays, which is supported bytheoretical analysis. SF RVM-DOA introduces a group of spatial filters to separate thesimultaneously impinging correlated signals and realize DOA estimation of them, so asto make up for the negative influence of the inter-signal correlation on the DOAestimation precision of the existing sparse reconstruction methods. SF RVM-DOAadapts to arbitrary array geometries and approaches or even reaches the Cramer-RaoLower Bound (CRLB) in scenarios of adequate SNR and snapshots, which has neverbeen achieved by the existing methods.When the incident signals are wideband and own typical temporal correlationcharacters, the directions of them can still be estimated by recovering the covariancevectors of the array outputs. Following this idea, two methods of WCV-RVM(Wideband CV-RVM) and STS-RVM (Sequential Temporal-Spatial RVM) areproposed for independent and multipath wideband DOA estimation, respectively. Theproposed methods do not require similar spectral decomposition and focusingprocedures as the subspace-based methods. WCV-RVM makes use of the spatialsparsity and modulation characters of the wideband signals, thus it well reserves thesuperiorities of its narrowband counterparts in superresoltion and adaptation to lowSNR and limited snapshots. It is also able to separate more signals than sensors inwell-designed arrays and owns a much relaxed restriction on the array geometry inavoiding DOA estimation ambiguity. Besides the spatial sparsity and modulationcharacters, STS-RVM also exploits the sparsity of the multipath signals in thetime-delay domain, it succeeds to estimate the time delays that are much smaller thanthe signal time-width, and its DOA estimation performance for all the multipathcomponents when more than one wideband signals impinge simultaneously surpassesthe subspace-based methods significantly.The widespread array imperfections, with mutual coupling, gain/phase uncertaintyand sensor location error being the most typical examples, play a significantly negativerole in the sparsity-inducing array processing methods. In order to enhance theadaptability of those methods to the array imperfections, we propose a joint arraycalibration and direction estimation method by taking the spatial sparsity of the incidentsignals into account. A unified framework of the uncalibrated array output is developedfirst in the presence of a single array imperfection type, it applies to any of theabove-mentioned typical array imperfections after reification, and can be easilyextended to scenarios when more than one type of array imperfections coexist. Thelower bounds of the array calibration and direction estimation precisions are thenanalyzed theoretically. The theoretical results also apply in any of the single-typeimperfection scenarios, and they have much compact expressions than the existingcounterparts. When compared with the previous array calibration methods, the proposed one dominates in adaptation to the much demanding environments, including low SNR,limited snapshots and spatially adjacent sources, and it exceeds with large margin inarray calibration and DOA estimation precisions.A sparse Bayesian joint reconstruction technique is finally studied for themulti-model multi-measurement (M4) reconstruction problems. The properties of the M4problem itself and the joint reconstruction method are analyzed theoretically to indicatethe general behavior of them, and the technique is then introduced to solve twoimportant array signal processing problems, including narrowband DOA estimation intime-varying array systems and wideband DOA estimation via spectral decomposition.The joint reconstruction technique and its applications help to enrich the spatialsparsity-based array signal processing theory largely.