【作者】 刘章孟；

【导师】 周一宇；

【作者基本信息】 国防科学技术大学 ， 信息与通信工程， 2012， 博士

【摘要】 随着低截获概率技术的广泛应用和空间辐射源数目的显著增加，阵列处理系统所面临的信号环境日趋复杂，低信噪比、小样本和空域邻近信号等非理想条件下的阵列处理需求也日益普遍，这些问题的出现给当前以子空间类方法为主体的阵列信号处理理论及方法的适用性带来了严峻挑战。结合入射信号的空域稀疏性在阵列处理领域所取得的初步探索成果已经显示了它们在上述非理想信号环境中实现超分辨测向的极大优势。然而，这些方法的性能受到了相应稀疏重构算法自身局限性等因素的制约，难以满足各种阵列处理系统在测向精度等方面的需求。本文从阵列处理和稀疏重构这两类问题的联系与区别角度出发，建立了以准确的信号空域特征重构为前提、以高精度波达方向估计为目的的稀疏重构阵列处理基本理论框架，据此提出了基于相关向量机的阵列测向方法RVM-DOA(Relevance Vector Machine based Direction-of-Arrival estimation)，并理论分析了其收敛性和可分辨信号数等性质。该方法充分利用入射信号的空域稀疏性，在重构过程中通过避免不同信号之间的相互耦合实现了对信号空域特征更准确的恢复，并结合后续精测向过程得到了高精度的波达方向估计结果。RVM-DOA方法可直接用于对窄带信号的波达方向估计，具有显著优于子空间类方法的低信噪比、小样本适应能力和超分辨能力，以及显著优于已有稀疏重构类方法的测向精度，而且在相关信号处理等方面也体现出了明显优势。为了更好地满足阵列测向系统在计算效率和对相关信号的测向精度要求，本文随后提出了基于阵列输出协方差向量空域稀疏重构的窄带独立/相关信号测向方法CV-RVM (Covariance Vector-exploited RVM)和基于空域滤波的窄带相关信号测向方法SF RVM-DOA (Spatial Filtering-based RVM-DOA)。CV-RVM方法利用协方差向量包含入射信号空域分布信息及其在适宜样本数条件下具有比原始阵列输出更高信噪比的特点，在深入分析协方差向量估计误差一阶和二阶统计特性的基础上，以牺牲一定的小样本适应能力为代价，得到了显著高于RVM-DOA方法的计算效率，以及明显增强的低信噪比适应能力和超分辨能力。该方法还可以通过阵列结构的优化设计，实现对多于阵列阵元数的同时入射信号的分辨，这一结论得到了严格的理论分析结果的支持。论文随后提出了用于窄带相关信号测向的SFRVM-DOA方法，以弥补各种稀疏重构类测向方法在相关信号测向精度方面所存在的不足。SF RVM-DOA方法借助一组依赖于信号方向的空域滤波器实现对多个时域混叠相关信号的分离，并通过滤波器参数与信号方向的联合优化得到高精度的测向结果。该方法适用于任意结构阵列，且在空时白噪声等典型信号环境中的测向精度十分逼近甚至达到了克拉美－罗下界，这是现有各种方法都无法做到的。针对雷达、通信等领域所使用的各种具有典型时延相关特征的宽带信号的测向问题，利用阵列输出协方差向量的空域稀疏性和时域调制信息，提出了分别适用于独立和多径宽带信号波达方向估计的WCV-RVM (Wideband CV-RVM)和STS-RVM (Sequential Temporal-Spatial RVM)方法，避免了常规子空间类宽带测向方法的频域分解与聚焦过程。WCV-RVM方法较好地继承了窄带信号稀疏重构类测向方法在低信噪比、小样本适应能力和超分辨能力等方面的优势，理论分析结果还证明了该方法借助阵列结构优化设计实现对多于阵列阵元数的同时入射信号的分辨，以及在保证无模糊测向的条件下显著放宽对阵列阵元间距要求的性质。STS-RVM方法进一步结合多径分量在时延域的稀疏性，实现对多径时延远小于信号时宽的多径分量的分辨，然后基于该时延估计结果完成对多个同时入射宽带信号所有多径分量的波达方向估计，相应的测向性能远优于已有宽带子空间类方法。实际系统中广泛存在的阵列互耦、幅相不一致和阵元位置不准确等模型误差会对稀疏重构类阵列测向方法的性能产生显著的负面影响。在充分利用入射信号空域稀疏性的基础上，本文随后研究了模型失配条件下的阵列误差校正与信号波达方向估计方法，以增强测向系统对上述各类典型阵列误差的适应能力。该方法以阵列互耦、幅相不一致和阵元位置不准确等误差条件下统一的阵列观测模型为基础，其模型和实现过程适用于其中任一阵列误差类型，并可以方便地推广至多种误差同时存在时的阵列测向环境。论文进一步分析了模型失配条件下阵列校准与信号测向精度的理论下界，该理论结果同时适用于上述三类典型误差类型，而且具有比已有结果更简洁和直观的形式。与传统阵列误差校正方法相比，新方法在低信噪比、小样本适应能力和超分辨能力等方面仍然具备显著优势，在典型信号环境中则体现出了更好的误差校正性能和更高的测向精度。最后，本文针对多模型多观测条件下的联合重构问题研究了相应的贝叶斯稀疏重构技术，并在充分分析重构问题本身和重构方法基本性质的基础上，将该技术应用于解决时变阵列中的窄带信号测向和基于频域分解的一般宽带信号测向等两类典型的阵列处理问题，相关模型、方法和理论成果进一步充实了基于信号空域稀疏性的阵列处理理论与方法体系。更多还原

【Abstract】 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.更多还原