稳健波束形成与稀疏空间谱估计技术研究
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摘要
阵列信号处理是现代信号处理技术的重要分支，在雷达、声纳、无线通信、医学成像等多种军事和国民经济领域具有广泛的应用。阵列信号处理可以分为波束形成和空间谱估计两大方面内容。针对这两方面内容，本文分别就非理想条件下的稳健波束形成技术，以及基于稀疏信号重建的空间谱估计方法展开研究。在对现有理论和方法进行调研的基础上，本文提出了一些新的稳健波束形成和高分辨空间谱估计方法。其主要创新性成果有：
1）针对波束形成方法中的导向矢量失配问题，提出了新的导向矢量矫正方法。该方法给出了一种基于二阶锥规划（Second-Order Cone Programming, SOCP）的迭代流程来近似原本的非凸（non-convex）优化问题，使问题可以有效的求解，并且该迭代流程的可解性和收敛性可以得到保证。与传统的算法相比，所提出的算法避免了使用等式约束，从而节省了系统自由度，进一步提升了波束形成器的性能。
2）针对宽带波束形成器中的来波方向（Direction of arrival, DOA）失配以及主瓣频率响应不一致的问题，提出了一种主瓣幅度响应可控的宽带波束形成方法。算法采用不等式约束而非等式约束来控制主瓣幅度响应，在获得对DOA失配稳健性的同时可以节省更多的系统自由度。算法给出一种基于SOCP的迭代流程，转化了原本的非凸优化问题，使问题可以有效求解，并且适用于任意类型阵列。此外，该方法引入了均方响应浮动元素，进一步克服了宽带波束形成器主瓣响应的频域不一致问题。仿真结果验证所提方法的有效性。
3）传统稳健波束形成方法大多基于Capon波束形成器框架下提出的。本文中，我们考虑在广义旁瓣相消器（Generalized Sidelobe Canceller, GSC）框架下设计稳健波束形成器。通过将传统GSC中的阻塞矩阵与自适应权值合并，我们发现这种框架带来的一个好处就是可以直接施加不等式凸约束来使波束形成器对DOA失配具有稳健性，避免了传统方法所经常涉及的非凸优化问题，使设计更为灵活和简便。另外，结合了最差性能最优化思想，算法进一步获得了对一般类型误差的稳健型。该方法可以将DOA失配和其他一般性误差分别对待，避免了传统最差性能最优化法设计容易过于保守的问题。
4）提出了一种基于稀疏重建干扰噪声协方差矩阵的稳健波束形成方法。该方法利用一种叫做SPICE（Sparse Iterative Covariance-based Estimation）的稀疏空间谱估计方法，矫正对期望信号的观察方向，然后重建无信号的协方差矩阵。与传统基于采样协方差矩阵的波束形成器不同，重构的协方差矩阵不包含期望信号成分，从而波束形成器的稳健性大大增强。所提出的方法由于进一步利用了协方差矩阵结构的稀疏性，因而比现有重建方法的精度更高。另外，基于SPICE重构的协方差矩阵对相干信号引起的秩缺损有稳健性，进而使得提出的波束形成方法可以处理相干干扰存在的情况。
5）针对现有的协方差矩阵重构法依赖于精确的阵列结构信息，无法处理阵列未知扰动的问题，作者提出了一种利用信号循环平稳性的协方差矩阵重构法。该算法在构造干扰噪声协方差矩阵时无需已知阵列的结构和响应信息，因而不受阵列中未知扰动的影响。另外，算法的设计基于信号的循环平稳信息，而不依赖于信号的空间位置信息，因此可用于干扰方向距离期望信号很近的情况。仿真结果表明，在阵列系统存在未知扰动时，所提出算法优于现有的协方差矩阵重构法，特别是在干扰信号能量较大或干扰距离期望信号很近的时候。
6）提出了一种联合利用信号空间稀疏性和循环平稳特性的空间谱估计算法。该算法考虑对信号的共轭循环自相关矩阵进行稀疏重建，并使用加权l1范数来约束稀疏性。由于利用了信号的循环平稳性，所提出算法可以仅对感兴趣的循环平稳信号进行方位估计而忽略干扰，因此其他干扰信号可以在距离期望信号任意近的位置。另外，所提出方法利用了信号的空间稀疏性，因此进一步提高了其空间分辨力。仿真结果证明了所提出方法的有效性。
Array signal processing techniques are widely applied to the fields of Radar, Sonarwireless communication, medical imaging, etc. It can be divided into two main parts in thearray signal processing: adaptive beamforming and spatial spectrum estimation techniques.Corresponding to each part, this dissertationion focuses on the issue of robust beamformingdesign and sparse-signal-reconstruction-based spatial spectrum estimation. Based on a deepstudy on the related theory and existing algorithms, the dissertation has developed some newmethods on the robust beamforming and high resolution spatial spectrum estimation. Themain contributions are as follows.
1) The problem of steering vector mismatch for the robust beamformer design isconsidered and a steering vector calibration method is proposed. The proposed technique canobtain the SV directly and efficiently by iterating second-order cone programming. Moreover,the feasibility and convergence of the proposed algorithms can be guaranteed. The proposedbeamformer avoids the equality constraints in the conventional method, thus more degrees offreedom are saved.
2) A wideband beamformer with mainlobe control is proposed. To make the beamformerrobust against direction of arrival (DOA) mismatch, inequality rather than equality constraintsare used to restrict the mainlobe response, thus more degrees of freedom are saved. Theconstraints involved are nonconvex, therefore are linearly approximated so that thebeamformer can be obtained efficiently by iterating a second-order cone program and can beapplied to arbitrary types of arrays. Moreover, the response variance element is introduced toachieve a frequency invariant beamwidth. The simulation results demonstrate theeffectiveness of the proposed method.
3) A robust beamformer is proposed by modifying the generalized sidelobe canceler(GSC) and using the concept of worst-case performance optimization. With the GSC-likestructure, convex constraints can be directly applied to make the beamformer robust againstDOA mismatch. Then, the beamformer is improved to be robust against arbitrary systemimperfections by applying the worst-case optimization method. The DOA mismatch and othergeneral imperfections can be treated separately in the beamformer, thus an over-conservativerobustness design may be avoided.
4）By introducing the sparse iterative covariance-based estimation (SPICE) approach, a robust beamformer with joint robustness against the desired signal mismatch and theinterference coherence is proposed. With the SPICE, we firstly calibrate the look directionmismatch, and then reconstruct the interference-plus-noise covariance matrix (INCM) toreplace the conventional sample covariance matrix. This is shown to greatly improve therobustness of adaptive beamformers since a quasi signal-free environment is provided.Moreover, since the SPICE is robust to signal coherence, the proposed beamformer cansuppress the coherent interferences.
5) An INCM reconstruction method is proposed by exploiting the cyclostationarity ofinterference signals. In contrast to the existing INCM reconstruction methods, the proposedtechnique is based on the knowledge of the interferences’ cycle frequencies and needs noinformation of the array structure, thus it can deal with unknown perturbations in the array.Moreover, the proposed technique is suitable to the case when the locations of theinterferences and desired signal are close. The numerical simulations show that the proposedmethod improves the robustness of adaptive beamformers and has superior performance to theexisting INCM reconstruction methods especially for strong interferences.
6) A DOA estimation technique is proposed by jointly exploiting the signalcyclostationarity and spatial sparsity. Based on the cyclic conjugate correlation matrix, theproposed estimator exhibits the signal selectivity at a desired cycle frequency, thus thenumber and characteristics of the interference can be arbitrary and unknown. Moreover, byusing the sparse representation framework with the weighted l1-norm minimization, theresolution and accuracy of DOA estimation can be greatly improved. The effectiveness of theproposed method is examined by numerical examples.
1）针对波束形成方法中的导向矢量失配问题，提出了新的导向矢量矫正方法。该方法给出了一种基于二阶锥规划（Second-Order Cone Programming, SOCP）的迭代流程来近似原本的非凸（non-convex）优化问题，使问题可以有效的求解，并且该迭代流程的可解性和收敛性可以得到保证。与传统的算法相比，所提出的算法避免了使用等式约束，从而节省了系统自由度，进一步提升了波束形成器的性能。
2）针对宽带波束形成器中的来波方向（Direction of arrival, DOA）失配以及主瓣频率响应不一致的问题，提出了一种主瓣幅度响应可控的宽带波束形成方法。算法采用不等式约束而非等式约束来控制主瓣幅度响应，在获得对DOA失配稳健性的同时可以节省更多的系统自由度。算法给出一种基于SOCP的迭代流程，转化了原本的非凸优化问题，使问题可以有效求解，并且适用于任意类型阵列。此外，该方法引入了均方响应浮动元素，进一步克服了宽带波束形成器主瓣响应的频域不一致问题。仿真结果验证所提方法的有效性。
3）传统稳健波束形成方法大多基于Capon波束形成器框架下提出的。本文中，我们考虑在广义旁瓣相消器（Generalized Sidelobe Canceller, GSC）框架下设计稳健波束形成器。通过将传统GSC中的阻塞矩阵与自适应权值合并，我们发现这种框架带来的一个好处就是可以直接施加不等式凸约束来使波束形成器对DOA失配具有稳健性，避免了传统方法所经常涉及的非凸优化问题，使设计更为灵活和简便。另外，结合了最差性能最优化思想，算法进一步获得了对一般类型误差的稳健型。该方法可以将DOA失配和其他一般性误差分别对待，避免了传统最差性能最优化法设计容易过于保守的问题。
4）提出了一种基于稀疏重建干扰噪声协方差矩阵的稳健波束形成方法。该方法利用一种叫做SPICE（Sparse Iterative Covariance-based Estimation）的稀疏空间谱估计方法，矫正对期望信号的观察方向，然后重建无信号的协方差矩阵。与传统基于采样协方差矩阵的波束形成器不同，重构的协方差矩阵不包含期望信号成分，从而波束形成器的稳健性大大增强。所提出的方法由于进一步利用了协方差矩阵结构的稀疏性，因而比现有重建方法的精度更高。另外，基于SPICE重构的协方差矩阵对相干信号引起的秩缺损有稳健性，进而使得提出的波束形成方法可以处理相干干扰存在的情况。
5）针对现有的协方差矩阵重构法依赖于精确的阵列结构信息，无法处理阵列未知扰动的问题，作者提出了一种利用信号循环平稳性的协方差矩阵重构法。该算法在构造干扰噪声协方差矩阵时无需已知阵列的结构和响应信息，因而不受阵列中未知扰动的影响。另外，算法的设计基于信号的循环平稳信息，而不依赖于信号的空间位置信息，因此可用于干扰方向距离期望信号很近的情况。仿真结果表明，在阵列系统存在未知扰动时，所提出算法优于现有的协方差矩阵重构法，特别是在干扰信号能量较大或干扰距离期望信号很近的时候。
6）提出了一种联合利用信号空间稀疏性和循环平稳特性的空间谱估计算法。该算法考虑对信号的共轭循环自相关矩阵进行稀疏重建，并使用加权l1范数来约束稀疏性。由于利用了信号的循环平稳性，所提出算法可以仅对感兴趣的循环平稳信号进行方位估计而忽略干扰，因此其他干扰信号可以在距离期望信号任意近的位置。另外，所提出方法利用了信号的空间稀疏性，因此进一步提高了其空间分辨力。仿真结果证明了所提出方法的有效性。
Array signal processing techniques are widely applied to the fields of Radar, Sonarwireless communication, medical imaging, etc. It can be divided into two main parts in thearray signal processing: adaptive beamforming and spatial spectrum estimation techniques.Corresponding to each part, this dissertationion focuses on the issue of robust beamformingdesign and sparse-signal-reconstruction-based spatial spectrum estimation. Based on a deepstudy on the related theory and existing algorithms, the dissertation has developed some newmethods on the robust beamforming and high resolution spatial spectrum estimation. Themain contributions are as follows.
1) The problem of steering vector mismatch for the robust beamformer design isconsidered and a steering vector calibration method is proposed. The proposed technique canobtain the SV directly and efficiently by iterating second-order cone programming. Moreover,the feasibility and convergence of the proposed algorithms can be guaranteed. The proposedbeamformer avoids the equality constraints in the conventional method, thus more degrees offreedom are saved.
2) A wideband beamformer with mainlobe control is proposed. To make the beamformerrobust against direction of arrival (DOA) mismatch, inequality rather than equality constraintsare used to restrict the mainlobe response, thus more degrees of freedom are saved. Theconstraints involved are nonconvex, therefore are linearly approximated so that thebeamformer can be obtained efficiently by iterating a second-order cone program and can beapplied to arbitrary types of arrays. Moreover, the response variance element is introduced toachieve a frequency invariant beamwidth. The simulation results demonstrate theeffectiveness of the proposed method.
3) A robust beamformer is proposed by modifying the generalized sidelobe canceler(GSC) and using the concept of worst-case performance optimization. With the GSC-likestructure, convex constraints can be directly applied to make the beamformer robust againstDOA mismatch. Then, the beamformer is improved to be robust against arbitrary systemimperfections by applying the worst-case optimization method. The DOA mismatch and othergeneral imperfections can be treated separately in the beamformer, thus an over-conservativerobustness design may be avoided.
4）By introducing the sparse iterative covariance-based estimation (SPICE) approach, a robust beamformer with joint robustness against the desired signal mismatch and theinterference coherence is proposed. With the SPICE, we firstly calibrate the look directionmismatch, and then reconstruct the interference-plus-noise covariance matrix (INCM) toreplace the conventional sample covariance matrix. This is shown to greatly improve therobustness of adaptive beamformers since a quasi signal-free environment is provided.Moreover, since the SPICE is robust to signal coherence, the proposed beamformer cansuppress the coherent interferences.
5) An INCM reconstruction method is proposed by exploiting the cyclostationarity ofinterference signals. In contrast to the existing INCM reconstruction methods, the proposedtechnique is based on the knowledge of the interferences’ cycle frequencies and needs noinformation of the array structure, thus it can deal with unknown perturbations in the array.Moreover, the proposed technique is suitable to the case when the locations of theinterferences and desired signal are close. The numerical simulations show that the proposedmethod improves the robustness of adaptive beamformers and has superior performance to theexisting INCM reconstruction methods especially for strong interferences.
6) A DOA estimation technique is proposed by jointly exploiting the signalcyclostationarity and spatial sparsity. Based on the cyclic conjugate correlation matrix, theproposed estimator exhibits the signal selectivity at a desired cycle frequency, thus thenumber and characteristics of the interference can be arbitrary and unknown. Moreover, byusing the sparse representation framework with the weighted l1-norm minimization, theresolution and accuracy of DOA estimation can be greatly improved. The effectiveness of theproposed method is examined by numerical examples.
引文
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