基于稀疏重建和压缩感知波束形成的高分辨DOA估计  

High Resolution Direction-of-Arrive Estimation Based on Sparse Reconstruction and Compressive Sensing Beamforming

作　　者：陈玉凤[1] 黄建国[1] 苏建军[1] 

机构地区：[1]西北工业大学航海学院,陕西西安710072

出　　处：《鱼雷技术》2013年第2期110-114,131,共6页Torpedo Technology

基　　金：国家自然科学基金(60972152);国家重点实验室基金(9140C230309110C23);西北工业大学基础研究基金(JC201027)

摘　　要：利用空域目标的稀疏性,建立了基于正弦域的DOA压缩感知模型,并根据压缩感知理论设计了一种随机压缩采样方式,从而构造了一种新的测量矩阵。同时将普适的高斯随机测量矩阵进行近似QR分解得到新的测量矩阵,使得该矩阵具有更好的约束等容(RIP)常数。应用新构造的测量矩阵,采用奇异值分解(SVD)提取信号子空间,得到低维形式的接收数据矩阵,从而提出了2种不同类别的DOA估计算法:基于QR分解和奇异值分解的多测量矢量欠定系统正则化聚焦求解算法(QR-SVD-MFOCUSS)和压缩感知波束形成算法(RSVD-CSB、QRSVD-CSB)。与多测量矢量欠定系统聚焦求解(MFOCUSS)等算法相比,QR-SVD-MFOCUSS算法在低信噪比条件下适用且运算量显著降低;与传统的最小方差无畸变响应(MVDR)算法和压缩感知(CS)波束形成算法相比,基于随机测量矩阵和奇异值分解的压缩感知波束形成算法(RSVD-CSB)和基于QR分解测量矩阵和奇异值分解的压缩感知波束形成算法(QRSVD-CSB)算法具有更高的角度分辨率、更低的均方根误差及更优的估计性能等。A novel compression perception model is established by making use of the spatial sparsity. A random com- pression matrix is constructed by designing a new compressive sampling way with compressive sensing（CS） theory. And another compression matrix is obtained by applying approximate QR decomposition to Gaussian random matrix in order to get a better restricted isometry property（RIP） constant. Singular value decomposition（SVD） is adopted on the data matrix to extract signal subspace for getting low dimensional form of receiving data matrix. Two different kinds of methods for DOA estimation are proposed based on the new compression matrices. One is for CS recovery, i.e. QR sin- gular value decomposition multi-vectors FOCal undetermined system solve（QR-SVD-MFOCUSS）; the other is for CS beamforming, i.e. random singular value decomposition compressive sensing beamforming（RSVD-CSB） and QR singu- lar value decomposition compressive sensing beamforming（QRSVD-CSB）. Simulation results show that, compared to the multi-vectors FOCal undetermined system solver（MFOCUSS） algorithms, QR-SVD-MFOCUSS is suitable for low signal-to-noise ratio（SNR） condition with significant reduction of computational burden; and compared to the minimum variance distortionless response（MVDR） algorithms and the CS bearnforming algorithms, the proposed method pos- sesses higher angular resolution, lower root mean square error（RMSE）, better estimation performance, and so on.

关 键 词：方位估计 压缩感知 QR分解 波束形成 

分 类 号：TJ630.34[兵器科学与技术—武器系统与运用工程] TN911.7[电子电信—通信与信息系统]