[发明专利]一种基于压缩协方差矩阵感知的鲁棒阵列波束形成方法

说明书

一种基于压缩协方差矩阵感知的鲁棒阵列波束形成方法，本发明涉及基于压缩协方差矩阵感知的鲁棒阵列波束形成方法。本发明为了解决阵列误差建模为SIRV模型及非理想压缩感知条件下现有波束形成算法波束空间谱主旁瓣比不高，以及自适应波束形成输出SINR值低的问题。本发明包括：一：构造信号协方差矩阵R_x的表达式，利用采样协方差矩阵及信号导向矢量矩阵和干扰导向矢量矩阵，并利用波束空间法求解信号协方差矩阵R_x；二：优化并求解鲁棒自适应波束形成算法模型，得到波束形成器权值w；三：将信号协方差矩阵R_x波束形成器权值w作为初始值迭代优化，直至收敛，得到最终的波束形成器权值w_opt。本发明用于智能天线技术领域。

技术领域

本发明涉及智能天线技术领域，具体涉及鲁棒阵列波束形成方法。

背景技术

几十年以来，自适应波束形成技术吸引了许多研究者的目光，这种技术广泛应用在雷达、通信、导航、宇航和生物医学中。根据计算方法的不同，自适应波束形成技术大体上能够分为两类。一类是基于参考信号的算法，如LMS算法(Widrow B,Mantey P E,GriffithsL J,and Goode B B.Adaptive antenna systems.Proc.IEEE,1967,55:2143-2159.GitlinR D,Weinstein S D.On the design of gradient algorithms for digitallyimplemented adaptive filters.IEEE Trans on CT,1973,2:125-136.[3]Nagumo J I,and Noda A.A learning method for system identification.IEEETrans.Autom.Control,1967,12:282-287)和DMI算法(Albert A E,and Gardner LS.Stochastic Approximation and Nonlinear Regression.MIT Press.1967.Widrow B,MeCool J,Ball M.The complex LMS algorithm.Proceedings of the IEEE,1975,4(63):719-720.)。另一类是基于DOA估计的算法，例如Capon提出的MVDR波束形成算法(DentinoM,McCool J,etc.Adaptive filtering in the frequency domain[J].IEEE Proc,1978,12(66):1658-1659)，LCMV算法(Xiaofei Zhang,Dazhuan Xu.Frequency Domain LMSBased Adaptive Beamforming Algorithm.Chinese Space Science andTechnology.2005,2:41-58)以及MSC算法(Reed I S.Rapid convergence rate inadaptive antenna.Aerospace and Electronic Systems,1974,10(6):853-863)。然而，考虑到实际情况，实际系统存在各种误差及非理想因素(O.Besson and P.Stoica.Decoupledestimation of doa and angular spread for a spatially distributed source.IEEETransaxtions on Signal Processing,2000,48:1872-1882)，这就要求算法具有足够的鲁棒性。文献(S.A.Vorobyov,Y.Rong,A.B.Gershman.Robust adaptive beamforming usingprobability-constrained optimization.In Proceedings of IEEE Workshop onStatistical Signal Processing.2005:934-939.S.A.Vorobyov,Y.C.Eldar,A.Nemirovski,and A.B.Gershman.Probability-constrained approach to estimationof random gaussian parameters.In Proceedings of First IEEE Inter.Workshop onComputational Advances in Multi-Sensor Adaptive Processing,2005:101-104.S.A.Vorobyov,Y.C.Eldar,A.Nemirovski,and A.B.Gershman.Probabilistically-constrained estimation random parameters with unknown distribution.InProceedings of 4th IEEE Sensor Array and Multi-channel Signal ProcessingWorkkshop,SAM'06,2006:54-57)中提出了估计高斯随机参数或鲁棒自适应波束形成的概率约束方法。文献(César C.Gaudes,Ignacio Santamaría,Javier Vía.Robust ArrayBeamforming With Sidelobe Control Using Support Vector Machines[J].IEEETransactions on Signal Processing,2007,55(2):574-584.Manel Martínez-Ramón,Christos Christodoulou.Support Vector Machines for Antenna Array Processingand Electromagnetics[M].MorganClaypool Publishers,2006,ch3:33-40.Amina ElGonnouni,Manel Martínez-Ramón,JoséLuis Rojo-A Support Vector MachineMUSIC Algorithm[J].IEEE Transactions on Antennas and Propagation,2012,60(10):4901-4910)将支持向量机(the support vector machines,SVM)应用在鲁棒阵列波束形成中。在某些场景中，压缩感知可以显著减少通信负载，这种技术有效利用了稀疏信号并以一个远低于奈奎斯特速率的采样频率采样(ALI CAFER GURBUZ,VOLKAN CEVHER,JAMESH.McCLELLAN.Bearing Estimation via Spatial Sparsity using CompressiveSensing.IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS.2012,2(48):1358-1369.Jian Jin,Yuantao Gu,and Shunliang Mei.A Stochastic GradientApproach on Compressive Sensing Signal Reconstruction Based on AdaptiveFiltering Framework.IEEE JOURNAL OF SELECTED TOPICS IN SIGNALPROCESSING.2010,4(2):409-420.Emmanuel J.Candès,Michael B.Wakin.AnIntroduction to Compressive Sampling.IEEE SIGNAL PROCESSING MAGAZINE.2008,(3):21-30)。Candes在文献(E Candès.Compressive sampling[A].Proceedings of theInternational Congress of Mathematicians[C].Madrid,Spain,2006,3:1433-1452)中证明了如果信号在一个正交空间中稀疏，那么这个信号可以低频率采样但可以高概率的恢复。文献(E Candès,J Romberg,Terence Tao.Robust uncertainty principles:Exactsignal reconstruction from highly incomplete frequency information[J].IEEETrans.on Information Theory,2006,52(2):489-509.E Candès.The restrictedisometry property and its implications for compressed sensing[J].Acadèmie dessciences,2006,346(I):598-592)中，Candes证明了这种恢复方法存在的充分必要条件是感知矩阵满足RIP(Restricted Isometry Property)。基于MP算法，OMP(J A Tropp and AC Gilbert.Signal Recovery from Partial Information by Orthogonal MatchingPursuit[OL].April2005,www.personal.umich.edu/_jtropp/papers/TG05-Signal-Recovery.pdf)，TMP(C La,M N Do.Signal reconstruction using sparse treerepresentation[A].Proceedings of SPIE[C].San Diego,CA,United States:International Society for Optical Engineering.2005.5914:1-11)以及StOMP(D LDonoho,Y Tsaig,I Drori,etc.Sparse solution of underdetermined linearequations by stagewise orthogonal matching pursuit[R].Technical Report,2006)等各种信号恢复算法相继被提出。然而，在某些场景中，压缩感知矩阵并不满足RIP，这被称为非理想压缩感知。