基于稳健最小二乘的鲁棒波束形成
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摘要
为解决Capon波束形成器在存在导向矢量失配时的性能急剧下降问题,提出了一种结合广义旁瓣对消器和稳健最小二乘的鲁棒波束形成算法.该算法利用广义旁瓣对消器原理将Capon波束形成器转化为最小二乘问题,然后在数据协方差矩阵误差的范数约束下将其转化为二阶锥规划问题,并利用高效内点法得到最优解.所提出的算法经推导证明属于对角加载类.仿真分析表明,该算法在导向矢量失配和快拍不足时仍具有较好的性能.
The performance of Capon beamformer degrades sharply in the presence of array steering vector errors.To solve this problem,a robust beamforming algorithm,which combines generalized sidelobe canceller(GSC)and robust least-square,is proposed.The Capon beamformer is converted to a least-square problem based on the principle of generalized sidelobe canceller,and then converted to a second-order cone program(SOCP)problem under the constraint on the norm of the error matrix.The well-established interior point method is adopted in order to obtain the optimal solution.Deduction proves that the proposed algorithm belongs to the diagonal loading sort.Simulation results show the efficiency of the proposed algorithm in the case of steering vector mismatch and snapshot deficiency.
The performance of Capon beamformer degrades sharply in the presence of array steering vector errors.To solve this problem,a robust beamforming algorithm,which combines generalized sidelobe canceller(GSC)and robust least-square,is proposed.The Capon beamformer is converted to a least-square problem based on the principle of generalized sidelobe canceller,and then converted to a second-order cone program(SOCP)problem under the constraint on the norm of the error matrix.The well-established interior point method is adopted in order to obtain the optimal solution.Deduction proves that the proposed algorithm belongs to the diagonal loading sort.Simulation results show the efficiency of the proposed algorithm in the case of steering vector mismatch and snapshot deficiency.
引文
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[2]Z L Yu,Meng Hwa Er.A robust minimum variance beamformer with new constraint on uncertainty of steering vector[J].Signal Processing,2006,86(9):2243-2254.
[3]宋海岩,朴胜春,等.矢量最优化稳健波束形成性能分析[J].电子学报,2012,40(7):1351-1357.SONG Hai-yan,PIAO Sheng-chun,et al.Performance analysis of robust adaptive beamforming based on vector optimization[J].Acta Electronica Sinica,2012,40(7):1351-1357.(in Chinese)
[4]Li J,Stoica P,Wang Z S.On robust Capon beamforming and diagonal loading[J].IEEE Transactions on Signal Processing,2003,51(7):1702-1715.
[5]Li J,Stoica P,Wang Z S.Doubly constrained robust Capon beamformer[J].IEEE Transactions on Signal Processing,2004,52(9):2407-2432.
[6]Vorobyov S A,Gershman A B,Luo Z Q.Robust adaptive beamforming using worst-case performance optimization:A solution to the signal mismatch problem[J].IEEE Transactions on Signal Processing,2003,51(2):313-324.
[7]Selen Y,Abrahamsson R,Stoica P.Automatic robust adaptive beamforming via ridge regression[J].Signal Processing,2008,88(1):33-49.
[8]Jian L,Lin D,Stoica P.Fully automatic computation of diagonal loading levels for robust adaptive beamforming[J].IEEE Transactions on Aerospace and Electronic System,2010,46(1):449-458.
[9]L E Ghaoui,H Lebret.Robust solutions to least-squares problems with uncertain data[J].SIAM J on Matrix Analysis and Applications,1997,18(4):1035-1064.
[10]J F Sturm.Using SeDuMi 1.02,a MATLAB toolbox for optimiazation over symmetric cones[J].Optimization Methods and Software,1999,11(1):625-653.
[11]Shahbazpanahi S,Gershman A B,et al.Robust adaptive beamforming for general-rank signal models[J].IEEE Transactions on Signal Processing,2003,51(9):2257-2269.