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针对标准Capon波束形成器在存在导向矢量失配时性能急剧下降问题, 提出了一种基于半定规划和秩-1分解的稳健波束形成算法. 该方法通过对实际导向矢量的估计提高自适应波束形成算法稳健性. 首先分别从干扰抑制和噪声抑制两个方面推导了新导向矢量应满足的约束条件, 并证明了利用矩阵滤波器构造约束条件的合理性; 构造了估计最优导向矢量的优化问题并将其转化为易于求解的松弛半定规划问题, 同时引入秩-1分解理论用于优化问题的求解. 仿真分析表明, 与目前较为常见的算法相比, 本文算法只需利用期望信号可能入射区间这一先验信息, 能获得更高输出信干噪比和功率估计精度.The performance of Capon beamformer degrades sharply in the presence of array steering vector mismatch. To solve this problem, a robust beamforming algorithm based on semi-definite programming and rank-one decomposition is proposed, which improves the robustness of the adaptive beamforming by estimating an actual steering vector. The constraints for estimating the steering vector are deduced under the requirement that the estimate does not weaken the ability to suppress interference and noise, and the analysis shows that the approach to formulating constraint using matrix pre-filter is reasonable. The optimization problem is constructed and converted into a semi-definite relaxation problem, and rank-one decomposition technique is adopted in order to obtain the optimal solution. The simulation results demonstrate that compared with the existing algorithms, the proposed algorithm offers high SINR (signal to interference plus noise power ratio) and accuracy of power estimation, with the sole prior information about the angular vector in which the actual signal lies.
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Keywords:
- robust adaptive beamforming /
- semi-definite programming /
- rank-one decomposition /
- steering vector estimation
[1] Shi J, Yang D S, Shi S G 2012 Acta Phys. Sin. 61 124302 (in Chinese) [时洁, 杨德森, 时胜国 2012 物理学报 61 124302]
[2] Yang D G, Li B, Wang Z T, Lian X M 2012 Acta Phys. Sin. 61 054306 (in Chinese) [杨殿阁, 李兵, 王子腾, 连小珉 2012 物理学报 61 054306]
[3] Shi J, Yang D S, Shi S G 2011 Acta Phys. Sin. 60 064301 (in Chinese) [时洁, 杨德森, 时胜国 2011 物理学报 60 064301]
[4] Gu Y J, Leshem A 2011 IEEE Trans. Sign. Process. 60 3881
[5] Li J, Stoica P, Wang Z S 2003 IEEE Trans. Sign. Process. 51 1702
[6] Li J, Stoica P, Wang Z S 2004 IEEE Trans. Sign. Process. 52 2407
[7] Sergiy A V, Gershman A B, Luo Z Q 2003 IEEE Trans. Sign. Process. 51 313
[8] Selen Y, Abrahamsson R, Stoica P 2008 Signal Process. 88 33
[9] Gu Y J, Zhu W P, Swamy M N 2010 Electron. Lett. 46 86
[10] Li J, Lin D, Stoica P 2010 IEEE Trans. on A&E 46 449
[11] Aboulnasr H, Sergiy A V, Wong K M 2008 IEEE Sign. Process. Lett. 15 733
[12] Arash K, Sergiy A V, Aboulnasr H 2012 IEEE Trans. Sign. Process. 60 2974
[13] Yang D G, Luo Y G, Li B, Li K Q, Lian X M 2010 Acta Phys. Sin. 59 4738 (in Chinese) [杨殿阁, 罗禹贡, 李兵, 李克强, 连小珉 2010 物理学报 59 4738]
[14] Feldman D D, Griffiths L J 1994 IEEE Trans. Sign. Process. 42 867
[15] Yan S F, Ma Y L 2009 Sensor Array Beampattern Optimization: Theory with Application (1st Ed.) (Beijing: Science Press) p53 (in Chinese) [鄢社锋, 马远良 2009传感器阵列波束优化设计及应用(第一版)(北京: 科学出版社) 第53页]
[16] Luo Z Q, Ma W K, Anthony M C S, Ye Y Y, Zhang S Z 2010 IEEE Sign. Process. Mag. 27 20
[17] Ai W B, Huang Y W, Zhang S Z 2009 Math. Program. 128 253
[18] Richard J V, Amit C, Brian F H 2004 J. Acoust. Soc. Am. 115 3010
[19] Louidor E, Marcus B H 2010 IEEE Trans. Inf. Theory 56 1624
[20] Li Y Z, Shi Q F, Wang Q 2006 Acta Phys. Sin. 55 1119 (in Chinese) [李运周, 史庆藩, 王琪 2006 物理学报 55 1119]
[21] He J B, Liu Z, Hu S L 2011 Acta Phys. Sin. 60 110208 (in Chinese) [贺静波, 刘忠, 胡生亮 2011 物理学报 60 110208]
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[1] Shi J, Yang D S, Shi S G 2012 Acta Phys. Sin. 61 124302 (in Chinese) [时洁, 杨德森, 时胜国 2012 物理学报 61 124302]
[2] Yang D G, Li B, Wang Z T, Lian X M 2012 Acta Phys. Sin. 61 054306 (in Chinese) [杨殿阁, 李兵, 王子腾, 连小珉 2012 物理学报 61 054306]
[3] Shi J, Yang D S, Shi S G 2011 Acta Phys. Sin. 60 064301 (in Chinese) [时洁, 杨德森, 时胜国 2011 物理学报 60 064301]
[4] Gu Y J, Leshem A 2011 IEEE Trans. Sign. Process. 60 3881
[5] Li J, Stoica P, Wang Z S 2003 IEEE Trans. Sign. Process. 51 1702
[6] Li J, Stoica P, Wang Z S 2004 IEEE Trans. Sign. Process. 52 2407
[7] Sergiy A V, Gershman A B, Luo Z Q 2003 IEEE Trans. Sign. Process. 51 313
[8] Selen Y, Abrahamsson R, Stoica P 2008 Signal Process. 88 33
[9] Gu Y J, Zhu W P, Swamy M N 2010 Electron. Lett. 46 86
[10] Li J, Lin D, Stoica P 2010 IEEE Trans. on A&E 46 449
[11] Aboulnasr H, Sergiy A V, Wong K M 2008 IEEE Sign. Process. Lett. 15 733
[12] Arash K, Sergiy A V, Aboulnasr H 2012 IEEE Trans. Sign. Process. 60 2974
[13] Yang D G, Luo Y G, Li B, Li K Q, Lian X M 2010 Acta Phys. Sin. 59 4738 (in Chinese) [杨殿阁, 罗禹贡, 李兵, 李克强, 连小珉 2010 物理学报 59 4738]
[14] Feldman D D, Griffiths L J 1994 IEEE Trans. Sign. Process. 42 867
[15] Yan S F, Ma Y L 2009 Sensor Array Beampattern Optimization: Theory with Application (1st Ed.) (Beijing: Science Press) p53 (in Chinese) [鄢社锋, 马远良 2009传感器阵列波束优化设计及应用(第一版)(北京: 科学出版社) 第53页]
[16] Luo Z Q, Ma W K, Anthony M C S, Ye Y Y, Zhang S Z 2010 IEEE Sign. Process. Mag. 27 20
[17] Ai W B, Huang Y W, Zhang S Z 2009 Math. Program. 128 253
[18] Richard J V, Amit C, Brian F H 2004 J. Acoust. Soc. Am. 115 3010
[19] Louidor E, Marcus B H 2010 IEEE Trans. Inf. Theory 56 1624
[20] Li Y Z, Shi Q F, Wang Q 2006 Acta Phys. Sin. 55 1119 (in Chinese) [李运周, 史庆藩, 王琪 2006 物理学报 55 1119]
[21] He J B, Liu Z, Hu S L 2011 Acta Phys. Sin. 60 110208 (in Chinese) [贺静波, 刘忠, 胡生亮 2011 物理学报 60 110208]
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