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存在条件失配时自适应波束形成器的性能急剧下降，凸优化技术的引入使稳健波束形成器的设计更加灵活，但同时带来了计算复杂度的增加和工程实现上的困难. 针对上述问题，提出了一种基于最小二乘估计的稳健波束形成算法，并推导得到一种基于一维搜索的求解方法. 首先利用广义旁瓣对消器的结构将标准Capon波束形成器转化为稳健最小二乘问题，并将该问题转化为二阶锥规划的形式. 为了减少计算量，利用二阶锥规划问题的原始问题和对偶问题的关系，将求解过程转化为一维搜索，并利用牛顿迭代法获得最优解，从而获得与标准Capon波束形成相近的计算复杂度. 仿真分析表明，该算法具有良好的抗导向矢量失配和快拍数不足的稳健性.Adaptive beamforming methods will be degraded sharply in the presence of steering vector errors. The design methods of robust adaptive beamforming become more flexible when the convex optimization technique is used. However, this leads to high computational-complexity and more difficulties for engineering applications. To solve these problems, a robust adaptive beamforming based on the least square estimation is proposed, and a laconic solution method using one-dimensional search is derived. The standard Capon beamformer (SCB) is converted to a robust least-square problem based on the principle of generalized sidelobe canceller, and is then changed into a problem of second-order program. In order to reduce the amount of computation, a one-dimensional search method is deduced using the relationship between the primal and dual problems of second-order program, and Newton iteration method is adopted to obtain the optimal solution. The computational complexity of the proposed algorithm is in the same order of magnitude as that of the SCB. Simulation results demonstrate the robustness of the proposed algorithm in the case of steering vector mismatch and snapshot deficiency.
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Keywords:
- robust adaptive beamforming /
- least square method /
- second-order program /
- Newton iterative method
[1] 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 61 054306]
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[1] 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 61 054306]
[2] [3] [4] 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 61 124302]
[5] Gu Y J, Leshem A 2012 IEEE Trans. Sign. Process. 60 3881
[6] [7] [8] 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 60 064301]
[9] Xiao X, Xu L, Li Q W 2013 Chin. Phys. B 20 094101
[10] [11] [12] Vorobyov S A, Gershman A B, Luo Z Q 2003 IEEE Trans. Sign. Process. 51 313
[13] Li J, Stoica P, Wang Z S 2004 IEEE Trans. Sign. Process. 52 2407
[14] [15] Li J, Stoica P, Wang Z S 2003 IEEE Trans. Sign. Process. 51 1702
[16] [17] Selen Y, Abrahamsson R, Stoica P 2008 Signal Process. 88 33
[18] [19] [20] Jian L, Lin D, Stoica P 2010 IEEE Trans. on A & E 46 449
[21] [22] Wang Y, Wu W F, Fan Z, Liang G L 2013 Acta Phys. Sin. 62 184302 (in Chinese) [王燕, 吴文峰, 范展, 梁国龙 2013 62 184302]
[23] Khabbazibasmenj A, Vorobyov S A, Hassanien A 2012 IEEE Trans. Sign. Process. 60 2974
[24] [25] [26] Rubsamen M, Gershman A B 2012 IEEE Trans. Sign. Process. 60 740
[27] Yu G J, Leshem A 2012 IEEE Trans. Sign. Process. 60 3881
[28] [29] [30] Somasundaram S D 2012 IEEE Trans. Sign. Process. 60 5845
[31] Wang J A 2011 Chin. Phys. B 20 120701
[32] [33] Lakshmanan S, Balasubramaniam P 2011 Chin. Phys. B 20 040204
[34] [35] [36] Shahbazpanahi S, Gershman A B, Luo Z Q, Wong K M 2003 IEEE Trans. Sign. Process. 51 2257
[37] Li X L, Li S L 2013 Chin. Phys. B 22 080204
[38] [39] [40] Stephen B, Lieven V 2004 Convex Optimization (Cambridge: Cambridge University Press) pp223–227
[41] [42] Yang J, Sun Q Y, Yang D S 2012 Acta Phys. Sin. 61 200511 (in Chinese) [杨珺, 孙秋野, 杨东升 2012 61 200511]
[43] Luo W, Zhang M, Zhou P, Yin H C 2010 Chin. Phys. B 19 084102
[44] [45] [46] Zhou L H, Gao X H, Yang Z J, Lu D Q, Guo Q, Cao W W, Hu W 2011 Acta Phys. Sin. 60 044208 (in Chinese) [周罗红, 高星辉, 杨振军, 陆大全, 郭旗, 曹伟文, 胡巍 2011 60 044208]
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