基于半定规划和秩-1分解的稳健波束形成

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. 关键词： 稳健自适应波束形成 半定规划 秩-1分解 导向矢量估计

Robust adaptive beamforming based on semi-definite programming and rank-one decomposition

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.
Keywords： robust adaptive beamforming semi-definite programming rank-one decomposition steering vector estimation