双约束稳健Capon波束形成算法的分析与求解

针对Capon波束形成算法在导向矢量的不确定集和模约束下的求解问题，提出了新的分析和求解方法。通过对最优化问题进行深入分析，发现不确定集约束决定该算法的性能，而模约束只是起辅助约束作用，因此可以通过对不确定集约束Capon波束形成算法的解进行标量化处理,使其满足模约束而获得该算法的最优解。所提出方法不仅使得不确定集约束参数的选择更加简单，同时使得波束形成算法的性能改善达到最优。发现不确定集约束参数选择得越大，算法的性能改善越接近于最优，而此时对应于负加载。仿真分析验证了方法的正确性和有效性。

Analysis and solution for double constraint robust Capon beamforming algorithm

For the problem of solving the Capon beamforming algorithm under the uncertainty set and norm of the steering vector, a novel analyzing and solving method is proposed. Via analyzing the characteristic of the optimization problem deeply, it is found that the uncertainty set constraint determines the performance, but the norm constraint is accessorial. Therefore, the optimal solution to this algorithm will be obtained by the solution of the Capon beamforming algorithm under the uncertainty set constraint scaling to meet the norm constraint. According to the proposed algorithm, the selection of the steering uncertainty constraint parameter becomes more simple. Moreover, the improvement performance of the beamforming algorithm can reach the optimal. It is also found that the greater the constraint parameter is selected, the more close to optimal is the performance of the beamforming algorithm. The simulation attests its correctness and effectiveness.