多维线性约束鲁棒自适应特征波束形成算法

Robust Adaptive Eigen-beam Beamforming Algorithm Subject to Multiple Linear Equality Constraints

以镶嵌在刚性圆柱体上的均匀圆阵为阵列模型,研究了一种鲁棒自适应特征波束形成算法。在分析了特征波束形成技术的基础上,将阵列优化问题描述为多维线性约束下的波束优化问题,进而在约束矩阵的正交线性子空间求解最优化问题,在满足鲁棒性约束条件下自适应地得到了阵列最优权向量,进而获得了与期望波束图较为一致的波束图,并分析了在满足鲁棒性约束条件下最大特征波束阶次的选择以及算法的收敛性。该算法具有收敛速度快、迭代误差不会累积的特点。计算机仿真验证了算法的有效性。

Multiple linear equality constraints are used in beamforming optimization and a robust adaptive eigen-beam beamforming algorithm is proposed based on the array model of a uniform circular array mounted on a rigid cylinder. The eigen-beam beamforming technology is analyzed firstly, and the array optimization is reformulated as the beamforming optimization subject to multiple linear equality constraints. Then, the optimization problem is resolved in the orthogonal subspace of the constraint matrix and the optimal beamformer weights are achieved subject to robustness constraint. The synthesized beampattern using the optimal weights is very similar to the desired beampattern. The selection of the maximal order of the eigen-beams and the convergence of the algorithm are analyzed. The proposed algorithm converges to the optimal performance quickly while the round-off errors do not accumulated. The validity of the proposed algorithm is verified by computer simulations.