Beampattern optimization for superdirective frequency-invariant beamforming with circular sensor arrays
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摘要: 提出了一种适用于圆环形传感器阵列的超指向性频率不变响应波束优化方法。首先,基于前期在最小均方误差准则下得到的不同频率处权值向量与期望波束权值向量的解析函数关系,将指向性因子、误差敏感度函数和最小均方误差进一步表达成了期望波束权值向量的函数;然后,构建了一个多约束优化问题,获得了满足指向性、稳健性、频率不变性等约束条件的最优期望波束,由此合成得到了最优宽带频率不变响应超指向性波束,并给出了相应的仿真和实验结果。Abstract: This paper proposes a beampattern optimization method for superdirective frequency-invariant beamforming with circular sensor arrays. Firstly, the previously proposed beampattern-synthesis-based superdirective beamforming method is briefly reviewed. Since the weighting vectors at different frequencies are all expressed as analytical functions of the desired weighting vector based on the criterion of minimizing the mean square error between the desired and synthesized beampatterns, the directivity factor, the sensitivity function, and the minimum mean square error can be all formulated as functions of the desired weighting vector. Then, a multi-constraint optimization problem is proposed, which can obtain the optimal desired beampattern subject to directivity, robustness, and frequency-invariance constraints. The superdirective frequency-invariant beampatterns at other frequencies can be directly synthesized using the previously derived analytical functions. The good performance of the proposed method is demonstrated using simulations and experimental data.
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