To diminish the performance degradation of coprime array beamforming arising from sensor gain and phase uncertainties, we propose a robust beamformer based on covariance matrix modification with augmented instrumental sensors. Initially, the received array data are split into two subarrays. Utilizing the instrumental sensors, we estimate the gain-phase errors of these two subarrays and then recombine them. Subsequently, error compensation is implemented to calibrate the received covariance matrix into a Toeplitz matrix relevant to the coprime array structure, in which the holes need to be further filled by means of some matrix completion operation. Then, the above covariance matrix modification is integrated into the classical beamforming procedure including MUSIC decomposition, spectral peak searching, power estimation, INCM (Interference-plus-Noise Covariance Matrix) reconstruction, thus yielding the final beamformer weight vector. Both theoretical analysis and simulations demonstrate that this method not only can accurately estimate the gain and phase errors, but also can effectively improve the beamformer’s output SINR (i.e., the robustness is enhanced), which presents the proposed beamformer with vast potentials in practical sparse-array involved applications.

中文翻译：

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基于传感器增益相位误差互质阵列的鲁棒自适应波束形成算法

为了减少由传感器增益和相位不确定性引起的互质阵列波束形成的性能下降，我们提出了一种基于增强仪器传感器的协方差矩阵修改的鲁棒波束形成器。最初，接收到的数组数据被分成两个子数组。利用仪器传感器，我们估计这两个子阵列的增益相位误差，然后将它们重新组合。随后，进行误差补偿，将接收到的协方差矩阵校准为与互质阵列结构相关的托普利茨矩阵，其中的空洞需要通过某种矩阵补全操作来进一步填充。然后，将上述协方差矩阵修改集成到经典波束形成过程中，包括MUSIC分解、频谱峰值搜索、功率估计、INCM（干扰加噪声协方差矩阵）重建，从而产生最终的波束形成器权重向量。理论分析和仿真都表明，该方法不仅可以准确估计增益和相位误差，而且可以有效提高波束形成器的输出SINR（即增强鲁棒性），这表明所提出的波束形成器在实际稀疏网络中具有巨大的潜力。数组涉及应用程序。