基于原子范数最小化的稀疏阵列稳健波束形成算法

A Robust Beamforming Algorithm for Sparse Array Based on Atomic Norm Minimization

为提高稀疏阵列在信号模型存在失配时的波束形成性能,提出一种基于原子范数最小化(Atomic Norm Minimization,ANM)的稳健波束形成算法。构建基于ANM的降噪问题模型,根据稀疏阵列的协方差矩阵结构将其转化为等价的半定规划问题,同时推导该问题的对偶问题以提高运行效率,求解得到阵列降噪后的接收数据和协方差矩阵。根据互质阵列的结构特性证明其空间谱的无模糊性,对所得的协方差矩阵直接使用多重信号分类算法获得入射信号的波达方向。利用虚拟填充技术得到与互质阵列孔径相同的均匀线性阵列的接收数据,最终获得阵列输出。通过计算机仿真实验,验证了所提算法的可行性和准确性,较其他被测算法输出的信干噪比至少提高1.5 dB。

Aiming at the performance degradation of the beamforming algorithm when some mismatches are present in the signal model.A robust beamforming algorithm based on atomic norm minimization(ANM)is proposed to improve the beamforming performance of sparse array during the mismatch of signal model.The proposed algorithm is used to construct an ANM-based noise reduction model and transform it into an equivalent semi-definite programming problem according to the covariance matrix structure of sparse array.Meanwhile,the dual problem of this model is derived to improve the computational efficiency,and the received data and covariance matrix of the array after noise reduction are obtained.The spatial spectrum is proved to be unambiguous based on the structural properties of a coprime array,and the directions of arrival of the incident signals are obtained directly by using the multiple signal classification algorithm for the resulting covariance matrix.The received data of a uniform linear array with the same aperture as the coprime array is obtained using the virtual filling technique,and the array output is ultimately obtained.Simulated results verify the feasibility and accuracy of the proposed algorithm,which improves the output signal to interference plus noise ratio by at least 1.5 dB compared to the other tested algorithms.