面向阵列互耦扰动DOA估计的原子范数方法

Atomic Norm Method for Array Mutual Coupling Perturbed DOA Estimation

互耦效应是天线阵列工作时阵元相互之间产生的一种干扰影响,会导致理想导向矢量与真实导向矢量之间存在偏差,严重影响参数的估计性能。本文针对阵列互耦扰动下的波达方向(Di-rection of Arrival,DOA)估计问题,提出了一种新的原子范数最小化方法MC-ANM,以提高参数估计精度。由于阵列互耦扰动下的原子结构不满足范德蒙德特性,原问题无法直接转化为半定规划程序。因此,文中基于对偶范数理论,推导了一个新的半定规划优化模型,作为原问题对应的对偶问题的充分近似,并构建了对偶多项式,以求解该半定规划优化中的DOA参数。仿真实验结果显示所提出的MC-ANM方法相较于传统原子范数最小化方法的估计性能有了明显的提升,同时估计精度要好于其他互耦扰动下的DOA估计算法。

The mutual coupling effect is an interference phenomenon among antenna array elements,which leads to deviations between ideal steering vectors and actual steering vectors,significantly affecting the performance of parameter estimation.In this paper,a new method called MC-ANM based on atomic norm minimization is proposed for direction of arrival(DOA)estimation under array mutual coupling to improve parameter estimation accuracy.Since the atomic structure under array mutual coupling does not satisfy the Vandermonde property,the original problem cannot be directly converted into a semidefinite programming problem.Therefore,based on the theory of dual norms,a new semidefinite programming optimization model is derived as a sufficient approximation to the dual problem corresponding to the original problem,and a dual polynomial is constructed to solve the DOA parameters in this semidefinite programming optimization.Simulation results show that the proposed MC-ANM method significantly improves the estimation performance compared to conventional atomic norm minimization method,with better estimation accuracy than other DOA estimation algorithms under mutual coupling.