In practice, adaptive beamforming usually faces non-ideal situations where a limited number of snapshots are available, the training data are corrupted by desired target signals, and the array mismatches exist. Traditional methods often degrade significantly under the above situation. In order to solve this problem, a new adaptive beamforming method based on atomic-norm optimization technique is proposed in this paper. In the proposed method, the interference subspace is estimated by minimizing the rank of interference data matrix while making the signals bounded within a ball of Frobenius norm around the observed data. This non-convex problem is solved using alternative optimization which decomposes it into two iterative steps. Each step can be formulated as semi-definite programming, and solved efficiently. Unlike traditional methods, the proposed method can estimate the target signals, target directions, and interference subspace simultaneously. This property guarantees that the proposed beamformer is free from the influence of target signals, and able to adjust pointing direction adaptively. Then it is derived theoretically that the estimation of interference subspace in the proposed method is consistent, and bounded. A fast implementation algorithm based on alternating direction method of multipliers is also derived. Compared with traditional methods, the proposed method not only performs better with target-contaminated training data, and erroneous prior of target direction, but also requires much less snapshots to work. The effectiveness of the proposed method, and its advantages over traditional methods are verified based on simulated, and actual measured radar data.

中文翻译：

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基于目标污染数据线性修正原子范数最小化的鲁棒自适应波束形成


在实践中，自适应波束形成通常面临非理想情况，即可用快照数量有限、训练数据被所需目标信号破坏以及存在阵列失配。传统方法在上述情况下往往性能显着下降。为了解决这一问题，本文提出了一种基于原子范数优化技术的自适应波束形成方法。在所提出的方法中，通过最小化干扰数据矩阵的秩来估计干扰子空间，同时使信号限制在观测数据周围的弗罗贝尼乌斯范数球内。这个非凸问题是使用替代优化来解决的，将其分解为两个迭代步骤。每个步骤都可以表示为半定规划，并有效地求解。与传统方法不同，该方法可以同时估计目标信号、目标方向和干扰子空间。这一特性保证了所提出的波束形成器不受目标信号的影响，并且能够自适应地调整指向。然后从理论上推导出该方法对干扰子空间的估计是一致的、有界的。还推导了一种基于乘法器交替方向法的快速实现算法。与传统方法相比，所提出的方法不仅在目标污染训练数据和目标方向错误先验方面表现更好，而且需要更少的快照。基于仿真和实测雷达数据验证了该方法的有效性及其相对于传统方法的优势。