Robust Adaptive Beamforming Based on Linearly Modified Atomic-Norm Minimization With Target Contaminated Data

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.