Fast compressive beamforming with a modified fast iterative shrinkage-thresholding algorithm

Compressive beamforming has been successfully applied to direction-of-arrival estimation with sensor arrays. The results demonstrated that this technique achieves superior performance when compared with traditional high-resolution beamforming methods. The existing compressive beamforming methods use classical iterative optimization algorithms in their compressive sensing theories. However, the computational complexity of the existing compressive beamforming methods tend to be excessively high, which has limited the use of compressive beamforming in applications with limited computing resources. To address this issue, this paper proposes a fast compressive beamforming method which combines the shift-invariance of the array beam patterns with a fast iterative shrinkage-thresholding algorithm. The evaluation shows that the proposed fast compressive beamforming method successfully reduces the number of floating-point operations by 3 orders of magnitude when compared with the existing methods. In addition, both the simulations and experiments demonstrate that the resolution limit for discerning closely spaced sources of the introduced fast method is comparable to those of the existing compressive beamforming methods, which use classical iterative optimization algorithms.