Joint Coprime Weights Optimization for Sub-Nyquist Tensor Beamforming

The emerging tensor beamformers are capable of structurally filtering multi-dimensional signals of sensor arrays. Although the popular sparse arrays have been utilized to enhance the resolution of beamforming, the existing tensor beamformers are only suitable for uniform arrays, which cannot handle the sub-Nyquist signals sampled by the sparse arrays. To address this issue, we propose a sub-Nyquist tensor beamforming method for coprime planar array, which is one of the typical sparse arrays. First, the coprime planar array signals are modeled as two sub-Nyquist tensors accompanied with a pair of tensor beamformer weights. Then, to suppress the sidelobes brought by the sparsity deployment of sensor arrays, a joint coprime weights optimization problem is proposed by imposing combined distortionless response constraints. Furthermore, the nonconvex joint coprime weights optimization problem is transformed into a pair of tensor decomposition-based sub-problems with convexity. As such, an alternating minimization approach is formulated to iteratively solve the interconnected sub-problems, which yields the optimum tensor beamformer design. The effectiveness of the proposed method is verified by simulations.