Tensor Beamforming for EMVS Coprime Planar Array

‍ ‍Compared to conventional uniform scalar sensor arrays， electromagnetic vector sensor （EMVS） sparse arrays can obtain multi-spatial electromagnetic information with reduced system costs， and the precise beam scanning offers improved direction-of-arrival （DOA） estimation performance. However， traditional matrix-based beamforming methods fail to exploit the structural characteristics of the signals received by an EMVS array， and cannot suppress the ambiguous sidelobes produced by a sparse sensor deployment. To cope with these issues， a tensor beamforming algorithm is proposed for an EMVS coprime planar array， where the coprime beam distribution and tensor processing are incorporated for accurate beam scanning. In particular， the multi-spatial electromagnetic signals received at the coprime subarrays are represented by a pair of tensors. The principle of tensor signal filtering was investigated， and tensor minimum-variance distortionless response optimization problems for a pair of tensor weights were designed. However， the tensor weight optimization problems could not be solved by conventional approaches. To overcome this challenge， the tensor weights were respectively decomposed via canonical polyadic decomposition， such that the original problems could be decomposed into interconnected sub-problems corresponding to the dimensions of the DOA and polarization information. Based on the local optimums of the sub-problems， the globally optimal tensor beamformer weights could be obtained through alternative optimization. Furthermore， based on the prime factorization theorem in the tensorial domain， the beam distribution property of the sparse subarrays was theoretically analyzed. The results were used as the basis for a coprime synthesis method to suppress ambiguous sidelobes. A tensor beam power pattern with a sharp mainlobe and suppressed sidelobes could be formulated to achieve an accurate DOA estimation. Simulation results demonstrated the effectiveness of the proposed algorithm.