Virtual Array Interpolation for 2-D DOA and Polarization Estimation Using Coprime EMVS Array via Tensor Nuclear Norm Minimization

In this article, we develop an interpolation-based algorithm for two-dimensional (2-D) direction-of-arrival (DOA) and polarization estimation with coprime electromagnetic vector-sensor (EMVS) array. First of all, we derive the tensor form coarray output of coprime EMVS array, and perform virtual array interpolation on the output components of the difference coarray. Subsequently, we construct a low-rank third-order augmented tensor using the interpolated uniform linear array output, and derive two important properties for this low-rank tensor in the Fourier domain. Based on these properties, we reconstruct a noise-free third-order augmented tensor by formulating a tensor nuclear norm (TNN) minimization problem. Finally, we derive the closed-form expressions of 2-D DOA and polarization estimates using the reconstructed tensor. Unlike the existing techniques, our approach not only avoids losses in array aperture and degrees-of-freedom, but also exploits the multidimensional structure inherent in the coarray output. Numerical results demonstrate the superiority of the proposed algorithm over the existing approaches.

I. Introduction

An electromagnetic vector sensor (EMVS), consisting of three orthogonally oriented electric short dipoles and three orthogonally oriented magnetically small loops, can measure the complete electromagnetic information of electromagnetic signals [1], [2], [3]. Compared with the scalar-sensor array, the EMVS array can offer higher parameter estimation accuracy, stronger anti-jamming ability and better target recognition performance by exploiting the polarization information of the incoming signals [4], [5], [6], [7], [8], [9]. Hence, the EMVS array is widely used in radar, remote sensing, satellite navigation, and wireless communications [10], [11]. Furthermore, the EMVS array is applicable in mobile communication systems, and the resulting polarization diversity can significantly improve the system capacity compared to classical dual-polarized communication systems [12]. In the past two decades, many algorithms have been proposed for two-dimensional (2-D) direction-of-arrival (DOA) and polarization estimation, including the vector cross product method [13], MUSIC method [14], propagator method [10] and quaternion-based method [15]. However, these methods usually address uniform EMVS arrays, while sparse EMVS arrays are rarely studied.