Geometric Algebra-Based ESPRIT Algorithm for DOA Estimation

Direction-of-arrival (DOA) estimation plays an important role in array signal processing, and the Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT) algorithm is one of the typical super resolution algorithms for direction finding in an electromagnetic vector-sensor (EMVS) array; however, existing ESPRIT algorithms treat the output of the EMVS array either as a “long vector”, which will inevitably lead to loss of the orthogonality of the signal components, or a quaternion matrix, which may result in some missing information. In this paper, we propose a novel ESPRIT algorithm based on Geometric Algebra (GA-ESPRIT) to estimate 2D-DOA with double parallel uniform linear arrays. The algorithm combines GA with the principle of ESPRIT, which models the multi-dimensional signals in a holistic way, and then the direction angles can be calculated by different GA matrix operations to keep the correlations among multiple components of the EMVS. Experimental results demonstrate that the proposed GA-ESPRIT algorithm is robust to model errors and achieves less time complexity and smaller memory requirements.

2D-DOA Estimation for EMVS Array with Nonuniform Noise

Electromagnetic vector sensor (EMVS) array is one of the most potential arrays for future wireless communications and radars because it is capable of providing two-dimensional (2D) direction-of-arrival (DOA) estimation as well as polarization angles of the source signal. It is well known that existing subspace algorithm cannot directly be applied to a nonuniform noise scenario. In this paper, we consider the 2D-DOA estimation issue for EMVS array in the presence of nonuniform noise and propose an improved subspace-based algorithm. Firstly, it recasts the nonuniform noise issue as a matrix completion problem. The noiseless array covariance matrix is then recovered via solving a convex optimization problem. Thereafter, the shift invariant principle of the EMVS array is adopted to construct a normalized polarization steering vector, after which 2D-DOA is easily estimated as well as polarization angles by incorporating the vector cross-product technique and the pseudoinverse method. The proposed algorithm is effective to EMVS array with arbitrary sensor geometry. Furthermore, the proposed algorithm is free from the nonuniform noise. Several simulations verify the improvement of the proposed method.

Electromagnetic Vector Sparse Nested Array: Array Structure Design, Off-Grid Parameter Estimation Algorithm

In this paper, a new array structure of sparse nested array (SNA) for electromagnetic vector sensor is designed. An electromagnetic vector sensor is composed of six spatially colocated, orthogonally oriented, diversely polarized antennas, which can measure three-dimensional electric and magnetic field components. By introducing sparse factor (SF) between every adjacent sensor, the proposed SNA has flexibility of extending the array aperture and reducing the mutual coupling effect. Meanwhile, a low-complexity multiparameter estimation algorithm is proposed for SNA. First, the vectorization operation for array manifold ensures the large degrees of freedom for multiparameter estimation, where the initial coarse estimates decrease search range. In addition, the improved off-grid orthogonal matching pursuit method obtains joint direction of arrival (DOA) and polarization estimates with a relatively small overcomplete dictionary because this off-grid method achieves high performance even if the estimates do not fall on the grid of the dictionary. Theoretical analysis and simulation results verify the superiority of the proposed array structure and the algorithm.