Three-Parallel Co-Prime Polarization Sensitive Array for 2-D DOA and Polarization Estimation via Sparse Representation

Co-prime array configurations are considered attractive due to the extension of degrees of freedom (DOFs) and the sparse placement of array elements. In this paper, a 2-D direction-of-arrival (DOA) and polarization estimation algorithm are proposed with the three-parallel co-prime polarization sensitive array which consists of the co-centered orthogonal loop and dipole. A novel cross-covariance matrix, that not contains the polarization parameters, is constructed to decouple the joint estimation problem of 2-D DOA angles and polarization parameters. Then, by using the vectorization operation and linear transformation, a virtual uniform linear array with larger DOFs is achieved. Meanwhile, a sparse representation-based algorithm is presented to estimate 2-D DOA angles with the only 1-D dictionary. To avoid the selection of regularization parameter in the sparse recovery process, we derive the constraint form of the optimization problem based on the upper bound of the data fitting error, which can reduce the effect of improper selection on regularization parameter. Finally, the polarization parameters are estimated via a least squares method. Since the proposed algorithm constructs the data vector with cross-covariance matrices between subarrays, the influence of noise is suppressed, and the estimation accuracy with low signal-to-noise ratio is enhanced. In the end, the simulation results demonstrate the effectiveness of the proposed algorithm.