Direction-of-arrival estimation for circular partial coprime array via nuclear norm optimization model after coprime interpolation

Abstract

This paper introduces a special nonlinear generalized coprime array, namely circular partial coprime array (CPCA). The antennas of CPCA are distributed on a circle, but after the antenna positions of CPCA are orthogonally projected to a certain baseline, the antenna spacing satisfies the coprime spacing characteristic of linear coprime array (LCA). Because the CPCA signal cannot be equivalent to the virtual difference coarray signal of LCA after vectoring the covariance matrix of incoming signals, the existing direction-of-arrival (DOA) estimation ideas of LCA model will be invalid in CPCA model. To make full use of the coprime information of CPCA model, the coprime interpolation method which can transform the steering manifolds of CPCA into the steering manifolds of expected LCA (ELCA) will be proposed. To alleviate the negative impact of interpolation error caused by coprime interpolation method on DOA estimation accuracy of CPCA model, a sparse Hermitian Toeplitz matrix (HTM) related to the spatial smoothed matrix will be recovered by the nuclear norm optimization model, where recovering the sparse part of HTM is equivalent to fitting the virtual hole data. Therefore, the recovered HTM can improve the virtual degree of freedom (DOF) of ELCA, and the high-precise DOA estimation can be obtained by combining the recovered HTM and MUSIC spectrum. In addition, the influence of inevitable interpolation error on the CPCA signal model is quantitatively analysed. Finally, simulation experiments verify the effectiveness and compatibility of the coprime interpolation method, and show the estimation performance advantages of the proposed method in CPCA model.