Direction-of-arrival of strictly non-circular sources based on weighted mixed-norm minimization

Weijie Tan,Lianyou Jing,Xinrong Ye,Xi’An Feng

doi:10.1186/s13638-018-1234-y

Abstract

In this paper, a super-resolution direction-of-arrival (DoA) algorithm for strictly non-circular sources is introduced. The proposed algorithm is based on subspace-weighted mixed-norm minimization. Firstly, we augment the array aperture for efficiently exploiting the non-circularity of signal source. Then, we transform the augmented array matrix to the real array matrix due to the centro-Hermitian of the augmented array matrix. To this end, a subspace-weighted mixed-norm minimization problem is formulated for the DoA estimation. In the proposed algorithm, we utilize singular value decomposition (SVD) to reduce the dimension of matrix, which improves the computational efficiency. We design the weighted scheme by utilizing the orthogonality of the noise subspace and the array manifold dictionary, which increases the reliability of the sparse DoA estimation. As shown by simulations, the proposed algorithm outperforms the state-of-the-art algorithms in difficult scenarios, such as low signal-to-noise ratio, small snapshots, and correlated source. Moreover, the proposed algorithm exhibits a superior performance for the DoA estimation in the underdetermined case.

Highlights

Direction finding has gained great interest in array signal processing field over the past decades, which is widely used in radar, underwater acoustics, wireless communication, and seismic [1,2,3]
Most of the studies have assumed that the signal follows complex circular Gaussian distribution, such as multiple signal classification (MUSIC) [4], estimation of signal parameters via rotational invariance technique (ESPRIT) [5]
A large number of subspace-based parameter estimation algorithm, which exploited the non-circular property of the signal, had been proposed in the literatures, for example, non-circular multiple signal classification (NCMUSIC) [9], polynomial rooting NC-MUSIC (NC-RootMUSIC) [10], fourth-order NC-Root-MUSIC (NC-RootFO-MUSIC) [11], and unitary ESPRIT for non-circular sources (NC-unitary-ESPRIT) [12], which aim to increase degree of freedom (DoF) and improve angular estimation accuracy

Summary

Introduction

Direction finding has gained great interest in array signal processing field over the past decades, which is widely used in radar, underwater acoustics, wireless communication, and seismic [1,2,3] In this area, most of the studies have assumed that the signal follows complex circular Gaussian distribution, such as multiple signal classification (MUSIC) [4], estimation of signal parameters via rotational invariance technique (ESPRIT) [5]. For the past two decades, the non-circular SSR-based algorithms have attracted a great number of researchers’ attention, [20,21,22], and by exploiting the non-circular property of the signal sources, the performance of the DoA estimation algorithms can be effectively improved. We propose a weighted subspace mixednorm DoA estimation algorithm for non-circular signal. M accounts for the M × M exchange matrix with elements 1s in its anti-diagonal and zeros elsewhere, and diag(u) represents a diagonal matrix, whose diagonal elements consist of the vector u

System model

Augmented array aperture and spatial smoothing processing

DoA estimation based on weighted mixed-norm minimization

Computational complexity analysis

Experimental simulations and discussion

Conclusions