Covariance Matrix Reconstruction for Direction Finding with Nested Arrays Using Iterative Reweighted Nuclear Norm Minimization

Weijie Tan,Xi’An Feng

doi:10.1155/2019/7657898

Abstract

In this paper, we address the direction finding problem in the background of unknown nonuniform noise with nested array. A novel gridless direction finding method is proposed via the low-rank covariance matrix approximation, which is based on a reweighted nuclear norm optimization. In the proposed method, we first eliminate the noise variance variable by linear transform and utilize the covariance fitting criteria to determine the regularization parameter for insuring robustness. And then we reconstruct the low-rank covariance matrix by iteratively reweighted nuclear norm optimization that imposes the nonconvex penalty. Finally, we exploit the search-free DoA estimation method to perform the parameter estimation. Numerical simulations are carried out to verify the effectiveness of the proposed method. Moreover, results indicate that the proposed method has more accurate DoA estimation in the nonuniform noise and off-grid cases compared with the state-of-the-art DoA estimation algorithm.

Highlights

Source localization is always a significant research direction in the past decades and today which is widely used in various fields including radar, sonar, wireless communication, and acoustics [1,2,3,4]
We assume that all the signals are far-field equal power uncorrelated signals; the additive noise is spatially nonuniform which is modeled as an independent complex Gaussian random vector with zero mean, and its covariance matrix is Rn = diag σ2n, since the input signal-to-noise ratio (SNR) can be defined as SNR = 10log10
We addressed the direction finding problem in the presence of unknown nonuniform noise over nested array

Summary

Introduction

Source localization is always a significant research direction in the past decades and today which is widely used in various fields including radar, sonar, wireless communication, and acoustics [1,2,3,4]. Two potential array configurations, i.e., coprime arrays (CPA) and nested arrays (NA), have drawn the researchers’ attentions since they have exactly closed-form expressions for sensor locations and it is easy to predict the attainable DOFs [7, 8]. Coprime arrays can resolve up to o MN sources with only M + N − 1 elements; the CPAs do not generate a filled coarray since CPA has holes in the difference coarray [7]. It cannot directly apply the augmentation techniques. The NAs and CPAs are not optimum lag arrays like MRAs, they are the most attractive array configuration because they are easy to build in the last decade

Objectives

Results

Conclusion