Gridless Multiple Measurements Method for One-Bit DOA Estimation with a Nested Cross-Dipole Array

Haining Long,Ting Su,Mengxing Huang,Xianpeng Wang,Daniele Pinchera

doi:10.1155/2021/6635220

Abstract

The gridless one-bit direction of arrival (DOA) estimator is proposed to estimate electromagnetic (EM) sources on a nested cross-dipole array, and the multiple measurement vectors (MMV) mode is introduced to improve the reliability of parameter estimation. The gridless method is based on atomic norm minimization, solved by alternating direction multiplier method (ADMM). With gridless method used, sign inconsistency caused by one-bit measurements and basis mismatches by traditional grid-based algorithms can be avoided. Furthermore, the reconstructed denoising measurements with fast convergence and stable recovery accuracy are obtained by ADMM. Finally, spatial smoothing root multiple signal classification (SSRMUSIC) and dual polynomial (DP) methods are used, respectively, to estimate the DOAs on the reconstructed denoising measurements. Numerical results show that our method one-bit ADMM-SSRMUSIC has a better performance than that of one-bit SSRMUSIC used directly. At low signal to noise ratio (SNR) and low snapshot, the one-bit ADMM-DP has an excellent performance which is even better than that of unquantized MUSIC. In addition, the proposed methods are also suitable for both completely polarized (CP) signals and partially polarized (PP) signals.

Highlights

Since electromagnetic (EM) source signal carries the complete information buried in the fields, the direction finding of the EM source signal has a wide application
The one-bit alternating direction multiplier method (ADMM) on a nested cross-dipole array with the measurement vectors (MMV) model is used to estimate the direction of arrival (DOA) of EM sources in this paper
Based on the properties of the cross-dipole array, one-bit ADMM is applied to the x-axis and y-axis dipole array and extended to the MMV model for solving the atomic norm minimization, the sign inconsistency will be solved and the basis mismatch will be avoided

Summary

Introduction

Since electromagnetic (EM) source signal carries the complete information buried in the fields, the direction finding of the EM source signal has a wide application. In [18], a nested cross-dipole array is used to estimate the DOA of EM source signals with spatial smoothing MUSIC (SS-MUSIC). The alternating direction multiplier method (ADMM) is proposed to solve the atomic norm minimization with one-bit quantization in the single measurement vector (SMV) model [23, 26, 27]. The atomic norm minimization with ADMM is extended for reconstructing the one-bit EM source signals using a nested cross-dipole array. The main contributions of this paper are as follows: (1) The formulas of one-bit ADMM are derived to estimate DOAs of EM source signals using a nested cross-dipole array, and the MMV model is used instead of SMV to improve estimation accuracy. X†, XH, XT , and X∗ denote the Moore-Penrose pseudoinverse, the conjugate transpose matrix, the transpose, and the conjugation of X, respectively. conjð⋅Þ means the conjugate operation on each entry of a vector or a matrix. e1 is a vector where the first element is 1, and the rest are 0. inf ð⋅ Þ means the infimum operator. convðAÞ is the convex hull of A. k⋅k∗A is the dual atomic norm

Signal Model

One-Bit Quantization

The Proposed Methods

Simulation Results

Conclusion