Two-Dimensional Direction-of-Arrival Estimation of Noncircular Signals in Coprime Planar Array with High Degree of Freedom

Haiyun Xu,Bin Ba,Daming Wang,Yankui Zhang,Size Lin

doi:10.1155/2019/3078376

Abstract

In estimating the two-dimensional (2D) direction-of-arrival (DOA) using a coprime planar array, there are problems of the limited degree of freedom (DOF) and high complexity caused by the spectral peak search. We utilize the time-domain characteristics of signals and present a high DOF algorithm with low complexity based on the noncircular signals. The paper first analyzes the covariance matrix and ellipse covariance matrix of the received signals, vectorizes these matrices, and then constructs the received data of a virtual uniform rectangular array (URA). 2D spatial smoothing processing is applied to calculate the covariance of the virtual URA. Finally, the paper presents an algorithm using 2D multiple signal classification and an improved algorithm using unitary estimating signal parameters via rotational invariance techniques, where the latter solves the closed-form solutions of DOAs replacing the spectral peak search to reduce the complexity. The simulation experiments demonstrate that the proposed algorithms obtain the high DOF and enable to estimate the underdetermined signals. Furthermore, both two proposed algorithms can acquire the high accuracy.

Highlights

Direction-of-arrival (DOA) is a significant research field in many applications, such as radar [1], underwater acoustics [2, 3], and indoor navigation
Considering the problems that existing methods for estimating DOAs of general uncorrelated signals using coprime planar arrays have huge computational complexity and low degree of freedom (DOF), we present an algorithm to estimate 2D DOAs of underdetermined noncircular signals with low complexity
This section performs the results of simulation experiments comparing the proposed algorithm using Unitary-estimating signal parameters via rotational invariance techniques (ESPRIT) with that using 2D-multiple signal classification (MUSIC) and partial spectral search (PSS) proposed in [14]

Summary

Introduction

Direction-of-arrival (DOA) is a significant research field in many applications, such as radar [1], underwater acoustics [2, 3], and indoor navigation. With the development of technology, the nonsparse array generally needs more sensors to expand array aperture to meet the requirement for more precise location determination This processing makes the systems more complicated and enhances the antenna mutual coupling interference, which increases the estimation errors. We have proposed a method in [15], which uses the covariance matrix of coprime planar array to estimate a new covariance matrix with matrix completion This processing has much improved DOF bigger than the number of sensors. Combining 2D spatial smoothing processing and Unitary-ESPRIT, we realize the fast estimation of 2D DOAs. Through constructing a virtual URA with more number of sensors than that of coprime planar array, we improve the DOF. The notations used in this paper are as follows: (∙)T, (∙)∗, and (∙)H, respectively, represent the transposition, conjugation, and conjugate transposition; E(∙) denotes the mathematical expectation; diag(∙) expresses the transformation of a vector to a diagonal matrix; ⊗, ∘, and (∙)+ denote the Kronecker product, Khatri-Rao product, and pseudoinverse operator, respectively

System Model

DOA Estimation for Noncircular Signals

DOF and Computational Complexity Analysis

Simulation Results

Conclusions