International Journal of Antennas and Propagation

Volume 2018 (2018), Article ID 3679494, 7 pages

https://doi.org/10.1155/2018/3679494

## Enhanced 2D-DOA Estimation for Large Spacing Three-Parallel Uniform Linear Arrays

Air and Missile Defense College, Air Force Engineering University, Xi’an, Shaanxi 710051, China

Correspondence should be addressed to Dong Zhang; moc.361@oaguotgnodgnahz

Received 15 September 2017; Revised 9 January 2018; Accepted 30 January 2018; Published 4 March 2018

Academic Editor: Elisa Giusti

Copyright © 2018 Dong Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

An enhanced two-dimensional direction of arrival (2D-DOA) estimation algorithm for large spacing three-parallel uniform linear arrays (ULAs) is proposed in this paper. Firstly, we use the propagator method (PM) to get the highly accurate but ambiguous estimation of directional cosine. Then, we use the relationship between the directional cosine to eliminate the ambiguity. This algorithm not only can make use of the elements of the three-parallel ULAs but also can utilize the connection between directional cosine to improve the estimation accuracy. Besides, it has satisfied estimation performance when the elevation angle is between 70° and 90° and it can automatically pair the estimated azimuth and elevation angles. Furthermore, it has low complexity without using any eigen value decomposition (EVD) or singular value decompostion (SVD) to the covariance matrix. Simulation results demonstrate the effectiveness of our proposed algorithm.

#### 1. Introduction

Two-dimensional DOA estimation has attracted extensive attention due to its wide range of applications [1–4], and there are many algorithms been proposed for DOA estimation. Among these algorithms, the subspace-based algorithms, such as MUSIC and ESPRIT, have received a lot of attention for its accurate estimation performance [5, 6]. However, the complexity of subspace-based algorithms is often too large because of the EVD or SVD. In [7], Marcos et al. put forward the well-known propagator method (PM) algorithm for 1D-DOA estimation. It uses linear partitioning instead of any EVD or SVD to reduce complexity. Then, Chen et al. [8] extend it to the DOA estimation of noncircular signal. References [9–11] extend the PM algorithm to 2D direction estimation. But these algorithms have some drawbacks. Reference [9] requires angle search operations. Reference [10] may fail in practical situation when elevation angle is between 70° and 90°. Reference [11] has worse estimation accuracy, because some element information is missing when calculating the propagation matrix (PMA). Based on this, Chen et al. [12] put forward an improved 2D angle estimation algorithm for three-parallel ULAs. It can solve all the problems mentioned in the above literature. But, it still has some shortcomings, that is, the array aperture is reduced because of the adoption of three parallel arrays with half wavelength spacing. And the estimation accuracy is reduced. References [13, 14] establish the “array of subarrays” idea and “cyclic ambiguity” idea to improve the estimation accuracy of 2D-DOA. According to this, we expanded the spacing between the ULA and proposed an enhanced 2D-DOA estimation algorithm. What needs to be stressed here is that our method is different from the method in [13, 14], although our algorithm and the method in [13, 14] both use the large array spacing to obtain high accuracy but ambiguous estimation. However, the principle of resolving ambiguity is different. References [13, 14] use coarse estimation without ambiguity or based on eigen space to resolve ambiguity. However, our algorithm uses the triangular relation between the three directional cosine to resolve the ambiguity. By doing this, we do not have to limit ourselves to using subarrays or eigen spaces to solve ambiguity problems. That is the main difference between our method and the method in [13, 14]. And it is also the main innovation of this paper. The flow of our algorithm is as follows: Firstly, we use the method in [12] to obtain the estimation of three directional cosines. Because of the large spacing between array elements, the estimated directional cosine is high precision and ambiguous. Then, we use the triangle relationship between the three directional cosines to eliminate the ambiguity. Then, we can get the true 2D-DOA of targets. Simulation results show that it cannot only avoid the problem in [8–11] simultaneously but also has better estimation accuracy than algorithm of [12] because of adopting large aperture. And the complexity of the algorithm is comparable to that algorithm of [12].

*Notations. *Superscripts , , , , and denote complex conjugation, transpose, pseudo-inverse, inverse, and conjugate transpose, respectively. is identity matrix. denotes the diagonalization of the entity inside. denotes take the absolute value of the element. denotes round the element to the nearest integers less than or equal to the element. denotes round the element to the nearest integers greater than or equal to the element. denotes the expectation operation. and denote the phase and the real part of a complex number separately.

#### 2. Problem Formulation

As shown in Figure 1, assume that there are three-parallel ULAs, namely, and . Array contains sensors. Array and array have sensors, respectively. The spacing between adjacent elements is The distance between array and array is and the distance between array and array is is the wavelength. It is assumed that far-field narrowband uncorrelated signals are incident onto the array. The elevation angle and azimuth angle of target are and respectively. Here, we assume that the range of 2D angle is the same with that of [12]. That is to say that the range value of is and the range value of is Then, the output of the three ULAs can be expressed as follows: where and contains the first N row of and and are assumed to be Gaussian white noise vectors whose mean value is zero and variance is Then a new vector with L snapshots, and can be represented as where and