Mathematical Problems in Engineering

Volume 2015, Article ID 613692, 12 pages

http://dx.doi.org/10.1155/2015/613692

## A Novel Virtual Time Reversal Method for Passive Direction of Arrival Estimation

Department of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China

Received 1 December 2014; Accepted 5 February 2015

Academic Editor: Roman Lewandowski

Copyright © 2015 Yongqing Fu 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

The paper presents a new method to estimate the two-dimensional (2D) direction of arrival (DOA) (the azimuth angle and the elevation angle) of electromagnetic signal emitted from a single communication station. This method is passive and accurate in the case of low signal-noise ratio (SNR) based on the virtual time reversal (VTR) theory. In order to illustrate its principle, the theoretical formulas of VTR direction finding with uniform circular array (UCA) are derived firstly. Based on these formulas, the implementation scheme for estimating azimuth angle and elevation angle passively is then provided. In the derivation, the strict mathematical proof for compressing planar search area to a curve line is proposed, reducing the complexity of VTR algorithm greatly. Finally, the simulation experiments are performed to validate the performance of VTR algorithm. The results show that the VTR method is effective and it delivers accurate DOA estimation in the case of low SNR.

#### 1. Introduction

It is very important to detect the direction of concealed enemy communication station passively and accurately under the condition of electronic warfare (EW). Until now, several commonly used methods for estimating the direction of arrival (DOA) have been developed, such as phase comparison direction finding method [1], multiple signal classification (MUSIC) [2], and estimation of signal parameters via rotational invariance techniques (ESPRIT) [3]. The performance of these methods in conventional electromagnetic environment is satisfactory, but it is not quite enough to estimate the DOA of weak electromagnetic signal in the case of modern EW environment. For example, the performance of phase comparison method is often affected by low signal-noise radio (SNR) levels, and there exists the ambiguity of bearing. The MUSIC method has high resolution, but it is difficult to implement in real time under the case of large sample. In order to improve the computation complexity, a hybrid MUSIC approach with uniform circular array (UCA) is proposed in [4]. The results show that the average runtime of this combined algorithm is reduced, but the error of elevation angle is almost 5° when the SNR is 0 dB, which is not satisfactory. A sparse MUSIC algorithm with UCA is provided in [5], and it gives more accurate DOA estimation than traditional MUSIC. However, it is impossible to get a root-mean-square error (RMSE) below 1° at SNR = 0 dB when the number of elements is less than 10. ESPRIT offers advantages over MUSIC algorithm by avoiding the spectrum peak search and reducing the effect of sensor performance variability. However, it cannot be used for UCA directly, and the estimation error of ESPRIT is greater than MUSIC under normal circumstances [6, 7]. Therefore developing a new method to estimate the DOA of weak electromagnetic signal accurately is the necessary to EW.

The time reversal (TR) direction finding method has some advantages, such as simple algorithm, accurate estimation result, and self-focusing without prior knowledge about medium characteristic and array distribution [8], so it has a potential ability to estimate the DOA of weak electromagnetic signal. It is worth mentioning that the TR technology accomplishes self-refocusing without knowing the distribution of TR array; therefore it is no limitation in the geometry of TR array. TR theory [9] is proposed by Fink in 1989, and it has been developed in various areas, such as nondestructive testing [10], lithotripsy [11], acoustics [12], imaging [13], civil engineering [14], radar [15], communications [16], and electromagnetic [17–19]. Although the focusing characteristic of TR method has been studied extensively, most of published papers applied the classic idea proposed by Fink [20]. In the classical TR theory, a physical backpropagation process for time-reversed signal is necessary, and a transducers array which is placed at the source to receive the backpropagated signal is needed for observing the refocusing process. Hence it is unsuitable to detect the direction of the enemy communication station because we cannot set up a receive array in the position of enemy communication station, and the physical backpropagation process for time-reversed signal is meaningless.

In order to solve the problem above, a virtual time reversal (VTR) passive direction finding method used for single communication station is proposed, which works with TR array only, and without receive array at source, and the physical backpropagation process for time-reversed signal is replaced by the virtual calculation. For verifying the performance of the proposed method, some experiments are performed. The simulation results show that the VTR DOA estimation method has a smaller root-mean-square error (RMSE) at low SNR levels than phase comparison method, spectral MUSIC, and real beam space MUSIC (RB-MUSIC).

The remainder of this paper is organized as follows. Section 2 proposes the VTR passive direction finding method for estimating azimuth angle and elevation angle. In Section 3, the time delay correction is given, and the steps of VTR algorithm are summarized. The simulation experiment results and performance analyses of the VTR algorithm are shown in Section 4. We summarize our works in Section 5.

#### 2. Fundamental of VTR Direction Finding Method

In this section, the direction finding method of azimuth angle is firstly given, and then under known azimuth angle the direction finding method of elevation angle is proposed.

##### 2.1. Model and Algorithm

With no limitation in geometry of TR array, we can establish the coordinate system as shown in Figure 1. The TR array is an antenna array, and it only receives signal. The antenna elements, assumed to be identical and omnidirectional, are uniformly distributed over the circumference of a circle of radius , and the number of antennas is 8. A cylindrical coordinate system is used to represent the arrival direction of incoming electromagnetic wave. The origin of the coordinate system is located at the centre of the array. The position of every element is , where m, , , .