International Journal of Antennas and Propagation

Volume 2016 (2016), Article ID 2598024, 12 pages

http://dx.doi.org/10.1155/2016/2598024

## Missile-Borne SAR Raw Signal Simulation for Maneuvering Target

College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China

Received 25 February 2016; Revised 28 April 2016; Accepted 10 May 2016

Academic Editor: Atsushi Mase

Copyright © 2016 Weijie Xia 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

SAR raw signal simulation under the case of maneuver and high-speed has been a challenging and urgent work recently. In this paper, a new method based on one-dimensional fast Fourier transform (1DFFT) algorithm is presented for raw signal simulation of maneuvering target for missile-borne SAR. Firstly, SAR time-domain raw signal model is given and an effective Range Frequency Azimuth Time (RFAT) algorithm based on 1DFFT is derived. In this algorithm, the “Stop and Go” (SaG) model is adopted and the wide radar scattering characteristic of target is taken into account. Furthermore, the “Inner Pulse Motion” (IPM) model is employed to deal with high-speed case. This new RFAT method can handle the maneuvering cases, high-speed cases, and bistatic radar cases, which are all possible in the missile-borne SAR. Besides, this raw signal simulation adopts the electromagnetic scattering calculation so that we do not need a scattering rate distribution map as the simulation input. Thus, the multiple electromagnetic reflections can be considered. Simulation examples prove the effectiveness of our method.

#### 1. Introduction

Synthetic aperture radar (SAR) raw signal generation and image simulation [1, 2] play a significant role in the development of SAR system. On the one hand, SAR raw signal generation is an effective and financial tool that enables us to obtain the echo data needed for the validation of the radar imaging algorithms; on the other hand, SAR image simulation provides a feasible way to establish a target feature database, which is the foundation of the target automatic recognition.

Because of the importance of SAR echo and image simulation, a lot of researches focused on the field have been carried out. In the published literature, approaches to simulating SAR echo signal can be divided into three categories: time-domain (TD) methods, two-dimensional (2D) frequency domain methods, and hybrid time/frequency (TF) domain methods [3]. Classical TD method was once employed by Mori to present an interferometric SAR simulator [4]. This algorithm has a high precision but is time consuming, and the scattering characteristic of the whole target is difficult to take into account. To improve the processing efficiency, the 2D method, taking advantage of the efficiency of fast Fourier transform algorithm, has been studied in many papers [5–8]. Unfortunately, this method cannot be directly employed under the situation of nonideal trajectory. As a tradeoff of the aforementioned two methods, hybrid TF simulation, with the ability to consider both the nonideal trajectory and the moderate computational efficiency, has also been an effective way to operate SAR simulation [9, 10].

So far, quite a lot of studies have been addressed to simulate SAR raw data [11–16]. However, unlike the traditional SAR configuration in which the platform travels an ideal trajectory, for realistic missile-borne SAR system, both the platform and the target move along curvilinear trajectories with acceleration and even jerk, which may result in two-order even high-order terms in the range history. With this special range history, the traditional approaches cannot be directly adopted to obtain its 2D frequency spectrum for the overall SAR system transfer function which depends on the azimuth and range coordinates of the target. Consequently, the improved SAR raw signal simulator with the ability to consider the curvilinear trajectory is strongly required. With respect to this, Franceschetti et al. [11] proposed an efficient SAR raw signal simulator based on full 2D Fourier transform, but this simulator is only effective for cases of narrow beam and slow trajectory deviation. Meng et al. developed a fast raw data simulator based on the effectual access of 2DFS [17], but there was still phase space variance which could lead to the inaccurateness of the raw signal. Besides, to our knowledge, the most important feature of the complex target, namely, the dynamic Radar Cross Section (RCS), has not been introduced to the echo generation so far in the literature, and available methods often need to know discrete reflectivity distribution map or digital elevation model (DEM) of the imaged scene as an input. Furthermore, there has not been an integrated method for dynamic target echo simulation which can deal with both monostatic SAR and bistatic SAR in the published literatures.

Aiming at the above problems, in this paper, we will fully take the target RCS feature into account to propose a novel RFAT echo generation method for missile-borne SAR. In this method, the high frequency electromagnetic scattering calculation method based on physical optics (PO), geometrical optics (GO), and Incremental Length Diffraction Coefficients (ILDC) is adopted to calculate the scattering characteristic of target; the SaG model and the IPM model are conducted into the real-time motion simulation; the 1DFFT based echo simulation method is used to generate SAR raw data; finally, the RDA (range-Doppler algorithm) is adopted to obtain the simulated SAR image; simulation results show that the method is effective and suitable for different kinds of SAR (monostatic and bistatic) and motion situations.

#### 2. Analysis of the Proposed Simulation Algorithm

##### 2.1. Signal Model

In this section, the main employed symbols (nomenclature) are defined as follows. : carrier frequency. : light speed. : carrier wavelength. : chirp duration. : target-to-antenna distance. : sensor position azimuth coordinate at . : chirp rate. : slow time. : fast time. : number of slow time samples. : number of fast time samples. : continuous form of .

Supposing that the radar is illuminating a point scatterer with a series of chirp signals, the received raw data for can be described by the following expression:where is the reflectivity function. For simplicity, replacing in (1) by , we obtainwhere is the spatial sampling interval in the range direction; let ; the echo equation of the point scatterer in the range-time domain can be written as follows:

Actually, the complex target consists of many point scatterers; the echo signal of the target can be calculated by summing up each point scatterer echo signal as follows:where is the overall reflectivity of all points at distance from the sensor. Through (4), we can simulate the SAR raw data in the time domain directly, but it suffers from the disadvantages of high computation complexity. Furthermore, it is hard to obtain the scattering center points of a complex target. To solve this problem, a Fourier transform is implemented in the range direction to (4):where represents the Fourier transformation of the scattering coefficient of the target which will be explained specifically in the next section and refers to the corresponding spatial frequency of the range coordinate variable with the unit of rad/m. According to the stretchable nature of the Fourier transform, the relationship between range frequency and spatial frequency can be described asSubstituting (6) to (5), we obtainwhich is the echo equation in the range frequency domain. Then, the original time-domain echo signal can be obtained after a 1D inverse Fourier transform.

##### 2.2. Dynamic Modeling for Electromagnetic Scattering

From the final expression described in (7), we can find that the key procedure of generating the echo data is the computation of . As mentioned in the previous section, is the Fourier transformation of the scattering coefficient, namely, the Radar Cross Section (RCS) of the target. Thus, in this section, the PO, GO, and ILDC based RCS calculation method is first introduced and then the Doppler correction method for dynamic target is given.

###### 2.2.1. The PO/GO and ILDC Method

The GO is a ray-based method intended for the consideration of electrically large structures, which employs ray-launching and transmission, reflection, and refraction theory to model the interaction between the dielectric regions [18]. The PO utilizes ray optics to estimate the field on a surface and then calculate the transmitted or scattered field through Stratton-Chu formulation [19]. The backscatter contributions are evaluated by both GO and PO, which can be used to compute multiple reflections effectively. Furthermore, the edge diffraction effect of electrically large scaled complex objects is also considered and calculated with the theory of Incremental Length Diffraction Coefficients (ILDC) [20].

###### 2.2.2. Doppler Correction Method

For dynamic missile target, the distance change between target and radar over time could lead to the Doppler effects in the echo [21]. Thus, it is needed for modified results of RCS calculation to take Doppler effects into account.

The modified RCS can be expressed asIn this formula, represents the distance from the geometric center of the complex target to the sensor, is the Doppler phrase term, denotes the electromagnetic wave frequency, and and are the RCS before phrase correction and the modified RCS, respectively.

##### 2.3. Dynamic Target Range History Analysis

In order to realize the phase correction described in (8), dynamic target range history analysis is presented in this section.

###### 2.3.1. Monostatic Radar

Consider the missile-borne SAR illuminating an aerial maneuvering target as shown in Figure 1. The missile-borne SAR platform denoted by moves along the nonideal trajectory which obeys a high-order polynomial-type representation as a function of the continuous time:where is the initial velocity vector, is the initial acceleration vector, and is the jerk vector. Similarly, the target denoted by moves along the nonideal trajectory which has the following expression:where , , and are the initial velocity vector, the acceleration vector, and the jerk vector, respectively.