1 Introduction

Synthetic aperture radar (SAR) is a core technology in the field of imaging, and the simulation technology is developing rapidly along with the computer technology and the signal processing technology developing by leaps and bounds. The simulation result is close to the actual result, which makes the simulation became one of the foundations of modern radar design and researching, and MATLAB software is better than any other software in radar simulation [1].

SAR is one kind of high resolution imaging radar, which rely on relative motion between radar and target. SAR imaging has all-time and all-weather advantages compared with other imaging, which has widespread application in the national economy and national defense construction. We often analyze and verify the results of the study through the computer simulation, due to the expensive cost for researching stage of SAR. This article summarizes the factors that affect the simulation results of SAR imaging from the range Doppler algorithm of SAR imaging using MATLAB software imaging of point target imaging, and finally analysis the results.

2 Wave Simulation of SAR Emission

Synthetic aperture radar is an important tool for the remote sensing the earth. Image resolution depends on the size of the lighting footprint on the ground in traditional radar systems. However, the SAR technology can realize the all-time and all-weather imaging with high resolution. This is based on emitting wide bandwidth of linear frequency modulation (LFM) signal in distance and using Doppler frequency shift information of orientation in the received signal.

The emission linear frequency modulation (LFM) signal of SAR is also called the Chirp signal, and it through the linear phase modulation to product bigger wide bandwidth, which is the earliest and most widely used pulse compression signal.

The LFM signal can be expressed as:

$$ s_{i} (t) = Arect\left( {\frac{t}{\tau }} \right)\cos \left( {\omega {}_{c}t + \frac{{\mu t^{2} }}{2}} \right) $$
(1)

Among them,

$$ rect\left( {\frac{t}{\tau }} \right) = \left\{ {\begin{array}{*{20}c} {1,} & {\left| {\frac{t}{\tau }} \right| \le \frac{1}{2}} \\ {0,} & {\left| {\frac{t}{\tau }} \right| > \frac{1}{2}} \\ \end{array} } \right. $$
(2)

The envelope of linear frequency modulation signal is rectangular pulse width with \( \tau \) width, and \( \mu \) is adjustable frequency, and \( \omega_{i} \) is instantaneous angular frequency, and the signal instantaneous frequency is linear change with time (Figs. 1, 2).

Fig. 1.
figure 1

LFM signal waveform

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Fig. 2.
figure 2

Relationship between the amplitude and time frequency spectrum of the LFM signal

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$$ \omega_{i} = \frac{d\phi }{dt} = \omega_{c} + \mu t $$
(3)

3 SAR Imaging Simulation

SAR transmits LFM signals in fighting, and it will meet the target and reflected echo signal, whose mathematical model is the basis of SAR imaging algorithm [2]. Echo signal is time delay of transmitted signal, and according to Eq. (1), we can be expressed the echo signal model as:

$$ s_{i} (t) = Arect\left( {\frac{{t - t_{0} }}{\tau }} \right)\cos \left[ {\omega {}_{c}\left( {t - t_{0} } \right) + \frac{{\mu \left( {t - t_{0} } \right)^{2} }}{2}} \right] $$
(4)

Among them, \( t_{0} \) is time delay, and \( \mu = \frac{\pi BW}{T} \) is linear frequency modulation rate, and \( BW \) is signal bandwidth, and \( t \) is fast time. The original echo signal waveform of 2 point target as shown in Fig. 3, and obtaining the baseband signal after mixing echo signal is as shown in Fig. 4.

Fig. 3.
figure 3

Two point target echo signal of SAR

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Fig. 4.
figure 4

Not correcting range migration of 2 point target imaging

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$$ m_{if} \left( t \right) = \frac{1}{4}\exp \left\{ {j\left[ {\omega_{0} + \mu \left( {t - t_{0} } \right)^{2} - \omega_{c} t_{0} } \right]} \right\} $$
(5)

Type in the \( \omega_{0} = \omega_{c} - \omega_{d} \), and \( \omega_{d} \) is Intermediate frequency.

SAR point target imaging simulation is based on the echo model, and then make it become an image point and display the picture effect using the range Doppler (R-D) algorithm doing range and azimuth compression of simulated point target for echo data. The basic SAR imaging R-D algorithm has been discussed in the literature [4, 5], here no longer. The simulation results of MATLAB SAR point target imaging as shown in from Figs. 4, 5 and 6, it directly and representatively reflects the principle of R-D algorithm.

Fig. 5.
figure 5

Correcting range migration of 2 point target imaging

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4 Simulation Analysis of Effect

In the SAR imaging simulation process, we analyze the factors which influence the simulation results.

  1. (1)

    The range resolution and azimuth resolution

    The SAR range resolution depends on bandwidth of transmitted signal, and the greater bandwidth, the better distance resolution. In the actual system, azimuth resolution is proportional to beam width of the antenna azimuth, and the resolution of synthetic aperture is inversely proportional to beam width of the azimuth.

  2. (2)

    Choosing of parameters of SAR system

    The most important parameters in SAR system is choosing the pulse repetition frequency, and PRF cannot be too low, otherwise it will cause the azimuth ambiguity, and it also cannot be too large, otherwise it will produce fuzzy distance.

  3. (3)

    Range migration

    RCM makes the range signal with frequency modulation characteristic, but if not corrects range migration, it will reduce the imaging resolution, especially deterioration of the range resolution.

  4. (4)

    Adding window of the distance and antenna beam of the azimuth

    A method of reducing the peak side lobe ratio is adding a window of the frequency matching filter in distance in frequency domain, which can smooth the spectrum. To Antenna beam can realize the spatial filtering, and it also can reflect the spatial filtering capability of radar.

5 Conclusion

The computer simulation has the extremely development prospects, but the factors impacting SAR imaging simulation results is various. In order to the better use of simulation software to analysis the SAR technology, this paper carries on MATLAB software to complete the point target imaging process. Through the simulation analysis, we summarize three important factors, which is seriously affecting the imaging quality.