A Two-Level Simulator for Spaceborne SAR

Chenhui Zhu, Zheng Xiang, Kaizhi Wang and Xingzhao Liu

Department of Electronic Engineering, Shanghai Jiaotong University, China phone: +86 021-34205435, email: donaldzch@sjtu.edu.cn

Abstract

A novel two-level simulator for spaceborne Synthetic Aperture Radar (SAR) is presented in this paper, and this simulator consists of two different simulation levels: the raw signal level and the image level and the implementations are discussed in detail. For the raw signal level, a new model with higher computation efficiency based on Graphic Processor Unit (GPU) to generate the radar echoes is proposed. For the image level, an efficient approach to create single-look image is processed. Finally some experimental results by the novel simulator are presented. These results demonstrate not only the validity of the proposed simulator but also the conformability of the two simulation levels.

Keywords: Spaceborne SAR, raw signal, GPU, single-look image

1. Introduction

Spaceborne Synthetic Aperture Radar (SAR) has become hotspot of all over the world because of its ability of all-time work, the high image resolution and wide availability, such as topographic survey, estimation of ocean currents, etc. [1][2]

In recent years, some references with regard to spaceborne SAR simulation have been published.[3][4][5][6] In these works, two simulation levels can be concluded: the raw signal level (RSL) and the single look complex (SLC) image level (SIL). Different simulation levels correspond to different system models and process complexities, therefore to be applied in different situations.

An RSL simulator generates the raw signals backscattered from an extended scene. Foreshortening, speckle noise, shadowing and other phenomena related to the real spaceborne SAR system can be involved in this simulation level. The discussions on this level focus two main aspects: the model of the complex backscattering coefficients (CBC) and the simulation approach in time domain (TD) based on GPU.

An SIL simulator assumes infinite system bandwidth in both the range and azimuth directions. The SLC image is obtained directly and quickly with some noises, such as speckle noise and additive receiver noise. Without considering errors caused by raw signal collecting and imaging processing, this simulation level is more applicable in analyzing some spaceborne SAR procedures.

A two-level simulator for spaceborne SAR is presented in this paper. Firstly, a framework of spaceborne simulator containing two different levels is established and modularized. Secondly, the RSL simulator presents a new model of time-domain simulation by GPU compute unified device architecture (CUDA) [7] technique. The SIL simulator

provides a fast method to obtain the SLC image with controllable error sources.

This paper is organized as follows. In section 2, the spaceborne SAR rationale and the simulator structure are presented. In section 3, simulation levels with some improvements are discussed. In section 4, we show and discuss a set of experimental results by the two-level simulator, and finally, a conclusion is drawn in Section 5.

2. Simulator Structure

We briefly describe the rationale of the spaceborne SAR principle. The geometry of a spaceborne SAR system has been analyzed in detail by many references. After heterodyne, the backscattered signal can be written as (1):

� � � �� �

� �� �

''' ' 2 ,, , ,

/ 2

exp 4 , /

r R x rx xs x r x y z w f

X c

j R x r dxdr

��

� �

� � � � �

� � � �

�� (1)

Fig.1. Structure of the two-level Spaceborne SAR simulator

where (.)� is the conventional CBC, (.)w is the normalized illumination function of the real antenna, (.)f is the transmitted impulse, X is the footprint in the azimuth direction, � is the impulse duration, � is the wavelength,

(.)R is the instantaneous slant range from an arbitrary ground point to the antenna, r is the distance from this point to the flight paths of platform, ( , , )x y z is the earth centric coordinate system.

The focused signal can be represented, in terms of non-normalized variables, as follows:

� � � � � �

� � � � � �

' '

' ' '

ˆ , . exp 4 /

sinc sinc . exp 4 /

x r dxdr j r

a x x b r r j r

� � � �

� � �

�

� � � � � � � � �� � � �

�� (2)

where a andb are system bandwidth in the azimuth and range direction respectively. If a and b are assumed to be infinite, the approximate expression in (2) is valid.

The proposed two-level spaceborne SAR simulator calculates (1) and (2). The expressions of the intermediate results in the simulators are consistent with (1) and (2). It is _____________________________

978-1-4244-2732-1/09/$25.00 ©2009 IEEE

explicitly noted that the modified CBC ''� and '� in Fig.1 incorporate the propagation factor � �exp 4 /j R� �� �� �

and

� �exp 4 /j r� �� �� �, respectively.

3. Module description

3.1. RSL simulator

In this section, we describe the RSL simulator. We first illustrate how to calculate the instantaneous slant range of Spaceborne SAR shown in Fig. 2.

For really simulating the echo signal, the satellite orbit employs the elliptical orbit model, and the earth take the elliptical ball model. In Fig.2, it has shown the process of calculating slant range and the transformation matrix have been discussed in [8].

Tranform ToEarth centercoordinate(x,y,z)

Satelliteposition S slant

range RTargetposition T

Fig.2. Process of instantaneous slant range evaluation

Then, we can calculate the SAR raw signal as shown in (1). As mentioned in the introduction, two issues are focused on in this simulation level: the model of the CBC and the simulation approach in TD based on GPU.

The geometry and height profile of the DEM can be approximated by planar rough facets which are larger than the wavelength but smaller than the radar resolution. Once the facets have been defined by the geometric model, the CBC is evaluated by some analytical or experimental models. [9] provides a method by using Kirchhoff approximation and physical optics solution. The electromagnetic model in this method is accurate enough in the simulated scene, however this method maybe more reasonable if it considered the following two: one is its high computation complexity, and the other is its unconformity in the real scene. [10] provides a set of fitted CBC models based on the measured intensity by radar. This method is much simpler than the former one, whereas the adoptive local slope angle (lower than 45 ) is inapplicable in the spaceborne SAR simulation. [11] also provides a backscattering model for a larger range of incident angle (lower than 80 ).The fitted model by lease square and non-linear curve is expressed as:

� � � � � �1 2 3 4 5 6exp coso dB P P P P P P� � �� � � � (3)

where � is the local incident angle, and 1 6P are constant values determined by both the frequency of electromagnetic wave and the type of the scene. The model in (3) works in the nearly vertical incidence region and this is suitable for the spaceborne SAR system. However, it only specifies the intensity of the CBC. A simple and approximate way to evaluate the phase by backscattered from the facets is to assume uniform distribution between 0 and 2� , as discussed in [12].

After we get the CBC with the deterministic amplitude calculated by (3) and the stochastic phase generated by random sequences, a TD technique to calculate the integral in (1) should be decided for it can easily consider the real orbit

of the platform and other effects discussed in [13]. Since the conventional simulation by the TD technique has high computational complexity, we utilize parallel computation of GPU using CUDA language to overcome this limitation. First we push the radar parameters and the two-dimension grid of DEM to GPU constant memory and input CBC into the global memory. Considering the mechanism of SAR raw signal collection, each azimuth line (i.e., pulse repetition time interval (PRT)) of raw signal is allocated to one block (1-dimension, indexed by the CUDA build-in variable blockIdx.y). Furthermore, for each platform location, the evaluated swath is processed by threads (2-dimension, indexed by the CUDA build-in variables threadIdx.x and threadIdx.y). Then for one PRT, evaluate the swath and loop it by a 16 16-threads block with variables in Fig.3 loaded into shared memory in the block and finish calculation the raw signal for the block as shown in Fig.4. Since the blocks are concurrently executed, the integral in (1) can be parallelized using the GPU CUDA language very easily. By GPU’s paralleling, the computational speed of the TD technique has increased significantly.

DEM heights

16 X 16

1 KB float

CBC (real)

16 X 16

1 KB float

CBC (imaginary)

16 X 16

1 KB float

Fig.3 Memory allocation for shared memory in a thread block

SystemParameters DEM

CBCPlatform location

per PRT

Evaluation of swath

Calculation of slant range

Integration equation (1)

Data from CPU to GPU

Data from GPU to CPU

Raw dataGPUCPU

Fig.4 Flowchart of the calculation of the Spaceborne SAR raw data

3.2 SIL simulator

The SIL simulator obtains the SLC image as shown in (2). The calculation of CBC shares the same block with RSL simulator which has been discussed in the previous part. Then the distance of each facet to the flight paths can be computed in grids of the DEM resolution. A transform from DEM resolution DEMd to the radar resolution radard is required. In general, we have:

cosDEM radard d �� � (4)

where � is the slope angle. Because of the non-linear relationship in (4) and discrete sampling, this transform is difficult to calculate accurately. [14] provides a method to solve this problem by iteration and interpolation. This method

is relatively accurate but time-consuming. In order to overcome this limitation, a fast method is proposed as follows:

Calculate the SLC in the DEM resolution and sort them in every range line according to the distance r . This method avoids interpolation and the precision is acceptable. Meanwhile, noise models derived by [6] are also employed in our simulator. Suppose the noise-free backscattering coefficient is � �,b x r� , and let the SLC image with multiplicative noise and additive receiver noise be � �,bma x r� :

� � � � � �� � � �, , 1 , ,bma b m ax r x r n x r n x r� �� � � (5)

where mn is the independent Gaussian random process with zero mean and standard deviation determined by the temporal and baseline decorrelation and an is also the independent Gaussian random process with zero mean but its standard deviation is determined by the noise level of the SAR image.

So the SLC image can be simulated with two controllable error sources above.

4. Experimental examples

In this section, we present some simulation results and evaluate the performance of the system under different simulation levels. To utilize practical parameters, we consider the existing ERS-1 system whose main parameters are listed in table 1. Some information referring to the geometry and obit is also listed in this table.

Table 1. Main system parameters System Parameters Numerical ValueCarrier frequency 9.6 GHz

Look angle 23ºPlatform height 400 km

Platform velocity 6692.5 m/sPulse length 37.12 µs

Chirp bandwidth 15.55 MHzSampling frequency 18.97 MHz

PRT 597.37 µsScene size 8 km×8 km

Orbit Altitude 246.26 kmInclination 96.6378º

Argument of Perigee 148.16ºEccentricity 1.06×10-3

Longitude of Ascending node 89.37º

Firstly, the computational complexity of the simulator is evaluated. Compared with the RSL simulator, the SIL runs nearly in no time. So only the computational efficiency of RSL simulator is evaluated. For each facet in the scene, a coherent sum of its backscattered radar signal leads to about 4NsNa real multiplications, where Ns=600 and Na=1198 are the numbers of samples of transmitted signal and the number of platform positions in the integration time, respectively. But based on GPU, the calculation acceleration in (1) is tested and the simulation time comparison between CPU and GPU is demonstrated in Fig. 5. Let us look at the simulation time in [13], where a number of 250000 facets require about 24 hours.

By inspecting Fig.5, only about 2 hours are cost in our RSL simulator. So we can see that the GPU based spaceborne SAR raw data simulation is much faster for a large number of facets, i.e., corresponding to different DEM size.

Fig.5 Simulation time comparison between CPU and GPU

Then in order to test the capacity of our two-level simulator, a pyramid DEM with its size of 8 km×8 km and height from 0 to 500 metres is simulated.

Now, let us look at the results by the RSL simulator. The amplitude map of the CBC generated by (3) is given in Fig. 6(a). It reflects clearly the truth that the face tilted toward the sensor is “brighter” than the one tilted backward. The amplitude image is shown in Fig.6(b), where speckle noise and foreshortening are apparent. The azimuth and range pixel spacing are about 4 and 8 metres respectively according to the ERS-1 parameters.

Then the SIL simulator gets the SLC image and the amplitude image with two types of errors is shown in Fig.7. Compared with the amplitude image (Fig.6(b)) generated by the RSL simulator, this one simulated by this level is consistent in shape, size and gray scale. This shows the effectiveness of the SIL simulator.

(a) (b) Fig.6 The results of RSL simulator where near rang is on the left. (a) the amplitude map of CBC for simulated DEM, (b)

single-look image

Fig.7 The result of SIL simulator with two types of errors

Finally, an experiment using the actual DEM data is performed. This terrain is surveyed by Shuttle Radar Topography Mission (SRTM) and the DEM (Fig.8(a)) is generated by NASA. Fig.8(b) and (c) display the image by the RSL and SIL simulator. It is clearly demonstrated that the three DEM sections are basically coincident except for some deviations.

As the summery of the examples, we can reasonably state that the proposed two-level Spaceborne SAR is valid and conformability to both the simulated and actual DEM.

(a) (b) (c)

Fig.8 (a) An actual DEM by SRTM (b) image generated by RSL (c) image generated by SIL

5. Conclusions

This paper presents a two-level Spaceborne SAR simulator which includes the raw signal level (RSL) and the SLC image level (SIL). Based on GPU, the RSL simulator can be chosen and evaluated in a very fast way to inspect Spaceborne SAR system with echoes collection and raw data imaging in spite of the large computational cost. Meanwhile, the SIL simulator is suitable to test Spaceborne SAR algorithms quickly and in a simplified way. Finally, the experiments on simulated and actual DEM testify the correctness and effectiveness of the two-level spaceborne simulator.

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