Analysis of Antenna Mispointing Effect on SAR Image Quality

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1 Journal o Computational Inormation Systems 1: Available at Analysis o Antenna Mispointing Eect on SAR Image Quality Yuhua GUO, Xiaoyuan YANG, Liuhe CHEN Department o Mathematics, Beihang University, LMIB o the Ministry o Education, Beijing 1191, China Abstract In this paper, the eect o antenna boresight mispointing on image quality is presented. The mathematical expression o SAR impulse response unction with satellite attitude jitter is studied using paired echo theory. The simulation results show that multi-paired echoes will apppear on the SAR image due to the coupling between the azimuth and range direction. In addition, the eect o antenna beam pointing errors on peak sidelobe ratio and integrated sidelobe ratio o impulse response unction are analyzed. Keywords: Synthetic Aperture Radar SAR; Satellite Attitude Jitter; Multi-paired Echoes 1 Introduction Synthetic aperture radar SAR is a remote sensing system used to achieve high-resolution microwave images o the illuminated area. High resolution in range is obtained via transmission o large bandwidth pulses. On the other hand, high resolution in the azimuth is the result o a raw data processing operation aimed at synthesizing an large antenna array 1 3]. For the satellite system, satellite attitude stability is a very important parameter or the design o satellite platorm o synthetic aperture radar. However, a wide side o causes including technological aspects and environmental conditions lead to antenna attitude variations 4 6]. Even very small attitude variations cause the antenna pointing errors. The antenna attitude variations may can be depicted by the roll θ R, pitch θ P and yaw θ Y angles. In generally, the azimuth mispointing is aected by yaw and pitch, while roll aects range pointing 7 9]. Both antenna azimuth and range boresight pointing errors aect the pulse compression, urthermore, they may degrade the SAR imaging qualities. Thereore, it is necessary to analyze the antenna boresight pointing instabilities eect on SAR image quality. The satellite antenna attitude pointing on Doppler parameters have been analyzed in 1 1]. A qualitative analysis has been given concerning the attitude vibration 13]. The mathematical expression o the single-requency attitude jitter based on paired echo theory has been studied 14]. Project supported by the National Nature Science Foundation o China No Corresponding author. address: [email protected] Yuhua GUO / Copyright 14 Binary Inormation Press DOI: /jcis1117 July 1, 14

2 573 Y. Guo et al. /Journal o Computational Inormation Systems 1: Fig. 1: The geometry o spaceborne SAR planar phased antenna A method has been developed quantitatively analyzing the relationship between spotlight SAR imaging quality and satellite attitude jitter 15]. In 16], the relationship between satellite attitude stability and spaceborne SAR imaging quality is investigated. In 17], the eect o antenna azimuth and elevation boresight pointing multi-requency jittering on image quality in a squint mode are discussed respectively. However, the cross coupling between the range and the azimuth direction is not taken into consideration. In this paper, the eect o antenna azimuth and range boresight pointing instability on SAR image quality is studied. The paper is organized as ollows. The mathematical expression o SAR impulse response unction with attitude jittering is investigated using paired echo theory. Then the eects o antenna beam mispointing on the main image quality parameters are given. Finally, several simulation results are presented to veriy the proposed scheme. Antenna Boresight Pointing Instability Eect on SAR Image Quality The geometry o the antenna attitude variations is depicted in Fig. 1. A planar phased antenna arrays is located in the XY plane. The X axis is along the light direction. The Y axis is perpendicular to X and is parallel to the short axis o the antenna. The Z axis is set ollowing the rule oight-hand coordinate. The antenna beam center perspective is α. Let radiation unit be coordinate system origin, i.e. phase reerence point. A set ootations yaw, pitch and roll in the reerence rame can be deined about respectively the Z, Y, and the X axis and are positive as deined by the arrows in Fig. 1. Since antenna attitude variations aects the antenna boresight pointing, the antenna pointing instability eect on SAR image quality is analyzed in the ollowing. In the processing o SAR data, the point target is modulated by the antenna pattern. We assume that all the excitation current amplitudes are equal, and in phase, then the expression o SAR raw signal ater range compression and range cell migration RCM is as ollows: S i t = wtexp{jπ dc t + t /} 1

3 Y. Guo et al. /Journal o Computational Inormation Systems 1: where wt is the antenna ground illumination pattern. dc is the doppler center requency, is the chirp rate. Since the satellite attitude variations are very complicated in practice, which contain various requency components. For brevity, we consider single-requency attitude jitter in both range and azimuth direction. Let the antenna attitude variations in the azimuth directions is: θa t = θ am sinπt + θ where θ am, and θ are the jitter amplitude, requency and the phase angle. The antenna attitude variations in range directions is: α r = α rm cosπt + α r 3 where α rm, and α r are the jitter amplitude, requency and the phase angle. antenna ground illumination pattern in the azimuth direction is w a t = sinc πla V ] g t t c λr c Suppose the 4 L a is the antenna length. λ is the wavelength, R c is the slant range between a point scatter and the antenna phase center, V g is the relative velocity between the satellite and the target. The antenna ground illumination pattern in the range direction is w r α r = sinc {πl r /λsinα r α sinα B α ]} 5 where α is the boresight angle. When the ollowing conditions are satisied: t Asinπt + θ, α r α r, 6 we have w a t Asinπt + θ w a t Asinπt + θ w at 7 w r α r α r w r α r α r w rα r 8 wherea = R c /V g θ am, w at and w rα r denote the irst order derivative o the antenna radiation diagram in the azimuth and range direction, respectively. The antenna ground illumination pattern in the presence o the antenna attitude variations in both azimuth and range direction can be expressed as: ] ] wt = w a t Asinπt + θ w at w r α r α rm cosπt + α r w rα r = w a tw r α r w a t α rm cosπt + α r w rα r Asinπt + θ w at w r α r + Asinπt + θ w at α rm cosπt + α r w rα r 9 Using the azimuth reerence unction h a t = Si t, we can obtain the signal ater azimuth compression is Ta S out t = expπ dc texp jπ t wt 1 expjπ tt 1 dt 1 T a = S t + S 1 t + S t + S 3 t 1

4 5734 Y. Guo et al. /Journal o Computational Inormation Systems 1: where S t = e jπt e jπ dct Ta is the point target image under ideal conditions. S 1 t = expjπ dc texp π t T a w a t 1 w r α r e jπtt 1 dt 1 11 Ta jπ dc T a w a t α rm cosπt + α r w rα r ] expjπ tt 1 dt 1 = w rα r { w r α r α ] r m exp jπ + t expjα r exp jπ dc S t + exp exp jα r exp S t } jπ t is the image caused by the jitter along the range direction. The paired-echoes are located on both sides o the main lobe: t 1 = ±. Let A r = w rα r w r α r ], then the amplitude are A rs t ] and A r S t + ], respectively. The third term S t = A π + π t exp{jπ + t]} exp{ jπ dc } S t + π π t exp{jπ t]}exp{jπ dc } S t ] Aexpjπ dc t exp{ jπ t }w a T a w rα r exp{jθ }sinπ T a t + ] exp{ jθ }sinπ T a t ] ] is the image caused by the jitter along the azimuth direction. It can be seen that the paired echoes are located on both sides o the main lobe, i.e. t = ±. The amplitude are Aπ ts t and Aπ + ts t +, respectively. The last term S 3 t = 1 expjπ dct exp jπ t A α rm w rα Ta r w a exp{jθ + α r } sin π T a t + exp{ jθ + α r } sinπ T a t ] ] 1 A α r m w rα r π t + ] exp{jθ + α r } exp{jπ + t ] ]} exp{j 4π dc } S t A α r m w rα r π t ] exp{ jθ α r } exp{jπ t ]} exp{j4π dc } S t + 1 exp{jπ dct} exp{ jπ t } A α rm w rα r jsinπ tt a w a T a sinθ α r jπ tsinθ α r expjπ t exp jπ dc t S t] 14 ] 1 13

5 Y. Guo et al. /Journal o Computational Inormation Systems 1: is the coupling eect o the azimuth and range boresigth pointing jittering. The location o the paired echo are t = ±, the amplitude are 1Aα rmw rα r π t + ]S t + and 1 Aα rmw rα r π t ]S t. The our contributions o S t, S 1 t, S t, S 3 t in Eq. 1 generate our contributions to the ocused response, where the sum o S t and S 1 t is the eect o antenna range boresight pointing jittering on images quality while the sum o S t and S t is is the eect o antenna azimuth boresight pointing jittering on image quality 1]. The term o S 3 t is due to the coupling eect between the range and the azimuth jittering. From the equations 11-14, we can conclude that the paired echoes are not only appeared in t = ±, but also appeared in t = ±. The ratio o both and inluence the position o paired echoes. The larger the ratio o, the paired echoes arther away rom the main echo. The amplitude are A r S t + Aπ + ts t + 1 Aα rmw rα r π t ] S t 15 and A r S t + Aπ + ts t + 1 Aα rmw rα r π t + ] S t + 16 Obviously, the paired echoes aect the image quality parameters, such as peak sidelobe ratio PSLR and integrated sidelobe ratio ISLR. The dierence SAR image quality parameters show dierent sensitive to mispointing. 1 3 position/xm Fig. : Antenna boresight pointing instability eect on SAR image quality unweighted 3 Numerical Experiments This section presents the experimental results regarding the processing procedure discussed in the previous section. We consider a typical X-band spaceborne SAR system, the main parameters are listed in Table 1. Suppose the antenna attitude variations are the same in both range and azimuth direction: the jitter requency is = 1Hz, the amplitude is α rm =.5 o, and the initial jitter angle is equal to zero. The signal S out t has been simulated or a single point placed in the center o the acquisition. Fig. shows the point target imaging result without windowing, while Fig. 3 is the point target image using Kaiser window. From Figs. and 3, we can see that the paired

6 5736 Y. Guo et al. /Journal o Computational Inormation Systems 1: position/xm Fig. 3: Antenna boresight pointing instability eect on SAR image quality with Kaiser weight S S1 7 1 position/xm Fig. 4: S portion o the point target response 7 1 position/xm Fig. 5: S 1 portion o the point target response S S position/xm Fig. 6: S portion o the point target response 9 1 position/xm Fig. 7: S 3 portion o the point target response echoes are located not only at x 1 = ±15.8m, but also located at x = ±51.6m. Moreover, the processing o weighting can reduce the sidelobe level, but it is almost not able to deal with paired echoes. Fig. 4-7 show the our contributions to the ocused response separately, that add up to orm the actual ocused image. The SAR image quality parameters are also aected by satellite attitude variations.

7 Y. Guo et al. /Journal o Computational Inormation Systems 1: azimuth and range azimuth range azimuth and range azimuth range PSLRdB 5 35 ISLRdB /Hz /Hz Fig. 8: The relationship between the PSLR and antenna attitude variations requency Fig. 9: The relationship between the ISLR and antenna attitude variations requency Fig. 8 and 9 show the comparison o PSLR and ISLR variations with antenna jitter requency, including the result o the algorithm in this paper and the ones proposed in 14]. Since the paired echoes are ar away rom the main lobe when requency increase, the eect o paired echoes at high requencies on PSLR are almost identical. However, there are apparent change or ISLR. This is because the coupling eect between azimuth direction and range direction results in the emergence multi-paired echoes. Table 1: Simulated sensor paramaters Midrange coordinate 61.64km doppler requency -56 Hz/s Platorm velocity 744.8m/s Azimuth antenna dimension 5.4m Pulse Repetition Frequency 355Hz Range antenna dimension 1m 4 Conclusion The paper shows the eect o the antenna mispointing in both azimuth and range direction on the SAR impulse response. The mathematical expression is given using paired echo theory. The eect o mispointing on the ISLR, PSLR is analyzed, which can be used as reerence or X band space-borne SAR mission. Reerences 1] G. Franceschetti and R. Lanari, Synthetic Aperture Radar Processing. New York: CRC, ] J. J. Kovaly, Synthetic Aperture Radar. Dedham, Mass: Artech House, ] G. Franceschetti, and G. Schirinzi, A SAR processor based on two-dimensional FFT codes. IEEE Transactions on Aerospace and Electronic Systems, pp ] P. W. Fortescue, J. P. W. Stark, Spaceborne System Engineering, New York: John Wiley & Sons Ltd, 1991.

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