Parameter Selection Procedure of Parabolic Reflector Antenna for the Optimum Synthetic Aperture Radar Performances
 Author: Yoon Seong Sik, Lee Jae Wook, Lee Taek Kyung, Yi Dong Woo
 Organization: Yoon Seong Sik; Lee Jae Wook; Lee Taek Kyung; Yi Dong Woo
 Publish: Journal of electromagnetic engineering and science Volume 13, Issue4, p251~258, 31 Dec 2013

ABSTRACT
A procedure for antenna parameter selections is proposed that considers the relationships between synthetic aperture radar performance and the antenna parameters of a parabolatype reflector antenna with a central flat dish. The effects of a central dish designed for weight reduction on the antenna beam pattern are also quantitatively analyzed using commercially available software based on the physical optics algorithm. The results of the theoretical analysis and simulation predict that a larger size of the central dish results in an increase in the sidelobe level, which is the reason for the increase in two important ambiguities, such as range ambiguity ratio (RAR) and azimuth ambiguity ratio (AAR). The dependence of RAR and AAR on Pulse repetition frequency is also analyzed and discussed.

KEYWORD
Azimuth Ambiguity , Backscattering Coefficient , Central Dish , PRF , Range Ambiguity , Reflector Antenna , Sidelobe Level.

Ⅰ. INTRODUCTION
In general, the images captured from real aperture radar systems can be acquired through the rearrangement of onedimensional (1D) radar signals obtained by the motion of the radar platform into 2D radar signals [1]. However, the image resolution in the azimuth direction is directly dependent on both the distance from the radar platform to target and the radiated beamwidth, so a narrower beamwidth has been required for the radiation pattern in the radar system as the altitude of the operating radar system increases. In addition, higher resolution at the mmlevel in a radar system operating at higher altitudes, such as a satellite, requires that the antenna mounted on the radar platform have a physical size that is too big and impractical to be realized.
The resolution in the azimuthal direction in synthetic aperture radar (SAR) systems could be improved by rearranging the detected 2D signals and carrying out signalprocessing in the azimuthal direction. The SAR system can operate under all weather conditions and covers a wide area with high resolution. Therefore, its use can lead to a size reduction in the overall radar system, which is an increasing trend in public needs, science, and military demands.
Many researchers have studied and investigated aspects of quality improvement in the detected signals and images [2,3]. The ambiguity level specified by the SAR performance evaluations is a particularly important parameter for testing the error rate that frequently occurs in the signal reception. Mistakes in image information due to potential ambiguity of the detected signal have been mentioned in [4,5].
Previous studies aimed at resolving this ambiguity problem have been conducted almost exclusively in the signal processing stage. However, if the ambiguity could be alleviated by a properly designed antenna, a significant reduction would be expected in the system complexity and processing difficulties. In this paper, we suggest parameter selection procedures for determining the antenna and electrical performance of an overall radar system that would reduce the ambiguity and improve image resolution as key parameters of SAR performance.
Section Ⅱ presents the structure and beam pattern analysis for the given geometry of reflector antenna for the SAR system. The parameter values affecting SAR performance are also derived, with the inclusion of backscattering coefficients into the ambiguity calculations, which leads to an increased reliability. In Section Ⅳ, the optimized antenna parameter values have been determined through parametric studies on the relationship between SAR performance and antenna parameters. Finally, conclusions are briefly described, together with the analysis results.
Ⅱ. REFLECTOR ANTENNA FOR SAR
In general, a satellite SAR antenna requires high gain and narrow beamwidth for high resolution of the detected image with pulsed transmitting/receiving transmission. Three wellknown candidates satisfy the requirements for SAR performance: the conventional waveguide, a patch using an organic substrate, and a reflector antenna with a metallic solid surface. For instance, a waveguide slot array antenna has been employed for TerraSARX, the representative German satellite system [6]. Another example is the phased array antenna with a patchtype organic substrate used on the Canadian Radarsat2 satellite, and the Italian Cosmo SkyMed satellite [7,8]. Reflectortype antennas have a drawback in their packaging efficiency relative to the waveguide or path array antenna, but they have advantages of high gain, narrow beamwidth, and easy implementation with transmit/receiving modules because of the possibility of a deployable mechanism [9].
This paper introduces a solid metal type of reflector antenna as a possible candidate for the SAR antenna system. In particular, the use of a flat dish with a given solid type of reflector antenna makes the antenna easy to manufacture and light weight, with low development costs. For instance, the center of the reflector antenna adopted in TecSAR system has been implemented with a flat surface [9].
Fig. 1 shows the ray tracing and moving path of the signal radiated from the feeding part, simulated and illustrated with a conventional and a modified reflector antenna structure. The electrical performance of these structures is analyzed using GRASP of TICRA, based on physical optics (PO). The dotted lines in Fig. 1 represent the equiphase plane of the reflected rays from the reflectors. At this time, a Gaussian beam pattern is considered as an input signal generated from conical horn antenna as a feeding structure.
Eqs. (1) and (2) represent the normalized electric field at the aperture and edge illumination, respectively, where
F_{f} is the normalized radiation pattern in the feeding antenna, andρ andF denote the axis of the aperture and focal distance, respectively [10].Fig. 2 shows that the edge illumination affects the radiation pattern and directivity of reflector antenna and determines the tradeoff between the aperture taper efficiency and spillover efficiency.
The conventional parabolic reflector antenna, as expected from Fig. 1(a), has all the rays reflected from the reflector propagating to the aperture plane with equal distance; consequently, the detected electric fields will have uniform phase distributions. On the other hand, Fig. 1(b) shows that the reflected signals from the flat surface do not propagate in parallel with each other and finally distort the wave propagating in other directions, leading to nonuniform phase distributions at the aperture plane.
Next, we will investigate the magnitude distribution of electric fields at the aperture plane. Fig. 3 shows the normalized electric field distribution at the aperture plane.
The magnitude of all the electric field distributions, according to the positions at the aperture plane, has been normalized to the maximum electric field intensity at the looking angle of feed horn, which means the direction of the shortest path.
It is conjectured from Fig. 3 that the field distribution of the parabolic reflector antenna of Fig. 1(a) forms a parabolic tapered shape because of the spherical radiation beam from the feeding part and the fallingoff characteristic, which is inversely proportional to the distance squared.
In contrast, in Fig. 1(b), the reflected wave from the flat surface at the center superposes on the other waves reflected from the other surfaces in a parabolic shape with different phase and magnitude.
As a result, the field distribution at the superposed region corresponding to ±0.2 ≤
ρ ≤ ± 0.75 shows only slight fluctuation as well as a relatively uniform distribution due to the summation of many other waves reflected from the surface.Table 1 describes the half power beamwidth and sidelobe level according to the aperture field distributions given in Fig. 4 [10]. The results of Table 1 and Fig. 4 predict that the normalized field distributions of the reflector antenna with a flat subreflector shown in Fig. 3 will give a narrow beamwidth and higher sidelobe level. The theoretical approach has been verified by simulating the radiation patterns and investigating them using the commercially available and POoriented software GRASP of TICRA.
Fig. 5 shows the radiation pattern according to the radii of the flat surface in the proposed reflector antenna. As the radius becomes longer, the sidelobe level increases and the mainlobe gain is reduced.
Ⅲ. SAR PERFORMANCE EVALUATION
This section describes two ambiguity ratios as a function of sidelobe level effects.
1. The Range Ambiguity Ratio
The range ambiguity is thought to be a signal contamination due to the antenna sidelobe and the range difference between the desired and the ambiguity signal. Fig. 6 shows the operating concept of the SAR system with data acquisition geometry in a stripmap mode. Each parameter related to range ambiguity and azimuth ambiguity is included in Fig. 6. In general, the range ambiguity condition and its corresponding look angle can be calculated, respectively, using the following equations [1],
where
ρ_{RA} (_{n}) is the range ambiguity slant range,H is the platform altitude, andR is the Earth radius. By newly defining the antenna angle,θ_{A} asthe range ambiguity ratio (RAR) can be written as follows,
where
G_{t} andG_{r} are gains of the transmitter and receiver antennas, respectively, andσ is the backscattering cross section depending on the incidence angle,θ_{I} .2. The Azimuth Ambiguity Ratio
Azimuth ambiguity contamination is often generated by the aliased signals of Doppler information, as indicated by Eqs. (9) and (10) [1].
The
V andθ_{AZ} refer to the velocity of the platform and the azimuth angle in the direction of the moving system, respectively. The azimuthal beam directionθ_{AZ} (n ) is determined from the integral multiple,n of the Pulse repetition frequency (PRF) in the Doppler centroid. From the obtained angle generating the azimuth ambiguities, azimuth ambiguity ratio (AAR) can be written as follows [1]:where PB means the Doppler processing bandwidth.
Ⅳ. ANALYSIS RESULTS
In this section, the relationship between SAR performance and antenna parameters is analyzed using the simulation results for the reflector antenna with the flat dish at the central part and applying the theoretical approach of SAR performance. Table 2 describes several parameters and values for the performance investigation of the SAR system.
1. Backscattering Coefficients
The backscattering coefficient is an important parameter for radar performance, and should be taken into account when considering the surface reflection characteristics coming back from the target. In addition, the backscattering coefficient,
σ is also dependent on the incidence beam angle and works as a multiplication factor with antenna gain. According to [11], the derived backscattering coefficient, as a function of the surface reflection characteristic and look angle, can be represented by using the surface reflectivity model [12]:Where
k _{1} andk _{2} represent the coefficients determined by the reflection characteristics of the target surfaces. The other parameters,a andb , are the standard deviations caused by the surface roughness, which were obtained from the least square approximation of numerous experimental data.2. SAR Performance Analysis
Investigation of the ambiguity signal level according to the electrical performance of the antenna requires determination of the angle,
θ_{A} which affects the signal contamination relative to the desired signal in the range direction.Fig. 7 shows the RARgenerating angle in the range direction with the 2D antenna beam pattern according to variations in PRF. The look angle is assumed to be 30°. As predicted from Eq. (5), the slant range changes uniformly while the ambiguitygenerating angle occurs at the beam illuminating angle (
θ_{A} = 0°) nearest to the positive integer,n . In addition, as the PRF increases, the range ambiguity signal also increases in the angle nearest to the mainlobe.Figs. 8 and 9 show the graphs of RAR values according to PRF, look angle, and radius of the central dish,
d . In general, the RAR increases as the PRF increases. The sidelobe level in the antenna beam pattern due to the size of central dish plays an important role in the RAR evaluation. Fig. 9 shows that increases in the look angle and PRF result in increases in the RAR.Fig. 10 shows the azimuth ambiguity generating angle according to PRF and processing beamwidth with the radiation pattern of the proposed antenna. The angle generating the azimuthal ambiguity is distant from the main beam angle as the PRF increases whereas in the case of RAR estimation, it was close. On the other hand, it seems that the ambiguitygenerating angle, based on the integer
n , has a constant interval.Fig. 11 shows the estimated results of the effects of the central dish on the PRF and AAR. In general, the AAR level is determined by the accumulation of the sidelobe level within the processing beamwidth. The results suggest that a lower AAR level might be predicted as the PRF and the size of
d decrease. An important result is that the AAR level is more dependent on the size of the central dish than on the PRF above 10 kHz. Fig. 12 shows the effects of look angle and PRF on the AAR values when the diameter,d of central dish is 0.8 m. In addition, it can be ensured from Fig. 12 that AAR values remain constant independent on look angle.The estimations of RAR and AAR depending on the PRF, the size of central dish, and the look angle confirm that an appropriate selection of PRF and
d (central dish) will lead to an optimum SAR performance. We propose 9 to 10 kHz and 0.6 to 0.8 m as the parameter values for PRF andd , respectively, in order to satisfy the requirement for an AAR level lower than ？20 dB.Ⅴ. CONCLUSION
This paper proposed a decision procedure for optimizing the antenna parameters that affect the ambiguity characteristics of SAR performance by carrying out a tradeoff on the structure of a parabolictyped reflector antenna with a central flat dish. The important parameters for SAR performance are RAR and AAR, which have been estimated by calculating the field distributions at the aperture and carrying out fullelectromagnetic simulations to obtain the beam pattern according to the variations in antenna parameters. Increasing the radius of the central flat dish was confirmed to increase the sidelobe level and the ambiguity signal level. One advantage of the addition of a central dish to the main reflector antenna is that the total weight will be reduced and the manufacturing process will be simplified. Hence, the selection of the antenna parameters (9 to 10 kHz and 0.6 to 0.8 m as the parameter values for PRF and
d , respectively) should be based on this relationship. Our approach will be a good strategy for the system designer when dealing with antenna parameters that affect the ambiguity level.

[Fig. 1.] Ray distributions in a conventional parabolic reflector antenna (a) and the proposed antenna with modification (flat surface) in its central part (b).

[Fig. 2.] The efficiency of reflector antenna according to the edge illumination.

[Fig. 3.] Normalized electric field distributions for two types of antennas.

[Table 1.] Antenna characteristics according to the circular aperture taper

[Fig. 4.] Aperture field distribution at the circular aperture.

[Fig. 5.] The radiation pattern according to the radii of a flat surface.

[Fig. 6.] The general concept of the synthetic aperture radar system.

[Table 2.] Parameters and values for SAR performance analysis

[Fig. 7.] Rrange ambiguity ratio generating angle in the range direction according to pulse repetition frequency (PRF). SAR =synthetic aperture radar.

[Fig. 8.] Range ambiguity ratio (RAR) according to pulse repetition frequency (PRF) and d (the radius of central dish) when the look angle is 30°.

[Fig. 9.] Range ambiguity ratio (RAR) according to pulse repetition frequency (PRF) and look angle when d is equal to 0.8 m.

[Fig. 10.] Azimuth ambiguity generating angle according to pulse repetition frequency (PRF).

[Fig. 11.] Azimuth ambiguity ratio (AAR) versus pulse repetition frequency (PRF) according to the variations in d when the look angle is 30°.

[Fig. 12.] Azimuth ambiguity ratio (AAR) as a function of pulse repetition frequency (prf) and look angle when d is equal to 0.8 m.