A low elevation sidelobe suppression algorithm based on the uniform physical theory of diffraction (PTD) is developed to simulate ground clutter prevention fences for boundary layer radars (BLRs). As applications to the algorithm, the most suitable fence is achieved for the lower troposphere radar (LTR) and the L-28 boundary layer radar, respectively. The developed algorithm can also be applied to other radar systems where reducing low elevation sidelobes is desired.
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 Boundary layer radar (BLR) has been operated for observing the whole lower atmosphere. However, one of the limitations to this function is clutter echo signals coming from any obstacle on the ground surface, which usually disturb and limit the detection capability of BLRs. It is well known that a radar with lower sidelobes has a better performance in blocking ground clutter. It is, therefore, important to suppress its low elevation sidelobes.
 A clutter prevention fence may result in lower sidelobes due to the field scattered by the fence. To analyze its effects on sidelobes, a fence needs to be first modeled as a scatterer in the radiation field of a radar, and furthermore, an optimum fence can be achieved after comparing the radiation patterns of the radar in the presence of and in the absence of the fence. Since a fence is often an electrically large polyhedral scatterer with several edges, the uniform physical theory of diffraction (PTD), compared to other numerical methods, such as finite element method, can often be more conveniently applied to simulate the scattered field in the view of saving memory and enhancing computation efficiency. According to the above procedures, a sidelobe suppression algorithm is developed to simulate the most suitable clutter prevention fences for two BLRs: the lower troposphere radar (LTR) and the L-28 boundary layer radar, they use electromagnetically coupled coaxial dipole (ECCD) array and disk array as radiation elements, respectively.
 The research in this paper involves the following aspects: Section 2 develops a sidelobe suppression algorithm based on the uniform PTD, and then Section 3 applies the algorithm to simulate the most suitable clutter prevention fence for the LTR. To certify the validity of the algorithm, Section 4 reports an experimental evolution of sidelobe suppression by the LTR fence. Furthermore, Section 5 applies the developed algorithm to the L-28 boundary layer radar. Finally, some discussions and conclusions are given.
2. Sidelobes Suppression Algorithm
 A sidelobe suppression algorithm based on the uniform PTD has been developed in this section to simulate ground clutter prevention fences for BLRs.
2.1. Physical Theory of Diffraction
 If a large antenna array in a radar is composed of M radiation elements, and the radiation far field of the ith element is , the total radiation field can be expressed as a superposition of the individual field contributed by every radiation element.
 To reduce low elevation sidelobes, a suitable fence needs to be installed around the antenna aperture. As a result, the total field in the presence of the fence is given using the uniform PTD [Pathak, 1992; Ando, 1985]
where Ei is the total radiation field from antennas, is the physical optics (PO) field scattered by the fence, and is called the fringe field due to finite edges, which is, in general, expressed as an integral form of equivalent edge current (EEC) along the edge.
2.2. Numerical Solution of Physics Optics
 Let a fence be divided into N segments; the induced current on each segment's surface can be assumed to be constant if the segment is small enough. Supposing the center of the ithsegment is located at (xi, yi, zi) the total field at the ith segment is summed by
where is the magnetic field associated with the electronic filed at the center of the ith segment and M is the total number of radiation elements in the array.
 The total induced current, also called physical optics current, on the ith segment is derived as below:
where is the normal unit of the ith segment. is the electric field of the k element at the ith segment; the radiation far field only in θ is given by
Considering the constant current on each segment, formula (7) is further represented by
where is Δsi the area of the ith segment, R is the distance from the coordinate origin to the observation point in space, (i) is the position vector of the ith segment, and ψi is the angle between the vector and ; the above parameters are expressed in terms of spherical coordinate
The total field scattered by the fence is therefore given by
It is shown from (10) that the field scattered by the fence can be obtained once the induced currents are known. However, PO solution in (10), which is based on the geometry optics and mainly employed to calculate the main beam and first few sidelobes of the reflected fence, becomes fundamentally poor near the shadow of the fence [Pathak, 1992; Ando, 1985]. To simulate accurately fields in full region, the fringe field, also called the corrected term to PO, needs to be introduced.
2.3. Fringe Field in the Closed Form
 As array elements in radars are usually arranged in a symmetrical aperture, we adopt a symmetrical polyhedral fence as a scatterer and symmetrical stationary points on the edges are treated as diffraction points to simulate diffraction fields. Consequently, the EEC integral in (2) is further simplified as a closed form with the stationary phase method [Ando, 1985]
where M is the total number of array elements, L is the total number of diffraction points, and and are the uniform geometry theory of diffraction field (UTD) and the uniform PO diffraction field in space, respectively, due to the kth element to the jth diffraction point.
2.4. Sidelobe Suppression Algorithm
 Sidelobe suppression (SS) is defined as the difference of the highest sidelobe in the low elevation region between in the cases of absence and presence of the fence as well. To achieve largest sidelobe suppression, an optimum configuration has been researched by try and error, where an iteration process is applicable and the times of iteration depend on the required level of low elevation sidelobes. The applications to the above algorithm will be given in the following sections.
3. Ground Clutter Prevention Fence for the LTR
 The most suitable ground clutter prevention fence for the lower troposphere radar (LTR) [Hashiguchi et al., 2003] is achieved using the sidelobe suppression algorithm developed in Section 2.
3.1. LTR and Electromagnetic Couple Coaxial Dipole (ECCD)
Figures 1 and 2 show the configuration of the LTR and its array elements. The LTR is a 1.36 GHz pulse-modulated monostatic Doppler radar with an active phased array system. The nominal peak power is 2 kW (the maximum average power is 400 W), which is produced by 24 solid state power amplifiers (transmitter modules). The antenna consists of two rectangular arrays mounted over a metallic reflected plate. They are perpendicularly superimposed corresponding to two linear polarizations. Each array is composed of twenty-four rows of electromagnetically coupled coaxial dipoles (ECCD) [Miyashita et al., 1999] where the metallic circular pipes act as radiation dipoles and their collinear arrangement in the vertical direction with in-phase excitation gives a line array performance as shown in Figures 2 and 3a. By controlling the phase of the phase shifter, we can steer the beam in the different direction. To reduce the ground clutter echoes, the radiation elements are left 20 cm over the ground surface. In addition, there is a metallic reflecting plate with holes, which is mounted 0.25 wavelengths under the antennas.
3.2. Radiation Patterns of the LTR
 Superposition approach is applied to obtain radiation pattern of the LTR after the electric current distribution of ECCD element is analyzed by moment method and the reflection plate under antennas is approximately modeled as an infinite perfectly conducting plate. The results are shown in Figure 3b.
3.3. Optimization of the Fence for the LTR
 Due to a symmetrical square array aperture in the LTR, a polyhedral fence is suggested and symmetrical stationary points on the top edges of the fence are chosen for calculating diffraction fields. Consequently, the most suitable clutter prevention fence for the lower troposphere radar (LTR) can be achieved using the described algorithm. For the LTR clutter surroundings, the accepted sidelobes in elevation angles (90°∼75°) should be less than −45 dB.
 Based on the procedures in the algorithm, an extensive set of sidelobe suppressions of the LTR with fences of different dimensions have been plotted. At first, let bottom width of a test fence be 2d, and its side length L be 1 m, 1.5 m and 2 m, respectively, the changed oblique angle α be from 0° to 45° with the step of 5°. As a result, a higher sidelobe suppression as shown in Figures 4–6 can be achieved for L = 2.0 m and d = 2.5 m, α = 20°. Thereafter, we introduce a small change in parameters L and d but leave α = 20°, the case of L = 2.05 m and L = 2.00 m shown in Figure 6 corresponds to higher sidelobe suppression in E plan and H plan, respectively, when and d = 2.5 m and the main beam is steered to zenith direction. A similar result can also be observed if the main beam is 15 deg. deflected away zenith angles. Therefore, the final choice for sidelength L is relative to the required sidelobe level in E plane or H plane. Figure 7 gives radiation pattern in the case of L = 2.05 m. Figure 8 shows comparisons of the corresponding radiation patterns simulated by using the GTD and the PTD, respectively. Figure 9 corresponds to an optimum fence obtained by using the above algorithm. As we can see, the agreement is very good. The validation of algorithm is theoretically certified.
4. Experimental Evaluation of the LTR Fence
 An experimental evaluation of sidelobe suppressions achieved by the clutter prevention fences of the lower troposphere radar (LTR) is presented. The results certify the validation of the fence simulated in Section 3.
4.1. Measurement Setup
 The measurement was conducted at Shigaraki MU Observatory of Kyoto University where the LTR antennas act as transmitter, and a half wavelength dipole as a receiver located at the low elevation far field of the LTR. The other characteristics for two antennas are listed in Table 1, and the corresponding environment for measurement is shown in Figure 10.
Table 1. Transmitter and Receiver Antennas for Test Fences
4 m by 4 m
4.0 degree (half-power)
zenith, north, south, east, and west
 To investigate effects of fence dimensions on low elevation sidelobes, we constructed several groups of four side fences; they are composed of aluminum plates and with different oblique angles and sidelengths. Several fences for testing are shown in Figure 11. Bottom width for each face is 2.5 m, the length from top to bottom of the fence is stepped from 0 m to 2.0 m where 0 m corresponds the absence of a fence, oblique angles changed from 0° to 35° in the step of 5°. Based on the above design, a group of test fences are listed in Table 2 where YV means that the polarization of LTR and the receiving antenna are parallel, while XV means that they are perpendicular, T means that the zenith angle of the main beams is 0 degree. The first number is the sidelength of a fence, and the second number is the oblique angle of a fence. Figure 9 in Section 3 shows a basic polyhedral fence.
Table 2. Testing Clutter Prevention Fences
4.2. Measured Results
 The measured results are shown in Figures 12–14, where a suitable fence can greatly reduce low elevation sidelobes of the LTR. From these results, we can also derive the conclusions as below, which are the exactly same as those from the simulations in Section 3:
Oblique angle of a polyhedral fence is strongly sensitive to low elevation sidelobes: In most circumstances, oblique angle of 0° for a polyhedral fence may not be the most suitable although it takes the small size of fence, but 20° oblique angle usually can result in lower sidelobes in the H and the E plane for BLRs in this application, simultaneously.
In general, a larger fence can induce higher sidelobe suppression. However, a polyhedral fence with relatively small dimension may also produce greater sidelobe suppression if its oblique angle and sidelength can be arranged optimally.
The most suitable fence for the LTR is the one with 20° oblique angle and 200 cm sidelength if the main beam is steered to zenith.
 It should be noted the discrepancy between the simulated and measured sidelobe suppression among the corresponded elevation angles is due to effects from environment around the LTR, such as reflection from MU radar fence and hills. As outside factors of the fence, which have not been considered in simulations. But it is indeed shown that the amount of their effects, being as clutter sources, can be greatly reduced once a suitable fence blocks the primary radiation from the LTR antennas to these outside obstacles. We will see that the similar situation would be certified by the following sections for the other BLR, called L-28 BLR.
5. Clutter Prevention Fence for the Boundary Layer Radar With Disk Array
 This section applies the sidelobe suppression algorithm to the L-28 boundary layer radar where array disks act as radiation elements.
5.1. Radiation Pattern of the L-28 Boundary Layer Radar (BLR)
 The L-28 boundary layer radar and its radiation elements are shown in Figure 15, where antennas are composed of 192 square disks, sidelength of each disk is 103 mm, height over ground plate (metallic plate) 10 mm, element spacing 0.75 wavelength. Main beam can be steered to zenith, east, south, west, and north, and the largest deflected angle of main beam is 10 degree away from zenith. Based on the cavity mode theory and superposition approach, radiation patterns of the L-28 BLR array in free space can be obtained. The pattern in Figure 16 corresponds to the case of the main beam steered to zenith.
5.2. Sidelobe Suppression for the L-28 BLR
 To reduce low elevation sidelobes, a clutter prevention fence needs to be around the L-28 radar. According to the sidelobe suppression algorithm, a suitable fence is found, and its bottom width is 4.6 m, the height from top to ground surface is 3 m, oblique angle is 20 deg., height of radiation elements over ground surface is 0.7 m, the simulated results shows that low elevation sidelobes can be greatly reduced as shown in Figure 17. Figure 18 gives the comparisons of radiation patterns obtained by the algorithm with those by GTD, a good agreement has theoretically certified the validation of algorithm again.
5.3. Measured Results
 To certify practically the validity of the designed fence, an experimental evaluation of the fences for the L-28 BLR was also conducted at MU Observatory of Kyoto University where the radar antenna aperture acts as a receiver, a horn antenna as a transmitter located in the far field of the radar. The test configuration is shown in Figure 19. We can see from Figure 19d that the measured low elevation power received by the radar is greatly decreased, compared to the received power in the absence of the fence. Therefore, just like the LTR fence in Section 2, the L-28 BLR fence designed by using the algorithm is also valid in blocking ground clutter.
 We also note the effects of diffraction and reflection from environments shown in Figure 10, such as the MU radar fence in the west-south of the L-28 BLR, a little hill covered by trees in east-south and the reflected ground surface, on the measured results. It is obvious that these effects have resulted in different sidelobes in west and east, which should be the same in an idea environment for the polarization of antenna is along a vector from south to north.
6. Discussions and Conclusions
 A low elevation sidelobe suppression algorithm is developed in this paper to simulate ground clutter prevention fences for boundary layer radars (BLRs). Theoretical comparisons and practical measurements for the LTR and L-28 clutter prevention fences have both shown that the expected results of simulations and designs for the fences are borne out in practice. The authors believe that the input of the following approximations should be important for accurate and efficient simulation in this paper.
 Neglecting multiple scattering: It should be noted that we neglected the effects of multiple scattering (involve the effect of reflection from surface of plate and diffraction from the edge of plate) among side fences on the induced current. The reasons for this approximation is that high-order scatter is much smaller than that of directly radiating one from the antenna, especially when the clutter fence is tilted, for the reflection rays, in this case, may directly proceed into space instead of being scattered by other plates. To certify this point, we also obtained results by using UTD, in which the effect of the first order multiple-reflecting rays has been added to the total scattered fields. But the results from PTD and UTD are almost the same except for the sidelobes of very low elevations. Of course, the authors agree that input of the reflection will be more accurate.
 Introducing stationary phased points: In PTD, the fields calculated by PO are corrected by adding the contributions from the correction edge current, that is, the error in PO diffraction coefficient associated with the peripheral edge of the fence are corrected. To obtain this part filed, stationary phased points provide a way to give the high frequency asymptotic expressions of the integrals for edge equivalent current (EEC). By the approximation, the diffraction integrals are simply the sum of the diffraction fields contributed by several stationary phased points along the edges. As a result, the stationary phased points not only enhance the computational efficiency of PO, but also extract the physical concepts and the PO error.
 Concerning sidelobes of antennas: The purpose to install a fence around the antennas is to prevent direct radiation from the antenna to obstacles on the ground. If the primary radiation to the obstacle is blocked or decreased, then the clutter returns from the obstacles to antenna can be reduced naturally. It is well known that low elevation- sidelobes can effectively reduce primary radiation from the antennas to obstacles. Therefore, the authors focus attention on the inside of clutter prevention fence rather than the outside problems of the fence. Although considerations of obstacles outsides of fences may be more closed to practical situations, characteristics of obstacles are different from each other due to different radar surroundings, and a full consideration for different obstacles is quite complicated and difficult; it is also outside the interests of this paper. Just because of the above outside effects, it is impossible to expect exactly the same results at any point in space for simulated and measured sidelobes in this paper, but we can obtain a very good agreement in tendency for the reduced sidelobes from simulations and measurements for two boundary layer radars, respectively. To accurately predict low elevation sidelobes of BLRs, environmental factors should be taken in account. As these factors involve quite special cases, the algorithm developed here is to involve radar system itself performances, so works related to environments will be reported in a separated paper in future.
 Sidelobe suppression algorithm in the paper has covered the developed reasonable approaches to solve practical complicated problems in engineering application, and it makes optimum fence dimension be possible so as to achieve lower elevation sodelobes of BLRs. Because the algorithm is developed by using a general procedure, it can be implemented on other radar systems where low sidelobes are desired. Actually, the clutter prevention fences developed by using the above algorithm have been in actual use with radars for the Japanese weather forecast system called WINDAS (wind profile network and data acquisition system), operated by the Japan Meteorological Agency, throughout the Japanese island, and they are working very well so far.
 The authors would like to thank the Mitsubishi Electric Corporation and Sumitomo Electric Industries, LTD. for their conducted measurements for the LTR fences and the L-28 fences, respectively. The authors are grateful to reviewers of this paper and Dr. Miyashita of the Mitsubishi Electric Corporation for their helpful comments. The first author (Q. Rao) was supported by a grant (99235) of the Japan Society for the Promotion of Science (JSPS) under the Postdoctoral Fellowship for Foreign Researchers.