A novel polyhedral cut-fence is proposed to reduce low-elevation sidelobes and maintain smaller radome size for lower-troposphere radars (LTRs). To optimize the design, radiation sidelobes of the LTR equipped with a cut-fence and a metallic circular disk on the top of a hemispheric radome were studied with high-frequency techniques. Special attention has been paid to the effect of the proposed structure on the LTR radiation sidelobes. The obtained results show that a suitable cut-fence can not only minimize radome size but also maintain the desired low-elevation sidelobes. Additionally, the disk on the top of a hemispheric radome needs to be taken into account for accurate far-field prediction. The proposed structure has been used successfully in designing fences and radomes for wind profiler radars throughout the Japanese islands. Our general conclusions may also be applicable to other radar systems.
 A polyhedral clutter prevention fence has been successfully introduced in front of the lower-troposphere radar (LTR) for blocking ground clutter contamination [Rao et al., 2003b]. To be used in various environments, the LTR with a clutter fence needs to be further covered by a hemispheric radome as shown in Figure 1a.
 This construction can effectively protect the antennas and the fence of the radar from the weather. However, it also produces some practical problems. For example, a larger radome that is needed to cover the whole antenna and a polyhedral fence will result in high construction cost. Moreover, if the LTR is operated in very cold regions, the radome may become heavily covered with ice and snow. This ice and snow build up act as an additional dielectric layer affecting the LTR radiation patterns. To reduce costs the simplest solution seems to make the wall of the polyhedral fence vertical up to the aperture of the radar antennas. This kind of structure requires the smallest size radome, but in most cases it may not be the best choice for suppressing the sidelobes of the radar [Rao et al., 2003b]. As for the ice and snow covering, there has not yet been an effective way to clear them.
 In this paper, we propose installing a vertical metallic axis on the metallic disk on the top of the radome and let one end of a long rope be attached to the axis as shown in Figure 1b. A person standing on the ground and holding the other end of the rope can move around the radome to effectively sweep the ice and snow off the surface of the radome. However, a disk may increase the sidelobe radiation level due to the scattered field from the disk, and it is also questionable whether or not the increased sidelobes will be larger than accepted values. Therefore it is of practical importance to accurately evaluate the effect of the disk on the far field of the radar system.
 As it is well known, more than a hundred wind profiler radars currently in use for lower tropospheric observations over the world are equipped with various clutter suppression fences. However, most of the fences are designed from experience or through simple calculation, we have found little extensive or precise calculations for those structures. Even though the authors' previous work [Rao et al., 2003b] did extensive research on clutter prevention fences, they didn't involve the effects of a disk, and also didn't consider the requirement of a radome.
 In order to solve the aforementioned problems, we developed a new fence design, called a cut-fence in section 2, that is compatible with a relatively small radome size and maintains reasonably low elevation sidelobes, even if a metallic disk is attached on the top of the radome. To effectively validate the proposed design, this paper is organized in the following sections. Section 3 presents the relevant analysis basic for cut-fences and a metallic disk. Sections 4 and 5 study the effects of both the cut-fences and the disk on low-elevation sidelobes. Section 6 describes an application where the LTR is equipped with a polyhedral cut-fence and a hemispheric radome with a metallic disk on its top. Finally, section 7 presents our conclusions.
2. LTR With a Clutter Prevention Fence and a Radome
 The LTR is a 1.36 GHz pulse-modulated monostatic Doppler radar with an active phased array system as shown in Figure 2 [Hashiguchi et al., 2004]. The nominal peak power is 2 kW (the maximum average power is 400 W) produced by 24 solid-state power amplifiers (transmitter modules). The antenna aperture is 4 m by 4 m and it consists of two rectangular arrays mounted over a metallic reflecting plate. The two arrays are perpendicularly superposed corresponding to two linear polarizations. Each array is composed of twenty-four rows of electromagnetically coupled coaxial dipoles (ECCDs) [Miyashita et al., 1999; Rao et al., 2003a] and the spacing between the two rows is 0.75 λ0, λ0 is wavelength in free space. Each ECCD is equivalent to 22 half-wavelength dipoles with the spacing of 0.75 λ0. The plate with electrically small holes can be modeled approximately as an infinite perfectly conducting plate.
 Owing to the square distribution of the LTR radiation elements, a square polyhedral fence can provide symmetric radiation patterns in E and the H planes. Figure 3 shows a basic LTR radar front system that consists of several possible fences associated with a hemispheric radome and a metallic disk on its top. It can be seen that a vertical fence requires a smallest radome if these polyhedral fences have the same bottom perimeter. However, compared to a vertical fence, usually an oblique fence can offer better sidelobe suppression [Rao et al., 2003b]. The above characteristics indicate the possibility of designing a novel fence to obtain a good compromise between small size and low sidelobes.
 From the geometry shown in Figure 3, an effective way to reduce the size of the radome is to cut the four-top corners of a square polyhedral fence. This will also retain the oblique walls of the fence. Although radiation from antennas leaks into the outside space of the fence, which may also result in the increased clutter return, it will be demonstrated that a “cut-window” with suitable dimensions and position on the sidewall of a fence can efficiently retain lower sidelobes.
3. Analysis Theory
 In this study, all metallic surfaces are modeled as perfectly conducting plates. To simulate the scattering fields of an electrically large scatterer, such as a polyhedral fence, the uniform physical theory of diffraction (PTD)has obvious advantages in reducing computational load and maintaining simulation accuracy. The basic relation between the incidence and the scattered field can be described below [Ando, 1985; Bhattacharyya, 1995; Pathak, 1992]:
Hi = the total radiation field from antennas.
 Here EPOs is the physical optics (PO) scattered field. EPTDd is the fringe scattered field due to the finite edges.
 Since EPOs in formula (2) is contributed by the induced currents on a scatterer and the induced currents are based on geometrical optics, high accuracy for formula (2) is expected only in the main radiation region of a scatterer or in its normal but it is degraded around the shadow region. The error around the shadow region is mainly due to the edge diffraction of the scatterer, and this part component can not be effectively described by formula (2). Therefore an additional modified component needs to be considered, which is called the fringe field. EPTDd in formula (3) is just for this purpose and generally an exact solution for it is presented in an integral form of equivalent edge current (EEC) within the framework of the PTD. It is well known, however, that the numerical evaluation of an integration not only imposes a large computational load but also prevents one from physical interpretation of the methodology. The stationary phase method [Ando, 1996; Copson, 1965; Felsen and Marcuvitz, 1973] for the asymptotic approximation of the integration offers an effective approach in the extraction of physical meanings as well as reductions in computation time. If there is a stationary point [Ando, 1996] along the edge line of a scatterer, the integration can be reduced to a simple closed form formula that allows physical interpretation by the generalized Fermat's principle. If the order of approximation is fixed, e.g., the first-order diffraction as in this paper, the stationary point is uniquely determined by the shape of a scatterer. In this paper, choosing the cut-fence on the top corners takes into account the two aspects: First, based on the obtained radiation patterns of the ECCDs [Rao et al., 2003b], this structure should have little radiation leakage into clutter space through this “cut-window,” therefore it will result in a little amount of clutter return; second, “cut-window” in the proposed position maintains a symmetric structure that can offer an easy set for the stationary phase points and reduces the complex in simulation. On the basis of the above principles, the contribution of the diffracted field can be reduced to a simple closed form formula:
where M is the total number of array elements, L is the total number of diffraction points, EUTD(k,j)d is the uniform theory of diffraction field (UTD), and EPOF(k,j)d is the uniform PO diffraction field. References [Ando, 1985; Bhattacharyya, 1995; Pathak, 1992] described more details for obtaining relative parameters involved in the above formula.
 As for a disk on the top of a radome, the UTD technique can be applied to obtain its scattered field in the presence of the antenna and the polyhedral cut-fence. As shown in Figure 4, to simplify simulation but without the loss of accuracy, it is assumed that the incident excitation to the scattered field of the disk comes from the two parts: one is the radiation of the antennas, and the other is the first-order scattering of the fence. In addition, we do not take account the disk into the physical optic scattered radiation of the fence described by formula (2), but include it into the edge diffraction of the fence described by formula (3). On the basis of the above approaches, one may concern that neglecting multiple scattering may result in the degraded results. However, the above approaches are practicable. The reasons are explained below.
 Strictly speaking, since there are actually multiple scattering among the disk, the antenna and the fence, an exact solution should include all possible scattering rays. However, actually taking all multiple rays for the proposed structure is not necessary due to the followings: (1) the disk aperture is very small relative to the fence; (2) the radiation from the disk is the second and the third-order scattered components as shown in Figure 4. Compared to the direct radiation from the antenna, they will be significantly reduced as the scattering distance increases. Moreover, we mainly focus on low-elevation sidelobes, but the physical optics scattered radiation considers mainly the region that is around the main beam. Considering the above three aspects, we can neglect the effect of the disk on the physical optic scattered radiation of the fence but consider its contribution to the edge diffraction of the fence. As shown in Figure 4, the two scattering rays, marked in the second and third order, propagate from the disk to the edge of the fence.
4. Effect of Geometric Parameters of a Cut-Fence
 In order to conveniently study the effect of the geometric structure of a polyhedral cut-fence on sidelobes, we need first define several geometric parameters. As shown in Figure 3, cut-height Hc is defined as the distance along the z axis from a cut-point on the oblique sidewall of the fence to the bottom of the fence or the ground plane, α is the oblique angle of the oblique wall away from the z axis. By adjusting the oblique angle α, various fence heights H can be set when the length L of the oblique sidewall is fixed. Dt and Db is the top and bottom width of one side in a polyhedral fence, respectively. For this study here, the length L of the oblique sidewall of the fence is set at 2 m and the bottom width Db is fixed at 5 m. The Db is little larger than the 4 m side length of the square antenna aperture used in the LTR. Other several parameters, such as cut-height Hc, top width Dt and oblique angle α are set as variable and their effects on sidelobes are studied below.
4.1. Effect of Cut-Height
 A 20° oblique angle is an optimum result in the authors' previous work [Rao et al., 2003b] where a polyhedral fence was proposed but without cut-slots on the oblique walls of the fence. Therefore choosing 20° oblique angle is useful in studying the effect of the cut-slots on the optimum results. For this study, three sample cut-points are chosen, they are 0.5 m, 0.7 m and 0.9 m, respectively. These points all correspond to an oblique angle of 20°.
Figure 5 shows the effect of several various cut-heights on low elevation sidelobes for a polyhedral fence where the top width is set at 1 m. The results show that cut-slots do not markedly affect radiation patterns, even in the 45° radiation plane just along the normal of the cut-slots. When the top width is increased to 1.5 m, as shown in Figure 6, the effect of cut-slots on the sidelobes is not obvious. Figures 5 and 6 also show the simulated low-elevation sidelobes for the above corresponding complete fence, the results show that a complete fence has almost the same low-elevation sidelobes as the corresponding cut-fence.
4.2. Effect of Top Width
Figure 7 shows the effect of the top width on low-elevation sidelobes with the oblique angle of 0°, where two top widths are chosen at 1.0 m and 1.5 m, respectively, and the cut-height is fixed at 0.9 m. From these curves shown in Figure 7, it can be observed that the top width of 1.0 m offers somewhat lower sidelobes than the 1.5 m top width in the E plane along 75° to 90° observation angles, but there is almost no difference for sidelobes in other directions. For another oblique angle, such as 20°, the two different top widths of 1 m and 1.5 m also offer almost the same low-elevation sidelobes as shown in Figures 5 and 6.
4.3. Effect of Oblique Angle
 As obtained in the authors' previous work [Rao et al., 2003b], sidelobes are very sensitive to the oblique angle of a complete fence. To conveniently study the effect of oblique angles on low-elevation sidelobes of a cut-fence, three oblique angles 0°, 10° and 20° are chosen, and they correspond to the cut-height of 1.0 m and the top width of 1.5 m. As displayed in Figure 8, low-elevation sidelobes are very sensitive to oblique angles, and an unsuitable oblique may increase low-elevation sidelobes. In addition, it can be observed that 0° oblique angle is not most suitable in this application although it costs the smallest. This conclusion is consistent with that of the authors' previous work [Rao et al., 2003b].
 On the basis of the obtained simulation results in sections 4.1–4.3, we conclude the following:
 1. Analogous to a polyhedral fence [Rao et al., 2003b], the oblique angle in a cut-fence is most sensitive to low-elevation sidelobes. An optimum oblique angle for a fence without a cut-slot is also basically suitable for the corresponding cut-fence if the cut-slots are set on its top corners.
 2. For a given oblique angle, cut-slots on the top corners of a polyhedral fence do not increase low-elevation sidelobes if the cut-height is set at a suitable height. This is because radiation leakage along the 45° plane exist due to cut-slots, but the amount lost through the slots is very small compared to that in the two principal planes. Therefore cutting the top corner of a polyhedral fence does not have to increase leakage significantly with respect to a complete fence. Also according to the PTD theory [Ando, 1985; Pathak, 1992], the edge of the fence diffracts fields into the shadow region, and the amount is related to the tilt angle, shape, dimension and materials of the fence. Certain field points in the shadow region of a complete fence will be in the illuminated parts of the corresponding cut-fence. As a result, a cut-slot on the fence may not greatly affect the sidelobe level in this direction since the total field is the vector sum of the various contributions. This not only shows the importance of optimizing these cut-parameters via theoretical simulations, but also indicates that cutting top corners of a polyhedral fence is theoretically acceptable.
5. Effect of a Metallic Disk
 A hemispheric radome is added to the LTR and a metallic disk is installed on its top as shown in Figure 3. The UTD technique is applied to the simulation of the LTR radiation field in the presence of a disk and a cut-fence. Figure 9 shows that the sidelobes oscillate with the height of the disk where the radius of the disk is 125 mm. Referring to Figure 9, it can be observed that the increased low-elevation sidelobe due to the disk may be 10 dB at most in a given plane. However, the reduced sidelobes with both the cut-fence and the metallic disk is adequate for data quality at some locations.
6. Practical Application
 On the basis of the basic structures described in this study, we have developed general in-home codes for further designing various cut-fences for the LTRs. These LTRs are covered by a reasonably sized hemispheric radome and have been successfully operated in heavy ice and snow regions in Japan. One of these practical applications is shown in Figure 10 where the antenna aperture is 4 m by 4 m and it is 250 mm over the reflection plate. In the primary design for the desired cut-fence, the sidelength of the fence is chosen at 1.5 m, the bottom width of one side is set at 4 m. To minimize radome size and retain low sidelobes, an optimized cut-fence has been obtained and it has the structure parameters below: the cut-height of 0.7 m, the top width of 1.0 m and oblique angle of 9°. As shown in Figure 1, this cut-fence was successfully installed around the LTR and was effectively covered by a radome where the radius of the radome is 3.75 m and a disk with the radius of 125 mm is on its top. Figure 11 shows the corresponding radiation patterns for the above design. From these results, it can be observed that the proposed cut-fence can effectively reduce low-elevation sidelobes.
 In this paper we describe a novel cut-fence developed for both minimizing radome size and maintaining lower sidelobes of the LTRs. In addition, a metallic disk on the top of a radome has been proposed to facilitate cleaning off any snow and ice gathered on the radome. Although simulation programs are based on the LTR, they are also be very helpful in designing a diversity of fences for other boundary layer radars (BLRs) operated in regions often heavily covered with snow and ice. Actually, these procedures have been used successfully in designing various fences and radomes for wind profiler radars throughout the Japanese island.
 The first author (Q. Rao) was supported by a grant (99235) from the Japan Society for the Promotion of Science (JSPS) under the Postdoctoral Fellowship for Foreign Researchers. The authors would like to thank the reviewers for their valuable comments and suggested improvement.