A Novel High-Gain Sum and Difference Conical Beam-Scanning Reflector Antenna

A novel sum and difference (SD) conical beam-scanning reflector antenna is proposed in this paper. The reflector surface, illuminated by two omnidirectional horns, is a body of revolution obtained by revolving the generating parabola about a symmetry axis. The horns stacked along the symmetry axis of the reflector are fed by a nest coaxial waveguide. Teflon lens is used to improve the side lobe levels and reflection coefficients of the feed horns. By tilting the generating parabola and using the offset feeding method, two conical beams, with different beam pointing angles, were generated. A compact feed network was also designed to feed the two horns, which includes two rectangular TE10 mode-to-coaxial TEM mode transitions and a Magic-T to implement SD beams. The scanning performance of conical beams can be achieved by mechanically moving the feed antennas along the symmetry axis and taking full advantage of offset focus characteristic of the parabolic reflector. The error in angle measurement was also discussed. The SD conical beam-scanning antenna was formed by a parabolic dish with a radius of $18~\lambda $ operating at 24 GHz. The proposed antenna was designed, simulated, and fabricated. The measured results show that the difference beam null-depth is −25 dB and the sum beam gain is 15 dBi at 40°. The sum beam gain varies by less than 1.5 dB across the scan coverage from 30.8° to 45.2°. The measured results are found to be in good agreement with the simulated ones.


I. INTRODUCTION
Of late, much attention has been paid to conical beam antennas, because they are good candidates for satellite communication, target detection, tracking or guiding system, and so on. Conical beam antennas are superior to phased array antennas and omnidirectional antennas in TACAN-tactical air navigation system, vehicles communication, etc., because of their low cost and better performance. Satcom on the Move (SOTM) system needs high-gain and wide-beam coverage to obtain good quality communication [1]. The conical beam-scanning antennas with sum and difference beams for tracking capability can give better performance-to-cost ratio.
Different from the traditional pencil beam monopulse antennas [2]- [4], the beam coverage of conical beam antenna is a ring area rather than a spot area. Therefore, conical beam antennas have intrinsic advantage of being wide beam coverage that is very important in many applications.
The associate editor coordinating the review of this manuscript and approving it for publication was Davide Ramaccia .
Consequently, unlike the pencil beam the gain reaches 15dBi with 40 • beam-pointing angle will be considered to be high gain. Conical beam patch antennas are reported to be switchable between a broadside and a conical radiating mode by exciting different modes of the radiator [5]- [9]. A hybrid topology optimization method, for designing an LP and CP conical-beam patch antennas, is proposed in [10]. Circularly polarized antennas with conical beam radiation patterns are introduced in [11], in which the feed networks are very simple, with no need for power divider. Slot antennas with conical-beam radiation are described in [12], whose angle of maximum gain depends on the tilt angle of the cone. In [13], [14], reconfigurable conical beam-pointing angle antennas with variable frequencies are reported. In [15], [16], nested horn antenna is proposed to produce conical beams with different beam-pointing angles by controlling the diameters of coaxial waveguide horn and circular waveguide horn. A helmet antenna with conical beams, based on artificial magnetic conductors, is presented in [17], which is wearable and compact.
In the above-cited references, the conical beam antennas are with either low-gain or small beam-pointing angle. To improve the gain of the conical beam antennas, three kinds of antennas are used: lens antenna, array antenna, and reflector antenna. The dielectric lens, used in high-gain conical beam antennas, is usually very large and bulky [18]. Array antenna proposed in [19]- [23] suffers from complex feeding network, complicated structure, high profile, and difficulty in beam-scanning. Reflector antennas, with single and dual reflectors, have been investigated for single high-gain conical beam [24]- [27]. In practical SOTM systems, conical beam-scanning antenna with high-gain and wide-beam coverage is desirable because of the relevant movement between the antenna and the satellite. The operation bandwidth of the STOM is too narrow to form a frequency-scanning conical beam. Conical beams have wide-beam coverage in azimuth plane. And tracking of the satellite in the elevation plane can be realized by sum and difference conical beams, as shown in Fig. 1. Therefore, conical beam-scanning characteristic of a fixed frequency is a good choice for SOTM. An omnidirectional dual reflector antenna is proposed in [26] for flexible coverage. It provides scanning conical beam by moving the sub-reflector along the common symmetry axis of the dualreflector. However, it lacks the capability of tracking, which is required for a high signal-to-noise ratio. To obtain the tracking capability in the SOTM system, the SD beams are introduced, which produce an error needed for tracking [28]. In addition, because of the rotational symmetric feature, the conical beams can only realize one-dimensional tracking.
In this paper, a SD conical beam-scanning reflector antenna, with the capability of tracking the beam-pointing angle, is proposed. Rotational symmetric reflecting surface, with parabolic generating curve, was illuminated by two primary omnidirectional horns (see Fig.2). By tilting the generating parabolic curve and using the offset feeding method, two conical beams, with different beam pointing angles, could be generated. To suppress the higher-order modes of the coaxial waveguide with large radius, four-way ridge waveguides have been used to feed the outer nested feeding horn. The inner horn was fed by a simple rectangularto-coaxial waveguide transition. In addition, a comparator network was also designed to coordinate with the horns and reflecting surface and to produce the high-gain SD conical beams. SD conical beams-scanning performance was realized by mechanically moving the total feed along the symmetry axis and taking full advantage of offset focus characteristic of the parabolic reflector. Thus, a reflector antenna with a radius of 18 λ was designed, fabricated, and tested. The measured gain of the sum conical beam, with 40 • beam-pointing angle, was 15 dBi, whereas the null depth of the difference conical beams could reach −25 dB at 24 GHz. Moving the feed horns along the symmetry axis allowed the sum conical beam to be scanned from 30.8 • to 45.2 • . This structure can make full use of the antenna aperture to obtain higher aperture efficiency and is easy to fabricate at K band.

II. GEOMETRY OF THE PROPOSED ANTENNA
The proposed antenna is composed of two nested omnidirectional horns and a reflector, and both of them are bodies of revolution with a common symmetry axis (the z axis), as depicted in Fig. 2. W a is the width of the antenna conical aperture and D M is the diameter of the reflector outer rim. The architecture of the feed of SD conical beam antenna is illustrated in Fig. 3. Feed network and omnidirectional feed horns are shown in Fig. 4. To produce a set of parallel omnidirectional beams, two horns are stacked along the z axis and fed by nested coaxial waveguide 1 and 2. The inner and outer radii of the coaxial waveguide 1 and the coaxial waveguide 2 are r 1 , r 2 , r 3 , r 4 , respectively. Teflon lenses (ε r = 2.1, and tanδ = 0.001) were placed at the apertures of the horns to improve the impedance matching and decrease the side lobe levels. Outer contours of the Teflon lens were generated by parabolas. The focuses O 1 and O 2 of the parabolas were placed at the phase center  of the horns, which were calculated by HFSS. The focus P of the reflector was set at the center of O 1 and O 2 . The traces of P, O 1 , and O 2 , spanning 360 • around z axis, form three ring. The focal length of the reflector is f . The primary radiation pattern of each feed horn was determined from the requirement of the −7-dB edge illumination and the details are given in Section III. Optimized dimensions of the relevant parameters in this design are listed in Table 1. Fig. 5 shows the structure of the magic-T and transition 1 of the rectangular-to-coaxial waveguide 1. The comparator network is stemmed by a traditional waveguide magic-T. For large impedance ratio between rectangular and coaxial waveguides and good return loss performance over a wide frequency band [29], a 4-section Chebyshev impedance  transformer was used in the matching transition. Optimized dimensions of the relevant parameters in this design are listed in Table 2.   6 shows the configuration of the coaxial-to-coaxial waveguide 2, that is, transition 2, which is a heartlike structure. For good return loss performance over a wide frequency band, arc trace connection between the single-ridge rectangular waveguide and Port 4 was used [30]. Moreover, four parallel 200-single-ridge rectangular waveguides were utilized to maintain the circular symmetry of the electromagnetic field required for excitation of pure TEM mode in the coaxial waveguide 2. In addition, two parallel 100-double-ridge rectangular waveguides were used to connect the 50-coaxial waveguide and 200-single-ridge waveguide. Optimized dimensions of the relevant parameters in this design are presented in Table 3.

III. ANALYSIS OF THE PROPOSED ANTENNA
This section introduces the analysis of the feed network and design of the reflector. The proposed structures were analyzed using HFSS and CST.

A. ANALYSIS OF THE FEED NETWORK AND THE HORNS
Magic-T is an important component of the feed network, which is used for the sum and difference outputs. To obtain SD characteristics, the difference-signal between Port 03 and Port 04 is excited at Port while the sum-signal is obtained at Port . Ports 03, 04, and form the H-arm T-junction of the magic-T. Similarly, Ports 03, 04, and constitute the E-arm T-junction of the magic-T. The process can also be viewed from the E-field distribution in magic-T shown in Fig. 7. Fig. 8 (a) shows the coaxial-to-rectangular waveguide transition 1. It has been observed that electromagnetic waves are transmitted mainly in TEM mode between the coaxial waveguide and the up wall of the ridged waveguide, and then radiate into the multistep impedance transformer, with just a little energy being propagated into the short-circuited waveguide cavity.
The ratio of the external radius to the inner radius of the coaxial waveguide 2 is smaller than the corresponding ratio  in the coaxial waveguide 1 because of the external position (r 4 :r 3 < r 2 :r 1 ). The widths between the inner and the outer conductors of the two nested coaxial waveguides should be the same to produce two similar patterns required from the illumination (r 2 − r 1 = r 4 − r 3 ). As a result, the characteristic impedance of coaxial waveguide 2 is only 17 , which is much smaller than that of the coaxial waveguide 1. Simultaneously, the higher-order modes of the coaxial waveguide 2 will appear. To solve these problems, a 50 to 17 continuously tapered coaxial waveguide impedance transformer was used, as shown in Fig. 8 (b).     The omnidirectional feed horns can be uniquely determined once the θ h and l h are given. θ h = 40 • and l h = λ are obtained based on [31]. Teflon lens was introduced to improve impedance matching. Fig. 11 shows E-field distributions in the omnidirectional feed horns with and without Teflon lens. The simulation results of these two cases are shown in Fig. 12 and Fig. 13. In comparison, the omnidirectional horns with Teflon lens not only exhibit more uniform illumination to the reflector from 48 • to 132 • but also feature lower lobes near z axis (see Fig. 12). In addition, the reflection coefficients improved significantly by adding Teflon lens (see Fig. 13), as described in [32]. It indicates that Teflon lens plays the role of phase adjustment and impedance matching.

B. DESIGN OF THE REFLECTOR
The contour curve of the reflector is generated by the left half of the parabola. Analysis of this axially symmetric reflector was carried out based on [24]- [27], [33]- [38]. The location of the focal point P can be determined by the phase center of the two nested feed horns as shown in Fig. 4. θ p is dependent on the beam width of the nested feed antennas. From the previous discussion in Section 2, the generating curve can be uniquely determined once the θ t , W A , and f parameters are given. θ t is specified beam pointing angle, W A is determined from the required gain, and f is calculated from θ p and W A .
The auxiliary y r Pz r coordinate system is defined by rotating and offsetting the yoz coordinate system, with its origin at the parabolic focus, as follows: where y P , z P are the y and z coordinates of the aperture focus point P in the yoz coordinate system. The auxiliary coordinate system and some pertinent geometric parameters are illustrated in Fig. 14. Assuming a uniform field distribution over the reflector's aperture, the maximum directivity D 0 at θ t is given VOLUME 8, 2020 approximately by the following formula [25]: This equation is valid for main-beam tilts at least 30 • from the vertical in this paper. When the feed of a parabolic reflector antenna is displaced laterally from the focal point, the beam shifts off-axis in the opposite direction [33]- [37]. As a result, two conical beams can be obtained by placing the two feed horns on both sides of the focus of the reflector, as shown in Fig. 15. θ O1 and θ O2 denote the angular displacements of the feed horns, and θ 1 , θ 2 the beam pointing angles of the two conical beams. Given that d is much less than f , the beam deviation factor (BDF) can be obtained by the following equation [38]: where κ = 0.5027 is the scale coefficient, whereas the values of f and W A can be taken from Table 1. Thus, it is established that BDF=0.9177. θ 1 , θ 2 can be calculated as follows:   It can be seen that, by moving the feed antennas along the z axis, the beam pointing angle can be continuously changed. Fig. 17 depicts the synthesis of sum and difference conical beams, obtained by the superposition of two conical beams. It can be found that a sum conical beam ( ) forms by adding the two conical beams (in phase), and a difference conical beam ( ) forms by subtracting the two corresponding conical beams (out phase). The difference in propagation path between coaxial waveguide 1 and coaxial waveguide 2 leads to an additional phase difference in the aperture of the horn 1 and horn 2. To compensate the corresponding phase difference, initial phase required at the output of the feed network should be adjusted by tuning the lengths of two co-linear arms of the magic-T (l 1 , l 2 ). Two omnidirectional horns produce two primary patterns, which are reflected by the reflection surface, and generate two high-gain conical beams. Sum and difference conical beams are obtained by the superposition of two conical beams through magic-T. Simulated 3-D radiation patterns are shown in Fig. 18. Mechanically movement of the feed is shown in Fig. 19. Fig. 20 shows the SD beams of the proposed antenna for feed  horns at different positions along the symmetry axis, which are synthesized by the corresponding conical beams shown in Fig. 16. The asymmetry of the difference beam at 30.8 • and 45.2 • was caused by the amplitude asymmetry and phase deviation from the patterns of the single horns.

IV. ERROR ANALYSIS ANGLE MEASUREMENT
As shown in Fig. 16, two conical beams produced by two single horns experience 4-dB crossover, when the spacing between primary-feed horns was set to 11 mm. To simplify the analysis, Gaussian function was used to fit the half part of the normalized conical beam in yoz plane at 40 • , as described in [39]: where θ tgt is the target elevation angle, θ l and θ r are the beam point angles of the two conical beams F l (θ ) and F r (θ), F l (θ tgt ) and F r (θ tgt ) are the output signal amplitudes of the two channels. θ 4dB is equal to the difference between θ l and θ r . Therefore: where θ s is the angle of null-depth. Accordingly, parameter α can be obtained thus: The monopulse error signal u can be obtained by the following [40]: where β is the phase angle between and beam outputs, and θ = θ tgt − θ s . The slope of the curve u error is called the monopulse error slope k m . It can be calculated thus: where x = θ/θ 4dB .The angular precision (standard deviation of angle error) can be calculated thus [28]: where θ bw is sum beam 4-dB beamwidth, and SNR is signalto-noise ratio. Accordingly, the monopulse error signal u error and angle measurement accuracy θ are plotted in Fig. 21 for the case where the SNR is 15 dB. This error signal can be used to estimate the target's position within the beam. In a tracking mode, since the angular position of the target is known, the antenna beam can be pointed directly at the target such that VOLUME 8, 2020 the target is in the center (or at least very close to the center) of the beam. As shown in Fig. 21, the maximum angle measurement accuracy θ is 0.2 • at θ/θ 4dB = 0 in the case of beam scanning from 30.8 • to 45.2 • . This scanning coverage is enough to search Starlink's satellite that launched by SpaceX [41]. Besides, compared with the SD conical beam reflector antenna without scanning ability (e.g., beam point angle is only at 40 • ), the SD conical beam-scanning reflector antenna gives a better sum beam gain at 30.8 • and 45.2 • , which is more than 15dBi. Based on the above-mentioned theoretical finding, a prototype was fabricated and tested. The experimental results are presented in the next section.

V. FABRICATION AND RESULTS
The assembly process of the prototype is illustrated in Fig. 22. Fabrication of the complete feed system and reflector antenna is shown in Fig. 23. The reflection coefficients of the antenna were measured by the network analyzer Agilent E8722ES, and the radiation patterns in an anechoic chamber.     curves present good agreement with measurement within the band 23.5 GHz and 25 GHz. The measurement operating frequencies are lower than the simulation ones are caused by fabrication errors (e.g. positive error of l h ) and the gap created by assembly. And the measurement differences between Port and in Fig. 24 are due to the fabrication errors between the two converters shown in Fig. 19 (e). Fig. 25 shows the simulated and measured radiation patterns of the fabricated SD conical beam reflector antenna at 40 • . It can be seen that cross-polarization levels remain below −25 dB. Low cross-polarization levels are because of the TEM mode feeding and complete symmetry. The measured radiation patterns of the designed antenna are given in Fig. 26, including three conical beam-scanning angles. The results show that the  (2)). sum beam gain varies by less than 1.5 dB, across the scan coverage. Fig. 27 shows the radiation efficiency and realized gain for the proposed antenna over the scan range. It can be found that whether the feed horns move upward from the reflector ring-focus or move downward, the efficiency will reduce. This is because when the feed antenna is off-focus, the spillover of the energy from the reflector increases. The measured and simulated results of the reflection coefficients and radiation patterns are found to be in good agreement, except for a small discrepancy, which might have been caused by manufacturing errors and experimental tolerance. The results show that the designed antenna can achieve high-gain SD conical beam-scanning.

VI. CONCLUSION
In this paper, a SD conical beam-scanning reflector antenna has been proposed. A compact feed network with equalpower-division, high isolation, and good phase-balance was developed for the proposed antenna. Coaxial waveguideto-rectangular waveguide transition was designed. The reflector, which is a body of revolution illuminated by nested coaxial horns, was analyzed by geometrical optics. As a result, 11% impedance bandwidth could be achieved for the whole SD conical beam-scanning reflector antenna. Two 16-dBi conical beams were obtained and used to generate SD conical beams by a comparator network. By mechanically moving the feed horns along z axis, 30.8 • to 45.2 • one-dimensional tracking of the SD conical beam reflector antenna could be achieved. With the proposed antenna, accuracy of 0.2 • could be achieved in measuring the SD amplitude comparison angle. A prototype of the proposed antenna was fabricated and tested. The test results demonstrate the validity of the proposed methodology. The advantages of the proposed antenna are its sum and difference conical beam-scanning, and low cost, besides the ease with which it can be fabricated and assembled. The proposed SD conical beam-scanning reflector antenna has the potential for applications in satellite communication systems.