Design of a High-Gain Single Circular Patch Radiator With a Cavity-Backed Structure Using Multiple SIW Feeders for Monopulse DF-Applications

This paper proposes the design of a gain enhanced single circular patch radiator (SCPR) with a cavity-backed structure using multiple substrate integrated waveguide (SIW) feeders for monopulse systems. We derive the equations of a radiation pattern for the multi-feed SCPR and compare it with the full EM simulation results. Based on the theoretical results, the proposed SCPR with multiple feeds is designed by adding the cavity-backed structure to obtain high gain characteristics. In the feeding network, four SIW structures are designed and circularly arranged, which can reduce loss and mutual coupling. Each pair of the SIW feeders can provide sum (<inline-formula> <tex-math notation="LaTeX">$\Sigma$ </tex-math></inline-formula>) and difference (<inline-formula> <tex-math notation="LaTeX">$\Delta$ </tex-math></inline-formula>) patterns to achieve the monopulse direction finding (DF) properties in both elevation and azimuth directions. To verify the feasibility, the proposed antenna is fabricated, and the antenna characteristics are measured. The measured reflection coefficient is −14.5 dB at 5.8 GHz, and the maximum gains are 4.9 dBi and 4.8 dBi in <italic>zy</italic>-plane. To observe the monopulse DF, the estimated direction of arrival (DOA) results are examined in both elevation and azimuth directions. In the whole estimated angle range, the estimation error is lower than 0.49, and the average error is 0.26.


I. INTRODUCTION
A monopulse system is one of the accurate and rapid direction finding (DF) systems for target tracking in radar and satellite technologies [1]- [5]. The monopulse system conventionally consists of an array antenna and pattern comparator that can compare the received signal simultaneously from the sum ( ) and difference ( ) channels [6], [7]. In general, the monopulse system requires four antenna elements to estimate a direction of arrival (DOA) for both azimuth and elevation directions. For an accurate monopulse DF, the antenna element requires a high bore-sight gain that can increase the ratio between the -and -patterns [8]- [10]. To obtain a high The associate editor coordinating the review of this manuscript and approving it for publication was Kwok Chung .
gain property, many studies on various radiator designs of monopulse system have been conducted by employing a horn antenna structure [11], [12], a slotted antenna structure [13]- [16], and a printed Yagi-Uda structure [17], [18]. Although these approaches can result in a high gain performance, the physical size of the antenna radiators are too bulky to implement in small platforms in various industrial fields, such as smart devices, small drones, and IoT applications. To overcome the problem, comprehensive efforts have been devoted to miniaturizing the radiator geometry, i.e., using a corrugated structure for a horn antenna [19], a high dielectric material for a patch [20], [21], and a slot loaded patch antenna [22], [23]. However, multiple radiators with complicated feeding structures and expensive fabrication costs are still required for the monopulse array antenna to estimate both azimuth and elevation angles.
In this paper, we propose a high-gain single circular patch radiator (SCPR) with a cavity-backed structure using multiple substrate integrated waveguide (SIW) feeders for monopulse direction finding (DF) applications. To obtain theoretical insights, we derive equations of a radiation pattern for the multi-feed SCPR based on the cavity model theory of the circular patch antenna with a single feed. The calculated radiation patterns for the SCPR with the multiple feeders are compared with the full EM simulation results for the circular patch antenna under the assumption of an infinite ground and substrate. Based on the cavity model results, the proposed SCPR is designed with the multiple SIW feeding network to minimize the distortion of the radiation patterns [24], [25]. In addition, a cavity-backed structure is added to the SCPR to obtain the high bore-sight gain by reducing the backradiation in the radiation pattern. In the feeding network, four SIW structures are designed to excite the fundamental mode to the SCPR and are circularly arrayed with an interval of 90 • . This feeding network can reduce transmission losses and mutual couplings between the adjacent ports. Each pair of the SIW feeders can provide -and -patterns in the azimuth and elevation directions to achieve the monopulse DF properties. To verify the feasibility, the proposed antenna is fabricated, and the antenna characteristics such as reflection coefficients, bore-sight gains, mutual couplings, and radiation patterns are measured in a full anechoic chamber. To observe the monopulse DF performance, the DOA estimation results using the monopulse amplitude comparison method are obtained by adopting the ratio of the -and -patterns in both azimuth and elevation directions. The results demonstrate that the proposed SCPR with multiple SIW feed structures is suitable for small monopulse DF applications.

II. PROPOSED ANTENNA WITH THE SIW FEEDING NETWORK
A. THEORETICAL APPROACH USING MULTI-FEED CAVITY MODEL Fig. 1(a) shows the conceptual geometry of a microstrip circular patch antenna with a cavity model for a single feed excitation. The circular patch with a radius of a is printed on an infinite substrate with a height of h. The substrate has a dielectric constant of ε r , and the ground of the antenna is also assumed to be infinite. These conditions allow the circumferential wall of the circular patch to be treated as a perfect magnetic conduction boundary by using the cavity model with the surface equivalent magnetic current density M φ When assuming the TM 11 mode field distribution under the patch radiator, the electric fields in the radial direction can be expressed using equations (1) to (4), as follows [24]: where E z is an electric field intensity along z-axis direction, and a e is an effective radius considering the substrate, and k 0 is a propagation constant. V 0 is the voltage induced from the uniform magnetic current as an approximation of a circular loop at φ = 0 • . In our research, the single feed circular patch with the cavity model is extended to the multi-feed with a single patch radiator. Fig. 1(b) presents the conceptual geometry of the SCPR with the multiple feeding ports. All ports (total number of N ) are circularly arranged and located at a uniform distance of d from the center of the patch antenna. Each port (port number n) has an angular position of φ n on the xy-plane.
The surface equivalent magnetic current density M n φ induced from each port can be calculated using the cavity model. From the magnetic current density, the radiating electric field is then obtained using the radiation equation for the circular aperture (5) to (9) [24]. where β d is the phase difference of the magnetic current density between the adjacent ports, and ε reff is the effective dielectric constant in terms of ε r expressed as [26], [27]: Therefore, the final forms of the electric field according to the θ and φ directions can be denoted in the equations (11) to (14) [28].
where E n θ and E n φ are the θ and φ-components of the electric field in the far-zone, and r is the distance to the observation point. J m is the Bessel function of the first kind in the m th order, and D n and S n represent the difference and sum of the Bessel functions of J 0 and J 2 . In Bessel function, the phase difference (β d ) and the angular position (cosφ n ) terms are included to derive the radiation electric field pattern considering the location of the multiple port excitations. To verify the theoretical derivations, we compare the EM simulation and the theoretical calculation of the normalized electric field as shown in Fig. 2. The comparative model is designed with variables a = 10.5 mm, h = 1.6 mm, d = 1.5 mm, and ε r = 2.2. The solid and dotted lines denote normalized electric fields in zx-and zy-planes based on the proposed theory. Dashed lines and dash-dotted lines show the results using the full-wave EM simulation. In EM simulation, the circular patch antenna is designed as a perfect electric conductor on an infinite substrate with a ground plate to similarly design the theoretical model. The electric field result is symmetric in zy-plane; on the other hand, the results in zx-plane are slightly steered to the positive azimuth direction due to the effect of the multi ports. Fig. 3 illustrates the geometry of the proposed circular patch antenna with the multi-port SIW feeding network based on the theoretical results. The proposed antenna is composed of the single patch radiator, the cavity-backed structure, and the four SIW feeders. To design the single radiator, the circular patch having a diameter of d 1 is printed on a TLY-5 substrate (ε r = 2.2, tanδ = 0.0009) that has a diameter of d 2 and a height of h 1 . The circumference of the cylinder substrate is surrounded by the cavity-backed structure with a height of h 2 and the ground plate. To assemble and fix the multi-feed network, a cross-groove on the cavity-backed   structure is designed with a width of w 3 and a length of l 4 . The distance from the ground to the radiator is designed to be about λ/4 to increase the radiation directivity, and the low mutual coupling characteristics of the proposed antenna can be obtained by shorting the cavity with the ground. To design the multi-feed network, four identical TE 10 mode SIWs are employed according to the following equation with the width w of the fundamental rectangular waveguide (15) [29].

B. IMPLEMENTATION USING THE SIW MULTI-FEED NETWORK
where s is the interval of the adjacent SIW via holes, and d 3 is the diameter of the SIW via holes. The SIW feeder has the dimensions of width × height × thickness (w 1 × l 1 × h 3 ). SIW structures preserve most of the advantages of conventional metallic waveguides, while realizing low loss performance in a compact size with low-cost. In addition, the SIW, which has a full-closed structure, is able to avoid the additional radiation coupling and interferences [30], [31].
To have a transition between the connector and the waveguide, the linear transition microstrip line is employed on the top plane of the SIW, where the feeding line excited by an SMA connector has a width of w 2 and a length of l 3 . Each SIW port is circularly arrayed for the four-port network, which can have low transmission losses and mutual coupling characteristics. The detailed design parameters are listed in Table 1. All ports have the maximum gains of 6 dB lower than those of the proposed antenna. We also measure 3D radiation patterns to observe the antenna pattern shape for each port, as shown in Fig. 9. The tilt of the active element pattern is occurred by the locations of the feeding points, the asymmetric structure of the feeding network in the measurement setup, and the mutual couplings. The array distance between the adjacent ports is a dominant parameter that affects the tilt angle of the active element pattern. For example, if the array distance is large enough, the active element pattern will become similar to a stand-alone antenna pattern. Thus, these tilted active element patterns directly affect the monopulse -and -patterns. When the tilt angles of the active element patterns are small, then the -pattern can have a narrow beam width. In the same manner, the -pattern can have a deep null depth. In addition, we simulated the proposed antenna to explain the field transition mechanism. Fig. 10(a) shows the simulated E-field distributions of the proposed antenna. The TE 10 mode E-field excited by the SIW feeder is gradually converted to the TM 11 mode of the circular patch radiator in the cavity-backed structure. Then, as shown in Fig. 10(b) and (c), the simulated H-field and surface current distribution confirm that the proposed antenna is operated as the TM 11 mode, which is obviously similar to the theoretical results of the TM 110 mode for the cavity model [32], [33]. The results demonstrate that the SIW multi-feeding network is appropriate with the proposed SCPR.

III. MONOPULSE DOA ESTIMATION
In general, the monopulse amplitude comparison method is used to estimate a signal direction using four squinted beams that are simultaneously generated. This method computes the amplitudes of -and -patterns. Then, the ratio between the -and -patterns, so called monopulse ratio, is calculated to estimate the angle direction of the received signal. For example, when a target is located on the boresight direction of the antenna, the monopulse ratio becomes zero. However, when the target is off the bore-sight direction, the monopulse ratio increases [34]. In the proposed VOLUME 10, 2022  multi-feeding network, port 1 and port 3 are used to have sum and difference patterns for the azimuth angle direction. Port 2 and port 4 are utilized to obtain the same pattern characteristics for elevation angle direction estimation. Fig. 11 presents the -and -patterns in zx-and zy-planes for the monopulse direction finding using the proposed antenna. The solid, dashed, dotted, and dash-dotted lines indicate the -and -patterns in zx-and zy-planes, respectively. To clearly observe the DOA estimation, the measured data of the radiation patterns are compensated by employing a   moving average filter to smooth the fluctuating noises [35], where the window size is 5. The null depths of the -patterns   ratios in the azimuth and elevation directions are calculated using the simulated and measured active element patterns, as shown in Fig. 12. The solid, dashed, and dotted lines represent the measured monopulse ratio results in zy-and zx-planes and the simulation results. Zero value of the measured monopulse ratio is slightly shifted from the bore-sight DOA because of the tilted null direction of the difference pattern, and the fluctuations of the measured DOA estimation results are caused by the shape of the measured patterns. In addition, the estimation errors between the monopulse ratios using the ideal isotropic pattern and the proposed antenna patterns are obtained in the azimuth and elevation angles. Fig. 13 illustrates the 2D estimation error map calculated based on the simulated and measured radiation patterns. The simulated and measured 2D estimation error map results show a similar tendency that the errors gradually become large when increasing the DOA angles. A large estimation error value is observed at DOA of 30 • because the sum and difference patterns of the patch antenna are more sharply curved than those of the ideal isotropic sources. In addition, the minimum and average estimation errors are 0.49 and 0.26 in the whole estimated angle ranges. The proposed antenna has a null depth of −34.1 dB using only a single radiator, and it can achieve the monopulse direction finding estimations in both azimuth and elevation directions with the SIW feeding network, as listed in Table 2.

IV. CONCLUSION
In this paper, the high-gain SCPR with a cavity-backed structure using multiple SIW feeders was proposed for monopulse DF applications. To obtain theoretical insights, the radiation pattern equations for the multi-feed SCPR were derived based on the cavity model theory of the circular patch antenna with a single feed. Based on the theoretical results, the proposed SCPR was designed with four SIW feeding networks with a cavity-backed structure to obtain the high gain property.
To verify the feasibility, the proposed antenna was fabricated and measured in a full anechoic chamber to obtain the antenna characteristics. The measured reflection coefficient and the mutual coupling of the proposed antenna were −14.5 dB and −11.8 dB at 5.8 GHz. The maximum gains for port 1 and port 3 were 4.9 dBi and 4.8 dBi at −22 • and 22 • in zy-plane, respectively. To observe the monopulse DF for the proposed antenna, the DOA estimation results using the monopulse amplitude comparison were obtained by adopting the ratio of the and patterns in both the azimuth and elevation directions. In the whole estimated angle range, the estimation error was lower than 0.49, and the average error was 0.26.