A Waveguide Slot Array Antenna With Reflection-Canceling Stairs for Sidelobes Suppression at 38 GHz

This paper presents a simulation and experimental study of a $10\times10$ alternating phase-fed single-layer waveguide slot array antenna with reflection-canceling stairs (RCSs) at 38 GHz. The aim of the study was to improve the aperture efficiency of the antenna. Two optimization methods were employed: 1) RCSs for each slot were proposed and optimized for height and position to minimize reflection, and 2) the broad wall width and slot offset were optimized to suppress grating lobes. A design procedure for the feed part was also presented. The characterization of the proposed antenna was found to be in good agreement with simulation results, with a measured S11 of less than −20 dB and a gain of more than 27.71 dBi at 38 GHz (corresponding to an aperture efficiency of 85.6%). The results of this study demonstrate the feasibility of using the proposed antenna in millimeter-wave communication systems.


I. INTRODUCTION
Single-layer slotted antenna arrays have gained increasing popularity in various millimeter-wave (mm-wave) applications, such as radar systems, satellite communication, and fifth-generation (5G) wireless communication [1], [2], [3], [4], [5], [6], [7], [8]. These antennas offer advantages, including an all-metal structure, low loss, high power, and a center-fed configuration that can double the bandwidth and eliminate the frequency dependence of the boresight beam direction [9]. However, previous studies have shown that conventional slotted waveguide antennas have a relatively low aperture efficiency of approximately 57%, primarily due to the presence of reflection-canceling inductive walls and an increasing offset of staggered slots towards the end of the waveguide [10], [11], [12], [13], [14].
To address these issues, several waveguide structures have been proposed, including nonuniform and asymmetric ridge waveguides [15], [16], [17], [18], [19], [20]. Recently, a single-layer slotted waveguide with RCSs The associate editor coordinating the review of this manuscript and approving it for publication was Giorgio Montisci . was introduced, demonstrating improved aperture efficiency at 38 GHz [21], [22], [23], [24], [25]. This novel strategy utilizes stairs to cancel reflections with minimal transmission phase delay, achieved by employing small and fixed slot offset. Moreover, radiation power can be compensated by implementing stairs towards the end of the waveguide.
Reference [21] proposed the concept of RCSs and numerically demonstrated reflection suppression by employing them in a 25.3-GHz slotted waveguide antenna. In addition, Reference [22] presented a detailed design procedure for slots and stairs. Furthermore, a reflection-suppressed slotted waveguide antenna based on the WR-28 standard at 38 GHz was numerically demonstrated in [22]. Reference [23] discussed the suppression of sidelobes in a 10 × 10 array. Subsequently, we utilized the designed 10 × 10 array in a single-layer alternative-phase-fed configuration in [24]. The detailed design procedure for the feed part was also introduced in [24]. Reference [25] addressed the sidelobe suppression issue in a 10 × 10 array and proposed the use of a waveguide with a broad wall width of 5 mm to mitigate the sidelobes.
The primary contribution of this paper is the characterization of the proposed single-layer slotted waveguide with RCSs. The entire antenna configuration is described in Section II, followed by a comprehensive presentation of the design procedure for the antenna array in Section III, encompassing broad wall width optimization, radiating part design, and feed part design. Section III-B discusses antenna fabrication, simulation, and characterization, with a focus on the measurement results. Finally, Section III-C concludes the paper and highlights the significance of the newly measured data for future applications of single-layer slotted waveguide antennas. Figure 1 shows the configuration of an alternating phase-fed single-layer waveguide slot array antenna with 10 × 10 slots. The design frequency is set to 38 GHz. The input aperture consists of a standard WR-28 waveguide [See Figure 1]. To facilitate fabrication and increase the manufacturing yield rate, the three parts of the antenna can be individually fabricated and connected with bolts. This modular design allows for easier assembly and adjustment.

II. DEVICE DESCRIPTION
In the input aperture part, a matching waveguide with a 1/4 guided wavelength is employed, along with a feed waveguide located between the input aperture (WR-28) and the 3 dB power divider for reflection suppression. The feed waveguide utilizes an alternative-phase configuration, wherein adjacent waveguides have a 180-degree phase difference and a uniform amplitude distribution. This arrangement effectively cancels the current on the side walls, eliminating the need for electrical connection between the top radiating plate and the waveguide-based layer.
Furthermore, each feeding aperture incorporates an inductive sidewall to enhance feeding efficiency by precisely tuning the amplitude and phase of the TE10 wave. To achieve a high gain, RCSs are employed for each slot on the radiating waveguides. The radiation section of the antenna features slots spaced at intervals of 1/2 guided wavelength along the longitude direction to mitigate the mutual coupling effect.
To design and estimate the structure, full-wave calculations were performed using the finite element method (FEM). We utilized Femtet (Murata Software Co., Ltd.) as the electromagnetic simulation tool, which accounts for various factors including mutual coupling effects and material loss with high accuracy.

III. ANTENNA DESIGN
A. BROAD WALL WIDTH OPTIMIZATION Figure 2 illustrates a 2-dimensional slotted array pattern. For simplicity, we fixed the width of a single waveguide as a and the offset as r · a. In the y-direction, the slots are allocated at a distance of half the wavelength in the waveguide. The wavelength of the radiating waveguide depends on the waveguide width a.
The relationship between the wavelength in free space (λ) and the wavelength in the waveguide (λ g ) can be calculated  Top view of arrayed antenna in X-Y plane. Broad wall width is a. Offset of slot is r · a, where 0 < r < 1. The slot can be represented by its coordinate (X n , Y n ).
using the following equation: By considering each slot as a small electric dipole antenna with an identical radiating amplitude and ignoring the mutual coupling effect, we can write the antenna factor as: Here, k represents the wave number in free space. The positions of each slot can be determined using the following formulas:  The grating lobe is mainly generated from two aspects. First, grating lobes are produced when adjacent slots are separated by distances greater than √ 2λ. Second, an asymmetrical slot distribution with multiple radiating centers also generates grating lobes. Thus, we can qualitatively conclude that obtaining low-sidelobe antenna arrays requires compact and symmetric slot distributions.
In Figure 3(a), the optimization results for minimizing the slot distance |O 1 O 2 | are presented. For the standard WR-28 (7.112 × 3.556 mm) waveguide, an offset of 1.38 mm is required to achieve 10% radiation. However, the designed waveguide (5 × 3.556 mm) only needs an offset of 0.28 mm to achieve the same radiating amount. Consequently, by reducing the broad wall width to 5 mm, smaller distances between adjacent slots and a symmetric configuration (smaller offset) are achieved.
Using equation (2), the corresponding antenna factor is calculated, and the radiation pattern in the φ = 45 • plane between the two waveguides is plotted in Figure 3(b). It is observed that the waveguide with a broad wall width of 5 mm exhibits lower sidelobes.

B. RADIATING PART DESIGN
Ten identical waveguides form a 10 × 10 antenna array, with each waveguide containing a linear slot allocation. The slot distribution on adjacent waveguides follows a mirror-symmetric pattern, creating an alternative-phase-fed configuration. In order to achieve a uniform radiating amount and minimize reflection for each slot, we employed a RCS for each radiating slot, as depicted in Figure 4. We used a 3-D finite element method (FEM) calculation to determine the complex S parameters for the model shown in Figure 4. Due to the inherent challenges in directly calculating the radiating power from a slot, we adopt an alternative approach. By evaluating the reflection coefficient (S11), transmission coefficient (S21), and propagation loss within the waveguide, we can indirectly estimate the radiation from the slot using the following equation: In our design process, we sequentially design 10 units from the input side to the end of waveguide, where each unit consists of a radiating slot and a RCS. The design of each unit utilizes the model shown in Figure 4 and undergoes full-wave FEM simulation. By specifying the waveguide height (h), slot length (Ls), slot offset (Lo), height of the RCS (hstair), and length of the RCS (Lstair), we calculate the reflection coefficient (S11) and the radiation from the slot. We begin by setting the slot offset to 0.28mm. Subsequently, the waveguide height of each unit is determined based on the height and hstair of the preceding unit. In this manner, we establish a cascading effect in the design process. By conducting parameter scanning of Ls, hstair, and Lstair, our objective is to attain the desired radiation level while simultaneously minimizing the reflection coefficient S11. 72944 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.
The reflection from an appropriately designed RCS has an equal amplitude and reverse phase to the slot reflection, effectively suppressing the total reflection [see Figure 5(a)]. Consequently, with the antenna parameters specified in Table 1, we obtained uniform amplitude and less than −30 dB |S11| for each slot [see Figure 5(b)].

C. FEEDING PART DESIGN
The feeding section of the 10 × 10 single-layer waveguide slot array antenna consisted of a standard WR-28 input aperture, a T-junction 50:50 power splitter, and two 1 × 5 alternating phase-fed radiating waveguides. Figure 6(a) illustrates the configuration of the input aperture and T-junction 50:50 power splitter, where a standard WR-28 waveguide connects to the T-junction using a matching waveguide. Due to the perfect symmetry of the structure in Figure 6(a), the waves coupled to the two directions of the T-junction exhibit precisely equal power amplitude and a 180-degree phase difference. Hence, by tuning the length (a), width (b), and height (h) of the matching waveguide to achieve impedance matching and suppress total reflection, we achieved a reflection of −53 dB at 38 GHz when setting (a, b, h) to (4.47 mm, 3.10 mm, 3.20 mm), as depicted in Figure 6(b).
The configuration of the 1 × 5 fed waveguides is illustrated in Figure 7. Initially, we set the length (l) to 5.225 mm to ensure that the half-wavelength in the waveguide (1/2 λg) is equal to 6.015 mm, which is the sum of the broad wall width (5 mm) and the sidewall thickness (1.015 mm) for the alternating phase-fed condition. Additionally, we precisely adjusted the width (w) and offset (d) of the feed waveguide port, as shown in Figure 7(b), to control the phase and amplitude of the fed wave. Furthermore, an inductive wall was incorporated to suppress total reflection, utilizing parameters (d 2 ) and (q) as depicted in Figure 7(b). Four parameters (d, w, d 2 , and q) were designed to achieve the two desired properties listed in Table 2. Firstly, we achieved less than −20 dB reflection for each port and nearly equal fed wave power distribution (with a power deviation of < 0.43 dB) across all ports, as shown in Figure 8(a). Secondly, we attained an alternating phase-fed  condition with a phase deviation of < 1 • , as demonstrated in Figure 8(b). VOLUME 11, 2023

IV. DEVICE FABRICATION, CHARACTERIZATION, AND DISCUSSION
The proposed antenna design parameters derived in Section III were utilized for the fabrication of the antenna by Oshima Prototype Engineering Co., Ltd. To serve as a reference, a traditional antenna array without RCSs was also manufactured. Both the device with and without RCSs has a broad wall width of 5 mm. Figure 9 presents top, back, and side views of the fabricated device, which features a compact single-layer configuration and a standard WR-28 aperture, ensuring ease of use.
To evaluate the performance of the fabricated antenna, the reflection coefficient S11 was measured using the Keysight (Agilent) N5234A PNA-L vector network analyzer covering a frequency range of 10 MHz to 43.5 GHz. Short-openload-through (SOLT) calibration was performed using an Agilent 85056D calibration kit. In addition, commercial  software Femtet was employed for finite-element method (FEM) simulations of the S parameters, enabling a comparison of the measurement and simulation results. Figure 10 illustrates the comparison between the RCS antenna array (red) and the conventional antenna array (black). The graph plots the S11 parameter (reflection) as a function of frequency from 37 to 39 GHz. Both experimental (solid line) and simulated data (dashed line) are presented, showing good agreement. The results validate the accuracy of the simulation and demonstrate the superior performance of the RCS antenna array, which exhibits reduced reflection losses (< 15 dB at 38 GHz). This graph provides compelling evidence supporting the advantages of the RCS design within the  specified frequency range, contributing to the overall findings of the study. Figures 11 and 12 illustrate the relative radiation patterns of the antenna array. The solid lines correspond to the measured results, while the dashed lines represent the simulated results. Specifically, the red lines illustrate the device equipped with RCSs, while the blue lines depict the device without RCSs. The strong agreement observed between the measured and simulated results in both Figure 11 and Figure 12 provides compelling evidence for the successful fabrication of devices with both configurations. Moreover, previous observations have highlighted that although the sidelobes on the E or H plane, resembling those of a cophase-fed antenna array, do not  significantly affect the antenna gain. In contrast, the presence of large sidelobes in the φ = 45-degree plane, arising from the increasing slot offset, heavily degrades antenna performance. Consequently, addressing this issue is important. In this context, Figure 12 focuses specifically on the relative radiation patterns on the φ = 45-degree plane. By incorporating RCSs, both the simulation and experimental results demonstrate a remarkable reduction in the first grating sidelobes near θ = ±60 • on the φ = 45-degree plane, with suppression levels ranging from −10 dB to −20 dB. These results suggest that the integration of RCSs holds great potential for enhancing antenna efficiency by effectively mitigating sidelobes.
To estimate the absolute maximum radiation power, a comparison was conducted between the measured radiation pattern of the Device Under Test (DUT) and that of a standard gain horn antenna (FLANN MICROWAVE Model 22240-25). Figure 13 illustrates the simulated gain between 37 to 39 GHz by solid lines, while the measured gains at 37, 38, and 39 GHz are represented by diamond marks, respectively. The dashed straight lines in the figure indicate the aperture efficiency (η), which is calculated using Equation (7) [5]: Here, λ represents the free-space wavelength, G denotes the linear gain, and A signifies the effective radiation area. , respectively, at the same frequency. Additionally, an aperture efficiency larger than 80% was achieved by incorporating reflection canceling structures (RCSs) within the frequency range of 37.5 to 38.5 GHz. Figure 14 shows the simulation results of ideal 10 × 10 arrays and full models, both with and without RCSs. It can be observed that within the range of 37.5 to 38.5 GHz, only a negligible loss of below 0.5 dB was incurred due to the design of the feeding component. However, outside this frequency range, the full model exhibited lower gain, indicating that the efficiency degradation beyond the range of 37.5 to 38.5 GHz is primarily attributed to limitations in the design of the feeding component.

V. CONCLUSION
In conclusion, this paper presented a simulation and experimental study on a waveguide slotted array antenna with RCSs for sidelobe suppression at 38 GHz. The main objective of the study was to improve the aperture efficiency of the antenna. Two optimization methods were employed: the use of RCSs to minimize reflection and the optimization of the broad wall width and slot offset to suppress grating lobes. The design procedure for the feed part of the antenna was also presented.
The proposed antenna design experimentally achieved a measured S11 of less than -20 dB and a gain of more than 27.71 dBi at 38 GHz, corresponding to an aperture efficiency of 85.6%. These results were in good agreement with the simulation results, confirming the feasibility of using the proposed antenna in millimeter-wave communication systems.
The alternative-phase fed configuration offers simplified fabrication, particularly for large-area antenna arrays. On one hand, a center-fed configuration can be employed with multiple 10 × 10 antenna arrays to enhance the overall gain [9]. On the other hand, the configuration presented in this study is also applicable to higher frequency regions such as (THz), allowing for the expansion of frequency resources.