## 1 Introduction  
Waveguide slot array antennas (WSAAs) are widely utilized in satellite communications and radar systems for many reasons, including their ability to handle high power levels, their high gain, their high efficiency, and their ability to control aperture distribution precisely [1, 2]. Many research studies have been conducted over the past few decades for the analysis and development of the WSAAs by means of analytical theories, numerical methods, and/or experiments [3, 4, 5, 6]. For synthesizing a slot array, a well-known and accurate design procedure was proposed by [PERSON] _et al._, taking into account all mutual coupling effects [7]. Using this method, the slot length and offset of each slot in the array could be determined for a given aperture distribution and input matching. Using this method, the slot length and offset of each slot in the array could be determined for a given aperture distribution and input matching. Since WSAA is typically realized on metallic waveguides, it is heavy, expensive, and difficult to fabricate precisely enough for mass production. To overcome these disadvantages, a substrate-integrated waveguide (SIW), which is realized by two rows of metallic via arrays in a metal-clad dielectric substrate by using a general PCB process, has been introduced and intensively investigated recently [8, 9, 10]. Like metallic waveguides, the SIW shows similar propagation characteristics. Additionally, it is low-cost, lightweight, mass-produced, and easily integrated with other planar circuits on the same substrate. Therefore, slot array antennas (SAAs) that utilize SIW technology are very attractive for use in satellite communications and radar systems. In high-performance radar and satellite communication applications, it is highly required to design an antenna with a low sidelobe level (SLL) to counter low-altitude attacks, anti-radar missiles, and so on [11]. However, only a few papers have been reportedto focus on the design of SIW-based SAAs with a low-SLL characteristic. Generally, the SLL of the SIW-based SAAs can be suppressed by appropriately tapering the amplitude distribution across all the radiating slots. This can be realized by either varying the offset value of the slots from the centerline of the SIW [12; 13] or tapering the SIW width [14]. As a result, these designs have reported the SLLs better than \(-28\) dB at the designed frequency. However, end-fed SAAs have the disadvantage of beam squinting versus frequency, so they do not meet the requirement of a stable boresight beam used in radar applications. Additionally, the beam squinting and long line effects are more noticeable as the array size increases, as is usually the case with traveling wave antennas [15]. To solve this problem, SAAs with a center feed are the most effective method since they provide a fixed boresight beam across their entire operating band due to their symmetrical structure and reduce the long line effect by half [16; 17; 18]. Double-layer center-fed SIW-based SAAs were introduced [16; 17], comprising a slot array implemented on the upper substrate and a feeding network implemented on the bottom substrate layer. By adjusting the slot positions and slot lengths to control the excitation coefficients for individual radiating slots, an SLL of \(-22.5\) dB was experimentally obtained in the \(H\)-plane at the center frequency [16]. A low-SLL of \(-17.9\) dB in the \(E\)-plane was realized with the help of the unequal power divider [17]. In another work [18], a center-fed SIW-based SAA realized on a single-layer substrate was reported by implementing the feeding network in a restricted slot-free area at the central portion of the array antenna. This design achieved an SLL of \(\leq\)\(-21\) dB in the \(H\)-plane by applying the tapered amplitude distribution over the slots, but the SLL suppression in the \(E\)-plane was not considered due to the difficulty of implementing an unequal power divider within the restricted slot-free area.