## 1 Introduction
However, sub-mode SIW cavity antennas only provide single to dual frequencies in Mw applications with a low frequency ratio [20; 22]. Figure 1: Simulated E-filed distributions of; (**a**) full mode SIW (FMSIW), (**b**) half-mode SIW (HMSIW), (**c**) quarter-mode SIW (QMSIW), and (**d**) eighth-mode SIW (EMSIW). Second, self-multiplexing SIW cavity-based antennas are a desirable option for multi-band antenna applications [23; 24; 25; 26; 27; 28; 29]. Self-diplexing [25; 26], self-triplexing [27; 28], and quadruplexing antennas [23; 24; 29] have been utilized to achieve dual-band, tri-band, and quad-band capabilities, respectively. However, these antennas are designed mainly using the multi-cavity, multi-port concept, where each individual-band cavity is powered by its own port, making the design more complicated and taking up more space [36]. Thus, the isolation between multiple-input multiple-output (MIMO) ports may require space diversity or external decoupling circuits, which increase the complexity and the occupied space. Additionally, self-multiplexing antennas generally have a large area and operate at two to four frequencies in the microwave bands with a low frequency ratio between them [25; 26; 27; 28; 29]. While only [24] proposed a self-multiplexing antenna for MMw bands. Third, the dual-mode composite approach has been used. This approach allows a full-sized SIW structure to act as a radiator for both Mw and MMw frequencies [37; 38; 39; 40]. This approach results in high aperture efficiency and can support multiple frequency bands; however, it requires a full-sized SIW (full-mode cavity), which causes the MMw antenna to have a large footprint [41]. In light of the aforementioned discussion, the current state of research shows two major gaps: (1) There is a lack of studies on multi-band single-sub-cavity antennas that can operate at different bands using only one feed point, particularly for MMw and sub-terahertz applications. (2) The published SIW-cavity antennas are unable to utilize sub-cavity structures with the dual-mode composite to serve as shared-aperture antennas for Mw applications. To overcome these gaps, the authors have designed a new antenna that addresses these limitations and provides solutions for both current and future applications with new and innovative features. This new design comprises a compact shared-aperture open-loop antenna using a quarter-mode SIW (QMSIW) based on structure-reuse technology. The proposed antenna covers four separate bands: 5.5 GHz, 28 GHz, 38 GHz, and 0.13 THz. Additionally, a \(4\times 4\) MIMO antenna system is created using four QMSIW cavity antennas at 28 GHz, 38 GHz, and 0.13 THz. The four QMSIW cavity antennas are arranged in a unique configuration to form a conventional open-loop antenna, which constitutes the antenna in the sub-6 GHz band (mainly 5.5 GHz). This design is the first of its kind and holds significant potential for future mobile communication systems. The following are the key novel features of the design:  
1. It is a multi-band, multi-application antenna that is integrated into a single-layer PCB with a quite small overall footprint area of only 6 \(\times\) 10 mm\({}^{2}\) (0.1\(\lambda_{0}\)\(\times\) 0.18\(\lambda_{0}\)), where \(\lambda_{0}\) represents the free space wavelength at 5.5 GHz. 2. For the first time, three distinct resonances with a high frequency ratio of approximately 23 are generated from a shared-aperture antenna that comprises integrated SIW sub-cavities. Furthermore, these sub-mode cavity antennas are used with the dual-mode composite to form sub-6 GHz Mw band antennas. This results in a very high reuse aperture utilization (RAU) efficiency of about 92%. The paper is structured as follows: Section 2 introduces the design of the proposed multi-band shared antenna and provides details on the design considerations. The evolution process of the proposed SIW antennas as well as a parametric study are investigated in Section 3.