## 1 Introduction  
Substrate-Integrated Circuits (SICs) are a technology designed to integrate all communication devices on a single substrate. This approach combines the advantages of both planar and non-planar circuits by embedding all communication components within one substrate, typically for use in microwave and millimetre-wave systems. Examples include Substrate-Integrated Waveguides (SIWs) [1], ESIWs [2] and Air-Filled Substrate-Integrated Waveguides (AFSIWs) [3]. ESIWs offer numerous advantages, including cost-effectiveness, light weight, simplified manufacturing, and low losses, making them ideal for various design applications [2, 4]. This technology has been used to develop many passive components [5, 6], but it has not been widely used for antennas. Patch antennas are already well known, and there are numerous examples [7, 8, 9] with different topologies. Generally, patch antennas are implemented using dielectric substrates and fed using microstrip lines, which leads to high losses due to the dielectric material used,reduced bandwidths, and poor electrical performance. In order to avoid the aforementioned problems, the concept of a floating patch antenna fed by a metallic rod was first introduced in [10], where the patch is fed using a microstrip line (a quasi-TEM line). However, the concept of the dielectricless patch antenna was previously introduced in other works, such as [11], where a dielectric probe placed at the centre of the patch holds the floating patch, allowing the removal of almost all of the dielectric filling of the patch (the probe itself is dielectric), significantly increasing the radiation efficiency and the electrical performance. Other works [12; 13] present air gaps in their patches to improve performance in terms of radiation efficiency and gain. All of them are implemented using microstrip lines, leading to an increase in losses in the feeding network. As has been demonstrated, in order to maximise efficiency, the dielectric in the patch should be completely removed. However, to achieve even higher efficiency, it is necessary to consider the technology used to feed the patch. This feeding technology should ideally operate in an empty (air-filled) medium in order to minimise losses. Some references, such as [14; 15; 16; 17], explore the use of empty structures for the feeding line. In [14], a configuration for feeding an ESIW dielectricals patch antenna was proposed, where a 3D-printed plastic frame supports the patch antenna, and a slot couples the electromagnetic signal to the patch. Although both the patch and feeding line are partially empty, the presence of the plastic frame affects the response, as there is a dielectric (plastic frame) between the patch and the ground plane, degrading the performance and not achieving a fully planar integration. In [15; 16; 17], empty structures such as ESIWs or AFSIWs are used as feeding mechanisms for patch antennas. In all of them, although the feeding structure is partially or completely empty due to the use of ESIW/AFSIW technologies, the patch itself remains filled with dielectric material, limiting their electrical response. Thus, in this paper, we propose for the first time a completely empty floating patch antenna fed by an Empty SIW. Both structures are empty; as a result, the radiation efficiency and electrical performance are significantly improved compared to traditional antennas implemented using dielectric substrates and fed using dielectric-filled waveguides or transmission lines. In addition, the proposed antenna is implemented using standard manufacturing processes of planar technologies. The prototype presented in this work provides a measured radiation efficiency of over 90% and a relative bandwidth of 20%. It is designed to operate in the X-band (8-12 GHz), with a resonance peak at 10 GHz. The antenna design follows the same principles as typical patch antennas [18; 19], with some key differences: air replaces the dielectric, and the feeding line is a non-TEM line instead of quasi-TEM.