# Meta Surface-Based Multiband MIMO Antenna for UAV Communications at mm-Wave and Sub-THz Bands
## 2 Materials and Methods
### Simulation  
#### 2.1.1 Design Process of the Antenna with a Single Port  
The proposed LWA incorporates two rectangular patches capacitively fed through the coplanar waveguide (CPW) technique, incorporating chamfered edges. Initially, fundamental equations, as provided by [33], are employed to determine the dimensions of the rectangular patch and transmission line, enabling the antenna's design at 8.5 GHz (where \(\lambda_{0}/2\leq 18\) mm). Despite well-established principles, these equations are presented again for more information. \[W\ =\ \frac{c}{2f_{0}\sqrt{\frac{(\epsilon_{r}+1)}{2}}},\ \epsilon_{eff}=\frac{( \epsilon_{r}+1)}{2}+\frac{(\epsilon_{r}-1)}{2}\Bigg{(}\sqrt{\left(1+\left( \frac{12h}{w}\right)\right)}\Bigg{)},\]  
\[\Delta L=0.412\ \mathrm{h}\frac{(\epsilon_{eff}+0.3)\left(\frac{w}{h}+0.264 \right)}{(\epsilon_{eff}-0.258)\left(\frac{w}{h}+0.8\right)},\ L_{eff}=\frac{c}{2 f_{0}\sqrt{\epsilon_{eff}}},\ \mathrm{L}\ =\ L_{eff}-2\Delta,\ L_{g}\ =\ L+(6h)\]  
\[W_{g}\ =\ W+(6h)\]  
where \(W\) is the width of the patch, \(c\) is the velocity of light, \(f_{0}\) is resonance frequency, \(\epsilon_{r}\) is the dielectric constant of the substrate, \(\epsilon_{eff}\) is effective dielectric constant, \(\Delta L\) is the extension length, \(L_{eff}\) is the effective length, \(h\) is the substrate thickness, \(L_{g}\) is the length of the ground, and \(W_{g}\) is the width of the ground. The calculated actual dimensions for the initial dimensions of the antenna are \(W=12.17\) mm, \(L=9.8\) mm, \(L_{g}=10.7\), and \(W_{g}=12.94\). Subsequently, the design process for the proposed LWA begins, adhering to the following rules, equations, and standards, which are essential for every LWA. Altering an antenna's length significantly affects its resonant frequency. Generally, the resonant frequency is inversely proportional to the antenna's length: increasing the length decreases the resonant frequency, and decreasing the length increases it. This relationship is governed by the principles of electromagnetic waves and the antenna's construction. The design of the leaky wave structure prioritizes high directivity and gain, low loss, and structural simplicity. LWAs belong to a class of traveling-wave antennas, characterized by a wave propagating along a long structure compared to the wavelength. They generate currents propagating along its longitudinal direction, resulting in end-fire and back-fire radiation patterns due to the open-stopband (OSB) phenomenon, as described in [34; 35]. These antennas can be effectively modeled using the balanced composite right-/left-handed (CRLH) transmission lines model, which combines the effects of capacitors and inductors. Enhancements are necessary to enable outward radiation from the antenna and the drone in a broadside direction. Before delving into the design process of the antenna, it is essential to understand the principles of the LWA antenna and how slots and stubs can influence its characteristics,such as impedance bandwidth and radiation pattern. The proposed LWA incorporates asymmetric elements. It includes longitudinal slots to enhance OSB suppression and transverse slots to resolve OSB issues. These slots function similarly to a series of left-handed capacitances (CLs). As a result, they alter the radiation pattern, favoring the broadside direction over the end-fire or back-fire directions. Additionally, these slots help mitigate the surface waves produced by LWAs. The characteristic mode method is utilized to analyze and design these slots, evaluating their impact on the radiation pattern throughout the design process while considering the principles of asymmetry radiation, as illustrated in Figure 1[36]. The periodic slots do not cover the entire width of the substrate (\(W_{s1}\)) and are positioned with an offset from one side (see Figures 1 and 2). Moreover, the waveguide port should be excited with the TE\({}_{10}\) mode instead of the TE\({}_{01}\) mode used in the dielectric inset.