# 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
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parameters** & **Values (mm)** & **Parameters** & **Values (mm)** & **Parameters** & **Values (mm)** & **Parameters** & **Values (mm)** \\ \hline \(L_{p}\) & 6 & \(L_{4}\) & 15 & \(W_{/2}\) & 0.75 & \(g_{3}\) & 0.12 \\ \hline \(L_{s}\) & 15 & \(L_{5}\) & 4.5 & \(W_{/3}\) & 1.25 & \(g_{4}\) & 0.12 \\ \hline \(L_{\frac{g}{2}}\) & 1.7 & \(L_{6}\) & 1.25 & \(W_{\frac{g}{2}}\) & 1.75 & \(g_{5}\) & 0.12 \\ \hline \(L_{/1}\) & 1.5 & \(L_{7}\) & 6.5 & \(W_{1}\) & 0.20 & \(g_{6}\) & 0.25 \\ \hline \(L_{/2}\) & 1.25 & \(L_{8}\) & 2.5 & \(g7\) & 0.125 & \(g8\) & 0.40 \\ \hline \(L_{/3}\) & 6.25 & \(L_{9}\) & 2 & \(s_{1}\) & 0.20 & \(s_{2}\) & 1.25 \\ \hline \(L_{1}\) & 4.5 & \(L_{10}\) & 1.75 & \(s_{3}\) & 1.75 & \(s_{4}\) & 1.85 \\ \hline \(L_{2}\) & 1.25 & \(W_{2}\) & 1.5 & \(s_{5}\) & 0.50 & \(s_{6}\) & 0.25 \\ \hline \(L_{3}\) & 5.5 & \(g_{1}\) & 0.12 & \(a\) & 0.40 & \(W_{s}\) & 16.5 \\ \hline \(W_{/1}\) & 0.5 & \(g_{2}\) & 0.12 & \(b\) & 0.65 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The optimized parameters of the proposed antenna. Figure 2: The design configuration of the single antenna and MIMO, including each step of the design and the proposed prototype (**(a)** step 1, **(b)** step 2, **(c)** step 3, **(d)** proposed, **(e)** front view of the MIMO, and **(f)** ground view of the MIMO). The proposed antenna is fabricated on a layer of Rogers 4830 substrate, with a dielectric constant of 3.2, a loss tangent of 0.0006, a dielectric thickness of 0.127 mm, and a copper thickness of 18 \(\upmu\)m. The primary concept behind this design is to create a semi-flexible antenna that seamlessly integrates into mm-wave sub-THz circuitry or packaging for drones. In addition, the proposed LWA design is fundamentally fed by a coplanar proximity technique [37], which employs an open-ended microstrip line. This feeding technique utilizes two distinct coupling mechanisms: capacitive and inductive coupling. In the configuration employing capacitive coupling, a square patch is positioned such that the central line of the patch aligns at a half wavelength from the tip of the open-ended feed line. This arrangement results in the maximum magnitude of the voltage standing wave on the feed line, coinciding at the center of the patch. As a result, a fundamental resonant current pattern (illustrated with arrows in Figure 3b) perpendicular to the feed line is excited through coupling across the gap. Consequently, this setup produces linearly polarized radiation in the distant area. Conversely, with inductive coupling (as depicted in Figure 3a), the edge of the square patch lines up with the tip of the feed line. In this scenario, the patch is powered by the highest amplitude of the current standing wave, which is 90\({}^{\circ}\) out of phase with the voltage standing wave. In contrast to capacitive coupling, this configuration's surface current and radiation polarization are perpendicular to their counterparts. Circular polarization (CP), essential for UAV communication compared to linear polarization, can be understood as a combination of two linear polarizations: spatially orthogonal and phase quadrature. By combining Figure 3a,b, the patch antennas can emit orthogonal linear polarizations as in step one of the designs shown in Figure 2a. In addition, this configuration requires two-element patches to resonate at slightly different frequencies. In this particular design, the shared feed line enables the application of two distinct coupling methods to the two patches, as previously described. As the voltage rises and the current diminishes along the open-ended feed line, depicted conceptually in Figure 4, a process ensues wherein the decreasing current along the feed line induces diminishing currents in the patch below it, utilizing inductive coupling (indicated by black arrows in Figure 4).