## 2 Design of MIMO Antenna
\begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Design Structure** \\ \hline Design structure—1 (DS-1) & **Top View** \\ \hline Design structure—2 (DS-2) & **Bottom View** \\ \hline Design structure—3 (DS-3) & **Top View** \\ \hline Design structure—4 (DS-4) & **Top View** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Four proposed models for the analysis. used in the design of antennas and R.F. circuits to reduce electromagnetic coupling and improve isolation between antenna elements in MIMO systems. The DGS in the ground plane helps in reducing coupling in MIMO antennas through the following mechanisms:  
* Electromagnetic isolation: In a MIMO system, each antenna element should ideally radiate and receive signals independently without interfering with each other. However, due to the close proximity of multiple antennas, there can be coupling between them, resulting in interference and the degradation of system performance. By introducing DGSs in the ground plane, the coupling between the antenna elements can be minimized. The DGS creates an electromagnetic barrier between the antennas, reducing the mutual coupling and enhancing isolation. * Surface wave suppression: DGSs can also suppress surface waves propagating on the ground plane. Surface waves can lead to increased coupling between antennas and reduce isolation. By incorporating DGSs in the ground plane, the surface waves can be attenuated, reducing their impact on the antenna elements and minimizing the coupling between them. * Impedance matching: DGSs can be designed to provide additional degrees of freedom in tuning the impedance of the antenna elements. By appropriately designing the shape and size of DGSs, the impedance seen by each antenna element can be adjusted. This helps in achieving a better impedance match between the antenna elements, minimizing reflections and optimizing the overall system performance. * Enhanced radiation efficiency: The presence of DGSs in the ground plane can also improve the radiation efficiency of the antenna elements. By reducing the coupling and surface wave effects, the energy that would otherwise be lost in coupling or surface wave propagation is efficiently radiated by the antennas. This leads to improved overall system performance and better signal quality. The fabrication of the proposed structures is carried out for analysis purposes, and indifferent proposed structures are shown in Figure 2. The dimensions of different regions are presented in Table 2.  
Figure 2: Fabricated proposed structures. (**a,b**) Proposed design structure—1. (**c,d**) Proposed design structure—2. (**e,f**) Proposed design structure—3. (**g,h**) Proposed design structure—4. The circular-shaped ring is cut in the hexagonal-shaped patch area. The width \(W\) of the patch is calculated using Equation (1) [25]. \[W=\frac{C_{0}}{2 fr}\sqrt{\frac{2}{\varepsilon r+1}} \tag{1}\]  
where \(C_{0}\) is the light speed, \(W\) is the patch width, \(fr\) is the resonating frequency, and \(\varepsilon r\) is the dielectric constant of the substrate. Fringing radio waves travel between patch and ground via air and substrate. Due to the difference in the dielectric constants of substrate and air, the practical dielectric constant calculation is required. The effective dielectric constant (\(\varepsilon_{\mathit{eff}}\)) is determined using Equation (2). \[\varepsilon_{\mathit{eff}}=\frac{\varepsilon r+1}{2}+\frac{\varepsilon r-1}{ 2}\bigg{[}1+12\frac{h}{w}\bigg{]}^{-0.5} \tag{2}\]  
The fringing effect changes the effective area of the patch. Therefore, variation in the area is represented by \(\Delta L\). The change is calculated using the following Equation (3). \[\frac{\Delta L}{h}=0.412\frac{\big{(}\varepsilon eff+0.3\big{)}\big{(}\frac{w }{h}+0.264\big{)}}{\big{(}\varepsilon eff-0.258\big{)}\big{(}\frac{w}{h}+0.8 \big{)}} \tag{3}\]  
where \(h\) is the substrate's height. The exact dimension of the patch can be calculated using Equation (4). \[L=\frac{1}{2 fr\sqrt{\varepsilon effh_{0}\varepsilon_{0}}}-2\Delta L \tag{4}\]