## 2 Configuration and Design of the Proposed UWB-MIMO Antenna
### Mava  
The MVA has a modified antipodal Vivaldi patch shape on both sides of the denim substrate to attain dual polarization and an improved directional pattern. Figure 1 and Table 1 show the MVA antenna's structure and dimensions. The ShieldIt conductive textile of the denim substrate has a \(\varepsilon_{r}=1.4\), a loss tangent of tan \(\delta=0.02\), and a h = 0.5 mm (thickness). Vivaldi antennas are typically low-frequency resonance structures. The resonance frequency varies with width at lower frequency. The substrate thickness is another element that might affect the performance of the antenna. When it is too huge, the undesirable modes are activated. The pattern is distorted, and the level of cross-polarization is enhanced when the modes that are not wanted. Thus, a low dielectric constant substrate and a modest thickness is desired. The length of the antipodal patch is also effective for antenna's performance improvement. Consequently, it can affect the gain, the lower and higher resonances [49; 50]. Figure 1 illustrates the suggested modified AVA model (MAVA), which is selected because of its favorable performing. Initially, a typical AVA was modified, simulated, and developed at 5-40 GHz, and next the dimensions were optimized. Particularly, exponential patch and feed line dimensions were calculated applying the formulas provided in [56; 57]. The proposed antenna includes two main tapered strips (conventional structure) and three additional curved-strip arms. It will be investigated how these additional curved-strip arms contribute to convert stopbands to passbands. In order to have a compact UWB antenna, four exponential curves (two as patch and three curved strips) are employed. The \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Values (mm)** & **Parameter** & **Values (mm)** \\ \hline L\({}_{\text{s}}\) & 15.00 & L\({}_{\text{p1}}\) & 10.00 \\ \hline L\({}_{\text{f}}\) & 8.60 & L\({}_{\text{p}}\) & 5.40 \\ \hline L\({}_{\text{g}}\) & 3.80 & W\({}_{\text{p}}\) & 6.00 \\ \hline W\({}_{\text{g}}\) & 6.50 & W\({}_{\text{s}}\) & 15.00 \\ \hline W\({}_{\text{1}}\) & 1.40 & W\({}_{\text{p1}}\) & 5.50 \\ \hline r\({}_{\text{1}}\) & 3.60 & L\({}_{\text{g1}}\) & 1.70 \\ \hline r\({}_{\text{2}}\) & 4.70 & r\({}_{\text{3}}\) & 4.70 \\ \hline W\({}_{\text{g1}}\) & 8.00 & r\({}_{\text{4}}\) & 2.00 \\ \hline L\({}_{\text{f1}}\) & 4.65 & L\({}_{\text{1}}\) & 1.25 \\ \hline W\({}_{\text{f1}}\) & 0.75 & W\({}_{\text{2}}\) & 1.25 \\ \hline L\({}_{\text{2}}\) & 5.00 & L\({}_{\text{3}}\) & 0.25 \\ \hline L\({}_{\text{4}}\) & 7.50 & L\({}_{\text{5}}\) & 9.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Optimized dimensions of MAVA. Figure 1: (**a**) front and (**b**) back view of the simulated prototype of the proposed antenna. conventional equations of these curves can be given as (Equation (1) for the patches and Equation (2) for curved strips):  
\[\left\{ \begin{array}{l}y(x)=A_{1}e^{A_{2}x}+A_{3}\\ y(x)=B_{1}e^{B_{2}x}+B_{3}\end{array} \right. \tag{1}\]  
\[y(x)=C_{1}e^{C_{2}x}+C_{3} \tag{2}\]  
\[y(x)=\pi\left(r_{2}^{2}-r_{2}^{2}\right) \tag{3}\]  
where \(A_{2}\), \(B_{2}\), and \(C_{2}\) demonstrate the degree of the exponential curves and \(A_{1}\), \(B_{1}\), \(C_{1}\), \(A_{3}\), \(B_{3}\), and \(C_{3}\), are related to the length and width of the arms and depend on the position of the origin of the Cartesian coordinate system in the antenna structure. To have the optimum reflection coefficient, the values of \(A_{2}\), \(B_{2}\), and \(C_{2}\), should be optimized to get the best matching.