## 3 Simulation Results and Discussion
### The Design and Optimization of the Proposed Design  
In Design-1 and Design-2, the DRA elements were placed side by side, and the feeding was executed from one end of the PEC ground plane. Although broadband S11 and 3 dB axial ratio was attained through Design-2, in parallel, this configuration did not significantly bring mutual coupling (MC) down. Hence, the main focus of this step was to reduce MC. At higher frequencies, MC is reduced by optimizing the spacing between two DRA elements. However, the tightly spaced DRA configuration led to high mutual coupling at a low-frequency range of 3.5-5 GHz. This high mutual coupling at a low-frequency range was reduced by rearranging the DRA elements and feeding network, as shown in Design-2. Finally, to further reduce mutual coupling toa level below \(-19\) dB for the entire band of interest, an S-shaped DGPS was introduced in the ground plane. The effect of the distance between the DR element on the S-parameters and the far-field parameters is shown in Table 4. The table presents the S11 bandwidth, mutual coupling reduction, 3-dB AR, return loss, and the fraction of intersecting bandwidths. The outcomes demonstrate that the 3-dB radiation bandwidth and isolation were easily enhanced throughout the range from 0.05 \(\lambda\) to 0.55 \(\lambda\), i.e., 4 mm-15.00 mm, that is a preferred element in a MIMO DRA design. On the other side, there was a noteworthy difference in the gain for the various lengths. On the basis of these results, the desired distance for the proposed design was 0.15 \(\lambda\) (12.15 mm), where \(\lambda\)0 was the wavelength concerning the lowest frequency of operation. Mutual coupling between antennas occurs also due to spreading surface waves or through radiation; it is evident from Figure 11 that, before deputing DGPS, the density of surface current was high on the entire DR. Consequently, after placing the DGPS at an optimized position and angle, a much smaller sum of current was connected to the another antenna, and because of this, the isolation between the ports was reduced significantly. In all of the above cases, port 1 was excited, which is on the left side of the configurations. Also, the surface wave-current changes from a counter-clockwise to a co-centric motion because of DGPS. This improvement in isolation between the two antennas could be easily explained with the help of surface current distribution at a minimum of an axial ratio of 3.89 GHz. Figure 10: Comparison of mutual coupling in Design-1 and Design-2. The simulated return-loss act of the desired MIMO RDRA is depicted in Figure 12. It is clear from the first resonant frequency remains the same as compared to that of Design-2, while the second resonance frequency marginally moved from 4.4 GHz to 4.5 GHz due to \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Distance** & **Return Loss** & **Axial Ratio (3 dB) \%** & **Gain dBi** & **Mutual Coupling (dB)** \\ \hline
0.05 \(\lambda\) (4) & 35.34 & nil & 5.8 & nil \\ \hline
0.10 \(\lambda\) (8) & 36.26 & 25.74 & 5.33 & \(-\)22.7 \\ \hline
0.15 \(\lambda\) (12) & **36.63** & **26.52** & **6.51** & \(-\)**28.40** \\ \hline
0.20 \(\lambda\) (16) & 35.69 & 25.53 & 5.60 & \(-\)26.24 \\ \hline
0.25 \(\lambda\) (20) & 34.05 & 25.59 & 5.80 & \(-\)23.45 \\ \hline
0.30 \(\lambda\) (24) & 34.76 & 24.59 & 5.89 & \(-\)24.10 \\ \hline
0.35 \(\lambda\) (28) & 32.39 & 24.62 & 5.95 & \(-\)24.85 \\ \hline
0.40 \(\lambda\) (32) & 32.20 & 24.87 & 6.09 & \(-\)25.17 \\ \hline
0.45 \(\lambda\) (36) & 31.05 & 25.47 & 6.10 & \(-\)26.14 \\ \hline
0.50 \(\lambda\) (40) & 30.12 & 23.44 & 6.51 & \(-\)26.40 \\ \hline
0.55 \(\lambda\) (44) & 29.22 & 22.24 & 6.00 & \(-\)27.14 \\ \hline \end{tabular}
\end{table} 
Table 4: S11, AR bandwidth, gain, and isolation at different spacings.