## 6 Quad Port MIMO Antenna Analysis  
The multiband single element antenna proposed is expanded to a four-port MIMO antenna place such that the adjacent elements are orthogonal to each other. The substrate size is 70 \(\times\) 70 mm\({}^{2}\) and 10 mm distance between orthogonal antenna elements, as shown in Figure 9. The current distribution at the center frequency of the six rejection bands is plotted and shown in Figure 10a-f to determine the antenna portion that is responsible for each notch. The first notch, at a center frequency of 3.24 GHz, is caused by the first two arms of the right bowtie portion, whereas the left feed line and the left bowtie portion have a dominant effect for creating the second notch at 4.64 GHz. At 5.48 GHz, which is the center of the third notch, the right feed line and the last arm of the bowtie are dominant. For the last three notches at 6.81 GHz, 7.51 GHz, and 8.7 GHz, the responsible potions are the lower portion of the feed line, the two feedlines, and the middle portion of the feedlines, respectively. The total active reflection coefficient (TARC) of the four-port MIMO antenna is depicted in Figure 11. TARC relates the total incident power to the total radiated power, and it is noticed that the MIMO antenna has a TARC similar to the reflection coefficient of the single element with a similar number of resonating bands and center frequencies. The mutual coupling between all four ports is plotted in Figure 12. The average mutual coupling between the elements at the operating bands center frequency is below \(-\)17 dB across the seven resonating bands, while it is a little higher (\(-\)13 dB) at the first resonant between the adjacent elements, and it is much lower between diagonal elements. The Envelope Correlation Coefficient (\(ECC\)) and diversity gain (\(DG\)) are useful metrics for assessing the diversity of MIMO antenna elements [4]. The ECC (much lower than 0.5) and DG (\(\cong\)10 dB) of the proposed MIMO are displayed in Figure 13, and they are calculated from the scattering parameters between the two ports of high mutual coupling as given by Equations (6) and (7), respectively. Other MIMO characteristics such as mean effective gain (\(\mathrm{MEG}\)) and channel capacity loss (\(\mathrm{CCL}\)) for the seven resonating bands are tabulated in Table 5, and the results are satisfying the determined limit for these quantities, such as  
\begin{table}
\begin{tabular}{c c c c c c} \hline R1 = 28.81 & R2 = 37.43 & R3 = 55.52 & R4 = 120.53 & R5 = 27.31 & R6 = 114.96 \\ \hline L1 = 3.80 & L2 = 31.96 & L3 = 47.75 & L4 = 5.52 & L5 = 40.02 & L6 = 147.98 \\ \hline C1 = 0.14 & C2 = 0.095 & C3 = 0.031 & C4 = 0.052 & C5 = 0.022 & C6 = 0.033 \\ \hline R7 the CCL, is below 0.4 bit/s/Hz; the MEG ratios between the investigated ports are close or equal to unity. \[ECC=\frac{\left|S_{11}*S_{12}+S_{21}*S_{22}\right|^{2}}{\left(1-\left|S_{11}\right| ^{2}-\left|S_{21}\right|^{2}\right)\left(1-\left|S_{22}\right|^{2}-\left|S_{12 }\right|^{2}\right)} \tag{6}\]  
\[DG=10\sqrt{1-\left|ECC\right|^{2}} \tag{7}\]  
Figure 9: Four-element MIMO antenna configuration. \begin{table}
\begin{tabular}{c c c c c} \hline  & **MEG 1 (dB)** & **MEG 2 (dB)** & **MEG 1/MEG 2** & **CCL (bit/s/Hz)** \\ \hline Resonant 1 & \(-\)3.57 & \(-\)3.52 & 0.99 & 0.38 \\ \hline Resonant 2 & \(-\)3.09 & \(-\)3.12 & 1.01 & 0.06 \\ \hline Resonant 3 & \(-\)3.22 & \(-\)3.21 & 1 & 0.14 \\ \hline Resonant 4 & \(-\)3.27 & \(-\)3.27 & 1 & 0.18 \\ \hline Resonant 5 & \(-\)3.07 & \(-\)3.03 & 0.99 & 0.03 \\ \hline Resonant 6 & \(-\)3.05 & \(-\)3.05 & 1 & 0.03 \\ \hline Resonant 7 & \(-\)3.15 & \(-\)3.16 & 1 & 0.09 \\ \hline \end{tabular}
\end{table} 
Table 5: Proposed MIMO antenna characteristics at the resonant frequencies. Figure 10: Current distribution at the rejection bands center frequency; (**a**) at 3.24 GHz, (**b**) at 4.64 GHz, (**c**) at 5.48 GHz, (**d**) at 6.81 GHz, (**e**) at 7.51 GHz, (**f**) at 8.7 GHz. Figure 11: The total active reflection coefficients of the MIMO antenna.