# Quad Element MIMO Antenna for C, X, Ku, and Ka-Band Applications
## 3 MIMO Performance of the Proposed Antenna
The mean effective gain (MEG) is a key measure for characterizing the performance of MIMO diversity. It compares the power received by the isotropic antenna to the power gained by the diversity antenna in a fade environment. The MEG of \(i^{th}\) element of the MIMO system can be evaluated using Equation (7) [47]. \[MEG_{i}=0.5\Big{[}1-\sum_{n=1}^{N}\lvert S_{in}\rvert^{2}\Big{]} \tag{7}\]  
where N is the number of elements in the MIMO system. The typical value of \(\left\lvert MEG_{i}-MEG_{j}\right\rvert\) should be less than 3 dB for a good MIMO antenna. The simulated and measured values of \(MEG_{i}\) over the frequency bands OFB1, OFB2, and OFB3 are depicted in Figure 9a. The value of \(\left\lvert MEG_{i}-MEG_{j}\right\rvert\) for distinct values of \(i\) and \(j\) are computed, where \(i\
eq j\), \(1\leq i\leq 4\) and \(1\leq j\leq 4\). The maximum simulated values of \(\left\lvert MEG_{i}-MEG_{j}\right\rvert\) over the frequency bands OFB1, OFB2, and OFB3 are 0.05 dB, 0.03 dB, and 0.082 dB, respectively; however, the maximum measured values of \(\left\lvert MEG_{i}-MEG_{j}\right\rvert\) over the frequency bands OFB1, OFB2, and OFB3 are 0.16 dB, 0.25 dB, and 0.2 dB, respectively, which promises a good MIMO antenna in investigated operating bands. Figure 9: Proposed MIMO system (simulated and measured): (**a**) MEG and (**b**) TARC. TARC is characterized as the square root of the overall reflected power divided by overall incident power. TARC provides a valid estimation of MIMO antenna efficiency since it contains information about the mutual coupling effect. The TARC for the N unit MIMO antenna setup can be computed using Equation (8) [48]. \[TARC=N^{-0.5}\sqrt{\sum_{i=1}^{N}\left|\sum_{K=1}^{N}S_{ik}e^{i\theta_{k-1}} \right|^{2}} \tag{8}\]  
The value of TARC is calculated with the assumption of \(\theta_{k-1}=0^{0},\ 30^{0},\ 45^{0},\ 60^{0}\) (where \(1\leq k\leq 4\) and k is an integer). For a better performance in investigated bands, the TARC should be from 0 to 1 and the ideal value of TARC should be less than \(-10\) dB. In this article, the simulated and measured TARC at \(\theta_{k-1}=0^{0},\ 30^{0},\ 45^{0},\ 60^{0}\) over the frequency ranges OFB1, OFB2, and OFB3 are below or about \(-10\) dB except for the frequency band 12-14 GHz (in this band average, TARC is \(-6.9\) dB). The simulated and measured TARC values are illustrated in Figure 9b. An additional fundamental diversity attribute measure that may be used to assess MIMO performance is CCL, which shows the greatest rate at which data can be delivered without experiencing significant losses. Equation (9) [49; 50] can be utilized to calculate CCL. The CCL ought to be below 0.4 bps/Hz throughout the operating frequency spectrum for the best MIMO antenna. Here, the greatest CCL (simulated and measured) value over the frequency ranges OFB1, OFB2, and OFB3 is less than 0.3 bps/Hz, indicating a strong candidate for use on the desired band. Figure 10a shows a CCL versus frequency plot. \[CCL=-\log_{2}\left[det\left(\varphi^{R}\right)\right] \tag{9}\]  
\[\textit{where}\ \varphi^{R}=\left( \begin{array}{ccccc}\alpha 11&\alpha 12 &\cdot&\cdot&\alpha 1N\\ \alpha 21&\alpha 22&\cdot&\cdot&\alpha 2N\\ \cdot&\cdot&\cdot&\cdot&\cdot\\ \cdot&\cdot&\cdot&\cdot&\cdot\\ \alpha N1&\alpha N2&\cdot&\cdot&\alpha NN\end{array} \right),\left(\alpha ii =1-\left(\left|\sum_{j=1}^{j=N}S_{ij}^{*}S_{ji}\right|\right)\right),\]  
\[\left(\alpha ik=-\left|\sum_{j=1}^{j=N}S_{ij}^{*}S_{jk}\right|\right),1\leq i \leq N,1\leq k\leq N\ \textit{and}\ N=4\]  
Figure 10: MIMO antenna (simulated and measured): (a) CCL and (b) CC. Ergodic channel capacity (CC), which is determined under the presumption of zero ECC among the transmitting antennas, is the most efficient diversity characteristics metric for a MIMO system. Equation (10) is used to evaluate the channel matrix \"H\".