## 2 Design and Analysis
### MIMO Assessment  
There are numerous metrics for evaluating the performance of the MIMO antenna systems. The envelope correlation coefficient (ECC) can be used to judge how well the envelopes of signals received by different antennas correlate with each other. The lower the value of ECC, the better the diversity performance, as this would imply that the antennas are receiving signals that are largely uncorrelated, thus enhancing the diversity gain. ECC evaluates the correlation between received signals by antenna pairs, normalized to their total received power. This evaluation parameter can be computed using the following expression:  
\[ECC=\frac{\left|S_{ii}^{*}S_{ij}+S_{ji}^{*}S_{ji}\right|^{2}}{\left(1-\left( \left|S_{ii}\right|^{2}+\left|S_{ji}\right|^{2}\right)\right)+\left(1-\left( \left|S_{jj}\right|^{2}+\left|S_{ij}\right|^{2}\right)\right)} \tag{1}\]  
where \(S_{ii}^{*}\) and \(S_{jj}\) represent the complex conjugate and complex values of the reflection coefficients for antennas i and j, respectively, while \(S_{ij}\) and \(S_{ji}^{*}\) denote the transmission coefficients between antennas i and j (with \(S_{ji}^{*}\) being the complex conjugate), describing the signal coupling between these antenna pairs in the scattering matrix. The diversity gain (DG) assigns a numerical value to measure the degree of improvement in the quality of the received signal using multiple antennas to mitigate fading effects by utilizing spatial diversity to enhance reliability. Considering the dependence of DG on ECC, it is computed using  
\[DG=10\sqrt{1-\left(ECC\right)^{2}} \tag{2}\]  
The mean effective gain (MEG) provides a good picture of how an antenna pattern performs with average power gain in all directions, thereby denoting the whole efficiency of the system in its mean transmission and reception of signals. Effective diversity gain (EDG) provides a comprehensive evaluation of system diversity performance by incorporating both diversity gain and antenna correlation effects. Meanwhile, the channel capacity loss (CCL) quantifies the decrease in the maximum attainable data rate owing to channel impairments such as noise and interference, reflecting their impact on the information-theoretic capacity limits. CCL is determined by computing the logarithm of the norm of the received signal coefficients. This calculation incorporates both the correlation between antenna elements and the received power distribution. The CCL can be expressed as  
\[\text{where}\] \[\beta^{R}=\begin{pmatrix}\beta_{11}&\beta_{12}&\dots&\beta_{1N}\\ \beta_{21}&\beta_{22}&\dots&\beta_{2N}\\ \vdots&\vdots&\vdots&\vdots\\ \beta_{N  
\(\beta_{R}\) represents a matrix of the received signal coefficients. \(\beta_{ii}\) denotes coefficients of power received by antenna i after computing powers received by other antennas. \(\beta_{ij}\) denotes correlation coefficients between signals received by antennas i and j, in which their values are counted from 1 up to N, where N signifies the number of antennas of the MIMO structure. Figure 5 displays ECC and DG concerning frequency variations. Notably, the ECC values exhibited in the plot are markedly below the conventional benchmark of 0.5 across the computed spectrum. Simultaneously, the DG is observed to approach approximately 10 dB, signifying robust signal reception and mitigation of the influence of fading. Moreover, the calculated CCL reveals promising results: at 28 GHz, CCL stands at 0.039; at 35 GHz, it rises slightly to 0.203; and at 38 GHz, it falls to 0.024. These computed CCL values notably outperform the standard reference of 0.4 bit/Hz/sec, indicating a significant CCL reduction. In Figure 6, the comparison between the gains of the MIMO antenna and the single-element antenna is illustrated across various frequencies. The results reveal a significantly higher gain for the MIMO antenna setup. Specifically, at 28 GHz, the MIMO antenna displays a gain of 9.6 dBi, slightly surpassing the gain of the single-element antenna, which is 9.2 dBi.