## 3 MIMO Configuration
These results indicate excellent electromagnetic isolation, even though the radiating elements are closely spaced. Figure 6: (a) 4-port MIMO configuration, scale in mm; (b) Simulated \(S\)-parameters. Figure 7: (**a**) E-field distribution at 5 GHz; surface current distribution at (**b**) 3 GHz, (**c**) 5 GHz, (**d**) 6 GHz, (**e**) 8 GHz, and (**f**) 10 GHz. On the other hand, a crucial metric for assessing MIMO performance is the Envelope Correlation Coefficient (\(ECC\)), which quantifies the similarity between the fields radiated by slightly spaced antennas. To obtain an optimized performance of the MIMO system, the \(ECC\) should be close to zero. (6) provides a means of calculating this metric based on the \(S\)-parameters. \[ECC=\frac{\left|S_{11}^{*}S_{12}+S_{21}^{*}S_{22}\right|^{2}}{\left(1-\left|S_{1 1}\right|^{2}-\left|S_{21}\right|^{2}\right)\left(1-\left|S_{22}\right|^{2}- \left|S_{12}\right|^{2}\right)} \tag{6}\]  
Another widely employed metric for characterizing the performance of MIMO antennas is the Total Active Reflection Coefficient (\(TARC\)). It provides a comprehensive assessment of the signal reflection from the entire array relative to the incident wave, taking into account the phase relationships among the received signals. This phase information is influenced by multipath propagation and offers a more realistic representation of the antenna's behavior in practical environments. By considering the array as a whole, rather than individual elements, \(TARC\) enables the determination of the system bandwidth. The bandwidth is typically defined as the frequency range where the \(TARC\) values are below  
Figure 8: (a) 8 MIMO antenna prototype; (a) Front view, (b) Back view. Figure 9: Measured \(S\)-parameters of the MIMO antenna; (a) \(S_{\text{ii}}\)-parameters, (b) \(S_{\text{ii}}\)-parameters. \(-10\) dB. (7) presents the general expression for calculating this metric in an \(N\)-element array, while (8) specifically addresses the case of \(N\) = 4 elements. \[TARC=N^{-0.5}\sqrt{\sum_{i=1}^{N}\left|\sum_{k=1}^{N}S_{ik}e^{i\theta_{k-1}} \right|^{2}} \tag{7}\]  
\[TARC=4^{-0.5} \left[\left|S_{11}+S_{12}e^{i\theta_{1}}+S_{13}e^{i\theta_{2}}+S_{14}e ^{i\theta_{3}}\right|^{2}+\left|S_{21}+S_{22}e^{i\theta_{1}}+S_{23}e^{i\theta_{ 2}}+S_{24}e^{i\theta_{3}}\right|^{2}\right. \tag{8}\] \[+\left|S_{31}+S_{32}e^{i\theta_{1}}+S_{33}e^{i\theta_{2}}+S_{34}e ^{i\theta_{3}}\right|^{2}\] Figure 8.0 Figure 8.1  
Given that a MIMO antenna array leverages spatial diversity, it is imperative to quantify the effectiveness of this technique. The diversity gain (\(DG\)) serves this purpose. Specifically, \(DG\) is a metric that quantifies the enhancement in the quality of a received signal resulting from the employment of multiple antennas in a communication system. \(DG\) values are typically bounded between 0 and 10, with 10 indicating the maximum attainable improvement in signal quality. The \(DG\) can be obtained with (9). Figure 8.2  
Another important metric in MIMO systems is the Mean Effective Gain (MEG), which is defined as the mean received power to the main incident power and can be determined as [13]  
Figure 8.3  
where \(e_{tot}^{i}\) is the total efficiency of the ith antenna, and this is calculated as  
Figure 8.4  
and \(e_{mis}^{i}\) is the antenna mismatch efficiency, and \(e_{rad}^{i}\) is the radiation efficiency, where  
Figure 8.5  
To evaluate the performance of the MIMO array, the \(ECC\) was calculated using (6), and the results are illustrated in Figure 10a using the 5-parameters method, while in Figure 10b, the results are given by using the E-filed method. The simulated and measured data reveal that the \(ECC\) values generally remain below 0.002 throughout the operating frequency band, with a peak of approximately 0.016 occurring at 4.5 GHz. On the other hand, using the E-filed approximation, the ECC reaches values of no more than 0.004. Nevertheless, these values are significantly lower than the 0.5 threshold commonly required for MIMO applications.