## 4 Results
### PCA with Antenna Radiation Patterns from Electromagnetic Simulations
The problem was confronted embedding an EBG lattice as shown in Figure 7. EBG lattices are commonly used in antenna structures as they can enhance their performance, increasing their frequency bandwidth, contributing to the decrease of their size and affecting their gain either increasing it or keeping its value constant within wide frequency ranges [21; 22; 23]. Besides these ways of influence, to the antennas' operation, the incorporation of EBGs, of mushroom or of other type in antenna arrays, can reduce significantly the isolation among their element reducing their electromagnetic mutual coupling. This result is very useful at MIMO antennas systems as it contributes to the reduction of correlation coefficients among their elements, thus enhancing the MIMO procedure ([24; 25; 26; 27; 28]). In the present work, the performance of the prototype of Figure 7 is presented via Figures 8-11. Figure 8 depicts the scattering coefficients \(\mathrm{S_{ii}}\) at the input of the antenna elements, confirming that they operate at the ISM band, which is under interest. Figure 9 illustrates the mutual signal scattering coefficients (\(\mathrm{S_{ij}}\)) among the elements and, for comparison, the respective coefficients of the same array without EBG are presented. It is observed that significant reduction, more than 5 dB, of the level of those of the \(\mathrm{S_{ij}}\) coefficients which correspond to pairs of elements that have the EBG between them, as the \(\mathrm{S_{23}}\), \(\mathrm{S_{24}}\) and \(\mathrm{S_{14}}\) can be achieved. Moreover, indicative results of the 3D and polar gain radiation patterns for one of the elements are shown in Figure 10. The patterns of all four elements are almost similar and the deviations from their maximum values do not exceed 3 dB inside the space angular section of utilization. The suitable orientation of the elements and the reduction of their mutual coupling lead to the reduction of the correlation of the respective coefficients, \(\mathrm{\rho_{ij}}\). It is validated by calculating them via the theory of [29] and Figure 11 depicts the results of these calculations for the cases of the array with EBG and without EBG. The comparison between the two arrays, shows a significant reduction of the \(\mathrm{\rho_{ij}}\) at the array with EBG especially when the elevation angle of the incoming signals are high, namely when they come from the space area at the broadside of the antenna. Among all four elements, of the EBG array, \(\mathrm{\rho_{ij}}\) values are less than 0.1, being a little higher in some cases. Figure 8: Scattering coefficients for the signals, at the input of the array elements, versus frequency. Figure 9: Mutual scattering coefficients of the signals, among the inputs of the array elements, versus frequency (With EBG in (**a**) and without EBG in (**b**)). In Figure 12, results are provided for two cases, considering a 4 \(\times\) 2 MIMO orientation, as well as one and six eigenvector and eigenvalues for covariance matrix formulation, respectively. They concern to two antennas. The first of them, Case A, represents an ideal system with an antenna having omni directional radiation pattern and channels modeled according to the Gaussian distribution which corresponds to zero correlation. The second one, Case B, is the realistic antenna array, of Figure 7, designed properly in order the correlation to be minimized. In this case, the channels were modeled according to 3 GPP specifications as described in Section 4 and Equation (25). In this equation, for the evaluation of the channel matrix elements, the antenna's radiation patterns are taken into account through the antennas' gain values which are calculated via simulation. The very low space correlation is impressed to these patterns and is inserted substantially to the channel estimation. As it can be observed, in Case B, for 18 power terms the mean BER is 3.142 \(\times\) 10\({}^{-4}\), while for 36 power terms the corresponding number is 3.109 \(\times\) 10\({}^{-4}\).