## 4 Optimization of Channel MIMO Capacity by Combining OSTBC and Polarization-Diversity with XPI
### Diversity Transmission Using OSTBC-MRRC MIMO Technique
\begin{split}\textbf{case1}:&\theta=0,\phi=0\Rightarrow A =0,B=1,C=0,D=0\\ \textbf{case2}:&\theta=0,\phi=\frac{\pi}{2}\Rightarrow A =1,B=0,C=0,D=0\\ \textbf{case3}:&\theta=\frac{\pi}{2},\phi=0\Rightarrow A =0,B=0,C=1,D=0\\ \textbf{case4}:&\theta=\frac{\pi}{2},\phi=\frac{\pi} {2}\Rightarrow A=0,B=0,C=0,D=1.\end{split}  \tag{17}\]  
Numerical Results of MIMO-Channel-Capacity, with OSTBC and MRRC, under Rain Distortions, Optimized by XPI Values  
In Figure 5, numerical results of the MIMO channel capacity of a communication system in mmWave with a combination of diversity techniques, XPI mechanism, under effects of rain distortion versus \(\frac{E_{b}}{N_{0}}\) are illustrated. This section refers to MIMO capabilities regarding OSTBC-MRRC diversification techniques according to the optimal XPI values given in (17). These optimal cases create polarization diversity and integrate with the application of OSTBC-MRRC techniques. Diversity techniques result in a low correlation between the DP MIMO paths. Thus, it is reasonable to assume that all the channel paths are independent of each other and can reduce the BER relative to system performance without the combination of these techniques (as we will see in Section 5). On the other hand, as we have seen in Section 4.2, the transmission of the same two symbols in two cycles of time causes a decrease in the transmission bit rate. This situation results in a reduction of the average channel capacity relative to the case without any diversity. Note that if for example we transmit power in directions \(u,v\) such that \(u\perp v\), with powers \(P_{u},P_{v}\) resp. then, the total received power is \(\sqrt{P_{u}^{2}+P_{v}^{2}}\) that becomes \(P_{u}\) if the direction \(v\) undergoes total destruction. However, if the directions are not perpendicular and have an angle \(0<\gamma<\pi/2\) between them, the total received power is \(\sqrt{\big{(}P_{u}+P_{v}\cos(\gamma)\big{)}^{2}+\big{(}P_{v}\sin(\gamma)\big{)} ^{2}}\), and under the above assumption, the destruction now is in direction \(v-\langle v,u\rangle u\) that is perpendicular to \(u\). Therefore, the value \(P_{v}\sin(\gamma)\) is lost and the total received power now is \(P_{u}+P_{v}\cos(\gamma)>P_{u}\). Therefore, the capacity in (11) lowers-down in the case of perpendicular paths, when part of the paths undergoes total destruction, as is seen from the comparison between Figures 3 and 5. In Figure 5, the red graph represents the average capacity achieved using optimal condition cases described in (17). The green graph represents the achieved average capacity by use interim condition cases (e.g., \(\phi=\frac{\pi}{8},\theta=\frac{3\pi}{8}\)). The blue graph represents the mostdestructive average capacity value by placing the worst condition values (e.g., \(\phi=\frac{\pi}{4}\), \(\theta=\frac{\pi}{4}\)). As we see in this section, the average capacity in all three scenarios in Figure 5 is on average less than \(\sim\)2 bit/s/Hz, compared to the performance of the three scenarios in Figure 3.  
From an analysis of Figure 5, the conservation of two trends can be seen compared to the previous section. The first one is that there is a complete match between the simulator results and the theoretical analysis, i.e., the optimal values lead to maximum values of the channel capacity, and the fit is also proper concerning the intermediate conditions and the destructive conditions. The second one is that in both graphs, the red and the green, a significant increase occurs with the rise in values of \(\frac{E_{b}}{N_{0}}\). Analysis Performance-BER of OFDM-Dual-Polarization Combined with/without Diversity-Techniques under MIMO-mmWave Channels with Rain Distortions  
The second part of this current study focuses on comparing the BER performance of a communication system without diversity techniques described in Section 3 to the performance of BER of a communication system with diversity techniques described in Section 4.