## 3 Optimization of Channel MIMO Capacity with Dual-Polarization and XPI Power Allocation  
In this section, we analyze and simulate the effect of rain distortion in 2 \(\times\) 2 MIMO-TTTO DP wireless communication systems, without any diversity techniques, on the channel capacity. We consider these processes as a reference model to lay the first milestone for presenting a base of conflict from the great ones in DP MIMO-wireless communication theory. The following facts make up the basis of the conflict: The first one, when the modern communication MIMO-system is combined with polarization diversity techniques, the MIMO channels with polarization diversity achieve a very low correlation between the sub-channels, which is beneficial for its capacity. Simultaneously, the spatial multi-paths created from the spatial-diversity techniques are extraordinarily vulnerable and experience decline in the Signal-to-Noise-Ratio (SNR), for example, in the diversity losses. This situation not only leads to detrimental BER performance but also affects the channel capacity and can lead to deterioration in the sum-rate capacity. However, the second fact is based on the scenario (proactively or in a physical design) that leads to a situation with high XPD. The high value of XPR helps to achieve better capacity for dual-polarized MIMO channels and create a few very good Single-Input-Single-Output (SISO) links. The conflict (in the perspective of DP) is considered when there is a destructive effect such as rain distortion. On the one hand, if we implement polarization diversity or transmit diversity in wireless MIMO-communication systems, the sub-channel power losses, in addition to the diversity losses, are, in general, detrimental to the capacity of MIMO channels (Although, in this situation, there is an increase in the rank order of the channel matrix). However, on the other hand, these configurations achieve a very low correlation between the sub-channels, which is beneficial to achieving common BER values. On the other side of the conflict, if we concentrate energy in the apparent direction of co-polarization without any diversity techniques, in addition to the increase in the bit-rate transmission compared to the OSTBC, for example (a situation that leads to an increase in the sum-rate capacity and the XPR value), the strong correlations can lead to a significant decrease in the BER performance (In addition to the lack of capabilities to deal with multi-paths phenomena). In this article, we not only settle for presenting the conflict, but we also offer a few solutions for resolving the conflict. Without any diversity techniques, this reference model, described in this section, will form a comparative basis against the model that includes the diversity method described in Section 4. The first step in the process of optimizing the MIMO channel capacity, is to extract from (2) the optimal values in terms of XPI values, where the function to be maximized is the square of the Frobenius norm of the \(H_{TR}\) that leads to optimal capacity. In Section 4.2, we find analytically 4 points of global maximum of the above-mentioned function. As the function is shown to be convex, we also find its global maximum (related to the worst destructed channel). Note that the mathematical analysis described in Section 4.2, is more general than needed here (since the \(H_{TR}\) matrix there is 4 \(\times\) 2 resulted from the application of the OSTBC), but its results are obviously applicable also here. By tuning the XPI mechanism in the transmitter and the receiver to the optimal values, it is possible to design the channels as optimal MIMO-TTTO channels, as is seen in the following Table 1. The table contains all the optimal channels with their related XPI values. The same optimal values are formed using matrices \(T\) and \(R\):In the second step, we propose a design of a simulator scheme based on the SIMULINK/MATLAB platform.