## 3 Optimization of Channel MIMO Capacity with Dual-Polarization and XPI Power Allocation
This simulator includes a transmitter-receiver OFDM mmWave architecture under wireless MIMO-TITO channels with rain distortion parameters based on [16]. The description of the general blocks scheme included the network wireless configuration is shown in Figure 1, and characterizing parameters are described in Table 1.  
The blocks scheme describe in Figures 1 and 2, included at the transmitter side, with the data-source block streaming data to the QPSK modulator. From the QPSK, the base-band data is split into two different OFDM transmitter schemes. These two transmitter paths stream the base-band data to two independent RF chain blocks. The blocks include the mmWave up-convert block, XPI mechanism, and two orthogonal (vertical-horizontal-linear-polarization) polarization transmission antennas. The block transmission, radiator, and propagation pass the \(2\times 2\) MIMO-TITO-channel matrix under the assumption of Quasistatic Flat-Rayleigh-Fading and rain distortion. On the receiver side, a collector RF block is situated at the receiver front. This block included two orthogonal (vertical-horizontal-linear-polarization) polarization antenna receivers, an XPI mechanism, and two RF chains, including a down-convert block. The data decoding passes through the OFDM receiver block and is decoded by QPSK demodulator. (Please note that the units and parameters used in the conducted simulations are described in Table 2). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(\mathbf{\theta=0}\) & \(\mathbf{\theta=\pi/2}\) \\ \hline \(\phi=0\) & \(H_{{}_{TR}}=\left(\sqrt{\frac{1}{1+k}}\right)\cdot\begin{bmatrix}h_{xx}&h_{xx} \delta_{x,y}\\ h_{xx}\delta_{y,x}&h_{yy}\end{bmatrix}\) & \(H_{{}_{TR}}=\left(\sqrt{\frac{1}{1+k}}\right)\cdot\begin{bmatrix}h_{yy}\delta_ {y,x}&h_{yy}\\ h_{xx}\delta_{x,y}&h_{xx}\end{bmatrix}\) \\ \hline \(\phi=\pi/2\) & \(H_{{}_{TR}}=\left(\sqrt{\frac{1}{1+k}}\right)\cdot\begin{bmatrix}h_{xx}\delta_ {x,y}&h_{xx}\\ h_{yy}&h_{yy}\delta_{y,x}\end{bmatrix}\) & \(H_{{}_{TR}}=\left(\sqrt{\frac{1}{1+k}}\right)\cdot\begin{bmatrix}h_{yy}&h_{yy} \delta_{y,x}\\ h_{xx}\delta_{x,y}&h_{xx}\end{bmatrix}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Definition of four optimal channels. Figure 1: Dual Polarization-MIMO Scheme. The MIMO-channel-capacity under the assumption of channel-state-information-at receiver only (CSIR) follows as [24,31]:  
\[C_{csi}=\mathbb{E}\left[log_{2}det\left(I_{N_{Y}}+\frac{P_{t}}{N_{t}\sigma_{n}^{ 2}}HH^{*}\right)\right]=\mathbb{E}\left[\sum_{i=1}^{N_{Y}}log_{2}\bigg{(}1+\frac {P_{t}}{N_{t}\sigma_{n}^{2}}\lambda_{i}^{2}\bigg{)}\right] \tag{7}\] \begin{table}
\begin{tabular}{l l l} \hline \hline
**Symbol** & **Parameter** & **Value/Description** \\ \hline \(c_{q}\) & Number of OSTBC component encoders in the transmitter & \(q=1,2\) \\ \hline \(N_{TX}\) & Total number of transmission antennas in the MGSTC transmitter & 2 \\ \hline \(N_{RX}\) & Sum of the total receiver antennas in the Receiver & 2 \\ \hline \(S_{c}=\left[\begin{array}{c}s_{c,1}^{-}\\ s_{c,2}^{-}\end{array}\right]\) & Row vectors of block transmission symbol matrix & \(s_{c,1}^{-}s_{c,2}^{-}\) \\ \hline \multirow{4}{*}{Antenna Design MATLAB Object} & Phased.shortDipole & AntennaElement \\ \cline{2-3}  & Simulation running time & 10 [ms] \\ \cline{2-3}  & Frequency operation & k-band 18–27 [GHz] \\ \hline \multirow{4}{*}{\(T_{S_{c}}\)} & Duplex mode & TDD \\ \cline{2-3}  & Sample time per frame & 16 [ms] \\ \cline{2-3}  & Modulation & \(QPSK\) \\ \cline{2-3} \(R_{b}\) & Transmission bit rate & 23.5 [Mbps] \\ \cline{2-3} \(SNR\) & Signal-to-Noise Ratio & 0 to 25 [dB] \\ \cline{2-3}  & Received power & \(-80\) to \(-90\) [dBm] \\ \cline{2-3} \(E_{s}\) & Energy to symbol & 1 [Watt] \\ \cline{2-3}  & FFT length & 64 \\ \cline{2-3} BW & Bandwidth & 6 [MHz] \\ \cline{2-3}  & Rain rate intensity range & 0 to 400 [mm/h] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Units and Parameters used in the conducted simulations. Figure 2: Block Diagram of The Simulator in The SIMULINK/MATLAB Platform.