# Practical 3-D Beam Pattern Based Channel Modeling for Multi-Polarized Massive MIMO Systems +
## 5 Experimental Results and Discussions
)_ denotes the determinant and \(I\) is the identity matrix. From the figure, it can be observed that the ECC does not only depend on the antenna dimension, but it also has a close relation to the antenna configuration of the antenna array. Similarly, in V and V/H polarized antennas, the capacity is much higher than H polarization, because the elevation angle in the E3-D model has a higher degree of freedom and the main DoT is perpendicular to the receiver array. In other words, the capacity of antenna elements polarization is lower than the others, causing the horizontally-receiving signals at an azimuth angle with a lower degree of freedom in elevation angle. This phenomenon occurs when the channel is linear to antenna elements, and the EAoA is constant for all elements. Therefore, based on the distance \(\mathbf{D}\) and increased dimension of the antenna at the RX, spherical waves are emitted in a spherical shape and consider as a plane wavefront. However, the beam patterns with different phase excitation toward different DoTs, contributes various correlation weights for rays related to the \(Qt\) clusters. Thus, providing different EAoAs for each antenna element that can be adapted to the improve the received SNR which in turn to increases the accuracy of the channel model. Figure 4:0 E3-D and C3-D compression capacity versus SNR for different polarization. Furthermore, an investigation of antenna correlation \(\rho\) versus space has been considered for the beam pattern as shown in Figure 4:1 It is shown that the correlation varies as the function of \(\rho(\varphi,\theta)\) changes with \(d^{UE}\) on \(\theta\) and \(\varphi\). Intuitively, the distance between two inter-elements is at the maximum, while the correlation remains minimal. The figure illustrated that the channel has less correlation in V and V/H configurations when the space between antenna elements increases. Also, H polarization varies slightly based on antenna space, because in H polarization the natural distance of elements from this kind of configuration is sufficient. Therefore, when space increase, the correlation result remains constant along the array axis. Finally, we investigated the effect of ECC versus antenna space at different polarization levels. Similar experimental observations can be found in Figure 8, where the capacity results also depending on the space between the antenna elements at the RX. It means that as space increases, correlation decreases and then capacity increases as well. The capacity of V and V/H polarization increases gradually as \(d^{UE}\) while the configuration with H polarization is almost constant. In summary, simulation results show that the H polarization antenna is not suitable for a 3-D model if, (A) uses plane wave front for the far-field effects, (B) the height of the user increases gradually, and (C) the dimension of antenna increases. In addition, the V polarization channel is sufficient when the only vertical angle is considered, and the spaces between antenna elements are enough for any reduction of correlation. This phenomenon happens in E3-D models when vertical degrees have higher wave dispersion from the beam pattern. Considering the same result, it is observed that correlation is not affected the channel in H polarization since the distance is enough and V polarization has the highest correlation result among others. Based on the results, having a dual polarization (V/H) at the RX while considering cross-polarization at the TX is a better option to have more accurate channels that can have at least one polarization at a certain time and direction of the user.