# Practical 3-D Beam Pattern Based Channel Modeling for Multi-Polarized Massive MIMO Systems +
## 5 Experimental Results and Discussions
As shown in Figure 5, the compression of the C3-D and E3-D massive MIMO model in different antenna configurations shows that the antenna polarization incorporated in the propagated channel cannot be ignored in channel modeling, especially when the distance between the TX and RX increasing. In addition, when DoT is not fixed along the axis but is switching from 0\({}^{\circ}\) to 90\({}^{\circ}\) or vice versa, it is also can be a polarization changing of antenna elements. This variation occurs due to the dynamic condition of the user between wave directions in relation to antenna polarization at the RX from time to time. For more details in Figure 5a-c show the massive MIMO channel variation based on H, V and V/H polarization where the waves are forced to lie in the same direction as the RX and the maximum pickup results when the RX antenna is oriented in the same direction as the TX antenna. The result also has shown that, in the C3-D, the conventional massive MIMO covering only an azimuth angle for far-field effect with providing equal AODs and AoAs, while in the E3-D model, the elevation angle has been considered with various phase excitation and different AoDs and AoAs for each antenna element. On the other side is shown in Figure 5d, when the cross-polarization antenna is configured at the TX, different polarization are assembled at the RX. The excellent agreement between the proposed MU-MIMO model and the measurement data demonstrates the utility of our MU-MIMO channel models. Figure 4: Overview of the measurement area at the campus of Shanghai Jiao Tong University, China. A spaced rectangular antenna array with 16 cross polarized patch antenna elements at the TX was placed on the rooftop of the Biomedical building during their respective measurement campaigns and a spaced uniform linear array as a user was moved around the international buildings acting as multiple-antenna user. Moreover, the ECC of the period of clusters at the receivers on the antenna array, including the effect of antenna polarization is illustrated in Figure 6. Here, we only considered the cross-polarization antenna at the TX with different polarizations (V, H, and V/H) at the RX based on DoT = 0\({}^{\circ}\). Then, we also investigated the influence of the channel noise on the achievable spectral efficiency. We defined the SNR for a non-stationary user as the ratio of the desired signal power to the noise power according to [26]  
\[SNR_{(V)}=\frac{(h_{V})^{T}h_{V}}{\sigma_{n}^{2}} \tag{55}\]  
\[SNR_{(H)}=\frac{(h_{H})^{T}h_{H}}{\sigma_{n}^{2}} \tag{56}\]  
\[SNR_{(V/H)}=\frac{(h_{V/H})^{T}h_{V/H}}{\sigma_{n}^{2}} \tag{57}\]  
where \(\sigma_{n}^{2}\) denotes the power of channel noise and \((h_{V})^{T}h_{V}\), \((h_{H})^{T}h_{H}\), and \((h_{V/H})^{T}h_{V/H}\) are the correlated channel matrix of complex path gains for V, H, and V/H polarized antennas,  
Figure 5: Performance comparison between E3-D and C3-D models based on different configurations, (**a**). V/H, (**b**). V, (**c**). H, receiving signals from TX with cross antenna elements polarization toward RX, in case there are polarization matching between TX and RX. And (**d**), in case there are polarization mismatching between TX and RX, the channel variations are based on the user movement with different DoT = 0\({}^{\circ}\) and DoT = 90\({}^{\circ}\). It is illustrated that the channel has been changed when the distance is increasing and also, the signal orientations do not match with the antenna polarization at the RX. Therefore, variation in polarization causes changes in the received signal level due to the inability of the antenna to receive such polarization changes. respectively. Therefore, a correlated capacity channel using the aforementioned expressions for different polarizations are derived as  
\[C_{(V)} =log_{2}\bigg{[}det\left(I+SNR_{V}\right)\bigg{]}bps/Hz \tag{58}\] \[C_{(H)} =log_{2}\bigg{[}det\left(I+SNR_{H}\right)\bigg{]}bps/Hz\] (59) \[C_{(V/H)} =log_{2}\bigg{[}det\left(I+SNR_{V/H}\right)\bigg{]}bps/Hz \tag{60}\]  
where, _det(.