# Practical 3-D Beam Pattern Based Channel Modeling for Multi-Polarized Massive MIMO Systems +
## 5 Experimental Results and Discussions  
In this section, the statistical properties of the proposed model and simulation model are evaluated and analyzed. Then, the proposed simulation channel model is further validated by measurements. As shown in Figure 4, an investigation has been made then to study such full characterization through field experimentation on 3-D massive MIMO systems at Shanghai Jiao Tong University (SJTU) campus network. Sixteen cross-dipole elements with \(+/-45^{\circ}\) slant polarization, and a movable user platform from the national instrument (NI) USRP-2943R with omnidirectional elements were implemented at the TX and RX, respectively. As shown in Figure 1, \((90/90)^{\circ}\) is a V polarization, \((0/0)^{\circ}\) is H polarization and \((0/90)^{\circ}\) is V/H polarization of omnidirectional antenna elements at the RX, and \(+/-45^{\circ}\) dipole antenna elements at the TX are configured. The height above the BS is about 40 m, and the reception antenna's height is 2.0 m with multiple receive antennas. To verify our proposed channel models, we use MU-MIMO measurement data to compare the non-stationary of a measured MU-MIMO channel with that of standard channel models such as IMT-A and WINNER II. The result in investigating the performance of the proposed model and comparing them with the theoretical model. In order to understand the compression part easily, we denoted our proposed model as (E3-D) and the theoretical model as (C3-D). To highlight the impact of the statistical properties, we first extracted the theoretical model as a reference and then, and then an investigation of C3-D was carried out. Later, to get a more quantitative understanding of how our proposed model (E3-D) would perform in the real propagation and measured data on the proposed model, we turned our attention to the RSC and ECC in the three measured scenarios, corresponding to their DoTs, where different polarizations were used at the TX and RX. It shows that the spatial correlation and capacity of the theoretical model and practical result. The model was based on EAoA \((\vartheta)\), AAoA \((\varphi)\), distance between the corresponding cluster to the antenna elements and arrays, elements spacing \((d^{BS},d^{UE})\), antenna polarization, user movements and non-stationary of clusters. It shows that the practical model provides a good approximation to the theoretical model especially at dull polarization. Figure 3: Phase difference between antenna elements for the varying (**a**) DoT = \(90^{\circ}\) and (**b**) DoT = \(0^{\circ}\). First, to understand the impact of the channel, we focused on the channel variation's case of the distance traveled as well as considering the antenna polarization match/mismatching between TX and RX, while we formulated and analyzed data based on Sections 3 and 4. The impact of the channel on the theoretical model and the corresponding proposed model of channel models affect the trends of the antenna polarization and spatial correlation properties considerably of the antenna elements. Second, RSC on ECC for correlation properties has been investigated, considering that the ASE had increased the spacing between elements. Consequently, as shown in the following figs, we are only going to investigate the performance of channel modeling with the effect of V, H, and V/H antenna polarization over E3-D channel, comparing with the C3-D model. This observation also was from the dynamic property of clusters on the array axis which may observe different sets of clusters with different \(\theta\) and \(\varphi\) to at least one antenna element including the adjacent ones in the E3-D model. In addition, they demonstrate that proposed model provides a good approximation to the statistical properties of the theoretical model.