# Practical 3-D Beam Pattern Based Channel Modeling for Multi-Polarized Massive MIMO Systems +
## 1 Introduction
Scenarios have a close relationship with channel modeling and measurements. Note that the measured data is based on the LTE specification as shown in Table 1, such as: using duplexing schemes as time division duplex (TDD) and frequency division duplex (FDD), with 10 (MHz) channel bandwidth, 1024 Sub-carriers, 80, 72 normal cyclic prefix length, 140 symbols, 50 Resource blocks for transmission block configuration, quadrature phase-shift keying (QPSK), 16-quadrature amplitude modulation (QAM) modulation schemes and orthogonal frequency-division multiplexing (OFDM) for multiple access schemes. Figure 1: Detailed of antenna configuration X\({}_{Pol}\), V, H, and V/H polarizations of an antenna elements in the horizontal and vertical angles. The major contributions of this paper are summarized as follows:  
* The impact of beam patterns has been proposed for 3-D massive MIMO channel model for different dipole and omnidirectional antenna elements. Therefore, the beam pattern provide different phase excitation towards different DoTs in the far-field. Given that, it also provides various AoDs and AoAs for each antenna element, contributing different correlation weights for rays related towards/from the clusters. As far as the author's knowledge is concerned, a practical 3-D channel model for massive MIMO using beam pattern assumption in the far-field has not been considered, yet. * A closed-form expression for AES has also been studied to reduce the RSC in the horizontal and elevation directions of the antenna array that can be accurately represented as an important aspect of a polarized antenna in 3-D space. Therefore, to design and evaluate a massive MIMO system, the investigation of correlations between antenna elements are necessary. This fact is possible in utilizing the SRAA and SULA, where all the antenna elements need to be addressed uniquely at the antenna array for investigating received spatial correlation. In fact, the model is providing an accurate observation to investigate the received spatial correlation based on the antenna polarizations. * The movement of the user and clusters make our channel non-stationary which is applied to both time and array axes. It means that the behavior of the clusters varies at different times of EAoAs and AAoAs. Therefore, receiving clusters are observed to at least one antenna element and its adjacent elements depend upon their distance to the clusters at the RX. A novel cluster evolution algorithm in the system level is developed in the antenna pattern. * The impact of the 3-D beam pattern channel model and elevation angle of the aforementioned channel properties is being investigated by comparing it with those of the 3-D conventional channel model. Statistical properties of the proposed massive MIMO channel model such as ECC and RSC, including signal-to-noise ratio (SNR) of the non-stationary channel model, were investigated. The proposed model has been valid for the far-field effects on the massive MIMO scenarios at the cell edge and the result looks convincing. This might provide a more accurate model for the current LTE-A system. Our good implementation models substantially facilitate the implementation of further techniques for different modeling, especially for massive MIMO antenna where the antenna space will affect the MIMO performance. This paper is organized as follows: Section 2 proposes the extension of 3-D massive MIMO antenna pattern considering both a 3-D beam pattern and the spaces between elements. This includes geometrical properties derived under the 3-D beam pattern as well as the AES technique which describes different configurations on the array axis, in practice. Section 3 presents the steps and methodology in generating a complete 3-D beam pattern channel model. In addition, the received spatial correlation in detail for massive MIMO systems is contained in Section 4. Furthermore, Section 5 shows the simulation results and conclusions are finally drawn in Section 6.