# Practical 3-D Beam Pattern Based Channel Modeling for Multi-Polarized Massive MIMO Systems +
## 1 Introduction
Prior to this, one of the reasonable ways to extract an additional degree of 3-D massive MIMO channels in the far-field is to adjust the beam pattern in the vertical direction for each individual user to improve the signal strength at the receiver. To improve the 3-D massive MIMO for the far-field effects, three important aspects should be considered to provide an accurate channel modeling in practice. **First**, nowadays, 3-D channel models show that spherical/plane wave-fronts cannot fulfill the elevation angles with an increased number of antenna elements at a wider space, especially when the user is in the same azimuth angle but at a different elevation. The 3-D beam pattern which is known to provide higher elevation angle is therefore proposed instead of spherical wavefronts. Based on the distance between transmitter (TX) and RX and increased dimension of antenna, spherical waves are emitted in a spherical shape and are considered as a plane wavefront. So, this paper contributes a phenomenon to investigate the beam waves to provide higher elevation angle is therefore proposed instead of spherical/plane wavefronts. Considering this fact, a 3-D massive MIMO in the far-field is assumed such that the phase of each antenna element is determined by the geometrical relationships and EAoAs and EAoDs on the antenna arrays are equal to each antenna element with same power angular spread (PAS). This fact is only possible in the theoretical view if we assumed that the wavefront for each wireless link is spherical. Therefore, in this paper, beam patterns with different PAS were considered to provide various phase excitations for different EAoAs toward different directions of travels (DoTs) on the antenna array with the higher degree of freedom on both the TX and RX. **Second**, in the massive MIMO antenna, an increase in the dimension of antenna array results in the high correlation between the antenna elements and inaccuracy of channel coefficients. Therefore, for the sake of massive MIMO system design and performance evaluation, it is indispensable to investigate the correlation between antenna elements. This leads us to utilize the spaced rectangular antenna array (SRAA) and spaced uniform linear array (SULA) on received spatial correlation (RSC), considering various elevation angle of arrivals (EAoAs) and azimuth angles of arrivals (AAoAs) for the different antenna elements. This technique provides more accuracy in generating the channel coefficients for a massive MIMO system, where all the antenna elements need to be addressed uniquely at the antenna array to recognize their paths from the elements to the clusters. Antenna element spaces (AESs) technique is an inter-element spacing where the SRAA and SULA are divided into the number of antenna elements in the horizontal and elevation direction of the dipole and omnidirectional antennas. This technique can also be used for any arbitrary choice of the antenna pattern and distribution of azimuth and elevation angles for the polarized massive MIMO antenna with the different configuration of vertical (V), horizontal (H), and Dual (V/H) polarizations as shown in Figure 1.  
**Third**, the appearance of clusters on the antenna array is another important characteristic of massive MIMO channel models. In conventional massive MIMO channel models, it is assumed that a cluster is always observable to the entire antennas elements. This model, on the other hand, proposes a non-stationary model based on the movement of the user where the cluster may appear as at least one antenna element and its adjacent elements. In this paper, we first give a comprehensive survey of the antenna campaigns conducted in different polarization patterns for different scenarios and address the recent advances of the LTE antenna pattern. Then, we propose a framework for deriving the statistical properties of these channels. This channel model is developed aiming to capture the far-field effects with beam pattern antenna arrays and non-stationary properties of clusters on both the time and array axes.