# Practical 3-D Beam Pattern Based Channel Modeling for Multi-Polarized Massive MIMO Systems +
## 1 Introduction  
Massive multiple-input multiple-output (MIMO) technology has gained lots of attention over the past decade since it provides improved link reliability and high system capacity without extra spectral resource. Towards the emergence of the fifth-generation wireless communication system, massive MIMO systems equipped with tens or hundreds of antennas have emerged to meet the increasing data-rate and high spectrum efficiency. In [1; 2; 3] massive MIMO systems with the increased number of the antenna was proven to give many benefits and advantages, such as increased channel capacity and reduced cost of implementation. In designing and evaluating massive MIMO systems, it is necessary to have an accurate and efficient massive MIMO channel model. Recently, several actions had been proposed which gave way to important channel models both for MIMO and massive MIMO. A lot of models classified more 2-D channels with a smaller number of antennas, such as [4], without considering the impact of antenna array on channel modeling. Many researchers have chosen the geometry-based stochastic model (GBSM), known as the ellipse model and one/two ring model in [5; 6], where the scatterswere distributed in regular shapes. Thus, the geometrical relationship between the scatter and the receiver (RX) determines the channel impulse response of these channel models. Very recently, the authors in [7] conducted a survey about MIMO on channel propagation models and signal processing single-cell/single-user. Although, in [8], a non-stationary model for massive MIMO communication systems was proposed; the work was based on a 2-D non-stationary multi-confocal ellipse model. In [9; 10] the works were based on the 3-D theoretical channel model. The authors assumed an infinite number of effective scattered with resulting infinite complexity that can hardly be put into practical use. The authors in [11; 12; 13] analyzed time-variant geometric properties such as angle of arrivals (AoA) and angle of departures (AoD), taking into account non-stationeries on the time axis. In [11], for an instance, they analyze shortcomings of a selected spatial channel model standard with respect to the identified requirements from other WINNER Work Packages. In [12], the model enables the simulation of the pure propagation channel behavior and the inclusion of the effects of different antennas and access schemes. In [13], the intra-path delay spread is considered which is the distance between user equipment (UE) and the last bounce scatter of each path for time-variant phases. A 3-D non-stationary twin-cluster channel model was proposed in [14] for massive MIMO systems considering their variation on both time and array axes. However, the impact of the cluster's appearance and disappearance in the elevation angles was only capable of a near-field condition based on the spherical wavefront. In [15], the author investigated antenna configuration and polarization for MIMO channels, without considering correlation at the antenna arrays for massive MIMO. In addition, in [16], the authors considered polarized antenna without investigating the antenna element spacing. Furthermore, the work in [17] was based on the multi-polarized fixed wireless channel based on 2-D omnidirectional antenna elements. To further enhance performance, the actual trend is to exploit the channel's degree of freedom in the elevation direction [18]. However, according to measurements observed in [19; 20; 21; 22], the above mentioned channel models [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17] are not sufficient accurate to capture certain characteristics of massive MIMO channels. Generally speaking, previous contributions on channel modeling have been surveying many subjects without tackling the capture of characteristics of 3-D massive MIMO channels in the far-field. Based on these references, we shed light on the current technique to develop a clearer understanding of the movement direction of the antenna array, space between antenna elements and cluster movements.