# The Impact of Antenna Height on 3D Channel:
## 1 Introduction  
One common feature of the research works on future wireless communication technologies is the pursuit of high spectral efficiency whilst multiple mobile stations (MSs) access the network. Multi-user (MU), multi-input-multi-output (MIMO) technology is expected to play a key role to achieve high spectral efficiency [1]. To thoroughly investigate MIMO, it is essential to have a good understanding of radio-propagation characteristics of transmission path between the base station (BS) and the MS [2]. Several models are proposed to describe the radio channel [3; 4; 5]. In [3; 4], the authors analyzed the channel characteristics by assuming the scatters are located uniformly within a circle or an ellipse. In [5], the authors argued that stochastic geometry and random graph theory are indispensable tools for the analysis of wireless networks. For the conventional study on channel model, linear antenna arrays were employed in the horizontal direction [6; 7; 8]. This assumption is valid since the distance between the MS and the BS is much larger than the distance between the height of the BS antenna and the scatterers around the MS [9]. However, considering 3D distributed MSs, a better coverage and capacity can be achieved by using a 3D antenna array [10]. Under this condition, the elevation angle of departure (EAoD) and elevation angle of arrival (EAoA), which significantly affect the performance of MU-MIMO, shouldbe considered for channel modeling. The original EAoD and EAoA model was proposed in [11]. In 1990, a measurement in Tokyo based on 900 MHz observed that the distribution of elevation angle is extremely close to be Gaussian [12]. In 2002, the PDF of the EAoD for multipath at the BS was derived by assuming that the scattering objects were located uniformly within a circle around the MS [13]. Then, more research works started to appear over 10 years later. In [14], the spatial channel model (SCM) was extended to 3D by considering the elevation angle at the MS. In [15], a 3D scattering model was generalized for the macrocell environment with an MS located at the center of a 3D scattering semispheroid and a BS employing a directional antenna, which is located outside of the semispheroid. Recently, the scattering behavior was studied in [16]. Some other works focusing on the elevation angle in different propagation environments can be found in [17; 18]. In [17], a new expression, which directly relates the PDF of the elevation angle, was proposed to the power spectral density of the received signal. In [18], the authors applied a novel technique for measuring the angular distribution in different environments. Although previous works have analyzed the distribution of the EAoD and the EAoA, the impact of antenna height on the EAoD and the EAoA has not been considered. Ultra-dense small cells, with various antenna heights, are widely investigated in 5G networks. Due to small coverage areas, the impact of antenna height on parameters of wireless propagation, especially the EAoD and the EAoA, becomes significant. Previous work indicated that the heights of the antennas at both the BS and the MS impact \(\backslash\) the distribution of EAoD and EAoA significantly [19]. However, they did not consider how the antenna height would affect the distribution of elevation angle. The main contributions of this paper are as follows. Firstly, the EAoD and the EAoA are characterized under typical scenarios against heights of antennas. Secondly, the PDFs of EAoD and EAoA are derived in closed-forms under each scenario. From the derived PDFs, we observe that the PDFs of EAoD and EAoA are almost linearly correlated with the antenna height under the straight street scenario. Meanwhile, the characteristics of PDFs change dramatically when the BS antenna height is half of the building's height under the forked road and crossroad scenarios. Finally, the effects of antenna height on the AS and the DS under the three typical scenarios are also discussed.