I.
Coordinate system
The 5G channel model will be built using the Cartesian coordinate, which is defined by
the zenith angle 𝜃 and the azimuth angle 𝜙 in Cartesian coordinate systems. Remember 𝜃 =0º
the x, y, and z axes, the spherical unit vectors illustrated in Figure 1. This figure also defines
points to the zenith and 𝜃 =90º points to the horizon. The field component in the direction of
θ^ and φ^ is given by Fθ and Fϕ respectively.
Figure 1. Definition of spherical angles and spherical unit vectors in a Cartesian coordinate system,
where nˆ is the given direction, θˆ and φˆare the spherical basis vectors [1]
ẏ axis is set as the original y-axis after the first rotation about z, the same goes for the ẍ
axis as the original x-axis after the first rotation about z and the second rotation about ẏ .
The antenna bearing angle is the first rotation of α about z, the down-tilt angle is the
second rotation of β about ẏ , and the antenna slant angle is the third rotation of γ about ẍ .
After three rotations, x, y, and z axes can also be presented as ⃛x , ⃛y , ⃛z . The angular ψ has the
duty to rotate to GCS as instructed in [1] and is shown in Figure 2:
Figure 2. Rotation of LCS concerning GCS [1]
II. Scenarios
To make the 5G channel model more precise, the measurement is taken place in 3
different areas:
- Umi (Street canyon, open area) with O2O and O2I: the BSs are being set below rooftop
levels of surrounding buildings. The purpose of the UMi is to capture lifelike scenarios at a
height of 50 to 100 m.
- Indoor: This scenario aimed to capture different types of typical indoor deployment
scenarios such as office environments, and shopping malls. The BSs are mounted at a height
of 2-3 m either on the ceilings or walls. The shopping malls are often 1-5 stories high and on
several floors.
- RMa: The rural deployment scenario concentrates on wider and constant coverage
supporting high-speed vehicles with noise-limited and/or interference limited, using macro
transmission reception points.
Below are the parameters for each scenario.
Table1. Parameters for Umi-street canyon [1]
Table 2. Parameters for indoor-office scenarios [1]
Table 3. Parameters for RMa [3]
III. The 5G’s correlation function’s properties for the NLOS situation
The impulse response function h(,) of s Base station(BS) antenna elements and u MS
antenna elements is described by the specifications of NLOS 5G simulators as in [1].
The Fourier transform of h(,) is the transfer function H(,) in the frequency domain. In this
case, the channel impulse response is calculated with the delay of the n cluster Tn.
The time average operator calculates the spatial-temporal correlation function of 2 x 2
antenna system using the following equation:
Besides using the time average operator, the correlation function can also be calculated by
using the average time of two transfer functions. The cross-correlation function in the case of
NLOS scenarios is used to illustrate the correlation of the channel. First, the spatial-temporal
frequency correlation function of the BS and the MS in the MIMO 2 x 2 system is calculated
antenna element u are F rx ,u ,θ and F rx ,u ,ϕ and have θ^ , ϕ^ as its direction and that of the transmit
using the time average operation with the equation (5). The radiant field of the receive
antenna element s are F tx , s ,θ , F tx , s ,ϕ with the same direction as the receive antenna. Next, we
have angle 𝜙𝑛,𝑚,𝐴𝑂𝐴 and 𝜃𝑛,𝑚,𝑍𝑂𝐴 with as the spherical unit vector and 𝑑̅𝑟𝑥,𝑢,
𝑑̅𝑡𝑥,𝑠 as the location vector of antenna element u, s.
With , the auto correlation TCF is illustrated using the equation below:
With , the auto correlation FCF is indicated as:
With Δ𝑡 = Δ𝑓 = 0 and Δ𝑑𝑢 = 0, the channel at the BS’s cross spatial correlation
function is illustrated as:
The same goes for that at the MS when Δ𝑡 = Δ𝑓 = 0 and Δ𝑑𝑠 = 0:
