# Realistic Channel and Delay Coefficient Generation for Dual Mobile Space-
Ground Links – A Tutorial

Hongzhao Zheng, , Mohamed Atia, , Halim Yanikomeroglu H. Zheng is with the
Embedded and Multi-sensor Systems Lab (EMSLab) and the Non-Terrestrial
Networks (NTN) Lab, Department of Systems and Computer Engineering, Carleton
University, Ottawa, ON, K1S 5B6, Canada (e-mail:
hongzhaozheng@cmail.carleton.ca).M. Atia is with the Embedded and Multi-sensor
Systems Lab (EMSLab), Department of Systems and Computer Engineering, Carleton
University, Ottawa, ON, K1S 5B6, Canada (e-mail: Mohamed.atia@carleton.ca).H.
Yanikomeroglu is with the Non-Terrestrial Networks (NTN) Lab, Department of
Systems and Computer Engineering, Carleton University, Ottawa, ON, K1S 5B6,
Canada (e-mail: halim@sce.carleton.ca).

###### Abstract

Channel and delay coefficient are two essential parameters for the
characterization of a multipath propagation environment. It is crucial to
generate realistic channel and delay coefficient in order to study the channel
characteristics that involves signals propagating through environments with
severe multipath effects. While many deterministic channel models, such as
ray-tracing (RT), face challenges like high computational complexity, data
requirements for geometrical information, and inapplicability for space-ground
links, and nongeometry-based stochastic channel models (NGSCMs) might lack
spatial consistency and offer lower accuracy, we present a scalable tutorial
for the channel modeling of dual mobile space-ground links in urban areas,
utilizing the Quasi Deterministic Radio Channel Generator (QuaDRiGa), which
adopts a geometry-based stochastic channel model (GSCM), in conjunction with
an International Telecommunication Union (ITU) provided state duration model.
This tutorial allows for the generation of realistic channel and delay
coefficients in a multipath environment for dual mobile space-ground links. We
validate the accuracy of the work by analyzing the generated channel and delay
coefficient from several aspects, such as received signal power and amplitude,
multipath delay distribution, delay spread and Doppler spectrum.

###### Index Terms:

Channel coefficient, delay spread, Doppler spectrum, multipath, Quasi
Deterministic Radio Channel Generator (QuaDRiGa), state duration.

##  I Introduction

Vertical heterogeneous networks (VHetNets) have garnered significant interest
in the community due to its potential to offer enhanced coverage and capacity,
improved spectrum utilization, lower latency, and support for diverse use
cases [1]. As such it is seen as a crucial facilitator in the forthcoming era
of 6G and beyond for a variety of usage scenarios, such as extremely reliable
and low latency communications (ERLLC), ultra-massive machine-type
communications (umMTC), long-distance and high-mobility communications
(LDHMC), and further enhanced mobile broadband (FeMBB) [4, 3, 2]. As
researchers explore the potential advantages and practical use cases of
integrating diverse vertical heterogeneous infrastructures, it is essential to
approach many research findings with caution due to the absence of realistic
signals in the scenarios they are investigating. These scenarios encompass
signals such as millimeter-wave (mmWave), terahertz (THz), and high altitude
platform station (HAPS) signals, spanning across space, air, ground, deep sea,
rural, and urban environments. This lack of realistic signals necessitates
numerous studies to focus primarily on the link level rather than encompassing
the broader system level.

With the increasing emergence of standardization efforts, technical
specifications, and reports from organizations such as the International
Telecommunication Union (ITU) and the 3rd Generation Partnership Project
(3GPP), which include channel models and line-of-sight (LOS) probability
models, there is growing interest within the community to develop a
comprehensive platform that enables the customization of various parameters.
These include antenna attributes like type, transmit/receive gain, pattern,
and dimensions, as well as vertical object placements, among others. Such a
platform would allow for an efficient and accurate generation of realistic
channel coefficients, time delays, and even pseudo signals for the target
infrastructures.

In general, there are two types of channel models in wireless communications:
deterministic and stochastic. Each of them comes with its own set of strengths
and weaknesses. For instance, as deterministic channel models are concerned
with an accurate modeling of the wave propagation by solving Maxwell’s
equations, they are expected to provide higher levels of accuracy. However,
deterministic channel models are specific to locations and demand detailed
information about the geometry and electromagnetic (EM) characteristics of the
propagation environment, leading to increased computational complexity [5, 6].
One commonly employed deterministic channel model is the ray-tracing (RT)
model [7, 8, 9]. However, this model often requires a huge amount of data
including but not limited to a high definition map of the environment and
surface parameters of the buildings, which brings not only the difficulty in
data access but also high computational cost [10, 11]. Additionally, the RT
method is generally not applicable for space-ground links due to the long
distance involved [12].

On the other hand, stochastic channel models primarily depend on the
statistics of the key parameters of the wireless channel, such as the number
of multipath components (MPCs), azimuth and elevation spread of arrivals and
departures, Ricean K-factor, shadow fading and so forth. Without the need for
the detailed information about the environment, stochastic channel models tend
to exhibit reduced computational complexity but offer relatively lower
accuracy compared to deterministic channel models [13]. Broadly, stochastic
channel models can be classified into two types: geometry-based stochastic
channel models (GSCMs) and nongeometry-based stochastic channel models
(NGSCMs). Similar to deterministic channel models, GSCMs consider the
geometrical component, such as scatterers. However, GSCMs differ in that the
locations of the scatterers are selected stochastically rather than
deterministically based on an environment database [14]. In contrast to GSCMs,
NGSCMs entirely rely on statistical parameters in modeling the wireless
channel. As a result, NGSCMs are unable to provide spatial consistency [5] and
accurate physical insights of the system, leading to lower accuracy when
applied to different scenarios unless the site-specific statistics are
available [15].

To achieve a balance between computational complexity and accuracy, the Quasi
Deterministic Radio Channel Generator (QuaDRiGa), which follows the GSCM
approach, is one of the stochastic models that has been widely adopted for
channel generation. This model is originally developed based on the Wireless
World Initiative for New Radio (WINNER) channel model proposed in WINNER 2
deliverable D1.1.2 v1.1 [16] and is now known as a 3GPP-3D and 3GPP 38.901
reference implementation [17]. It offers features such as continuous time
evolution, spatially correlated large and small-scale fading, transitions
between varying propagation scenarios, and so on. QuaDRiGa is also considered
a statistical ray-tracing model, as such it can be used to effectively and
efficiently model multipath, channel fading, and Doppler effect. Due to the
mechanism of the QuaDRiGa channel generator, this tutorial is expected to be
applicable for the dual mobile air-ground links, which facilitates a realistic
simulation for an integrated signal processing, such as urban positioning
[18], mmWave communications, THz communications [19], and multiple-input
multiple-output (MIMO) communications [20] in a vertical heterogeneous network
(VHetNet)[21]. We clarify that QuaDRiGa currently lacks support for THz
communications due to inadequate measurements. Nonetheless, it is anticipated
that QuaDRiGa will expand into the THz band once sufficient measurements
become available.

Although QuaDRiGa provides numerous tutorials for different channel
simulations, none of them takes into account the realistic state transitions
that occur in the real world. Typically, a state, either LOS or non-line-of-
sight (NLOS), would persist for a certain duration before transitioning to the
other state. To accurately model the signal propagation in a multipath
environment, it is therefore necessary to consider a realistic state
transition, especially when a long period of simulation is desired or
synchronization problems are of interest. A traditional approach to model the
state transition is by employing a Markov model, wherein the subsequent state
is determined by a transition probability model without considering the past
occurrences. However, due to the fact that the channel properties are assumed
to be quasi-stationary only for a short period of time and that state
durations follow an exponential distribution, the Markov models may yield
unrealistic state durations [22]. Therefore, the statistical state duration
model that follows a semi-Markov approach has gained a greater acceptance in
embodying the practical duration of different states. This approach has
received endorsement from the ITU and is documented in ITU-R P.681-11 [23].

Space-ground links involve the communication between satellites in space and
ground-based receivers, while air-ground links pertain to the communication
between aircraft or drones and ground-based receivers. Both links cover
substantial distances and share similar propagation characteristics and
challenges. The insights gained from studying space-ground links, including
signal propagation, attenuation, multipath effects, and interference, can be
applied effectively to model air-ground links. Moreover, the methodologies
used for space-ground link modeling can be adapted and extended for air-ground
link analysis. On the other hand, space-ground links present additional
challenges, such as longer propagation distances, orbital dynamics, and
significant Doppler effects, particularly in cases where both terminals are in
motion. Consequently, it is more rational to begin by modeling the scenario
involving dual mobile space-ground links and subsequently extend these models
to air-ground links.

Multipath propagation has consistently posed a noteworthy obstacle in wireless
communications, particularly in demanding conditions like indoor spaces,
wooded regions, and urban environments. In these settings, signals become more
vulnerable to phenomena like reflections, refractions, and scattering. Due to
multipath, multiple copies of the same signal arrive at the receiver with
different time delays and amplitudes, posing many issues such as intersymbol
interference (ISI), signal fading, and degraded signal quality[24]. Hence, it
is crucial to develop a platform that can emulate a system which incorporates
signal processing in a multipath environment like urban areas.

In this paper, we have developed a scalable tutorial that enables the
generation of realistic channel and delay coefficients for dual mobile space-
ground links in urban areas. We utilize the combined capabilities of the
Matlab Satellite Communications Toolbox, Skydel GNSS Simulator, and QuaDRiGa
channel generator. While QuaDRiGa provides tutorials for dual mobile ground-
ground links and single mobile space-ground links, simulating scenarios
involving dual mobile space-ground links presents additional challenges. For
example, a cautious manipulation of the spatial coordinates of satellites with
respect to the receiver is required in consideration of the Earth curvature
and coordinate transformation. Moreover, the choice of channel update rate
should be carefully considered in order to accurately capture the Doppler
effect caused by the rapid movement of satellites. To examine the accuracy of
the tutorial, we analyze the generated channel and delay coefficients from a
variety of angles, such as the received signal power and amplitude, multipath
delay distribution, delay spread, and Doppler spectrum. Due to the
unavailability of actual GPS data that aligns with our statistical model, we
compare certain aspects of our work with the findings of others who have
access to real GPS measurements. This work serves as a tutorial for potential
QuaDRiGa users and enhances the available resources for simulating dual mobile
space-ground links with time-varying channels. The key contributions of this
paper are listed as follows:

  1. 1.

In the preparation of terminal trajectories with designated propagation
scenarios, we integrate a practical phenomenon in signal reception by
employing both a LOS probability model and a state transition model and
following the semi-Markov approach.

  2. 2.

By leveraging the combined capabilities of the QuaDRiGa channel generator, the
Matlab Satellite Communications Toolbox, and the Skydel GNSS simulator, a
tutorial for dual mobile space-ground links has been meticulously crafted.

  3. 3.

To serve the purpose as a tutorial, we outline several challenges that we
encounter in the channel modeling for the scenario we consider. In addition,
we point out a few possible mistakes/typos in the source code provided by
QuaDRiGa.

  4. 4.

To verify the accuracy of the generated channel and delay coefficient, we
provide a comprehensive analysis on the received signal power and amplitude,
multipath delay distribution, delay spread, and Doppler spectrum. The results
of this analysis show a high degree of agreement with previous researches that
incorporate real GPS measurements.

The rest of the paper is organized as follows: The simulation descriptions,
such as satellite scenario, receiver position, and channel modeling are
introduced in Section 2. The challenges encountered in developing this
tutorial as well as the possible mistakes and typos in the source code
provided by QuaDRiGa are enumerated in Section 3. The analytical metrics used
to examine the fidelity of the channel and delay coefficient are described in
Section 4. A brief description of the simulation setup is given in Section 5.
Section 6 presents the detailed analysis of the simulation results concerning
the received signal power and amplitude, multipath delay distribution, delay
spread, and Doppler spectrum. Finally, the conclusion, the implications of the
work, and an outline of the future work are provided in Section 7.

This manuscript serves an instructional purpose, and as such, it is structured
to facilitate focused study in specific areas of interest. Those seeking
insights into received signal power and amplitude are directed to Section IV-A
and VI-A. For an understanding of multipath delay distribution, Section IV-B
and VI-B should be referenced. Inquiries regarding delay spread are
comprehensively addressed in Section IV-C and VI-C. Finally, for readers with
a focus on the Doppler spectrum, Section IV-D and VI-D offer detailed
exposition and analysis.

##  II Simulation Descriptions

In this section, the descriptions on the channel modeling using the QuaDRiGa
channel generator, the creation of satellite scenarios using the Matlab
Satellite Communications Toolbox, and the generation of receiver positions
using the Skydel GNSS simulator are presented.

###  II-A Channel Modeling - QuaDRiGa

In order to utilize QuaDRiGa channel generator effectively, users are expected
to provide three essential inputs. These inputs encompass terminal
trajectories assigned with specific propagation scenarios, a network layout
that outlines transmitter positions and includes the carrier frequency
information, as well as the necessary antenna parameters. A terminal
trajectory can be divided into multiple segments, each of which needs to be
assigned with a propagation environment. There are many propagation scenarios
prepared as configuration files provided by QuaDRiGa, such as the non-
terrestrial-network (NTN) urban LOS, 3GPP 38.901 urban macrocell (UMa) NLOS,
3GPP 37.885 highway LOS, and so on. The scenarios supported by QuaDRiGa
include 3GPP NR UMa, 3GPP NR urban microcell (UMi), highway, indoor, rural
macrocell (RMa), rural microcell (RMi), MIMO communications, NTN
communications, and so forth. In this work, we employ the NTN urban LOS and
NTN urban NLOS. With these two propagation scenarios, we can simulate
scenarios not only for satellites but also for other vertical infrastructures
such as HAPS and unmanned aerial vehicles (UAVs).

It is important to note that in QuaDRiGa, the LOS scenario incorporates both
the direct path and MPCs, whereas in the NLOS scenario, only MPCs are
considered. For each segment the channel parameters, such as delay spread,
angle spread, shadow fading, cross-polarization ratio and so on, are
stochastically determined based on the statistical distributions derived from
channel measurement campaigns [16, 25]. In addition, a number of scattering
clusters are generated based on the corresponding channel parameters and the
receiver position in each segment. There are 20 sub-paths associated with each
cluster. The arrival angles are calculated for each sub-path and for each
position of the receiver along the trajectory. Based on the antenna parameters
assigned to the transmitter (TX) and the receiver (RX), the complex-valued
coefficients that contain phase information for all sub-paths are generated.
Finally, the channel coefficients and the path delays are generated by summing
up the coefficients of sub-paths and merging the adjacent segments. This
approach facilitates the observation of realistic phenomena, such as
constructive and destructive interference, within the generated channel and
delay coefficients. The data flow of QuaDRiGa channel model is shown in Fig.
1.

Figure 1: Data flow of QuaDRiGa channel model (parameters on black lines are
constant, they are either provided by the user or the model; parameters on
blue lines are updated once per segment; parameters on red lines are updated
once per snapshot) [17].

To emulate a realistic LOS/NLOS conditions for satellites, the LOS probability
model proposed in [26] and [27], which is a function of satellite elevation
angles, is implemented to determine the visibility condition for each
satellite at the very first epoch. The QuaDRiGa channel generator
automatically simulates multipath and channel fading. Based on this mechanism,
we categorize the propagation state into two categories: GOOD and BAD. A GOOD
state includes both a direct path and MPCs, while a BAD state only involves
the MPCs. The state transition is implemented by following the semi-Markov
approach proposed in [23]. There is a potential error in this document,
wherein a factor of 2 is omitted under the square root in the denominator, and
there is a minus sign missing in the exponent. As a result, the equation is
corrected as follows:

$p_{\text{lognormal}}(x)=\frac{1}{\sigma_{i}x\sqrt{2\pi}}\exp(-\frac{(\ln(x)-\mu_{i})^{2}}{2\sigma_{i}^{2}})$
(1)

where $i$ denotes the binary state which can either be GOOD or BAD, $\mu_{i}$
denotes the mean duration in meter for state $i$, $\sigma_{i}$ denotes the
standard deviation of the duration in meter for state $i$. Both $\mu_{i}$ and
$\sigma_{i}$ are scenario specific and are provided in Annex 2 of [23]. In
order to simulate a realistic state duration, it is essential to consider the
scenario-specific minimum state duration, denoted as
$dur_{(\mathrm{min})_{i}}$, which is dependent on the elevation angle $\alpha$
as mentioned in [13]. The summarized values of the minimum state duration are
presented in Table 1.

TABLE I: Minimum State Duration Frequencies between 1.5 and 3 GHz
---
$\alpha$ [degrees] |  $\text{dur}_{(\text{min})_{\text{GOOD}}}$ [m] |  $\text{dur}_{(\text{min})_{\text{BAD}}}$ [m]
20 |  3.9889 |  10.3114
30 |  7.3174 |  5.7276
45 |  10.0 |  6.0
60 |  10.0 |  1.9126
70 |  118.3312 |  4.8569
|  |

###  II-B Satellite Scenario - Matlab Satellite Communications Toolbox

The position of the transmitter or satellite constitutes a crucial input for
the QuaDRiGa channel generator. Ensuring utmost precision in the system
dynamics necessitates an accurate simulation of satellite positions across
various time epochs. To facilitate this, the Matlab Satellite Communications
Toolbox offers tools that adhere to established standards. These tools enable
an efficient creation of a comprehensive satellite scenario by specifying
simulation start and end times, pinpointing the receiver or ground station
location, and supplying a two-line element (TLE) file that encompasses a
compilation of the orbital elements for operational GPS satellites. From this
satellite scenario, we can gather information such as satellite positions over
a predetermined time frame, the availability of satellites based on their
elevation angles at a particular instance of time, and the duration for which
each satellite remains accessible to the receiver. This is achieved by
establishing a designated Earth surface location as the ground station and
setting an elevation mask. Consequently, any satellites that fall below the
defined elevation mask at any given point in time will be automatically
disregarded. Fig. 2 presents a screenshot depicting the simulated satellite
scenario. Refer to this figure, the satellites with a blue line joining itself
and the receiver have an elevation angle greater than the elevation mask,
indicating that they are available for reception by the receiver.

Figure 2: A snapshot of the satellite scenario simulated using the Matlab
Satellite Communications Toolbox.

###  II-C Receiver Position - Skydel GNSS Simulator

As another key input to the QuaDRiGa channel generator, we generate the
receiver positions in the Earth-centered Earth-fixed (ECEF) coordinate system
using the Skydel GNSS simulator. This software offers multiple methods for
generating receiver positions, including selecting the starting and ending
points on the Skydel GNSS simulator map or importing a keyhole markup language
(KML) street map into the software.

The Skydel GNSS simulator is a software-defined global navigation satellite
system (GNSS) simulator that emulates the signals and behavior of various
satellite navigation systems, such as GPS, GLONASS, Galileo, BeiDou, and more.
It is designed to create realistic and customizable scenarios for testing and
evaluating GNSS receivers and systems in a controlled and repeatable
environment. To the best of our knowledge, the simulation approach employed by
the Skydel GNSS simulator does not adequately replicate the intricate
complexities of real-life multipath effects. As a result, the primary utility
of the Skydel GNSS simulator lies in generating receiver positions. It is
worth mentioning that this software can also generate satellite scenarios.
However, given the specific focus of this study which is to efficiently
identify available satellites within a defined time frame, we find it more
effective to utilize the Matlab Satellite Communications Toolbox for
simulating satellite scenarios.

##  III Challenges and Possible Mistakes/Typos in QuaDRiGa

In this section, we present a number of technical challenges encountered in
the channel modeling using QuaDRiGa to simulate dual mobile space-ground
links, followed by a few possible mistakes/typos that we have identified in
the source code provided by QuaDRiGa.

###  III-A Challenges in Channel Modeling using QuaDRiGa

Other than the primary challenge in using the QuaDRiGa channel generator,
which is understanding the overall data flow and the methods adopted in the
provided source scripts, a number of additional technical challenges are
enumerated as follows:

  1. 1.

Coordinate Transformation: In the QuaDRiGa reference coordinate system, the
origin (0,0,0) corresponds to the position of a chosen receiver at time zero.
As a result, the initial position coordinates of all the other receivers and
transmitters, if present, need to be adjusted relative to this reference
position.

  2. 2.

Antenna Orientation: To correctly generate channel information, the transmit
antennas equipped on satellites should be oriented such that they are pointing
toward the receiver at all time. This is accomplished by calculating the
elevation and azimuth angle of the satellite and considering the geometric
orientation of the antenna defined in QuaDRiGa in conjunction with the
reference system for aircraft principal axes.

  3. 3.

Compatibility with State Transition Model: As the occurrence of a state
transition not only depends on the state transition model governed by (1) but
also the minimum state duration, it is advisable to sample the terminal
trajectory at a fine granularity while comparing the cumulative distance
travelled by the receiver with the minimum state duration.

  4. 4.

Parameters in Class Track: The class track in QuaDRiGa is defined to describe
the movement of a mobile terminal. While certain parameters within this class
lack detailed information, supplementary details for selected parameters are
furnished as follows:

    1. (a)

initial_position: The initial position of an object should be adjusted
relative to the reference position.

    2. (b)

positions: The positions of an object should be adjusted relative to its
initial position.

    3. (c)

movement_profile: This parameter stores the distance values in the second row
with the corresponding timestamp in the first row. It is used to describe the
distance travelled by an object between the current timestamp and the previous
one. Consequently, it is updated based on the position at the previous time
epoch.

###  III-B Possible Mistakes/Typos in Source Code

In the process of developing the channel modeling tutorial for our target
scenario, we identify the following possible mistakes and typos in the source
code provided by QuaDRiGa:

  1. 1.

“get_channels.m” in @qd_layout: The line 184 in this script serves to
determine the current speed of an object based on its movement profile. We
believe it should be corrected as follow:

$v=(mp(2,2:end)-mp(2,1:end-1))\\\ ./(mp(1,2:end)-mp(1,1:end-1)).$ (2)

  2. 2.

“get_pl.m” in @qd_builder: The line 496 of this script is utilized to
calculate atmospheric attenuation. We suspect that there should be a transpose
sign followed when invoking the function $qf.interp()$.

  3. 3.

“merging_cost_fcn.m” in private folder of @qd_builder: The line 98 in this
script aims to calculate the mean square error (MSE) of the delay spread. The
original code employs a denominator that encompasses the summation of the
target delay spread, thereby exhibiting characteristics more aligned with
normalization rather than averaging. Therefore, this line of code is modified
as follows:

$mse=10*\log 10(sum((ds\\_target-ds).^{2})\\\ ./numel(ds))$ (3)

where $ds$ is the name of a parameter storing delay spreads and $numel(ds)$
denotes the number of samples in the parameter $ds$. The revised code serves
to calculate the correct MSE value of the delay spread.

##  IV Analytical Metrics

In this section, the method for calculating the received signal power and
amplitude, the general approach adopted by QuaDRiGa in generating channel and
delay coefficient, the method for analyzing the delay spread, and the
technique for computing the Doppler shift are discussed. Among these, the
received signal power and amplitude, the multipath delay as well as its
distribution, the root mean square (RMS) delay spread, and the Doppler shift
collectively serve as the key analytical metrics to validate the accuracy of
the generated channel and delay coefficient.

###  IV-A Received Signal Power and Amplitude

TABLE II: Constant Parameters for Satellite Pathloss Model |  NTN Urban LOS |  NTN Urban NLOS
---|---|---
$A$ |  20 |  20.05
$B$ |  32.55 |  54.85
$C$ |  20 |  27.9
$D$ |  0 |  -11
|  |

Received power serves as an indicator of the pathloss experienced by the
signal along its propagation path. In QuaDRiGa, the satellite pathloss model
is derived from [28] which is a combination of the 3GPP-NTN pathloss model and
the clutter-loss model. This pathloss model is formulated as follows:

$\textsf{PL}=A\log_{10}(d_{\text{3d}})+B+C\log_{10}(f_{\text{c}})+D\log_{10}(\alpha)+\textsf{PL}_{a}$
(4)

where PL denotes the pathloss of a satellite signal, $d_{\text{3d}}$ denotes
the 3D distance between the TX and the RX in meter, $f_{\text{c}}$ denotes the
carrier frequency in GHz, $\alpha$ denotes the elevation angle of the TX with
respect to the RX in rad, $A$ is a scaling factor that is dependent on the 3D
distance between the TX and the RX, $B$ is the reference pathloss at a carrier
frequency of 1 GHz and an elevation of 1 rad or 57.3°, $C$ is a frequency
dependent scaling factor, and $D$ is a elevation angle dependent sacling
factor. These four constant parameters, $A$, $B$, $C$, and $D$, are scenario
specific and are provided in Table 2. $\textsf{PL}_{a}$ is used to account for
the absorption attenuation due to atmospheric gases, which can be neglected
when frequencies are below 10 GHz and elevation angles are above 10 degrees
[17, 29]. The channel coefficients are scaled based on the computed pathloss
in conjunction with K-factor and shadow fading.

With the genereted channel coefficient $h$ of dimension $L\times T$, where $L$
denotes the number of paths and $T$ denotes the number of snapshots, the
received power of a satellite can be calculated as follows:

$P^{i}_{t}=\sum_{l=1}^{L}|h_{l,t}^{i}|^{2}$ (5)

where $P^{i}_{t}$ denotes the received power of satellite $i$ at snapshot $t$,
$l$ denotes the path index, and $h_{l,t}^{i}$ denotes the channel coefficient
of the $l^{th}$ path at snapshot $t$ for satellite $i$. The received signal
amplitude of a satellite can be calculated using the generated channel
coefficients as follows:

$A^{i}_{t}=\sum_{l=1}^{L}|h_{l,t}^{i}|$ (6)

where $A^{i}_{t}$ denotes the received signal amplitude of satellite $i$ at
snapshot $t$. One way to validate the propagation scenarios employed by
QuaDRiGa is to observe the distribution of the received signal amplitude. When
the received signal involves both direct/LOS path and multipaths, the PDF of
the signal should follow the Rician distribution as follows:

$f(a)=\frac{a}{\sigma^{2}}\text{exp}(-\frac{a^{2}+z^{2}}{2\sigma^{2}})I_{0}(\frac{az}{\sigma^{2}})$
(7)

where $a$ denotes the signal amplitude as a random variable, and $\sigma^{2}$
denotes average multipath power, $z$ is the LOS signal amplitude, and
$I_{0}(\cdot)$ is the modified Bessel function of zeroth order. When the
received signal involves multipaths only, the PDF of the signal reduces to the
Rayleigh distribution as follows:

$f(a)=\frac{a}{\sigma^{2}}\text{exp}(-\frac{a^{2}}{2\sigma^{2}}).$ (8)

Both Rayleigh and Rician distribution are employed to fit the histogram of the
received signal amplitude in Section 6.

###  IV-B Multipath Delay Distribution

Multipath delay distribution refers the statistical distribution of the
multipath delay relative to the direct path. It is a crucial analytical metric
for understanding the channel characteristics and has been shown to be mainly
subject to the receiver’s environment [30]. In [31], the authors conduct a
statistical analysis on the GPS multipath in the urban environment. They
reveal a notable likelihood of encountering short-delay multipaths compared to
those with longer delays in urban areas. This observation will be employed as
one of the benchmarks to validate the precision of the channel model we have
adopted, by comparing it with the multipath delays in our study. Moreover, we
conduct a comparison of the relationship between multipath delay and elevation
angle, as well as the multipath delay distribution, with the findings
presented in [30], which utilizes real GPS measurements collected in a dense
urban area, and [32], which relies on the real GPS measurements collected in
urban areas as discussed in [33]. There are three distribution functions which
are commonly employed to characterize multipath delays: the gamma distribution
[30], the exponential distribution [32], and the Rayleigh distribution [34].
These distribution functions are employed to fit the multipath delay histogram
presented in Section 6.

###  IV-C Delay Spread

TABLE III: Parameters for Initial Delay Spread Calculation Note: $\mu_{\textnormal{DS}}$, $\sigma_{\textnormal{DS}}$, $\alpha_{\textnormal{DS}}$, $\gamma_{\textnormal{DS}}$ are calculated using $\mathrm{log}_{10}()$ |  LOS |  NLOS
---|---|---
$\mu_{\textnormal{DS}}$ [dB] |  -7.8 |  -6.85
$\sigma_{\textnormal{DS}}$ [dB] |  0.3 |  0.15
$\alpha_{\textnormal{DS}}$ [dB] |  0.5 |  N/A
$\gamma_{\textnormal{DS}}$ [dB] |  -0.4 |  N/A
$d_{\lambda}$ [m] |  50 |  40
|  |

Delay spread describes the temporal spreading or spreading in time of a signal
due to multipath propagation in a communication channel. It is another key
parameter used to characterize wireless communication channels, particularly
in environments with reflections, scattering, and refractions, leading to
multiple signal paths arriving at the receiver with different time delays. In
QuaDRiGa, for a given carrier frequency, the initial delay spreads for the NTN
urban LOS, $\text{DS}_{\text{LOS}}$, and NLOS scenarios,
$\text{DS}_{\text{NLOS}}$, are calculated as follows:

$\text{DS}_{\text{LOS}}=\mu_{\text{DS}}+\gamma_{\text{DS}}\mathrm{log}_{10}f_{\text{c}}+\alpha_{\text{DS}}\mathrm{log}_{10}\alpha+\sigma_{DS}X^{\text{DS}}$
(9) $\text{DS}_{\text{NLOS}}=\mu_{\text{DS}}+\sigma_{\text{DS}}X^{\text{DS}}$
(10)

where $\mu_{\text{DS}}$ denotes the reference value of the delay spread at a
carrier frequency of 1 GHz and an elevation of 1 rad or 57.3°,
$\sigma_{\text{DS}}$ denotes the standard deviation of the delay spread at the
reference value, $\gamma_{\text{DS}}$ denotes a frequency dependent scaling
factor, $\alpha_{\text{DS}}$ denotes an elevation dependent scaling factor,
and $X^{\text{DS}}$ denotes a random variable that follows a spatially
correlated normal distribution with zero mean, unit variance, and an
autocorrelation function which is a mixture of a Gaussian and an exponential
autocorrelation function:

$\rho(d)=\left\\{\begin{array}[]{ll}\exp(-d^{2}/d_{\lambda}^{2}),&\text{if
}d<d_{\lambda}\\\ \exp(-d/d_{\lambda}),&\text{if }d\geq
d_{\lambda}\end{array}\right.$ (11)

where $d_{\lambda}$ represents the decorrelation distance and $d$ is the
distance between two mobile terminals (MTs), in our case, the TX (e.g.,
satellite) and the RX (e.g., ground user). Due to the large distance between
the TX and the RX in our simulation, the condition $d\geq d_{\lambda}$ is
always satisfied. The parameters used for the calculation of the initial delay
spread are provided in the source code of QuaDRiGa and are summarized in Table
3. To consider the relationships among large-scale parameters including delay
spread and others such as Ricean K-factor, shadow fading, azimuth spread of
departure, azimuth spread of arrival, elevation spread of departure, elevation
spread of arrival, and cross-polarization ratio, an inter-parameter
correlation model is employed. The detailed information on generating the
spatially correlated large-scale parameters can be found in [17]. The
spatially correlated large-scale parameters are employed to generate initial
delays, cluster powers, and drifting angle of arrivals. These parameters are
then combined with the defined antenna patterns and array geometries to
generate channel and delay coefficients.

The resulting channel and delay coefficients are validated by examining the
RMS delay spread that is computed by

$\text{DS}_{\text{rms}}=\sqrt{\frac{1}{P}\sum_{l=1}^{L}P_{l}\tau_{l}^{2}-(\frac{1}{P}\sum_{l=1}^{L}P_{l}\tau_{l})^{2}}$
(12)

where $P$ denotes the sum of all path power $P_{l}$, and $\tau_{l}$ denotes
the $l^{th}$ path delay.

###  IV-D Doppler Spectrum

Figure 3: Doppler angle illustration (red solid line: upper and lower bounds
of the Doppler angle; red dash line: the 90° Doppler angle).

Doppler spectrum refers to the distribution of the signal power as a function
of the Doppler shift. It is commonly used in wireless communications and
navigation systems to analyze the frequency shift of signals caused by the
relative motion between the transmitter and the receiver. In this work, the
Doppler spectrum is found by calculating the frequency response of the
channel, followed by an inverse Fast Fourier Transform (iFFT). The detailed
steps can be found in [17].

To validate the Doppler effect, the most prominent Doppler shift depicted in
the Doppler spectrum is compared with the estimated Doppler shift for each
satellite, which is given as follows:

$\delta f^{i}=\frac{f_{\text{c}}}{c}\delta v^{i}$ (13)

where $\delta f^{i}$ denotes the Doppler shift for satellite $i$, $c$ is the
speed of light, and $\delta v^{i}$ denotes the radial relative velocity
between satellite $i$ and the receiver, which can be calculated by

$\delta v^{i}=v^{i}\cos{\theta^{i}}+v_{\text{RX}}\cos{\theta_{\text{RX}}^{i}}$
(14)

where $v^{i}$ denotes the speed of satellite $i$, $\theta^{i}$ denotes the
angle between the movement direction of satellite $i$ and the LOS between
satellite $i$ and the receiver, which is commonly referred to as the Doppler
angle of satellite $i$, $v_{\text{RX}}$ denotes the speed of the receiver, and
$\theta_{\text{RX}}^{i}$ denotes the angle between the direction of receiver’s
motion and the LOS between satellite $i$ and the receiver, or the Doppler
angle of the receiver. A visual illustration of the Doppler angles for the
satellite and the receiver is depicted in Fig. 3. It should be noted that the
sign of radial relative velocity is determined by the motion trajectories of
the satellite and the receiver. Refer to Fig. 3, suppose the distance between
the satellite and the receiver at position 1, denoted as $d_{1}$, is greater
than the distance at position 2, denoted as $d_{2}$, meaning that the
satellite is approaching the receiver, then the sign of radial relative
velocity should be positive. Based on the fact that the maximum radial
relative velocity between a stationary receiver and a GPS satellite is about
929 m/s [35], the upper and lower bounds of the Doppler angle at varied
satellite speeds can be determined. Therefore, we conduct a sanity check on
the celestial mechanics by verifying the correctness of the Doppler angles for
the simulated GPS satellites. According to (14), a satellite with a Doppler
angle of 90° would yield no radial velocity. The upper bound and lower bound
of the Doppler angle along with the 90° Doppler angle are also shown in Fig.
3.

##  V Simulation Setup

In this study, a tutorial for the channel modeling of an urban dual-mobility
scenario for the space-ground links is developed. The simulation is carried
out for a duration of 1 second. The elevation mask is set to 15 degrees. The
carrier frequency of the transmitted signal (GPS L1) is 1,575.42 MHz. Since
satellites are moving at a great speed (e.g., 3,000 m/s), the channel update
rate needs to be sufficiently large in order to satisfy the sampling theorem
and accurately capture the Doppler effect. We choose to use a sample density
of 5 samples per wavelength for the dual-mobility scenario. This is the
default value recommended by QuaDRiGa to correctly capture the Doppler
characteristics. As the longest distance travelled by a satellite in this work
is around 3,500 meters, we can calculate the minimum channel update rate,
$R_{\text{ch}}$, required for the simulation as follows:

$R_{\text{ch}}=1\times 3500\times
5\times\frac{f_{\text{c}}}{c}=91.963~{}\mathrm{kHz}.$ (15)

Figure 4: Satellite visibility plot (blue line indicates a LOS scenario).

To simplify the computation, we opt for a channel update rate of 100 kHz. A
propagation scenario, either NTN urban LOS or NTN urban NLOS, is assigned to
each satellite every 1 ms. In this simulation, the speed of the RX (e.g.,
vehicle) is 50 km/h, thence the distance travelled by the vehicle for one
second is about 14 meters. It can be observed that a transition between states
can occur within a simulation time of 1 second, as evident from the minimum
state duration values presented in Table 1. All satellite antennas are
featured with a parabolic dish antenna with right-hand circular polarization
(RHCP), an aperture radius of 3 meters, and a gain of 40 dBi. A 0 dBm transmit
power is applied to the satellite. A patch antenna pointing to the sky is
equipped on the receiver. It is worth noting that we perform the entire
simulation using Matlab, however, the channel modeling by QuaDRiGa can also be
performed in Octave where graphics processing unit (GPU) can be utilized to
accelerate the simulation. In the calculation of the Doppler spectrum for the
satellites, a Doppler analysis window size of 1 second is chosen to optimize
frequency resolution. Following the typical parameter selection for GPS L1 C/A
code, a channel bandwidth of 2 MHz is considered[36, 37]. To render a
considerably good performance, a Fast Fourier Transform (FFT) point of 1024 is
adopted. The key simulation parameters are summarized in Table 4.

TABLE IV: Key Simulation Parameters Parameter |  Value
---|---
Simulation duration |  1 s
Elevation mask |  15 deg
Carrier frequency |  1,575.42 MHz
Sample density |  5 samples/wavelength
Channel update rate ($R_{\text{ch}}$) |  100 kHz
Vehicle (receiver) speed |  50 km/h
Transmit antenna gain |  40 dBi
Transmit power |  0 dBm
Channel bandwidth |  2 MHz
FFT-point |  1024
|

##  VI Simulation Results

TABLE V: Starting and Ending Elevation Angle for Satellites Satellite ID |  $\alpha_{i}$ [deg] |  $\alpha_{f}$ [deg]
---|---|---
PRN 14 |  72.6560 |  72.6638
PRN 08 |  15.7490 |  15.7431
PRN 30 |  47.7190 |  47.7120
PRN 01 |  63.4044 |  63.4049
PRN 07 |  21.6368 |  21.6290
PRN 17 |  47.8612 |  47.8676
PRN 19 |  17.7293 |  17.4352
PRN 21 |  45.7599 |  45.7546
|  |

Under the simulation setup elucidated in the preceding section, the simulation
time required by QuaDRiGa for channel modeling turns out to be 36 minutes. A
total of about 600 MB (in binary) data for the network layout and the channel
information is collected for post-processing. The satellite visibility over a
simulation period of 1 second is depicted in Fig. 4. All satellites shown in
this figure are considered available to the RX. Notably, we can observe that
the LOS condition is eventually established for the satellite with the pseudo
random noise (PRN) code 21 due to the state transition model. The frequency of
state transitions may increase if the simulation is prolonged over an extended
time frame. The starting and ending elevation angles, $\alpha_{i}$ and
$\alpha_{f}$, of each satellite are summarized in Table 5. To validate the
generated channel and delay coefficient, the received power, multipath delay
distribution, delay spread, and Doppler spectrum are analyzed in this section.
It is worth noting that we have the knowledge of the positions for both
satellites and the receiver, sampled at a rate optimized by QuaDRiGa for
efficient channel modeling. However, it is important to mention that this
sampling rate may not align with the channel update rate utilized for
generating channel and delay coefficients. As a result, the position data for
satellites and the receiver corresponding to each generated path delay might
not be accessible.

###  VI-A Received Signal Power and Amplitude

The received power of the simulated satellites is shown in Fig. 5. We can
observe from this figure that when the LOS condition is established between
the satellite and the receiver, the received power exhibits larger amplitude
and reduced noise. This observation is logical since the received power of the
direct/LOS path is typically much higher than that of the multipath. Using (4)
and the constant parameters for the satellite pathloss model provided in Table
2, we can estimate the pathloss for each satellite. For instance, the
propagation scenario for satellite PRN 21 is urban-NLOS at the start of the
simulation. At this moment, the 3D distance $d_{\text{3d}}$ between satellite
PRN 21 and the receiver is roughly found to be 21,954.8287 km and the
elevation angle is 45.7599 degrees. The pathloss of satellite PRN 21 can then
be computed as follows:

$\textsf{PL}=20.05\log_{10}(21{,}954{,}828.7)+54.85\\\
+27.9\log_{10}(1.57542)-11\log_{10}(45.7599\times\frac{\pi}{180})\\\
=208.63~{}\mathrm{dB}.$ (16)

Knowing that the transmit power is 0 dBm and the transmit antenna gain is 40
dBi, we can roughly determine the received power for PRN 21 at the start of
the simulation, which is -168.63 dBm. This matches with the received power for
PRN 21 shown in Fig. 5. A similar analysis is carried out for an urban-LOS
case, in particular, PRN 14 at the start of the simulation. At this moment, we
determine that the 3D distance $d_{\text{3d}}$ between the satellite and the
receiver is 20,408.4785 km. The pathloss for this satellite is then computed
as follows:

$\textsf{PL}=20\log_{10}(20{,}408{,}478.5)+32.55+20\log_{10}(1.57542)\\\
=182.69~{}\mathrm{dB}.$ (17)

Following the same analysis, the received power is computed to be -142.69 dBm.
This again roughly matches with the received power for PRN 14 as shown in Fig.
5.

|  |  |
---|---|---|---
|  |  |
Figure 5: Received power for GPS satellites. |  |  |
---|---|---|---
|  |  |
Figure 6: Histogram of the received signal amplitude with fitted Rayleigh and
Rician distribution.

Fig. 6 presents the histogram of the received signal amplitude for simulated
satellites, alongside the fitted Rayleigh and Rician distributions. This
illustration reveals that the Rician distribution converges to the Rayleigh
distribution when the received signal is solely influenced by multipath.
However, in the presence of a LOS path in the received signal, the Rayleigh
distribution is not a suitable fit for the histogram of the received signal
amplitude. The histogram of the received signal amplitude for PRN 21 exhibits
two distinct distributions. This is attributed to the initial NLOS propagation
scenario for PRN 21, which later transitions to a LOS scenario. To validate
the propagation scenarios for this satellite, we divide the corresponding
received signal amplitude into two datasets where the first one contains low
amplitude values, corresponding to the NLOS scenario, and the second one
contains high amplitude values, corresponding to the LOS scenario. Both groups
are fitted using Rayleigh and Rician distributions. The first dataset shows
the Rician fit overlapped with the Rayleigh fit, while only the Rician
distribution can be used to fit the second dataset. In summary, the amplitude
distribution for all simulated satellites aligns with theoretical predictions,
demonstrating the accuracy of the propagation scenarios employed by QuaDRiGa
channel generator.

###  VI-B Multipath Delay Distribution

|
---|---
|
Figure 7: Multipath delay histogram for LOS satellites PRN 01, PRN 14, PRN 19,
PRN 30.

Due to different sampling rates adopted by QuaDRiGa in position interpolation
and delay generation, the positions for satellites and the receiver associated
with each generated path delay are unavailable. In other words, the delay of
the direct path in the NLOS scenarios is unknown to us. Therefore, we will be
analyzing the multipath delay distribution for the LOS satellites: PRN 01, PRN
14, PRN 19, and PRN 30. Three candidate distributions mentioned in Section 3
are used to fit the histogram for each satellite in order to find out which
distribution is the best for multipath delay in the urban scenario considered
by QuaDRiGa channel generator. Based on the least squares criteria, the
regressive curve fitting method is used to determine the optimal coefficients
for all possible distribution functions. The histogram and the corresponding
root mean square error (RMSE) for each distribution curve fitting, along with
the elevation angle $\alpha$, the average multipath delay,
$\tau_{\text{avg}}$, and the median multipath delay $\tau_{\text{med}}$ for
each satellite are depicted in Fig. 7. From this figure, the following
information can be observed:

  1. 1.

The average multipath delay $\tau_{\text{avg}}$ and the median multipath delay
$\tau_{\text{med}}$ decrease as the elevation angle increase in general. This
finding is consistent with the observation made in [30] in general. However,
there can be exceptions to this trend, particularly at high elevation angles.
This is because a higher elevation angle may not necessarily correspond to the
shortest distance between the satellite and the receiver.

  2. 2.

The exponential distribution is the best fit among the three considered
distributions as it has the lowest RMSE value. This result matches with the
multipath delay distribution proposed in [32], where actual GPS measurements
collected from urban areas are utilized. The dominance of the exponential
distribution remains consistent across all elevation angles, indicating that
the multipath delay is primarily influenced by the receiver’s surrounding
environment. This also corresponds with the observation made in [30].

  3. 3.

With QuaDRiGa channel models for the NTN-urban scenario, there is a notably
greater likelihood of encountering short-delay multipaths compared to those
with longer delays. This observation is in accordance with the conclusion
presented in [31].

###  VI-C Delay Spread

Figure 8: Delay spread for PRN 19 at the initial epoch. |  |  |
---|---|---|---
|  |  |
Figure 9: RMS delay spread for the simulated GPS satellites.

Fig. 8 illustrates the delay spread at the initial epoch for satellite PRN 19,
in which a LOS condition is established between itself and the receiver. This
plot highlights that the signal along the direct path exhibits the most robust
signal amplitude. Furthermore, it is noticeable that a multipath signal
characterized by a shorter delay does not necessarily align with a stronger
amplitude. This demonstrates a successful simulation of the occurrence of
constructive and destructive interference which can occur in real life. The
RMS delay spread of the simulated satellites is shown in Fig. 9. The x-axis in
the delay spread plots denotes the distance travelled by the RX. Using (9),
(10) and the extracted parameters given in Table 1, the reasonable range of
the delay spread of each satellite can be calculated. For example, the delay
spread of satellite PRN 14 in the urban scenario with an elevation of 72.6560°
can be calculated by substituting $\mu_{\text{DS}}=-7.8$,
$\sigma_{\text{DS}}=0.3$, $\alpha_{\text{DS}}=0.5$, and
$\gamma_{\text{DS}}=-0.4$ into (9), resulting

$\text{DS}_{\text{LOS,urban}}^{\text{PRN 14}}=-7.8274+0.3X^{\text{DS}}.$ (18)

Since $X^{\text{DS}}$ is a random variable that follows a normal distribution
with zero mean and unit variance, we could consider $X^{\text{DS}}$ to be any
value in between $-3\sigma$ and $+3\sigma$ in estimating the range of the
delay spread. Therefore, the range for
$\text{DS}_{\text{LOS,urban}}^{\text{PRN 14}}$ is found to be between 1.8733
ns and 118.1952 ns, which is consistent with the delay spread for PRN 14 shown
in Fig. 9. As an example for the NLOS case, the delay spread of PRN 08 is
found using (10) as follows:

$\text{DS}_{\text{NLOS,urban}}^{\text{PRN 08}}=-6.85+0.15X^{\text{DS}}.$ (19)

By the same analysis, the delay spread for PRN 08 falls into the range between
50.1187 ns and 398.1072 ns. We notice that in this case, the calculated range
of delay spread does not match perfectly with the delay spread shown in Fig.
9. This is likely due to a significant Doppler shift of this signal (see Fig.
10), rendering a prominent time varying channel for the link between PRN 08
and the receiver. Since we assume a nominal carrier frequency when applying
(9) and (10) to estimate the initial delay spread, it is reasonable to
anticipate the calculated range for delay spread to be more accurate for the
ones with less Doppler shift (i.e., frequency shift).

###  VI-D Doppler Spectrum

The Doppler spectrum of the simulated satellites is shown in Fig. 10. From
Fig. 10, it is evident to see that the Doppler shifts of all satellites lie in
between -5 kHz and +5 kHz. This observation aligns with the expectation of the
Doppler shift for a space-ground link that involves a stationary or a slow
moving receiver [38, 35]. Additionally, we can observe that the intensity of
the Doppler spectrum in the LOS scenario appears to be stronger compared to
the NLOS scenario. Furthermore, the Doppler shift in the NLOS scenario
exhibits more noise when contrasted with the LOS scenario. This aligns with
the anticipated behavior as the power of MPCs is considerably lower than that
of the direct path in general. A specific instance illustrating both of these
characteristics can be observed in the case of PRN 21. To validate the
accuracy of the Doppler spectrum generated using the channel and delay
coefficient, we compare the strongest Doppler shift in the spectrum with the
one calculated using (13). For instance, by knowing the positions of both
satellite PRN 21 and the receiver at two consecutive epochs with known time
interval, the radial relative velocity for this specific satellite-receiver
pair is estimated to be -434.5713 m/s. Based on this information, the Doppler
shift for satellite PRN 21 can be calculated as follows:

$\delta f=\frac{1{,}572.42\times
10^{6}}{299{,}792{,}458}\times-434.5713=-2{,}283.69~{}\mathrm{Hz}.$ (20)

This roughly aligns with strongest Doppler shift of satellite PRN 21 in the
Doppler spectrum as shown in Fig. 10. By assuming the receiver is stationary,
the plot of the Doppler angle for the simulated satellites along with the
upper and lower bounds of the Doppler angle for different satellite speeds is
shown in Fig. 11. As we can observe from this figure, the Doppler angle bound
approaches 90 degrees as the satellite speed increases. Furthermore, it is
evident that the Doppler angles of all the simulated satellites fall within
the specified upper and lower bounds, demonstrating the fidelity of celestial
mechanics involved in the system model.

|  |  |
---|---|---|---
|  |  |
Figure 10: Doppler spectrum for the simulated GPS satellites. Figure 11:
Doppler angles for the simulated GPS satellites (black dots: simulated GPS
satellites; red solid lines: upper and lower bound of the Doppler angle for
GPS satellites; red dash line: the Doppler angle at which zero radial velocity
is contributed by the satellite).

##  VII Conclusion

In this paper, we have developed a scalable tutorial that can generate
realistic channel and delay coefficients for dual mobile space-ground links.
This is achieved by utilizing the Matlab Satellite Communications Toolbox, the
Skydel GNSS simulator, and the QuaDRiGa channel generator. Although the
QuaDRiGa channel generator is complex, essentially, users must provide three
key inputs: the trajectory of the terminal along with specified signal
propagation scenarios, a network layout, and details of antenna parameters.
For simulating realistic signal quality conditions in different propagation
scenarios, recognized models for LOS probability and state transition are
utilized. QuaDRiGa then automates the remaining channel modeling processes.

The statistical nature of QuaDRiGa eliminates the need for high-resolution
maps and surface parameters, enabling fast deployment while maintaining
sufficient accuracy. We validate the generated channel and delay coefficients
by analyzing the received signal power and amplitude, multipath delay
distribution, delay spread and Doppler spectrum. With the intention of
functioning as a tutorial, we highlight several technical obstacles that users
could encounter while utilizing QuaDRiGa, particularly when simulating the
dual mobile space-ground connections. Several possible errors and
typographical errors present in the source code supplied by QuaDRiGa are
identified to enhance the reliability of the open source.

As the propagation scenario files provided by QuaDRiGa can be utilized for any
NTN scenario, we anticipate the applicability of this tutorial to extend to
dual mobile stratospheric-ground links and air-ground links. This versatility
becomes valuable for integrated signal processing within VHetNets. By
convolving the generated channel coefficients with any type of signals, such
as satellite and HAPS, and incorporating different delays to the same signal,
we can generate pseudo signals in a statistically reliable multipath
propagation environment.

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|  Hongzhao Zheng (Member, IEEE) received the B. Eng. (Hons.) degree in
engineering physics from the Carleton University, Ottawa, ON, Canada, in 2019.
He is currently a PhD student at Carleton University. His research interest is
urban positioning using sensor-enabled heterogeneous wireless infrastructure.
Mr. Zheng received the best paper award at IEEE WiSEE 2022.
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|  Mohamed Atia (Senior Member, IEEE) received the B.S. and M.Sc. degrees in
computer systems from Ain Shams University, Cairo, Egypt, in 2000 and 2006,
respectively, and the Ph.D. degree in electrical and computer engineering from
Queen’s University, Kingston, ON, Canada, in 2013. He is currently an
Associate Professor with the Department of Systems and Computer Engineering,
Carleton University. He is also the Founder and the Director of the Embedded
and Multi-Sensory Systems Laboratory (EMSLab), Carleton University. His
research interests include sensor fusion, navigation systems, artificial
intelligence, and robotics. Dr. Atia received the best paper award at IEEE
WiSEE 2022.
---|---
|  Halim Yanikomeroglu (Fellow, IEEE) received the BSc degree in electrical
and electronics engineering from the Middle East Technical University, Ankara,
Turkey, in 1990, and the MASc degree in electrical engineering (now ECE) and
the PhD degree in electrical and computer engineering from the University of
Toronto, Canada, in 1992 and 1998, respectively. Since 1998 he has been with
the Department of Systems and Computer Engineering at Carleton University,
Ottawa, Canada, where he is now a Chancellor’s Professor. Dr. Yanikomeroglu’s
research interests cover many aspects of wireless communications and networks,
with a special emphasis on non-terrestrial networks (NTN) in the recent years.
He has given 110+ invited seminars, keynotes, panel talks, and tutorials in
the last five years. He has supervised or hosted over 160 postgraduate
researchers in his lab at Carleton. Dr. Yanikomeroglu’s extensive
collaborative research with industry resulted in 40 granted patents. Dr.
Yanikomeroglu is a Fellow of the IEEE, the Engineering Institute of Canada
(EIC), the Canadian Academy of Engineering (CAE), and the Asia-Pacific
Artificial Intelligence Association (AAIA). He is a Distinguished Speaker for
the IEEE Communications Society and the IEEE Vehicular Technology Society, and
an Expert Panelist of the Council of Canadian Academies (CCA—CAC). Dr.
Yanikomeroglu is currently serving as the Chair of the Steering Committee of
IEEE’s flagship wireless event, Wireless Communications and Networking
Conference (WCNC). He is also a member of the IEEE ComSoc Governance Council,
IEEE ComSoc GIMS, IEEE ComSoc Conference Council, and IEEE PIMRC Steering
Committee. He served as the General Chair and Technical Program Chair of
several IEEE conferences. He has also served in the editorial boards of
various IEEE periodicals. Dr. Yanikomeroglu received several awards for his
research, teaching, and service, including the IEEE ComSoc Fred W. Ellersick
Prize (2021), IEEE VTS Stuart Meyer Memorial Award (2020), and IEEE ComSoc
Wireless Communications TC Recognition Award (2018). He received best paper
awards at IEEE Competition on Non-Terrestrial Networks for B5G and 6G in 2022
(grand prize), IEEE ICC 2021, IEEE WISEE 2021 and 2022.
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