#  Emulating UAV Motion by Utilizing Robotic Arm for mmWave Wireless Channel
Characterization

Amit Kachroo, Collin A. Thornton, Md Arifur Rahman Sarker, Wooyeol Choi, He
Bai, Ickhyun Song, John O’Hara, and Sabit Ekin∗ A. Kachroo, C. Thornton, Md.
Sarker, W. Choi, I. Song, J. O’Hara and S. Ekin are with the School of
Electrical and Computer Engineering, Oklahoma State University, OK, USA
(e-mail: {amit.kachroo, collin.thornton, msarker, wchoi, isong, oharaj,
sabit.ekin}@okstate.edu), *Corresponding author: Sabit Ekin.H. Bai is with the
Department of Mechanical and Aerospace Engineering, Oklahoma State University,
OK, USA (email: he.bai@okstate.edu).

###### Abstract

In this paper, millimeter wave (mmWave) wireless channel characteristics
(Doppler spread and path loss modeling) for Unmanned Aerial Vehicles (UAVs)
assisted communication is analyzed and studied by emulating the real UAV
motion using a robotic arm. The motion considers the actual turbulence caused
by the wind gusts to the UAV in the atmosphere, which is statistically modeled
by the widely used Dryden wind model. The frequency under consideration is 28
GHz in an anechoic chamber setting. A total of 11 distance points from 3.5
feet to 23.5 feet in increments of 2 feet were considered in this experiment.
At each distance point, 3 samples of data were collected for better inference
purposes. In this emulated environment, it was found out that the average
Doppler spread at these different distances was around -20 Hz and +20 Hz at
the noise floor of -60 dB. On the other hand, the path loss exponent was found
to be 1.843. This study presents and lays out a novel framework of emulating
UAV motion for mmWave communication systems, which will pave the way out for
future design and implementation of next generation UAV-assisted wireless
communication systems.

###### Index Terms:

mmWave, UAV, Doppler, Channel emulation, Path loss, Dryden wind model, Path
loss

##  I Introduction

Rapid proliferation of smart devices below 6 GHz has lead to a massive amount
of data traffic, thus creating a tremendous burden on the limited frequency
spectrum available to the public. To overcome this spectrum crunch,
technologies such as cognitive radios[1], multiple-input and multiple-output
(MIMO)[2], and non-orthogonal multiple access (NOMA)[3] etc. were proposed.
However, the demand still continues to outpace the spectrum availability. In
2015, the Federal Communications Commission (FCC) released millimeter wave
(mmWave) frequencies for licensed and unlicensed use. The newly licensed
frequencies are 28 GHz, 37 GHz, and 39 GHz, while the unlicensed bands are
64$\sim$71 GHz[4]. Access to these mmWave frequencies allows multi gigabit
wireless communication which enables fifth generation (5G) and beyond fifth
generation (B5G) communications[5]. In addition to the high data rates, small
antenna size, and circuits at millimeter wavelength provides reliable, highly
directional and secure communication links against any eavesdropping and
jamming.

On the other hand, unmanned aerial vehicles (UAVs), also referred to as
drones, have seen a lot of interest from academia, industry, and from the
general public at large over the past decade. The main reasons behind this
large scale popularity are the ease of operability (remote or autonomous),
easy deployment, higher maneuverability, and lower operating and maintenance
costs of UAVs. UAVs are now extensively used in smart farming, disaster
responses, military, smart logistics, and recreation (filming)[6, 7, 8, 9,
10]. Advancements in UAV technology are also fuelling the interest of its
application in wireless communication technology. UAVs are capable of
providing a highly reliable and cost effective mode of technology[7, 11, 12,
13, 14], and can also be easily deployed as a flying base station (BS) to
provide ubiquitous wireless communication access. They also provide an
alternative support for 5G and B5G cellular mobile communication. Furthermore,
UAVs can be used as mobile relays to provide wireless connectivity among
partitioned user equipment (UE) that lack any direct line of sight (LOS)
communication between the BS and UE. Apart from using as a flying BS and/or
relaying node, UAVs have also found application in areas such as aerial data
collectors, aerial caching, and aerial power source etc. Multiple UAVs can
also coordinate, and self organise to form different network architectures,
such as flying adhoc networks (FANETs), internet of drones etc. All these
applications of UAV assisted wireless communication have been studied assuming
Wi-Fi, or at fourth generation (4G) cellular communication frequencies.
Lately, mmWave communication with UAVs have been a topic of great interest[15,
16, 7].

Recent studies[16, 17, 18, 19, 15, 7] suggest that the successful deployment
of UAV-assisted mmWave wireless communication hinges on accurate and realistic
propagation channel modeling. While considerable research on terrestrial
propagation channels has been conducted for the last few decades, propagation
channel modeling for UAVs has not been extensively studied[15]. Existing
channel modeling studies mainly use 1) analytical modeling, e.g., two-ray
model, or 2) ray-tracing simulations, or 3) empirical modeling using channel
sounding methods. The first two methods are deterministic, cost-effective and
require less effort, but they are fundamentally sub-optimal approaches given
the complexity and dynamicity of the wireless channels. On the other hand,
empirical modeling that uses the channel sounding method could provide more
realistic channel models but requires a large amount of statistical data that
needs to be collected from multiple channel observations, and numerous
measurement campaigns by using advanced channel sounding equipment. Moreover,
microwave measurements to validate such models are inadequate because of
fundamental differences between mmWave and microwave channels (e.g.,
propagation loss, directivity, sensitivity to blockage). The UAV operating
environment also introduces unique atmospheric and terrain challenges[15]. Due
to UAV restrictions (e.g., pointing, payload, power, equipment-cost
constraints) and the requirement of advanced channel-sounding equipment, to
our knowledge no studies have been reported that conduct empirical modeling
for UAV-assisted mmWave channels. Available studies mainly use ray-tracing
simulations or analytical modeling[19, 15], e.g., for frequencies of 28 GHz
and 60 GHz. Also, due to differences in channel scattering environment and
operating frequencies, the propagation channel models used for higher altitude
aeronautical communications generally cannot be utilized directly for low
altitude (small) UAV-assisted mmWave communications[15]. Distinct structural
and flight characteristics for low-altitude UAVs could be expected such as
different airframe shadowing features, and potentially sharper pitch, roll,
and yaw rates of change during flight. Empirical data is therefore required to
determine accurate analytic and stochastic models of mmWave wireless channels.

Utilization of a robotic arm to emulate UAV motion can 1) help overcome these
challenges, 2) efficiently emulate the motion of UAV in different
environments/scenarios, and 3) enable rapid collection of channel measurements
by using channel sounding method to create a database for UAV-assisted mmWave
channel models. In this work, a novel way to incorporate UAV motion in
studying UAV assisted mmWave communication is conducted by emulating the UAV
motion by a robotic arm in an anechoic chamber. This method, as compared to
other studies which mostly depend on the software simulation, captures the
real UAV dynamics in the UAV motion111Rotor motion is not considered in this
scenario, which can be a part of future work.. This study, therefore, is an
important first step in realizing a real mmWave communication system for UAVs
in the near future. Designing a channel emulator by using vector network
analyzer (VNA) based channel sounder with real UAV motion emulated by a
robotic arm to develop a first-of-its-kind, experimental, wireless channel
emulator for UAV-assisted mmWave communications can produce accurate and
realistic propagation channel models for a wide range of environments and
scenarios. Using the robotic arm to produce atmospheric turbulence effects on
UAV position and stability, we can produce the first empirical mmWave channel
models that account for path loss/shadowing, Doppler spread due to UAV motion.

Before moving on to the measurement set up in the next section, it is very
important to understand the different challenges associated with the mmWave
communication itself. mmWave communication suffers extensively from the
propagation attenuation, shadowing effect (blocking), beam misalignment, and
Doppler shift[17, 20, 21, 22] because of small wavelength in the order of
millimeter. Doppler spread effect is the most critical one, when there is a
motion attributed to the movement of transmitter (Tx) or receiver (Rx) or
both. In addition to that, with the wind gusts in the atmosphere for UAVs,
Doppler effects are more aggravated. It is also well known that in a given
mobile and multipath environment, each multipath component (MPC) will
experience a different Doppler shift according to the motion. This leads to
the spectral broadening at the receiver that causes erroneous signal reception
or communication failure. Therefore, modeling physical UAV motion as close to
a real life UAV motion is very crucial in understanding the design
constraints, and performance of a mmWave based UAV communication system.
Techniques to analyze and combat the Doppler effects have been studied earlier
but as mentioned previously, almost all of them are based on simulations that
ignore the actual UAV motion dynamics and the wind gust conditions in the
atmosphere[15, 7, 13]. Therefore, in this paper, the focus is to analyze and
study the Doppler and channel power characteristics by emulating the real UAV
motion under wind gusts. This close to actual UAV motion is emulated by using
a robotic arm in an anechoic chamber environment.

This study will: 1) empirically characterize the time-variant radio
propagation channel of a UAV-assisted communication in mmWave range, 2)
underpin novel control and aerospace designs for next-generation UAVs and UAV-
assisted communications, and 3) provide the stepping stone for future channel
emulators of high-complexity to analyze next-generation communication systems.
In summary, the main contributions of this paper are as follows,

  * •

Doppler spread analysis of mmWave communication system by emulating UAV motion
under the Dryden wind conditions in an anechoic chamber.

  * •

De-embedding of phase variations caused by the cable movement from collected
data in this VNA based measurement.

  * •

Determination of path loss exponent value under anechoic chamber settings222It
is important to note that these results cannot be generalized as such for any
indoor or outdoor environments, and will require extensive data measurement
campaigns in that regards..

This paper is organized as follows, Section II discusses the measurement
setup. In Section III, details of the UAV motion emulation is discussed.
Analysis of Doppler spread and corresponding signal processing are presented
in Section IV. Finally, conclusions are drawn in Section V.

##  II Measurement Setup

The successful deployment of wireless communication systems requires a solid
understanding and accurate modeling of wireless channel conditions
(propagation characteristics) between the transmitter (Tx) and receiver (Rx).
Channel sounding is a measurement technique used to gain that understanding.

Figure 1: Top view of the measurement setup. The receiver is placed on the
robotic arm and connected to VNA by a phase stable short cable, while the
transmitter is hooked on the tripod with a long cable.

The channel sounding measurement method used in this study is based on
continuous wave (CW) mode of VNA [23, 24]. The Rx is hooked up on the robotic
arm, while the Tx is placed on a tripod. The Tx is positioned at different
distances from the Rx (3.5 ft to 23.5 ft) depending on measurements plan. The
Tx is connected at port-1 of the VNA, while the Rx is connected at port-2. At
each distance point (11 points in total, with 2 feet increments between the Tx
and Rx), three samples of S21 parameters are recorded on the VNA. These
multiple samples of S21 parameters are recorded to get a better redundant
value in the Doppler spectrum calculations, and in channel path loss modeling.
The measurement setup is shown in the Fig. 1 with the details of all the
measurement equipment in Table I.

Table I: The measurement equipment with the specifications. Equipment | Specifications
---|---
| Vector Network
---
Analyzer
| Keysight PNA-X (N5247A),
---
10 MHz to 67 GHz
Antenna (horn type) |  | Cernexwave (CRA28264015),
---
26.5 GHz-40 GHz
Gain: 15 dBi, HPBW:18∘
Waveguide transition |  | Cernexwave (CWK28264003F), WR-28,
---
Brass/Copper
Cables |  | Fairview microwave (50 feet),
---
Mini-Circuits (5 feet)
Robotic arm |  | Rethink Robotics (Sawyer), software: Intera,
---
1 arm x 7 degree of freedom

The VNA is operated at a frequency of 28 GHz with the intermediate frequency
(IF) bandwidth set at 300 Hz. This IF frequency is selected carefully in such
a way that the expected Doppler frequency can be covered within the selected
IF range. In addition, a total of 4096 points were selected in this CW
(carrier wave) mode. It is worth to mention that increasing the IF bandwidth
will definitely decrease the time required to capture the data at each
distance for a given run, however, the scattering parameter data will suffer
from higher noise floor as the noise floor level is linearly proportional to
the IF bandwidth. Therefore, taking multiple readings with moderate IF
bandwidth was a main factor in this measurement scenario. With this selected
4096 sample points, the sampling time is, $Ts=4.4$ ms. Thus, the Doppler range
that could be captured with these settings will be in the range of
$-fs/2=-114.49$ Hz to $+fs/2=+114.49$ Hz. Fig. 2 shows the equipment, and the
actual measurement setup in an anechoic chamber. The Tx is at a height of 4
feet 4 inches on a tripod, while the Rx is initially at the height of 4 feet 6
inches (at the beginning point) on the robotic arm. The robotic arm is
connected to a computer that executes a Python script to emulate the UAV
motion with the wind turbulence model. The corresponding scattering parameter
data generated under such motion is captured on the VNA, and analyzed on a
workstation later on. In the next section, we will dwell more into the details
on the UAV motion emulation part with the robotic arm.

(a) Equipment description.

(b) Actual setup in an anechoic chamber.

Figure 2: Actual measurement setup with the transmitter on the tripod, and
receiver hooked up at the robotic arm in an anechoic chamber.

##  III UAV Motion Emulation

To emulate a real UAV motion under wind turbulence is not only a very
challenging but also an interesting problem. This problem can be solved by
using methods from robotics area, where the real UAV motion with the wind
turbulence can be easily emulated by a robotic arm. The motion of this robotic
arm is controlled by robotic operating system (ROS) from a computer. To create
the turbulence experienced by UAVs in atmosphere, a wind generation model is
used.

The UAV motion is first simulated in MATLAB®using a stochastic wind gust model
(Dryden wind model) and a 6 degree-of-freedom (DOF) quadcopter dynamic model
together with closed-loop controllers are used for hovering motion models.
Then, the positions and altitude of the quadcopter generated from the
simulations are emulated by the end-effector (end point) of the robotic arm.
The simulation framework and the arm control is briefly discussed in the
following subsections.

###  III-A Simulation of Quadcopter Motion with Wind

We model the wind as a combination of a 3D mean wind
$(\bar{u},\bar{v},\bar{w})^{\top}$ and a 3D turbulence wind $(u,v,w)^{\top}$.
The mean wind is specified in the north-east-down (NED) coordinates, while the
turbulence wind is specified in another different frame (discussed later). In
particular, the Dryden turbulence model [25, 26] is used to generate
turbulence. This popular Dryden model has been extensively used for practical
aviation applications (see e.g., [27] for its application in small fixed-wing
UAV). It is based on a stochastic formulation that incorporates knowledge of
the energy spectrum of turbulence [28] and assumes a homogeneous frozen
spatial turbulence. The Dryden turbulence model is implemented through
filtering operations on white noise signals.

Let the 3D turbulence velocity be $(u,v,w)^{\top}\in\mathbb{R}^{3}$. The $u$
component is aligned with the direction of the horizontal mean wind, i.e.,
$(\bar{u},\bar{v},0)$, the $w$ component is aligned with the vertical (down)
direction, and the $v$ component is aligned with the direction that completes
a right-handed coordinate frame with the $v$ and $w$ directions. As shown in
Fig. 3, the 3D velocities $u$, $v$, and $w$ in time domain are obtained by
passing three independent white noise signals through three filters described
by the following transfer functions [27, Section 4.4]

$\begin{split}H_{u}(s)&=\sigma_{u}\sqrt{\frac{2V_{a0}}{L_{u}}}\frac{1}{(s+\frac{V_{a0}}{L_{u}})},\end{split}$
(1)
$\begin{split}H_{v}(s)&=\sigma_{v}\sqrt{\frac{3V_{a0}}{L_{v}}}\frac{(s+\frac{V_{a0}}{\sqrt{3L_{v}}})}{(s+\frac{V_{a0}}{L_{v}})^{2}},\end{split}$
(2)
$\begin{split}H_{w}(s)&=\sigma_{w}\sqrt{\frac{3V_{a0}}{L_{w}}}\frac{(s+\frac{V_{a0}}{\sqrt{3L_{w}}})}{(s+\frac{V_{a0}}{L_{w}})^{2}},\end{split}$
(3)

respectively, where $(\sigma^{2}_{u},\sigma^{2}_{v},\sigma^{2}_{w})$ are the
variances of the turbulence, $V_{a0}$ is an estimate of the quadrotor’s
airspeed, and $(L_{u},L_{v},L_{w})$ are the turbulence length scales. In our
experiments, we focus on horizontal, low turbulence effects and set
$\sigma^{2}_{u}=0.53$, $\sigma^{2}_{v}=0.53$, and $\sigma^{2}_{w}=0$. For low
altitude, $L_{w}$ is set to the altitude in feet.

In our experiments, we set $(L_{u},L_{v},L_{w})$ to $(200,200,50)$ ft. Since
the quadcopter is controlled in the hover mode, we set $V_{a0}$ to be the mean
wind speed, i.e., $\sqrt{\bar{u}^{2}+\bar{v}^{2}+\bar{w}^{2}}$, where
$\bar{u}=2$ m/s, $\bar{v}=-1$ m/s, and $\bar{w}=0$ m/s. The output of the
three filters is a time-series representation of the turbulence, which is
further combined with the non-zero mean wind
$(\bar{u},\bar{v},\bar{w})^{\top}\in\mathbb{R}^{3}$. The resulting 3D wind in
the NED frame is given by

$V_{w}(t)=(\bar{u},\bar{v},\bar{w})^{\top}+\mathcal{R}(u(t),v(t),w(t))^{\top},$
(4)

where $\mathcal{R}\in\mathbb{R}^{3\times 3}$ is a 3D rotational matrix that
converts $(u(t),v(t),w(t))^{\top}$ to the NED frame. The process of generating
the Dryden wind is shown in Fig. 3 below.

Figure 3: The Dryden wind is generated by combining the mean wind
$(\bar{u},\bar{v},\bar{w})^{\top}$ and the turbulence wind $(u,v,w)^{\top}$.
$*h_{\star}(t)$ denotes the convolution with the impulse response of
$H_{\star}(s)$ in (1)–(3), where $\star=u,v,w$.

We use a standard formulation of the quadcopter dynamics [29], with the
addition of a nonlinear drag term $f_{d}\in\mathbb{R}^{3}$ to model the wind
effect. The dynamics of the quadcopter is given by,

$\displaystyle\begin{bmatrix}\ddot{p}_{n}\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\ddot{p}_{e}\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\ddot{p}_{d}\\\ \vskip
3.0pt plus 1.0pt minus 1.0pt\dot{\phi}\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\dot{\theta}\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\dot{\psi}\\\ \vskip
3.0pt plus 1.0pt minus 1.0pt\dot{\omega}_{p}\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\dot{\omega}_{q}\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\dot{\omega}_{r}\\\
\end{bmatrix}=\begin{bmatrix}(-\cos\phi\sin\theta\cos\psi-\sin\phi\sin\psi)\frac{F}{m}+\frac{f_{d,n}}{m}\\\
\vskip 3.0pt plus 1.0pt minus
1.0pt(-\cos\phi\sin\theta\sin\psi+\sin\phi\cos\psi)\frac{F}{m}+\frac{f_{d,e}}{m}\\\
\vskip 3.0pt plus 1.0pt minus
1.0ptg-(\cos\phi\cos\theta)\frac{F}{m}+\frac{f_{d,d}}{m}\\\ \vskip 3.0pt plus
1.0pt minus
1.0pt\omega_{p}+\sin\phi\tan\theta\,\omega_{q}+\cos\phi\tan\theta\,\omega_{r}\\\
\vskip 3.0pt plus 1.0pt minus
1.0pt\cos\phi\,\omega_{q}-\sin\phi\,\omega_{r}\\\ \vskip 3.0pt plus 1.0pt
minus 1.0pt\frac{\sin\phi}{\cos\theta}\leavevmode\nobreak\
\omega_{q}+\frac{\cos\phi}{\cos\theta}\leavevmode\nobreak\ \omega_{r}\\\
\vskip 3.0pt plus 1.0pt minus
1.0pt\frac{J_{y}-J_{z}}{J_{x}}\omega_{q}\omega_{r}+\frac{1}{J_{x}}\tau_{\phi}\\\
\vskip 3.0pt plus 1.0pt minus
1.0pt\frac{J_{z}-J_{x}}{J_{y}}\omega_{p}\omega_{r}\dot{\psi}+\frac{1}{J_{y}}\tau_{\theta}\\\
\vskip 3.0pt plus 1.0pt minus
1.0pt\frac{J_{x}-J_{y}}{J_{z}}\omega_{p}\omega_{q}+\frac{1}{J_{z}}\tau_{\psi}\\\
\end{bmatrix},$ (5)

where $m$ and $(J_{x},J_{y},J_{z})$ are the mass and the moment of inertia of
the quadcopter, respectively, $(p_{n},p_{e},p_{d})$ are the north, east, and
down positions in the inertial frame, $(\phi,\theta,\psi)$ are the roll,
pitch, and yaw angles, respectively, $(\omega_{p},\omega_{q},\omega_{r})$ is
the angular velocity in the body frame,
$(F,\tau_{\phi},\tau_{\theta},\tau_{\psi})$ are the force and the moments in
the designated directions, and $f_{d}=(f_{d,n},f_{d,e},f_{d,d})^{T}$ is the
drag force in the north, east and down directions. The pitch, roll, and yaw
axis are also shown in Fig. 4. The drag force $f_{d}$ is modeled in a
quadratic form as $f_{d}=C_{d}(V_{w}-\dot{p})|V_{w}-\dot{p}|$, where $\dot{p}$
is the ground velocity of the quadcopter equal to
$(\dot{p}_{n},\dot{p}_{e},\dot{p}_{d})$ and $C_{d}$ is a drag coefficient
matrix.

Figure 4: Pitch, roll and yaw axis of a UAV.

In the quadcopter dynamics, we have also included motor dynamics and several
secondary aerodynamic effects, such as blade flapping and air-relative
velocity effects. Closed-loop PID (Proportional-Integral-Derivative)
Controllers are designed to achieve tracking of a given waypoint. We refer
interested readers to [30, 31] for details on the quadcopter dynamics and the
controller design.

###  III-B Emulation of Quadcopter Motion using the Sawyer Robotic Arm

The MATLAB simulator generates NED positions, and the yaw, pitch, roll (YPR)
orientations, as well as their time derivatives, at a rate of 10 Hz. These
state variables are formatted and dumped to a raw text file. A Python program
reads these NED and YPR coordinates and uses them to generate a series of
time-dependent waypoints for the Sawyer robotic arm. The Intera software
development kit (SDK) is used as an interface between the desired waypoints
and the ROS messages needed to command the Sawyer robotic arm. For this
application, the Intera Motion Controller Interface is implemented in a joint
control mode. This mode generates trajectories based on a series of joint
commands. The native inverse kinematics solver is used to convert waypoints
from the end-effector frame to a given set of joint positions.

###  III-C Emulation of Linear Motion using the Sawyer Robotic Arm

The MATLAB software is used to generate the waypoints from the Dryden motion
generation profile. In order to precisely control the velocity, the Joint
Velocity Control mode was implemented in the Intera SDK. This contol mode
accepts velocity commands in the joint frames, not the end-effector frame, and
as such the Jacobian matrix $J(\theta_{1},\theta_{2},...,\theta_{7})$ is
needed to translate commanded velocities between frames. Specifically, the
psuedo-inverse Jacobian matrix is needed to convert velocities from the end-
effector frame to the joint frames as follows,

$\displaystyle
J(\theta_{1},\theta_{2},...,\theta_{7})=\begin{bmatrix}\frac{\partial
x}{\partial\theta_{1}}&\frac{\partial
x}{\partial\theta_{2}}&...&\frac{\partial x}{\partial\theta_{7}}\\\ \vskip
3.0pt plus 1.0pt minus 1.0pt\frac{\partial
y}{\partial\theta_{1}}&\frac{\partial
y}{\partial\theta_{2}}&...&\frac{\partial y}{\partial\theta_{7}}\\\ \vskip
3.0pt plus 1.0pt minus 1.0pt\frac{\partial
z}{\partial\theta_{1}}&\frac{\partial
z}{\partial\theta_{2}}&...&\frac{\partial z}{\partial\theta_{7}}\\\ \vskip
3.0pt plus 1.0pt minus
1.0pt\frac{\partial\phi}{\partial\theta_{1}}&\frac{\partial\phi}{\partial\theta_{2}}&...&\frac{\partial\phi}{\partial\theta_{7}}\\\
\vskip 3.0pt plus 1.0pt minus
1.0pt\frac{\partial\theta}{\partial\theta_{1}}&\frac{\partial\theta}{\partial\theta_{2}}&...&\frac{\partial\theta}{\partial\theta_{7}}\\\
\vskip 3.0pt plus 1.0pt minus
1.0pt\frac{\partial\psi}{\partial\theta_{1}}&\frac{\partial\psi}{\partial\theta_{2}}&...&\frac{\partial\psi}{\partial\theta_{7}}\end{bmatrix},$
(6)

$\displaystyle Q=J^{-1}V,$ (7)

where $J^{-1}$ is a $7\times 6$ matrix representing the psuedo-inverse of the
Jacobian, $V$ is a $6\times 1$ matrix representing the linear and angular
velocities of the end-effector, and $Q$ is a $7\times 1$ matrix representing
the joint velocities.

Figure 5: Arm motion dynamics.

This method provides precise control of the arm’s velocity at speeds under 0.5
m/s. However, drift was introduced in the x-axis as the arm reached higher
speeds and the end-effector reached its outer boundaries. As such, a P
(proportional) controller was used to minimize the drift along the x-axis.
This whole UAV motion emulation dynamics333Note that this motion doesn’t
include the propeller motion which causes amplitude modulation in the received
signal. is summarized in Fig. 5. An actual snapshot of the UAV motion can also
be visualized in this GitHub repository444https://github.com/amitkac/uavSim.
Once the robotic arm is emulating the real UAV motion under turbulence, the
next step is to measure scattering parameters from the VNA.

###  III-D De-embedding the Phase Changes Caused by Cable Movement

One important point to consider is that because of this robotic arm motion,
the cable connected to VNA and antenna on the arm will also move, and this
will result in phase changes at the received signal. To take care of such
scenario, it is therefore very critical to utilize a phase stable cable, and
also the cable effects need to be taken out from the final measured data. The
de-embedding [32, 33] of phase can be performed by first determining two-port
S-parameters of the cable from the measurements with short, open, and load
standards while doing the same motion. The process is similar to “Adapter
Characterization” function within Keysight VNAs [33], which involves Short-
Open-Load calibrations at two different reference planes. The only difference
is that this process is performed over time-swept data rather than frequency-
swept data.

Figure 6: Magnitude variations of S21 data collected in the repeatablity test.
Figure 7: Phase variations of the S21 data collected in the repeatablity test.

A repeatability test (5 times with same motion) was also performed to check
the variance in the S-parameters. In our case, it was found that the phase
variation (min-max) after de-embedding ranged from -4 degree to +0.6 degree,
while the magnitude variation (min-max) ranged from -0.033 dB to -0.007 dB for
the phase stable cable in an anechoic chamber. Fig. 6 and Fig. 7 show these
variations in our scenario. Later on, offset calibration was also done by
removing S21 of the cable from the measured data.

In the next section, the signal processing of this processed data, and the
corresponding analysis to determine the Doppler spread and path loss modeling
will be presented in detail.

##  IV Analysis of Doppler Spread and Path Loss Modeling

In this section, first the data processing of the pre-processed (de-embedded
and offset-calibration) VNA data (S-parameters), and its correlation with the
motion profile extracted from the ROS logs will be analyzed, and then the
analysis of Doppler spread and path loss will be discussed in detail. Let the
transmitted signal, $x(t)=\Re\\{b(t)e^{j2\pi f_{c}t}\\}$, where
$b(t)=x_{I}(t)+jx_{Q}(t)$ is a complex baseband signal with in-phase and
quadrature components as $x_{I}(t)$ and $x_{Q}(t)$, and $f_{c}$ is the carrier
frequency. The signal $b(t)$ is also known as the complex signal envelope or
an equivalent low pass signal of $x(t)$. Ignoring the noise in the system, the
corresponding received signal with the line of sight (LOS), and all resolvable
multipath is given as [34],

$\begin{split}y(t)&=\Re\bigg{\\{}{\sum}_{n=0}^{N(t)}\alpha_{n}(t)b(t-\tau_{n}(t))e^{j2\pi[f_{c}(t-\tau_{n}(t))+\phi_{d_{n}}+\phi_{0}]}\bigg{\\}},\end{split}$
(8)

$\begin{split}y(t)&=\Re\bigg{\\{}\bigg{[}{\sum}_{n=0}^{N(t)}\alpha_{n}(t)b(t-\tau_{n}(t))e^{-j(2\pi
f_{c}\tau_{n}(t)+\phi_{d_{n}}+\phi_{0})}\bigg{]}\\\ &\leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \times e^{j2\pi f_{c}(t)}\bigg{\\}}.\\\ \end{split}$ (9)

which can be further written as,

$\begin{split}y(t)&=\Re\bigg{\\{}\bigg{[}\int_{-\infty}^{+\infty}h(t,\tau)b(t-\tau)d\tau\bigg{]}e^{j2\pi
f_{c}(t)}\bigg{\\}},\end{split}$ (10)

where $h(t,\tau)$ is the channel impulse response,

$\begin{split}h(t,\tau)&={\sum}_{n=0}^{N(t)}\alpha_{n}(t)e^{-j(2\pi
f_{c}\tau_{n}(t)+\phi_{d_{n}}+\phi_{0})}\delta(\tau-\tau_{n}),\end{split}$
(11)

where $\alpha_{n}(t)$ is a function of path loss and shadowing, $N(t)$ is the
$N$-th resolvable multipath, $\tau_{n}$ is the $N$-th path delay, $\phi_{0}$
is the phase offset, and $\phi_{d_{n}}$ is the Doppler phase shift of this
$N$-th path. Now, when the Tx or Rx is moving, the change in the distance over
a short time interval $\Delta t$ will cause the phase to change as
$\phi_{d_{n}}\approx 2\pi(v/\lambda)\Delta t\cos\theta$, where $\theta$ is the
arrival angle of the received signal relative to the direction of motion, and
$v$ is the velocity of receiver towards transmitter in the direction of
motion. Therefore, the corresponding Doppler frequency will be then given as,

$\begin{split}f_{D}&=\frac{1}{2\pi}\frac{\phi_{d_{n}}}{\Delta
t}=\frac{v}{\lambda}\cos{\theta},\end{split}$ (12)

where $\lambda$ is the wavelength of the signal. The data collected at VNA
during the measurement campaign are the S-parameters, also known as scattering
parameters, over time (CW mode).

Since the Tx is connected at port-1 and Rx at port-2, therefore, the S21
parameter will represent the channel transfer function (channel power). These
S-parameters depend on time, distance and frequency. Thus, S21 parameter as a
channel transfer function of time, distance, and frequency can be written
as[18, 35],

$\begin{split}\text{S21}_{dB}(t,f,d)&=20\log_{10}(|H(t,f,d)|)\end{split}$ (13)

As the VNA is set in CW time mode with frequency kept fixed at 28 GHz, the
only variable in (13) would be the discrete time points at a given distance.
Therefore, at a given distance $d$, (13) can be rewritten as,

$\begin{split}\text{S21}_{dB}(t,f,d)&=\text{S21}_{dB}(t)\\\ \end{split}$ (14)

Figure 8: Measurement data with noise floor at 3.5 feet over time. Figure 9:
One sided autocorrelation of S21 data at 3.5 feet over delay.

These discrete points of S21 parameter can be written in a complex vector form
as, $x[n]=\text{S21}_{dB}(t)\delta(t-t_{i})$, where $t_{i}$ is the discrete
time point, $\delta(\cdot)$ is the delta function, and the index $i$ goes from
0 to 4095. Because, the S21 parameters are complex numbers, therefore, the
frequency response after taking the fast Fourier transform (FFT) would also be
complex in nature. Therefore,

$\begin{split}X[k]=\frac{1}{N}{\sum}_{n=0}^{N-1}x[n]e^{-j2\pi
kn/N},\end{split}$ (15)

where $k$ is the point in the frequency domain, $n$ is the point in time
domain, and $x[n]$ is the discrete time domain input (vector of all 4096
points). Fig . 8 shows a sample S21 data with noise floor collected at 3.5
feet.

Moreover, the UAV motion in general, and the current emulated motion of the
UAV by the robotic arm is very dynamic in nature. The motion not only
considers the modelled wind gust (Dryden wind model) in the atmosphere but
also considers the UAV structure. For a process to be assumed wide sense
stationary with uncorrelated scattering (WSSUS)[36, 37, 38, 39], the mean
should be constant over time, and the autocorrelation function should be
independent of the time. On closer inspection of the measured data (Fig . 8
and Fig. 9), it was observed that this condition can be assumed true in
anechoic chamber settings555In real scenario of outdoor or indoor environment,
the WSSUS conditions may not be true..

###  IV-A Doppler Spread

As mentioned, in our set up, 4096 points were set in CW time mode, this number
was chosen so that the Discrete Fourier transform (DFT) can be efficiently
calculated by using the FFT algorithm as the data points will be in the form
of $2^{n}$. As $N$=4096, (15) can be rewritten as follows,

$\begin{split}X[k]=\frac{1}{4096}{\sum}_{n=0}^{4095}x[n]e^{-j2\pi
kn/4096},\end{split}$ (16)

where $k=0,1,\dots 4095$. Doppler spectrum after taking the FFT of S21
parameters at a distance of 5.5 feet is shown in Fig. 10.

Figure 10: Doppler spectrum at 5.5 feet. Figure 11: Controlled linear change
of the arm speed in an anechoic chamber.

To demonstrate the accuracy of the collected data for the Doppler analysis, we
reprogrammed the robotic arm to do a controlled motion (to and from) with a
pre-defined linear speed in an anechoic chamber. The robotic operating system,
also known as ROS, captures various fields of the end point (velocity and
displacements) of the arm in the system logs in .bag format. These files are
later converted to .csv format to process with the MATLAB software.

Figure 12: Velocity distribution over time. Figure 13: Theoretical Doppler
with Measured Doppler at 5.5 feet.

On close analysis, it can be observed that the velocity of this control system
will go from 0 m/s to 0.58-0.63 m/s and will stay at this peak there for some
time in one direction and the same while going back (0 m/s to -0.58 to -0.61
m/s). The corresponding probability density function (pdf) of velocity change
over time (Fig. 11) is shown in Fig. 12. Intuitively, since velocity is
proportional to the ideal Doppler observed, the frequency corresponding to the
peaks in the velocity pdf will also be seen in the Doppler spectrum. For
example, speed at the peak of 0.59 m/s to 0.64 m/s will correspond to a
theoretical Doppler of 55.1 Hz to 59.7 Hz, while the speed of -0.58 m/s to
-0.64 m/s will correspond to Doppler of -54.17 Hz and -59.7 Hz, which can be
seen in the Doppler spectrum666The theoretical Doppler power is offseted by 4
dB to fit the measured Doppler spectrum plot. as shown in Fig. 13.

Figure 14: Doppler spread at 11.5 feet in the Anechoic chamber environment. Table II: Maximum Doppler spread with distance in Anechoic chamber. Noise floor | Distance [feet] | -ve freq. [Hz] | +ve freq.[Hz]
---|---|---|---
-60 dB | 3.5 | -25.3844 | 24.9763
5.5 | -20.5687 | 20.3328
7.5 | -18.5282 | 21.14
9.5 | -26.0374 | 19.9157
11.5 | -16.4876 | 22.446
13.5 | -20.3238 | 20.6503
15.5 | -20.079 | 20.5687
17.7 | -18.5282 | 19.5076
19.5 | -16.0795 | 17.5487
21.5 | -17.4671 | 20.6503
23.5 | -20.6503 | 20.4871
Average Doppler [Hz] | -19.4750 | 20.3204

The resulting maximum positive Doppler spread (motion towards the receiver)
and negative Doppler spread (motion away from the receiver) at each distance
in an Anechoic chamber is shown in Table II with respect to the noise floor of
-60 dB. The average Doppler spread in the Anechoic chamber was found to be
around +20 Hz to -20 Hz. Fig. 14 shows an example of the Doppler spectrum at
11.5 feet. These Doppler spread parameters are paramount in designing the
symbol duration in a wireless communication system. Specifically, the
coherence time depends on this Doppler spread, and if not properly designed
for it, will result in frequency selective fading.

###  IV-B Path Loss Modelling

The next part is to statistically model the path loss characteristics of the
wireless channel777Note that in this work, the effect of variation of
elevation, and elevation angle on the Doppler is not considered.. As mentioned
in earlier section, at each distance point, 3 samples of scattering data were
recorded. An example of such 3 samples of 4096 data points appended with each
other is shown in Fig. 15. The first initial points (highlighted in Fig. 15)
in these S21 power samples represent no-motion or idle motion of UAV.

Figure 15: No motion portion in the appended data at 3.5 feet.

These points can be filtered from the appended samples for each distance, and
therefore, can be utilized to determine the distance dependent path loss
exponent value in an anechoic environment.

The path gain as a function of distance can be modelled as[34, 18],

$\begin{split}\text{PG}_{dB}(d)&=\text{PG}_{dB}(d_{0})-10n\log_{10}\bigg{(}\frac{d}{d_{0}}\bigg{)}+X_{\sigma}(d),\end{split}$
(17)

where $\text{PG}_{dB}(d_{0})$ is the path gain at a reference distance
$d_{0}$, which is 1 meter in our scenario. $d$ is the distance between
transmitter and receiver, $n$ is the distance dependent path loss exponent,
and $X_{\sigma}(d)$ is the Gaussian distributed shadowing factor with zero
mean in dB, and a variance of $\sigma^{2}$ in dB.

Figure 16: Linear fitting to determine distance dependent path loss.

The path gain as a function of distance is plotted in Fig. 16. A linear
fitting model is used to find the slope of the plot which is nothing but the
path loss factor $n$. The path loss factor in our anechoic scenario888The path
loss factor derived in this work is specific to the measured data in this work
and will require extensive set of measurements to be generalized for any
environment as such. using this linear fitting model was found to be 1.843.
Similar close values have been reported in different indoor environments[40,
41, 42]. This path loss modeling shows the applicability of such novel
platform for mmWave channel characterizations.

##  V Conclusion

In this work, a novel mmWave channel emulation method to analyse the Doppler
spread, and path loss modeling are presented and discussed in detail. The UAV
motion was emulated by a robotic arm considering the effect of wind gusts,
which was modelled by the famous Dryden wind model. Doppler spread in both
positive and negative frequency axis were determined at the noise floor of -60
dB in an anechoic chamber. A total of 11 distance points were considered, and
in average, the Doppler spread was found to be around +20 and -20 Hz. No-
motion data points were then selected to determine the path loss exponent for
this anechoic chamber environment, which in our scenario came out to be 1.843.
These results and the application of such novel platform to study next
generation wireless communication systems will definitely help propel the
development, and design of such UAV assisted communication systems in the near
future. As a future work, multi-beam phase array antenna will be considered
for 3D scattering channel models with this type of emulation setup. Also,
depolarization effect because of wind, attenuation and scattering over time is
in the future scope of this work.

## Acknowledgment

The authors would like to thank Dr. Charles Bunting and Dr. Mehdi Bahadorzadeh
for their great support in conducting measurements in the anechoic chamber.
Also, the authors would like to thank Mohammed Musaqlab, Paul Hodgden, and
Scott Walker for their kind and generous help during the measurement campaign.
This work was supported in part by the Qatar National Research Fund under
Grant NPRP13S-0130-200200 (a member of The Qatar Foundation), and in part by
the National Science Foundation (NSF), USA under award number 1925147.

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|  Amit Kachroo (S’14) received his B.Tech degree in Electronics and
Communications Engineering from NIT, Srinagar, India (2005-2009), and M.Sc
degree from Istanbul Sehir University, Istanbul, Turkey (2015-2017)
respectively. From 2010 to 2014, he worked as a project engineer with Nokia
Networks, India on GSM, WCDMA, LTE, and RF technologies. In 2017, he joined
Oklahoma State University, Stillwater, USA to pursue his Ph.D. degree in
Electrical and Computer Engineering. In summer of 2020, he worked as an
Applied Scientist Intern at Wireless Technology Group of Amazon Lab126,
California, USA in the domain of IoT localization with AI/ML technology. Prior
to that, in summer of 2019, he worked as a software intern at Tensilica R&D
group of Cadence Design Systems, California, USA in mmWave radar technology.
His research interest are in statistical modeling of wireless channels, mmWave
channel modeling, statistical learning, machine learning, and cognitive
radios. He also serves as a reviewer in IEEE Communications Magazine, IEEE
Transactions on Wireless Communications, IEEE JSAC, IEEE Access, and IEEE VTC
Conference among others.
---|---
|  Collin A. Thornton is a Honors College junior in the Department of
Electrical and Computer Engineering at Oklahoma State University. He joined
OSU as both a CEAT Scholar and a Freshman Research Scholar, and he is pursuing
dual degrees in Electrical and Computer Engineering. He was selected as an
Institutional Nominee for the Goldwater Scholarship during his sophomore year.
During his first semester at OSU, he began work in the Control, Robotics, and
Automation lab in the Department of Mechanical and Aerospace Engineering. His
work focuses on the development and application of path planning algorithms in
unmanned aerial vehicles.
---|---
|  Md Arifur Sarker received the B. Sc degree in Electrical & Electronic
Engineering from Rajshahi University of Engineering & Technology, Rajshahi,
Bangladesh in 2017. He is currently working toward the Ph. D. degree in
Electrical and Computer Engineering at Oklahoma State University, Stillwater,
OK, USA. He is currently with Systems on New Integrated Circuits (SONIC)
group. His current research interests include radiation effects in RF
circuits, phase array antenna and radar system and wideband circuit design for
future communication system.
---|---
|  Wooyeol Choi (M’11-SM’19) received the B. S. degree in Electronic
Engineering from Yonsei University, Seoul, Korea, the M. S. and the Ph. D.
degrees in Electrical Engineering from Seoul National University, Seoul,
Korea. From 2011 to 2018, he was with the Texas Analog Center of Excellence
(TxACE) at the University of Texas at Dallas, Richardson, Texas, USA, first as
a Research Associate later as an Assistant Research Professor. From 2018, he
has been an Assistant Professor in the School of Electrical and Computer
Engineering at Oklahoma State University, Stillwater, Oklahoma, USA. His
research is focused on design and characterization of integrated circuits and
systems for various applications from RF to terahertz frequency range.
---|---
|  He Bai (M’15) received his B.Eng. degree from the Department of Automation
at the University of Science and Technology of China, Hefei, China, in 2005,
and the M.S. and Ph.D. degrees in Electrical Engineering from Rensselaer
Polytechnic Institute in 2007 and 2009, respectively. From 2009 to 2010, he
was a Post-doctoral Researcher at the Northwestern University, Evanston, IL.
From 2010 to 2015, he was a Senior Research and Development Scientist at
Utopia Compression Corporation. He was the Principal Investigator for a number
of research projects on sense-and-avoid, cooperative target tracking, and
target hand off in GPS-denied environments. In 2015, he joined the Mechanical
and Aerospace Engineering Department at Oklahoma State University as an
assistant professor. He has published over 70 peer-reviewed journal and
conference papers related to control and robotics and a research monograph
“Cooperative control design: a systematic passivity-based approach” in
Springer. He holds one patent on monocular passive ranging. His research
interests include multi-agent systems, nonlinear estimation and sensor fusion,
path planning, intelligent control, and GPS-denied navigation.
---|---
|  Ickhyun Song (S’07-M’11)  received his B.S. and M.S. degrees in electrical
engineering from Seoul National University, Seoul, Republic of Korea, in 2006
and 2008, respectively, and his Ph.D. degree in electrical and computer
engineering from Georgia Institute of Technology, Atlanta, GA in 2016. From
2008 to 2012, he was Design Engineer at Samsung Electronics, Hwasung, Republic
of Korea, where he contributed to the development of next-generation memory
products. From 2017 to 2018, he was Research Engineer at Georgia Institute of
Technology. In 2018, he joined the faculty at Oklahoma State University, and
is currently Assistant Professor in the School of Electrical and Computer
Engineering. His research interest includes extreme-environment electronics,
radiation effects, RF/millimeter-wave devices and circuits, and CMOS/SiGe HBT
device physics. Dr. Song was a recipient of the 2007-2008 Samsung
Semiconductor Scholarship, the Silver Paper Award at the 2007 IEEE Seoul
Section Student Paper Contest, the Gold Prize at the 2008 Samsung HumanTech
Paper Award, the 2012-2013 Fulbright Graduate Study Award, and the 2016 GEDC
(Georgia Electronic Design Center) Best Poster Award.
---|---
|  John F. O’Hara (SM’19) received his BSEE degree from the University of
Michigan in 1998 and his Ph.D. (electrical engineering) from Oklahoma State
University in 2003. He was a Director of Central Intelligence Postdoctoral
Fellow at Los Alamos National Laboratory (LANL) until 2006. From 2006-2011 he
was with the Center for Integrated Nanotechnologies (LANL) and worked on
numerous metamaterial projects involving dynamic control over chirality,
resonance frequency, polarization, and modulation of terahertz waves. In 2011,
he founded a consulting/research company, Wavetech, LLC. In 2017, he joined
Oklahoma State University as an Assistant Professor, where he now studies
metamaterials, terahertz communications, photonic sensing methods, and
Internet of Things applications. He has around 100 publications in journals
and conference proceedings.
---|---
|  Sabit Ekin (M’12) received the B.Sc. degree in electrical and electronics
engineering from Eskişehir Osmangazi University, Turkey, in 2006, the M.Sc.
degree in electrical engineering from New Mexico Tech, Socorro, NM, USA, in
2008, and the Ph.D. degree in electrical and computer engineering from Texas
A&M University, College Station, TX, USA, in 2012. He was a Visiting Research
Assistant with the Electrical and Computer Engineering Program, Texas A&M
University at Qatar from 2008 to 2009. In summer 2012, he was with the
Femtocell Interference Management Team in the Corporate Research and
Development, New Jersey Research Center, Qualcomm Inc. He joined the School of
Electrical and Computer Engineering, Oklahoma State University, Stillwater,
OK, USA, as an Assistant Professor, in 2016. He has four years of industrial
experience from Qualcomm Inc., as a Senior Modem Systems Engineer with the
Department of Qualcomm Mobile Computing. At Qualcomm Inc., he has received
numerous Qualstar awards for his achievements/contributions on cellular modem
receiver design. His research interests include the design and performance
analysis of wireless communications systems in both theoretical and practical
point of views, interference modeling, management and optimization in 5G,
mmWave, HetNets, cognitive radio systems and applications, satellite
communications, visible light sensing, communications and applications, RF
channel modeling, non-contact health monitoring, and Internet of Things
applications.
---|---