IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 1
Distributed Communication and Sensing System
Co-Design for Improved UAV Network Resilience
Iuliia Tropkina, Bo Sun, Dmitri Moltchanov, Alexander Pyattaev,
Bo Tan, Rui Dinis, and Sergey Andreev
Abstract—The progress in wireless technology over the past
decade led to the rapid adoption of Unmanned Aerial Vehicles
(UAVs) for various applications. As the interest in UAVs is
accelerating, increased attention is paid to the reliability and
resilience of UAV-based systems with respect to the collision
avoidance. One of the ways to improve this aspect is to utilize
the RADAR functionality. In this work, we consider a cellular
network employed for communication jointly with RADAR oper-
ation. The critical parameter that affects the RADAR algorithm
is the radar cross-section (RCS). Since the task of obtaining the
RCS of a complex-shaped object is extremely challenging, we
first propose a novel, accurate, and fast method of scattered
field assessment. We further perform radio network planning
for the cellular deployment, as well as link budget estimations
for the RADAR system that co-exists with it. Under this system
model, we carry out detailed Monte-Carlo simulations of the
RADAR detection process to obtain reliable statistical results and
answer the question of how the actual bistatic RCS model affects
the detection algorithm. We then apply mathematical modeling
based on stochastic geometry to estimate the collision probability
without the need to simulate an extensive number of flight-hours.
Our numerical results confirm the robustness to RCS pattern
nulls, which is crucial for safety-centric applications such as
collision avoidance.
Index Terms—5G New Radio, Bistatic radar, Multistatic Radar,
UAV resilience, Radar Cross-Section.
I. INTRODUCTION
A. Motivation and Rationale
I t is expected that unmanned aerial vehicles (UAVs) willsoon play a major role as part of public infrastructure
within cities. Use-cases such as parcel delivery, law enforce-
ment, environmental monitoring, and more have thus been
proposed [1]. However, prior to the mass adoption of UAVs
within densely populated urban areas, their safety must be
ensured. To this end, regulators attempt to assure safety of
UAV usage in terms of individual reliability as well as their
ability to avoid collisions with each other.
By design, the payload of UAVs is limited. Hence, any
sensing equipment such as LIDARs or cameras for collision
This work was supported by the Academy of Finland (projects ACCESS,
RADIANT, and IDEA-MILL), by the JAES Foundation via the STREAM
project, and by Fundação para Ciência e Tecnologia and Instituto de Teleco-
municações under the project UIDB/50008/2020. I. Tropkina is funded by the
EDUFI Fellowships program.
I. Tropkina, B. Sun, D. Moltchanov, B. Tan, and S. Andreev are with
Tampere University, (e-mail: firstname.lastname@tuni.fi), Tampere, Finland.
A. Pyattaev is with YL-verkot Oy, (e-mail: ap@yl-verkot.com), Finland.
R. Dinis is with FCT-UNL, Instituto de Telecomunicações (e-mail: rdi-
nis@fct.unl.pt), Caparica, Portugal.
avoidance cuts into payload significantly. Therefore, the steps
toward assurance of UAV safety in an urban environment
should, if possible, be based on the integration of sensing and
communication capabilities [2]. Employing communication
signals from terrestrial cellular network jointly with sensing
allows to save on the mass, cost, control circuitry, and power
consumption that would be required to build a separate sensing
system.
There are various proposals reported in recent literature to
co-design and analyze the converged sensing and commu-
nication functionalities within city infrastructure that target
application of RADAR for UAV collision avoidance. As a
feasible approach to this challenge, studies address the de-
ployment of multiple monostatic RADARs on the facades of
buildings and/or street lamps to ensure the coverage of the area
between buildings [3]. As another more complex example,
there are proposals to exploit a dynamic RADAR network
(DRN) composed of UAVs able to intelligently adapt and
share the sensed information with their neighbors via multi-
hop networks [4], [5]. Apparently, both of these options require
dedicated spectrum resources, as well as massive investments
in either infrastructure or communications protocol design.
The coexistence of communication and RADAR systems
has been extensively studied over the past decade, with a focus
on developing efficient interference management techniques,
such that the two individually deployed systems can oper-
ate concurrently [6], [2]. However, by utilizing a converged
sensing-and-communication approach, one should be able to
arrive at a more balanced solution. We expect that in a city
with dense cellular infrastructure, there are plentiful signals
transmitted by the base stations (BSs) that could, in principle,
be utilized for sensing. It has been demonstrated that it
is indeed possible to use conventional 5G waveforms for
localization [7].
In our study, we consider a system where BSs on the ground
form a distributed RADAR transmitter (TX), while UAVs are
receivers (RXs) only. Such a system has multiple advantages,
as it requires no extra infrastructure other than more advanced
RX on the UAVs. By combining signals from several TX sites
over time, one can perform multiple perspective observations
to improve spatial resolution [8]. Despite these benefits, as a
standalone system, distributed RADAR may be prohibitively
expensive. In our envisaged solution, however, it is seamlessly
integrated with the cellular infrastructure at minimal additional
expenses.
While simple in principle, numerical evaluation of such
system’s performance requires the detailed knowledge of radar
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content may change prior to final publication. Citation information: DOI 10.1109/TVT.2022.3206863
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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2
TABLE I
SUMMARY OF ACRONYMS.
Abbreviations Definition
UAV Unmanned Aerial Vehicle
RCS Radar Cross-Section
DRN Dynamic RADAR Network
BS Base Station
CIR Channel Impulse Response
PPP Poisson Point Process
MTC Multi-Temporal Coherence
UMi Urban Micro
SINR Signal to Interference plus Noise Ratio
PO Physical Optics
GO Geometrical Optics
MoM Method of Moments
FEM Finite Element Method
ODE Ordinary Differential Equations
FDTD Finite-Difference Time-Domain
AVX Advanced Vector Extensions
GPU Graphics Processing Unit
PDF Probability Density Function
CDF Cumulative Distribution Function
SNR Signal-Noise Ratio
SRS Sounding Reference Signal
RV Random Variable
CFAR Constant False Alarm Rate
CA-CFAR Cell-Averaging CFAR
CUT Cell Under Test
TP/FP/TN/FN True Positive/False Positive/True Negative/False Negative
cross-section (RCS) [9], [10] for accurate results. Hence, in
addition to the system design, we propose a new method
for accurate estimation of the RCS for curved objects with
complex shapes, such as drones. This further allows us to
answer the question of how the accuracy of the RCS model
affects the converged sensing and communication system’s
performance.
B. Delivered Contributions
First, in Section II, we consider system design and model
co-design for an integrated cellular/RADAR scenario. We
perform radio network planning for the cellular deployment, as
well as aim to conduct link budget estimations for the RADAR
system that co-exists with it.
Further, to perform qualitative analysis, we need an accu-
rate and robust method for high-precision calculation of
the reflected electric field from objects with a complex shape
(i.e., UAVs). This is necessary to compute the bistatic RCS,
which affects how well does a UAV reflect a signal toward a
certain RX point when illuminated from a certain TX point.
It is important to note that most works on UAV detection tend
to avoid the need for accurate RCS by focusing on Doppler
patterns of the UAVs [11], [12].
As the calculation of a bistatic RCS pattern for a complex
object is extremely challenging [13], many researchers resort
to using a constant RCS value for their simulations [14], [5], or
abandon the bistatic RADAR setup entirely. In Section III, we
demonstrate a new method that achieves highly accurate
bistatic RCS computation with adequate computational
complexity, and thus becomes well-suited for large-scale
simulation studies. We further illustrate how it can be used to
compute 3D channel impulse response (CIR), or other desired
parameters of interest.
Further, in Section V, we perform a system-level mathe-
matical modeling based on stochastic geometry to obtain
the estimates of collision probability without simulating the
extensive volumes of flight-hours. This helps understand which
parameters of our model are the most impactful w.r.t. the
overall performance in terms of the final collision probability.
Further, in Section VI, we embed the proposed scattering
model into the system model and conduct detailed Monte-
Carlo simulations of the RADAR detection process to
obtain reliable statistical results. Finally, we assess the results
and discuss possible extensions of the proposed methodology.
We present the essential acronyms in Table I. The main param-
eters and the description of employed notation are collected
in Table II.
II. SYSTEM DESIGN CONSIDERATIONS
In this section, we introduce our key system design consid-
erations. Overall, we seek to capture the case where multiple
UAVs are aiming to leverage the existing cellular network
deployment for sensing purposes. To this end, we introduce the
basic assumptions of the considered system. First, we assume
that a 4G/5G network is deployed in the area where UAVs
are operating. For this first-order evaluation, we require the
spectrum to be non-overlapping because we use the sounding
reference signal (SRS), which features Zadoff-Chu sequences
[15] as a reference signal for RADAR processing: each of the
BSs has its own orthogonal sequence.
We further assume that the interference between the adjacent
BSs is on that level that there is a possibility to distinguish dif-
ferent BSs using code division. Because of the high robustness
of these sequences to radio interference, one does not need to
TABLE II
NOTATION OF THIS WORK.
Abbreviations Definition
L Inter-site distance in cellular structure
λB Deployment density
hA Height of all BSs
A0 BS plane
λb Density of buildings on the ground
hb Height of building
wb Width of building
A1, A2 Planes constraining the altitude of all UAVs
hL UAV minimum flight altitude
hU UAV maximum flight altitude
VUAV Speed of a UAV
t Fixed time instant
λU Density of UAVs
Fc Cellular frequency
GA(
−→
d ) BS antenna gain−→
d OA Direction of arrival−→
d OD Direction of departure
wm,n, vm,n Weighting factors
NH Numbers of antenna elements (horizontal)
NV Numbers of antenna elements (vertical)
GE(
−→
d ) Single element pattern
GE Maximum directional gain
AEH Values of attenuation (horizontal)
AEV Values of attenuation (vertical)
Am Front to back ratio
PA TX power
GRX(
−→
d ) RX antenna gain
RCSUAV (
−→
d OA,
−→
d OD) UAV 3D RCS function of incident ray
RCSb(
−→
d OA,
−→
d OD) Building 3D RCS function of incident ray
r1, r2 Distances from the target to the RX
Aeff Effective antenna area
λ Wavelength
RTX Distance between the TX and the target
RRX Distance between the RX and the target
Pd Probability that the target is detectable by the RX
PRX Received signal power
S RADAR sensitivity level
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content may change prior to final publication. Citation information: DOI 10.1109/TVT.2022.3206863
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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 3
Fig. 1. Geometric illustration of considered scenario.
take into account the interference in the simulation of sensing
operations. Our proposed system may operate in either 4G or
5G environment, as long as BS antenna has acceptable amount
of radiation toward the UAVs and does not employ beacon
beamforming. For the sake of exposition, however, below we
only consider 5G systems.
Importantly, the flight of UAVs is restricted in altitude to
a narrow range. This is justified by the existing regulations
on the maximum UAV altitude, which are present e.g., across
the EU [16], and a reasonable expectation that drones would
need to reside sufficiently above the buildings to be able
to maneuver in emergencies. Hence, we do not consider
buildings as possible collision threats. The UAVs in question
are expected to be large, bulky devices incapable of abrupt
turns; for analysis purposes, we assume that the UAVs fly
along straight lines, unless performing collision avoidance, and
that their flight paths are therefore random.
A. Detailed Network Model
We now discuss the 5G network model in detail, and
focus on specific parameters that impact the numerical results.
For reference, an overview of the considered deployment is
illustrated in Fig. 1.
The terrestrial BSs are assumed to follow cellular structure
in ℜ2 with inter-site distance of L, thus, resulting in the
deployment density of λB units/km2. Regarding the height
of the BSs, we argue that there are plenty of buildings whose
height is around 30m for BS deployment even in the cities
seeing an average height of 10m. Moreover, the LTE BS
heights range from approximately 23m to 32m, with the
average height being 27.81m. Therefore, the height of all the
BSs hA is required to be similar and, on average, equal to 30m.
The corresponding "BS plane" in Fig. 1 is denoted by A0.
There are also uniformly distributed square buildings on the
ground with the density of λb units/km2. The height and width
of the buildings are denoted as hb = 12m and wb = 30m,
correspondingly. We utilize the same object model for all
buildings in the scene, however, they have random orientation.
The altitude of all the UAVs is constrained within the
allowed limits, (see above), thus, placing them between the
planes A1 and A2. The height under A0 of the lower UAV
flight level is set to hL = 10m. The height of the permitted
UAV flight region is set to hU = 25m. The approximate speed
of all the UAVs (VUAV ) is 20mps. However, this value may
vary because of the changing direction of the UAVs. Therefore,
the approximate maximum Doppler shift for our system is
equal to ±100Hz. We assume that the speed of the UAVs
is much lower compared to the measurement window of any
RADAR. This allows to consider a fixed time instant t in
our model for analysis purposes. The trajectories of the UAVs
are assumed to form a Poisson line process in ℜ2. Hence, at
any given time instant t, the UAVs constitute a homogeneous
Poisson point process (PPP) in ℜ2 with the density of λU
units/km2.
To assess the system performance, we randomly choose one
UAV ("UAV A" in Fig. 1), at which the RX is located. All
other UAVs are thus designated as targets, and in what follows,
we are interested in characterizing the detection performance
of UAV A w.r.t. all possible targets around it.
B. Radio Part Specifics
In a RADAR-centric system, to improve the detection
probability, one may prefer to use the lowest frequency band
available. Hence, we consider the lowest available cellular
frequency of Fc = 800MHz, which would normally be used
in the networks to ensure that there are no gaps in coverage
and/or MTC.
1) Antenna Model: Where possible, we follow the 3GPP
recommendations from TR 37.840 [17]. In particular, a crucial
component of our system is the BS antenna model, GA(
−→
d ),
which specifies the gain as a function of the signal propagation
direction
−→
d . In our scenario, the direction of arrival
−→
d OA and
the direction of departure
−→
d OD are illustrated in Fig. 1.
The antenna patterns are modeled as
GA(
−→
d ) = GE(
−→
d ) + 10log10
[
1+ (1)
+
∣∣∣∣∣
NH∑
m=1
NV∑
n=1
wm,nvm,n
∣∣∣∣∣
2
− 1
],
where wm,n, vm,n are the weighting factors, while NH and
NV are the numbers of antenna elements in horizontal and
vertical dimensions. The first term in (1), GE(
−→
d ), is a single
element pattern given by
AE(
−→
d ) = GE −min[−(AEH (
−→
d ) +AEV ), Amax], (2)
where GE is the maximum directional gain, which is set
to 8dBi, while AEH and AEV are the values of attenuation
in horizontal and vertical planes, and Am = 30dB is the
front/back ratio. The reception pattern of the UAV RX antenna
is modeled similarly. To capture the radio propagation for radio
network planning purposes, we utilize the 3GPP urban micro
(UMi) model [18].
With the above considerations in mind, and for the purposes
of numerical evaluation, we select a generic target inter-site
distance of L = 350m, TX power PA of 40dBm, antenna
downtilt of 10 degrees, and frequency reuse scheme 1/3/3. The
values for wm,n, vm,n, NH , and NV are then adjusted through
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content may change prior to final publication. Citation information: DOI 10.1109/TVT.2022.3206863
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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 4
Fig. 2. RX signal strength map in cellular network.
the parameter search to match the desired average SINR of
20dB within each cell subject to reasonable fluctuations. The
resulting distribution of the RX power is demonstrated in
Fig. 2. However, our key findings are expected to hold across
a wide range of system parameters.
The UAV antennas affect the performance of the target
system, and an antenna with high directivity is preferable
to reduce the parasitic reflections from the ground clutter,
as well as from objects that are behind the UAV. Therefore,
for the considered in this section antenna model, we use
such parameters that make it highly directional. However, an
improved UAV antenna may also provide better performance
in the proposed system.
2) Propagation Model: For UAV RADAR path loss cal-
culation, one can utilize the free-space model, since events of
interest occur above the rooftop level, and thus multipath is in-
significant. In our analysis, we employ the free-space model in
Fig. 3. Example of BS antenna gain.
its linear form ( 4π·Fc·xc )
−γ = Ax−γ , where A ≈ 11229416.5
and γ = 2.0.
For collision avoidance, the UAV RX antenna needs to
provide the horizontal field of view (FoV) of 90 degrees,
with the vertical FOV of 10 degrees (to minimize the impact
of buildings). Maximum isolation is required otherwise, thus
offering the gain of GRX(
−→
d ) toward the UAVs in front of
the RX, while attenuating all other possible targets by at least
20dB.
However, in practice, for the carrier frequency of interest
such antenna may not realistically be expected to yield a
significant gain (or high front/back ratio), and thus may be
approximated with an isotropic antenna for the first-order
analysis purposes. By contrast, for the numerical assessment,
a realistic antenna designed under the above constraints is
employed. Another concern is the dependence of the TX
antenna gain on the UAV altitude (due to cellular antenna
downtilt), but that turns out not to be an issue for low-flying
UAVs, as illustrated in Fig. 3. Specifically, at larger distances
R, the BS antenna does not have sufficient angular "resolution"
to significantly attenuate the signals toward UAVs flying near
the ground.
The illuminating signal is reflected by all the UAVs ac-
cording to the 3D reflection function RCSUAV (
−→
d OA,
−→
d OD)
specified in Section III. We define RCSUAV (
−→
d OA,
−→
d OD)
as the 3D RCS function of incident ray
−→
d OA and re-
flected ray
−→
d OD directions. Similarly, the RCS of a building
RCSb(
−→
d OA,
−→
d OD) follows for a given direction of incident
and reflected rays.
The overall power available at the RX for a link is deter-
mined according to the radar equation
PRX =
PAGA(
−→
d )
4πr21
RCS(
−→
d OA,
−→
d OD)
4πr22
GRX(
−→
d )Aeff , (3)
where r1 and r2 are the distances from the target to the RX
and from the target to the TX, respectively, and Aeff = λ
2
4π
is the effective antenna area. Its size depends on the relative
BS locations, as well as the form and structure of the objects
themselves as discussed in Section III.
C. Bistatic RADAR Operation
The most conventional RADAR system is monostatic,
wherein TX and RX are colocated in one device, thus making
them conceptually simpler. In hardware terms, however, most
monostatic RADARs require a specialized transciever and
RF components, and therefore are not suitable candidates for
integration into concentional communications RX. In contrast,
our distributed RADAR system is a superposition of multiple
bistatic RADAR configurations, which require at least two
nodes to operate, one transmitter and one receiver, and is thus
more complex. On the other hand, bistatic configurations can
be implemented with current communication hardware, as no
individual node needs to act as TX and RX at the same time.
Due to bistatic operation of our system, the RX receives an
original pulse from the BS and sees reflections from all the
environmental objects. Hence, if UAV A aims to specifically
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content may change prior to final publication. Citation information: DOI 10.1109/TVT.2022.3206863
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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 5
detect other UAVs, it needs to contend with: (i) direct leakage
signal from the BS to UAV, which can in principle be removed
by signal processing, (ii) desired UAV reflections, which in our
case are the objects we actually need to avoid collisions with,
(iii) reflections from buildings, which are treated as clutter.
To perform separation between buildings and UAVs, there
are two components of information available for each potential
target: (i) Doppler shift and (ii) power level. While the power
level is straightforwardly computed using (3), the Doppler shift
for bistatic RADAR is obtained as
f = − 1
λ
d
dt
(RTX +RRX), (4)
where λ is the wavelength, RTX is the distance between the
TX and the target, and RRX is the distance between the RX
and the target.
D. Metrics of Interest
Our parameters of interest follow from the safety concerns,
in particular, UAV collision probability. Specifically, we seek
the probability Pd that the target is detectable by the RX,
given that the distance between the RX and the target is less
than a certain value Rmin = 20m. This probability is affected
by two key factors: (i) the probability that the received signal
power is sufficient PRX > S, where S = −120dBm is the
RADAR sensitivity level, and (ii) the probability that the RX
can separate the target from the background, i.e., that it has
a sufficiently different Doppler shift. These two can then be
combined to determine the successful detection probability Pd.
Based on the successful detection probability, one can then
infer the likelihood of the situation that two UAVs remain
unaware of each other while approaching dangerously close,
thus creating a collision risk. From the system analysis point of
view, we are further interested in the following considerations:
1) Understand the impact of the quality of a UAV RCS
model on the predicted system reliability.
2) Quantify the probability of a false detection, i.e., the
chances that a certain UAV is reported as a potential
collision threat, whereas in reality it is not (e.g., it is
farther away than estimated, or it is not a UAV at all).
III. CALCULATION OF BISTATIC RCS FOR UAV
In this section, we present a novel method for calculating
the scattered electromagnetic field under the assumptions of
physical optics (PO). Then, we demonstrate that our approach
converges to selected closed-form solutions, while offering
superior speed w.r.t. GO. Our method is thus shown to be
most helpful when the existing solutions cannot be applied
due to their slow speed or poor accuracy.
A. Related Studies
There are three main approaches to obtaining the RCS of
an object. First, it can be produced using direct measure-
ments. This method requires an anechoic chamber and fairly
expensive equipment [19], [20], but remains in use due to its
accuracy.
The second approach relates to "full-wave" simulation tools
that include Method of Moments (MoM), Finite Element
Method (FEM), and Finite-Difference Time-Domain (FDTD).
For MoM and FEM, the idea is to apply numerical analysis
to Maxwell’s equations in the form of ordinary differential
equations (ODEs). This, in turn, requires a subdivision of
the environment surfaces into smaller elements (cylindrical,
rectangular, or triangular) [21], [22]. While being reasonably
accurate, these methods face restrictions on scene complexity.
The number of the corresponding ODEs needed to repre-
sent complex or non-homogeneous scenes increases signif-
icantly, thus causing growth in computational and memory
burden [23]. This makes MoM and FEM solvers challenging
to use where the scene is large relative to the wavelength.
For the FDTD method, the algorithms are based on a
discrete-time solution to Maxwell’s equations, and thus call for
a voxel (aka "Yee lattice") scene representation [24]. Similarly
to MoM and FEM, a typical performance bottleneck of FDTD
is in the voxel size, which must be made much smaller than the
wavelength used in the modeling [23]. Therefore, similar to
MoM/FEM, FDTD is best suited for smaller scenes (or longer
wavelengths). A key feature of all full-wave methods is that
once the solution is found for a given driving wave, the entire
reflected field is known. Hence, if the TX location is fixed,
their computational complexity may be acceptable.
The third alternative approach is analytical. Closed-form
expressions for the RCS of simple targets, such as a sphere or a
corner reflector, have long been available [25]. However, when
the shape of an object is more complex, it becomes nearly
impossible to obtain a closed-form solution. Because of this,
much effort is devoted to studying a set of approximations
named physical optics (PO). PO takes into account wave
effects, such as interference, diffraction, and polarization, but
does not consider the impact of induced fields. The rationale
behind the PO approach is that the modeling outcome is
close to that of the full-wave solutions [26], but is much less
computationally expensive.
The PO approximation allows calculating the transmitted
or scattered field [27] by solving the PO integral over the
surfaces illuminated by the incident wave. The latter is the
most computationally intensive part of the PO procedure.
There are different techniques for the calculation of the said
integral. Some authors propose an analytical solution for the
PO integral, such as transformation of the surface integral to
line integrals under certain constraints [28]. In other works,
authors consider analytical expressions to calculate the PO
scattered field with plane triangular patches [29]. Others put
forward discretization of a surface as quadratic patches in such
a way that the amplitude and phase terms of the PO integral
change in quadratic form [30]. In [31], the authors offer a way
for converting these quadratic patches to square patches.
B. Description of Proposed Method
The key idea behind the PO is that one only needs to
model possible transformations of a wavefront at the interfaces
between different media, which are represented by integral
over all surfaces. We now proceed by describing our numerical
method for its evaluation.
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content may change prior to final publication. Citation information: DOI 10.1109/TVT.2022.3206863
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Fig. 4. Signal propagation example.
According to the proposed method, we replace the integra-
tion over a surface with the sum of the fields of tiny segments
of the surface. For this, we associate each segment with its
own RCS. For simplicity, it can be represented by a square
shape. The RCS of a square plate is expressed as [26]
RCSsegment = 4π
(
a2
λ
)2
, (5)
where a is the side of the square segment that the point
represents and λ is the wavelength in the current media.
To accurately capture the geometry of a region on an
object’s surface, each segment carries a normal vector of that
fragment of the surface. To take into account the normal
direction, we introduce a directivity coefficient
Dsegment = cos
2(θref ), (6)
where θref is the angle between the point’s normal vector and
the direction to the RX.
In practice, any macroscopic object can be readily repre-
sented as a uniformly distributed point cloud, wherein every
point is the center of one segment as exemplified in Fig. 4.
The power carried by a reflected spherical wave at the RX
location using the radar equation for each segment [32] can
be estimated as follows
Qi =
PTXDsegmentRCSsegmentAe
16π2Dt2iDr
2
i
, (7)
where PTX denotes the power of radiation at the TX, Dti is
the distance between the TX and i-th point, Dri is the distance
between the RX and i-th point, and Ae = λ
2
4π is the effective
antenna area at the RX (assuming ideal isotropic RX).
Finally, the overall electric field at the RX point can be
derived as a coherent sum of the fields from each point as
−→|E| = |
∑
i
√
Qi(cos(ϕi) + jsin(ϕi))|, (8)
where ϕi = 2π dλ is the phase of i-th component at the RX.
Hence, surface subdivision followed by summing over mul-
tiple elements allows us to approximate the final electric field
at the RX location, thus transforming the evaluation of the
PO surface integral into a sum over multiple points, which is
well-suited for vector processing, such as AVX and GPU. Our
following objective is to verify that the results obtained with
this approximate method remain sufficiently accurate for RCS
calculations.
IV. VALIDATION OF PROPOSED METHOD
In this section, we report the validation scenarios, the se-
lected modeling conditions, and the comparison of our method
with the theoretical expressions. In most examples, we are
interested in validating the results for the RCS, as those are
key for RADAR processing.
A. Validation Scenarios and Conditions
We compare the performance of our proposed method with
the analytical expressions for which closed-form RCS solu-
tions are known [26]. There are certain constraints imposed
by the closed-form solutions: (i) the incident wave has to be a
plane wave, (ii) the calculations are performed in the far-field
and for this we ensure the separation of 200λ, (iii) the sizes of
objects should be more than ≈ 2λ, (iv) all objects are perfect
electric conductors.
We consider the following validation scenarios: flat plane of
different size, sphere, cylinder, and concave object. One can
estimate the RCSplane for the bistatic RCS of a flat plane [26]
via the following
RCSplane = 4π(
cd
λ
)2cos2(θref )× (9)
×
sin
[
βd
2 (sinθref ∓ sinθinc)
]
βd
2 (sinθref ∓ sinθinc)
2 ,
where c and d are the sides of the plane, θinc is the angle
of incidence (the angle between the surface normal and the
vector to the TX point), and β = 2·πλ is the wavenumber.
The monostatic RCS of a metal sphere and a cylinder,
respectively, can be assessed as [26]
RCSsphere = πr
2
s , (10)
where rs is the radius of the sphere, and
RCScylinder =
2πrch
2
c
λ
, (11)
where rc is the radius of the cylinder and hc is its height.
B. Validation Results
First, we assess the reflected power as a function of the
angle of reflection for a square flat plate, since the theoretical
expression for the latter is known (9) [26]. We fix the grid
step at 4mm, and the carrier frequency is 300MHz. As can
be observed in Fig. 5, for the plate size of 5λ, our method
demonstrates adequate agreement with the exact solution.
When the plate size is set to 20λ (see Fig. 6), the obtained
result for the proposed approach remains similar to the exact
solution. Therefore, for a range of sizes, we demonstrate that
the proposed method captures both the main reflection lobe as
well as all the side lobes correctly.
Second, we compare the results for the spheres of different
radii [26]. We set rs = 3, 4, 5m, and consider different
distances between the sphere and the TX/RX point. For a
sphere, only monostatic results are known in closed-form;
hence, TX and RX have to be collocated. Here, our approach
continues to demonstrate excellent agreement with theory, as
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Fig. 5. Received power as a function of angle of reflection for flat square
plate under different angles of incidence. Plate size is 5λ.
Fig. 6. Received power as a function of angle of reflection for flat square
plate. Plate size is 20λ.
seen in Fig. 7. It is important to note that it is extremely
difficult to obtain similarly accurate results with a geometric
optics (GO) solver (such as a ray tracer) due to smooth convex
shape of the object in question.
Further, we consider a cylinder. Its height is fixed at
8m, while the radius is being varied (rc = 3, 4, 5m). The
dependence of the reflected power on the distance from the
TX/RX to the object surface is displayed in Fig. 8. The curves
demonstrate a perfect match.
The final validation is done with a concave object, specifi-
cally, a parabolic reflector with the radius of 5m. As we can
see in Fig. 9, the maximum of power is at the focus point for
various shapes of the reflector, which matches expectations.
In Table III, we present the theoretical values of the gain
for a parabolic reflector at the focus point together with our
numerical results. These match the analytical expression.
In summary, for a wide variety of shapes, our method
produces results that are very close to those obtained via exact
Fig. 7. Received power as a function of distance from TX/RX to object
surface for spheres of different radii.
Fig. 8. Received power as a function of distance from TX/RX to object
surface for cylinders of different base radii. Cylinder height is 8m.
solutions. It has to be noted, however, that while our approach
is far superior to GO (i.e., ray tracing and its variants), it does
have its own limitations [33]. Specifically, for those cases
where the objects are smaller than the wavelength, one can
expect induced currents to affect the applicability of PO in
general, thus making the proposed approach unreliable.
Similarly, for extremely high frequencies, the density of
the point cloud needed for accurate calculations becomes
rather high, thus straining the memory budget. Despite these
shortcomings, the proposed method is observed to be superior
to the MoM in terms of scalability, by approaching that of
typical GO solutions, while providing accuracy far superior
to what is possible with GO, especially for smooth, organic
shapes common for UAVs.
C. Computational Complexity
Here, we consider the computational complexity of the
proposed method. First, one needs to assess how many points
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Fig. 9. Received power as a function of distance from TX/RX to object
surface for parabolic reflector with different focus distances. rp = 4m.
per object are required. As an example, the well-known
NEC++ [34] engine may represent a sphere of radius 5λ
with about N = 1000 elements using the MoM, where each
element is internally an ODE. However, to solve the system
of N equations, one needs at least O(N2) operations, and a
substantial amount of memory to store the intermediate results.
In our case, a sphere of the same size has N = 20, 000
points, but the solution speed is O(N), with no extra memory
requirements. In addition, with the proposed approach, one
does not need to represent free space in the scene, unlike
in FDTD; therefore, this reduces the computational cost as
well. Further, in our method, while more points are required
to represent an object, the volume of computations per point
is reduced, and the code has no branching. Overall, there is a
difference in the runtime speeds on the order of 1000 for the
RCS of a sphere as compared to e.g., NEC++.
V. STOCHASTIC GEOMETRY ANALYSIS
In this section, we continue by outlining a stochastic geom-
etry framework tailored to the performance assessment of our
UAV-based communications-and-RADAR system.
A. Analysis Principles
The proposed analysis is based on stochastic geometry con-
siderations. The overall framework comprises of thee stages.
In the first one, we determine the probability that the target
is actually distinguishable from the clutter. To this aim, we
TABLE III
THEORETICAL AND MODELED AVERAGE POWER GAIN AT FOCUS POINT
FOR PARABOLIC REFLECTOR.
Radius, m Modeled average power gain, dB Theoretical power gain, dB
3 25.53 25.5
4 29.55 29.94
5 30.1 29.94
R
r
Tx
L2
L1L3
Target
Rx
Scatterers
Fig. 10. Top view of considered scenario.
assess whether the difference between the Doppler shift from
the target at the RX is sufficiently different as compared
to the Doppler shift from all the scatterers located in the
environment.
Distinguishing the target from the scatterers alone is not
sufficient for a successful target detection. Hence, at the second
stage, we determine the probability that the received signal is
actually higher than the detection threshold. To this end, we
account for the reflection profile of the target to characterize
the probability density function (PDF) of the received signal
strength and then obtain the sought probability of signal
detection by numerical integration.
Finally, at the last stage, we deliver the overall target de-
tection probability. Accordingly, we exploit the independence
property for the events that (i) the received signal is greater
than the threshold and (ii) the target is distinguishable from
the clutter. In the end, the target probability of signal detection
is obtained as a product of the probabilities of these events.
B. Target Visibility Probability
With the metrics of interest specified in Section II, we
consider the top view of the scenario geometry illustrated in
Fig. 10. Here, we assume that the RX positions are uniformly
distributed across the coverage area of a cell with radius R.
The targets of interest are uniformly distributed within a circle
around the RX having radius r < R.
To determine the target detection probability, one needs to
ensure that: (i) the target is distinguishable from the clutter and
(ii) the received power is sufficient to perform a detection. For
the former to hold, the Doppler shift from the target at the RX,
DRX , has to be sufficiently dissimilar from all the Doppler
shifts DSc from the scatterers located in the environment, i.e.,
buildings.
1) Doppler Spread from Stationary Scatterer: The Doppler
spread from a scatterer can be written as
DSc = fc
(
1− 1 + v
TX,Sc
rel
1 + vSc,RXrel
)
, (12)
where fc is the carrier frequency, v
TX,Sc
rel is the relative speed
of the TX and the scatterer, vSc,RXrel is the relative speed of
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the scatterer and the RX. Since both TX and scatterers are
assumed to be stationary, we may simplify (12) as
DSc = fc
(
1− 1
1 + vSc,RXrel
)
. (13)
Observing the structure of (13), one may notice that DSc
is the function of a single variable vSc,RXrel . Due to our
assumption on random UAV trajectories, the latter is a random
variable (RV), even for a constant speed of the UAVs, v. By
utilizing Fig. 11(a), we determine this component as
vSc,RXrel = v sinα, (14)
where α is uniformly distributed in (0, 2π) and (13) reads as
DSc = fc
(
1− 1
1 + v sinα
)
. (15)
Note that (15) implies that DSc is the function of a single
RV. Recall that the PDF of RV Y , w(y), expressed as a
function y = ϕ(x) of another RV X with the PDF f(x) is
given by [35]
w(y) =
∑
∀i
f(ψi(y))|ψ′i(y)|, (16)
where x = ψi(y) = ϕ−1i (x) is i-th branch of the inverse.
Observe that applying the transformation directly to (15) is
difficult. However, one can apply it initially to the component
U = v sinα and then to the overall function. Under this
transformation, each value of U located in the interval (−v, v)
corresponds to multiple values of α, i.e.,
αk = πk + (−1)k arcsin
(
U
v
)
, k = 1,±1,±2. (17)
By applying the transformation in question, we arrive at
wU (x) =
1
a
√
1− (xv )2
∞∑
k=−∞
f(πk+ (18)
+ (−1)k arcsin
(x
v
)
), x < v.
As α is distributed uniformly in (0, 2π), one may notice that
there are only two non-zero components in (18): (i) k = 0,
x < v and (ii) k = 1, 0 < x < v. Hence, the final pdf of
U = v sinα takes the following form
wU (x) =
1
vπ
√
1−
(x
v
)2
, x < v. (19)
With the distribution of U = v sinα at hand, we are now
able to determine the pdf of DSc. Since the transformation at
hand is a bijection, and observing that the derivative of the
inverse function is given by ψ′(x) = fc(fc−x)2 , we arrive at the
following pdf
wDSc(x) =
1
vπ
√
1−
(
fc
v(fc − x)2
)2
fc
(fc − x)2 . (20)
v
vrelSc,Rx
α Scatterer Rx
(a) Scatterer case.
Tx
Rxv
vrelSc,Rx
α
v
urelSc,Rx
β
(b) Target case.
Fig. 11. Illustration of relative speeds of involved entities.
2) Doppler Spread from Actual Targets: We now determine
the distribution of the Doppler spread from any of the actual
targets. Accordingly, we have
DTg = fc
(
1− 1 + v
TX,Tg
rel
1 + vTg,RXrel
)
. (21)
Contrarily to the Doppler spread from a scatterer, here both
components vTX,Tgrel and v
Tg,RX
rel are RVs. The former one can
be determined similarly to (14), as vTX,Tgrel = v sinα, where
α is uniformly distributed in (0, 2π).
To obtain the component vTg,RXrel , we need to account for the
relative speed between the target and the RX, which are both
moving. By considering the projection of the RX trajectory
onto the line connecting the RX and the target, see Fig. 11(b),
we obtain the speed of the RX with respect to the target as
uTg,RXrel = v sinβ, (22)
where β is uniformly distributed in (0, 2π).
The resultant relative speed is thus the vector sum of v
and uTg,RXrel . To operate with scalar variables, one needs to
supplement uTg,RXrel with an appropriate sign. Furthermore,
since the trajectories of the target and the RX are assumed to
be independent, α and β are mutually independent. With these
observations in mind, the Doppler spread from the target can
be written as
DTg = fc
(
1− 1 + v sinα
1 + (v + v sinβ)
)
, (23)
thus implying that it is a function of two independent RVs.
By following the same technique as the one we utilized
to establish the Doppler spread from a scatterer, we first
determine the pdfs of two independent RVs, U = v sinα and
Z = v sinβ, where both α and β are uniformly distributed in
(0, 2π). We thus have
wU (x) = wZ(x) =
1
vπ
√
1−
(x
v
)2
, x < v. (24)
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Note that by applying the RV transformation technique,
no closed-form expression for wDTg (x) is feasible. However,
one can readily determine the cumulative distribution func-
tion (CDF) of DTg by numerically estimating the following
integral
FDTg (x) =
∫∫
f(x,y)≤z
wU (x)wZ(y)dxdy, (25)
where f(x, y) = fc(1 − [(1 + x)/(1 + (v + y))]) as in (23),
while wU (x) and wZ(y) are available in (24).
As an alternative solution, one may first perform linear
transformations of the numerator and the denominator as
U ′ = 1 + U and Z ′ = 1 + v + U in (21) to obtain
wU ′(x) = wU (x − 1), wZ′(x) = wZ(x − 1 − v). Then, to
estimate the ratio U ′/V ′, one needs to numerically solve the
following integral:
FU ′/V ′(y) =
∫∫
x1/x2≤y
wU ′Z′(x1, x2)dx1dx2 = (26)
=
∫ 0
−∞
[∫ ∞
yx1
wU ′Z′(x1, x2)dx2
]
dx1+
+
∫ ∞
0
[∫ yx1
−∞
wU ′Z′(x1, x2)dx2
]
dx1,
where wU ′Z′(x1, x2) = wU (x− 1)wZ(x− 1− v).
By differentiating (26), one can obtain
wU ′/V ′(y) = −
∫ 0
−∞
x1wU ′Z′(x1, yx1)dx1+ (27)
+
∫ ∞
0
x1wU ′Z′(x1, yx1)dx1,
which is easier to estimate than (25). To complete the deriva-
tion, one needs to perform a linear transformation of U ′/V ′
according to f(x) = fc(1− x), where x = U ′/V ′.
3) Probability of Target Visibility: After determining the
pdfs of DSc and DTg, we aim to establish DTg ∈ {DSc −
∆D, DSc +∆D}, where ∆D is the Doppler threshold, which
can be straightforwardly derived from the RX UAV ground-
speed. Mathematically, we seek the probability
pV = 1− Pr{|DTg −DSc| < ∆D}. (28)
By utilizing (28), the task of quantifying pV thus reduces
to determining the CDF of the modulo of the difference
between DTg and DSc. The pdf of the difference D− is readily
available by performing a convolution of the RVs DTg and
−DSc, i.e.,
wDdif (x) =
∫ ∞
∞
wDTg (t)wDTg (t− x)dt. (29)
The pdf of the absolute value |Ddif | is made available by
utilizing a transformation of the RV Ddif with respect to the
modulo function. In this case, the inverse function has two
branches ϕ1(y) = −y and ϕ2(y) = y, thus leading to the
sought pdf in the following form
f|Ddif |(x) = fDdif (−x) + fDdif (x). (30)
To obtain the CDF of |Ddiff |, one needs to integrate (30),
and then the sought probability in (28) readily follows.
Recall our assumption that the scatterers follow a homo-
geneous PPP in ℜ2. Hence, by employing the properties of
the PPP, the target visibility probability in a field of scatterers
with density λC is given by
qV = e
−Λ +
∞∑
i=1
Λk
k!
e−ΛpkV , (31)
where the first component provides the probability that there
are no scatterers in the region covered by the BS antenna,
A, (i.e., the void probability of the PPP), while the second
component specifies the probabilities that there are k scatterers
in the region A but none of those occlude the visibility of the
target according to (28).
The only unknown in (31) is the mean number of scatterers
in the region covered by the BS antenna, Λ. This parameter
is related to the density of scatterers as SAλC , where SA is
the area of the region covered by the BS antenna. In general,
SA depends on the type of the BS antenna, the operating
frequency, and the frequency reuse plan. For example, for a tri-
sector antenna, the area SA can be approximated by a triangle
with 120◦ angle. If the carriers utilized in all the sectors are
the same, then the region of interest can be well approximated
by a circle.
C. Power Detection Probability
Observe that the visibility of the target does not guarantee
that the latter is detected successfully. Even when the target
is visible in a field of scatterers, the received power may be
insufficient to successfully detect it. Hence, here we derive the
probability that the received power at the RX is higher than a
certain threshold ∆P , i.e., qP = Pr{PRX ≥ ∆P }.
The received power at the RX can be written as
PRX = PTXGTX(ζ, θ)Gcs(ζ, θ, ζ
′, θ′)GRX(ζ ′′, θ′′)×
×A(L1 + L2)−γ , (32)
where PTX is the BS transmit power, GTX(ζ, θ) is
the BS transmit gain toward the current target location,
Gcs(ζ, θ, ζ
′, θ′) is the RCS, GRX(ζ ′′, θ′′) is the receive gain
at the RX, γ is the propagation exponent, A is the frequency-
dependent attenuation factor, L1 and L2 are the distances
shown in Fig. 10, ζ, ζ ′ and θ, θ′ are the elevation and az-
imuth angles, respectively, in the appropriate direction. These
parameters are illustrated in Fig. 12.
By analyzing the structure of (32), we observe the following.
The RCS is derived in Section III as a function of the
azimuth and elevation angles. The parameters GTX(ζ, θ) and
GRX(ζ
′, θ′) are available as part of the problem formulation.
It is important to note that by assuming fixed BS and UAV
heights, the elevation angle ζ equals ζ = arccos([hU −
hA]/L1), while ζ ′ = 0. Furthermore, both azimuth angles
θ and θ′ are RVs with the densities wθ(x) = 1/2π and
wθ′(x) = 1/2π, respectively.
The only remaining unknown in (32) is the distance (L1 +
L2). Let us denote the projections of these segments L1,
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hA
Ground plane
BS plane
UAV plane
hU
z
θ φ
x
y r
GA(ζ,θ)
GU(ζ',θ')
GR(ζ,θ,ζ',θ')
L1
TargetL2
L3
L1,x
L3,x L2,xζ
θ
θ'
Fig. 12. Components of received power analysis.
L2, and L3 onto the xOy axis by L1,x, L2,x, and L3,x,
respectively. We see that L2 = L2,x, while
L1 =
√
(L1,x)2 + (hU − hA)2,
L3 =
√
(L3,x)2 + (hU − hA)2, (33)
where L2,x is the RV with pdf wL1,x = 2x/r
2, 0 < x < r,
L3,x is the RV with pdf wL3,x = 2x/R
2, 0 < x < R, while
the distribution of L1,x is unknown. We can also express ζ as
ζ = arccos
(
[hU − hA]/
√
(L1,x)2 + (hU − hA)2
)
. (34)
By combining the above facts together, we establish that
the received power at the RX in (32) is a function of four
RVs, L2,x, L3,x, θ, and θ′. However, since Gcs(ζ, θ, ζ ′, θ′)
is not available in the closed form, a direct application of
the RV transformation technique does not lead to a closed-
form solution. However, one can estimate the CDF of PRX
via numerical integration as
FPRX (x) =
∫∫
f(x1,x2,x3,x4)≤y
wθ(x1)wθ′(x2)wL3,x(x3)wL2,x(x4)dx1 . . . dx4 =
=
∫∫
f(x1,x2,x3,x4)≤y
x3x4
πr2R2
dx1 . . . dx4, (35)
where f(x1, x2, x3, x4) is the received signal strength. Ac-
cordingly, the probability that the received signal strength at
the RX exceeds a certain threshold is given by
qP = Pr{PRX ≥ ∆P } = 1− FPRX (x). (36)
Finally, if the mutual orientations of the mobile objects are
known a-priori (e.g., the considered target and the RX are part
of a fleet moving in the same direction), θ1 and θ2 become
constants. Then, the received power depends only on two RVs,
L2,x and L3,x, thus leading to a simpler form
FPRX (x) =
∫∫
f(x1,x2)≤y
wL3,x(x1)wL2,x(x2)dx1dx2 =
=
∫∫
f(x1,x2)≤y
4x1x2
r2R2
dx1dx2. (37)
Note that our analysis can be extended to incorporate variable
BS heights as follows. First, one needs to make the said height
a random variable. Hence, the variables L1, L3, and ζ will
become functions of more than one RV. Second, solutions for
L1 and L2 in (33) can be obtained in a closed form for some
suitable distributions of BS heights (i.e., those having a single
exponential term, such as exponential, Rayleigh, and Weibull).
D. Successful Detection Probability
Having both the target visibility probability and the proba-
bility that the received signal strength at the RX is lower than
a certain threshold, we are now in a position to determine the
probability of successful target detection given that it is located
closer than a certain distance r. Recalling that the two derived
parameters are implicitly conditioned on the target being closer
than r, and by combining (31) and (36), we arrive at
pS = (1− Pr{|DTg −DSc| < ∆D})Pr{PRX ≥ ∆P } =
=
(
e−Λ +
∞∑
k=1
Λk
k!
e−ΛpkV
)
[1− FPRX (x)], (38)
where ∆D and ∆P are the Doppler and power thresholds.
VI. SIGNAL RECEPTION AND TARGET DETECTION
In Section V, we presented a RADAR detection probability
analysis based on stochastic geometry. While useful for first-
order system-level assessment, that approach has limitations in
capturing finer details. In fact, the detection of a target relies
on the specific signal waveform, receiver design and signal
processing algorithms. In this section, we elaborate the signal
reception and target detection procedure. It is then used in our
Monte Carlo simulations of target detection probability.
A. Matched Filter Reception
The first step in the RX processing is the matched filter,
which maximizes the signal-to-noise ratio (SNR) in the pres-
ence of additive stochastic noise. The timing of the maximum
value of the matched filter outcome characterizes the distance
to the detected target, while its magnitude is used for signal
detection. Typically, matched filtering is implemented by cor-
relating the signal with the conjugation of a known waveform
(or sequence, if digital processing is used) as
x(τ) =
∫ ∞
∞
r(t)s∗(t− τ)dt, (39)
where s(t) is the transmitted waveform, r(t) = r(t)⊛ h(t) is
the received signal, and (·)∗ denotes the conjugation operation.
From (39), the waveform s(t) determines the SNR gain of
the matched filter. To illustrate the detection capability for
the conventional communication signals, we employ the SRS
defined in the 3GPP specifications [36], which is typically
based on a Zadoff-Chu sequence and brings approximately a
20dB SNR gain.
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CUT
Guard cells
Training
cells
Frequency (Doppler) cell index
R
an
g
e
ce
ll
i
n
d
e
x
Ambiguity
Surface
Fig. 13. Cell average CFAR on ambiguity surface x(τ, fd).
B. Range Doppler Profile of Received Signal
The outcome of the matched filter represents a power-range
profile of the environment. In our case, however, since the
UAV antenna is not perfect, the range alone may not be able
to discriminate the targets from the clutter. Hence, we further
explore the power-frequency (Doppler) domain profile jointly
with the power-range profile to improve the discrimination
capability of the detection system. The range-Doppler profile
is obtained via cross-ambiguity processing as
x(τ, fd) =
∫ ∞
∞
r(t)s∗(t− τ)ei2πfdtdt. (40)
The output of (40) characterizes the power distribution of
the received signal in frequency (Doppler) and time (range)
domains as compared to the transmitted waveform. x(τ, fd)
is also known as the ambiguity surface. The time delay and
Doppler shift carried by the reflections from the UAVs can be
represented by the value of x(τ, fd) at the specific time instant
and frequency point, which is the peak (local maximum) value
on the ambiguity surface x(τ, fd).
C. Detection Rate with Constant False Alarm Rate (CFAR)
The local maximum values of x(τ, fd) indicate the delay
and Doppler shift of a reflected signal. In this work, we
utilize a cell averaging CFAR (CA-CFAR) detector to capture
the local maximum (see Fig. 13). The CA-CFAR detector
compares the intensity of the cell under test (CUT) with a
dynamic threshold that is calculated via the following steps.
First, the threshold factor is chosen according to the ex-
pected CFAR level Pfa and is given by
α = N(P
−1/N
fa − 1), (41)
where N is the total number of the selected training cells.
Further, the threshold is determined by the threshold factor
α and the estimated noise level nest according to
Th = αnest = α
nsum
N
, (42)
where nsum is the sum of all the training cell values. To avoid
signal leakage into adjacent cells, this method exploits guard
cells to isolate the CUT.
Once the threshold is determined, the detection decision is
made based on
pCUT
detect
≷
miss
Th, (43)
where pCUT is the value (power) of CUT. The CA-CFAR
procedure is applied to the ambiguity surface x(τ, fd) cell by
cell for determining the detection status of every cell.
Regarding the computational complexity of our RADAR
algorithm, which we use for determining the detection state
of every cell on the ambiguity surface, the CFAR procedure
averages the values of the selected cell and the training cells
around it (see Fig. 13). Since the averaging process repeats
for every cell that appeared on the ambiguity surface, the
computational complexity of RADAR detection depends on
the total size of the cells on the surface. In other words,
the CFAR complexity is determined by the multiplication
of frequency domain cell numbers (NumF ) and the range
domain cell numbers (NumR). This work employed 1024 and
2048 for NumF and NumR, respectively, and the complexity
is thus O(NumFNumR).
VII. SELECTED NUMERICAL RESULTS
In this section, we aim to verify the scattering model
proposed in Section III with the RADAR detection metrics.
By utilizing this approach, we can obtain the bistatic RCS of
the UAV model in any direction, see Fig. VI-B.
A. Simulation Setup for Radar Detection
The specific 5G waveform used is the SRS, which features
Zadoff-Chu sequences [36]. We consider a system with 2048
subcarriers having 15kHz subcarrier spacing. The overall
spectral span of the signal is 30MHz. By analyzing a total of
400 SRS symbols, the range and Doppler resolution can reach
9.76m and 30Hz, respectively, which is adequate for UAV
systems. To reduce sensing times, one may increase the SRS
Fig. 14. RCS of UAV (monostatic).
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content may change prior to final publication. Citation information: DOI 10.1109/TVT.2022.3206863
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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 13
-400 -200 0 200 400
d. Doppler Frequency (Hz)
1900
2000
2100
2200
2300
2400S
ig
n
al
P
ro
p
ag
at
io
n
R
an
g
e
(m
)
-400 -200 0 200 400
c. Doppler Frequency (Hz)
1900
2000
2100
2200
2300
2400S
ig
n
al
P
ro
p
ag
at
io
n
R
an
g
e
(m
)
-400 -200 0 200 400
b. Doppler Frequency (Hz)
1900
2000
2100
2200
2300
2400S
ig
n
al
P
ro
p
ag
at
io
n
R
an
g
e
(m
)
-400 -200 0 200 400
a. Doppler Frequency (Hz)
1900
2000
2100
2200
2300
2400S
ig
n
al
P
ro
p
ag
at
io
n
R
an
g
e
(m
)
-125 dBW
-135 dBW
-110 dBW
-130 dBW
-120 dBW
Fig. 15. a. Example range-Doppler plot with 5 reflections from buildings and UAVs. Propagation path range is 1900m to 2400m and Doppler frequency of
all marked spots is between ±200Hz. Ground truth of reflection is marked by red ellipse. b. CFAR detection results, FAR = 10−5. c. FAR = 10−6. d. FAR
= 10−7.
0 2 4 6 8 10 12 14 16 18 20
Base Station Number
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
D
et
ec
tio
n
Ra
te
FAR = 10-3
FAR = 10-4
FAR = 10-5
FAR = 10-6
FAR = 10-7
Fig. 16. Detection rate of one UAV if using multiple reflections from different
BSs jointly. Carrier frequency is 800MHz.
rate at the BSs. After propagation modeling, the range-Doppler
profile is obtained via ambiguity processing. The noise floor of
the RX is assumed to be -130dBW. In the CA-CFAR, 5 guard
cells and 25 training cells are applied on the range-Doppler
surface.
The simulation environment follows the description in Sec-
tion II with 19 BSs, 33 UAVs (one drone is chosen as the
tagged RX), and 100 buildings. We collect all the parameters
used by our simulation setup in Table IV. The locations of
TABLE IV
PARAMETERS USED IN SIMULATIONS.
Parameter Value
Carrier frequency 800MHz
Number of subcarriers 2048
Subcarrier spacing 15kHz
Spectral span of the signal 30MHz
Number of SRS symbols 400
Range 9.76m
Doppler resolution 30Hz
Noise floor of the RX -130dBW
Guard cells 5
Training cells 25
Number of BSs 19
Number of UAVs 33
Number of buildings 100
Independent Monte-Carlo runs 5000
Number of signal paths in every run 2508
Subcarrier spacing 15kHz
the UAVs and buildings are randomly generated in 5000
independent Monte-Carlo runs. Hence, the data set of the
reflection channel model has 5000 independent instances and
19× 132 = 2508 signal paths in every run.
Fig. 15(a) presents an example range-Doppler profile of the
signals reflected from the UAVs and buildings with marks. The
strongest area in Fig. 15 corresponds to -110dBW, while the
weakest reflections are below -150dBW. To select the local
maximum values from the range-Doppler plot, CA-CFAR is
adopted, which calculates the threshold factor α according to
the pre-defined FAR level Pfa as per (41). Then, the actual
threshold level is determined according to (42).
The detection probability of CA-CFAR at 10−5 FAR level is
demonstrated in Fig. 15(b). The highlighted region embodies
the reflections from targets. The FAR is utilized to control
the impact of noise, where higher acceptable FAR directly
influences the probability of detection. In our case, owing to
the matched filter, a signal with the power of ≈ 20dB below
the noise floor of −130dBW remains detectable; hence, the
true sensitivity is −150dBW.
When using a single nearest BS as the illuminator, we note
around 20% UAV detection probability, even with the very
high FAR of 10−3, primarily due to nulls in the RCS patterns.
However, due to diversity in bistatic geometries, RX power
from different BSs varies widely. In this situation, a target
(UAV or building) that is "invisible" when using one BS may
be easily detectable with another BS. Hence, multiple illu-
minators provide extra robustness for the detection purposes.
The detection performance with multiple illuminators may be
improved if the detection of the same target with different
illuminators is independent, which is generally true, as:
Pmultiple_BS = 1−
M∏
1
(1− PM ), (44)
where PM is the detection probability by using M -th BS as
an illuminator. With fewer BSs, the detection rate of targets is
less than 25%. Taking advantage of multiple BSs, the detection
rates are improved to over 80% even at low FAR levels.
B. Discrimination of UAVs and Buildings
The detection rate evaluated above does not differentiate
between UAVs and buildings, neither is it straightforward with
power alone. Further, from a single range-Doppler plot like
Fig. 15, one may not discriminate the types of targets. In
This article has been accepted for publication in IEEE Transactions on Vehicular Technology. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/TVT.2022.3206863
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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 14
0 5 10 15 20
b. Base Station Index
-145
-140
-135
-130
-125
-120
-115
-110
-105
M
ea
n
V
al
u
e
o
f
R
ef
le
ct
io
n
P
o
w
er
Drones
Buildings
Selection Thresholds
0 5 10 15 20
c. Base Station Index
0
0.2
0.4
0.6
0.8
1
P
er
ce
n
ta
g
e
Percentage of TP
Percentage of TN
Percentage of FP
Percentage of FN
-130 -125 -120 -115 -110 -105 -100
a. Power dBW
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
R
el
at
iv
e
P
ro
b
ab
il
it
y
Buildings
Fig. 17. a. Power probability for UAVs and buildings reflection power with fixed RCS, BS index 2. b. Mean reflection power comparison. c. Hypothesis
testing results.
0 5 10 15 20
a. Base Station Number
0
0.2
0.4
0.6
0.8
1
D
e
te
c
ti
o
n
R
a
te
Correct Detection Rate
Miss Detection Rate
0 5 10 15 20
b. Base Station Number
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
C
la
s
s
if
ic
a
ti
o
n
R
a
te
Correct Classification Rate
Miss Classification Rate
Fig. 18. Classification performance using reflections from multiple BSs: a. Constant RCS. b. Realistic RCS.
-150 -140 -130 -120 -110
a. Power in dBW
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
R
el
at
iv
e
P
ro
b
ab
il
it
y
Buildings
Drones
0 5 10 15 20
c. Base Station Index
-150
-145
-140
-135
-130
-125
-120
M
ea
n
V
al
u
e
o
f
R
ef
le
ct
io
n
P
o
w
er
Drones
Buildings
Selection Thresholds
Fig. 19. Power probability for UAVs and buildings reflection power with realistic (varying) RCS: a. BS index 1. b. BS index 3. c. Mean reflection power
with realistic RCS and corresponding threshold.
what follows, the profiles of different types of targets are
investigated and the strategies for target discrimination are
discussed. Fig. 16 depicts the detection rate of one UAV if
using multiple reflections from different BSs jointly.
1) Target Discrimination with Constant RCS: For the fixed
RCS parameters of UAVs and buildings (as we set the mean
values of the actual RCS distributions), the reflected signal
power from the UAVs and buildings is distinguishable as
confirmed in Fig. 17(a). The mean values of the reflected
power for all 19 BSs are collected in Fig. 17(b). It is apparent
that the mean signal power from the UAVs is higher than
that from the buildings most of the time; hence, one can
discriminate based on the signal power. By setting the middle
point of the UAV and building reflection power as a threshold,
the ’Hypothesis Testing’ analysis is applied to the CFAR
output for each BS. The ’Hypothesis Testing’ observes the
power of all the detected signals and compares these values
with the threshold, which is plotted as the yellow line in
Fig. 17(b). If the power is above the threshold, we treat the
detection outcome as a UAV, otherwise it is a building.
The "Hypothesis Testing" results for all the single illumi-
nator cases are demonstrated in Fig. 17(c). As the reflection
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content may change prior to final publication. Citation information: DOI 10.1109/TVT.2022.3206863
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power gap between the UAVs and the buildings is large for
BS 1 to 10, we observe that the percentage of ’TP’ remains
higher than 60%. When building reflections become stronger
and power gap reduces, as shown by the remaining cases in
Fig. 17(b), incorrect discrimination occurrences like ’FN’ and
’FP’ in Fig. 17(c) emerge. To support stable discrimination,
we extend to multiple illuminators at the discrimination stage.
With the discrimination based on each individual BS, majority
voting is applied. The joint discrimination output is offered in
Fig. 18(a), where we see that the correct discrimination rate
improves from around 76% to over 90% via combining more
signals from different BSs. In comparison, the misclassifica-
tion rate reduces at the same time from 25% down to 10%.
2) Target Discrimination with Realistic RCS: Fig. 19(a)
and (b) report the distribution of the reflection power from
buildings and UAVs when using the signals from BS 1 and
BS 3, and a realistic RCS. We notice in Fig. 19 that the power
from a given type of target tends to reside within a certain
range for any given BS. We extend the discrimination strategy
proposed above to improve over this. We plot the average
reflection power from different BSs in Fig. 19(c) together with
the discrimination threshold. With the realistic RCS, one can
see that the reflection power from the UAVs and buildings
does not show distinguishable features as in the constant RCS
cases.
Therefore, we jointly analyze the detection results with
multiple BSs, and the output in Fig. VI-C(b) reaches 65% of
the correct discrimination rate if we use 8 BSs as illuminators
in total. It should be noted that the varying and weak reflection
power in Fig. 19(c) limits the maximum correct discrimination
rate to around 65% even if we leverage all 19 BSs. Moreover,
this strategy may not be generalized because the power dis-
tribution varies as the bistatic geometry changes. Hence, to
discriminate different types of targets with realistic RCS, one
needs to exploit the time and frequency shift properties of
the continuously detected targets from the (time) series of the
range-Doppler plots.
VIII. CONCLUSIONS
In this article, we introduce a novel approach to the design
and analysis of an integrated sensing and communication
UAV system. This co-design methodology allows for concep-
tualizing an efficient converged solution that permits UAVs
within a city to perform resilient RADAR collision avoidance
without significant investments into RADAR hardware on each
UAV, and with a possibility to reuse the ground network
infrastructure. As a potential future research direction, our
system model may be complemented by a detailed BS-to-
BS interference model, which then requires a cellular network
deployment model.
A key enabler to this work is our novel RCS calculation
algorithm, which allows approaching the challenge of bistatic
distributed RADAR modeling. This RCS characterization
method demonstrates highly accurate results under moder-
ate computational complexity. Our deterministic approach to
channel modeling may be extended further by considering the
multi-bounce effect for capturing more than one reflection
component in multipath environments. For this, a highly
efficient voxel cone tracing algorithm can be combined with
our introduced point-cloud method.
Moreover, we demonstrate how analytical modeling can
be applied to such a complex scenario, all while taking into
account the details of RCS patterns and Doppler processing
in the RADAR receivers. Finally, we illustrate the system
performance and scaling with extensive numerical results, thus
conclusively demonstrating the robustness of our method to
RCS pattern nulls, which is crucial for safety-centric UAV
applications such as collision avoidance.
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Iuliia Tropkina received her B.Sc degree in Elec-
tronics and Nanoelectronics from Peter the Great
Saint Petersburg Polytechnic University, Saint Pe-
tersburg in 2018 and M.Sc in infocommunication
technologies and communication systems. Now she
is with the Unit of Electrical Engineering at Tampere
University, Finland. Her research interests include
radio propagation, channel modeling, machine learn-
ing, and millimeter-wave communication.
Bo Sun completed his Master of Science (MSc)
in the field of Wireless Communication and RF
from Tampere University in 2019. He then joined
the Faculty of Information Technology and Com-
munication Sciences, Tampere University, to con-
tinue studying to Doctor of Philosophy (Ph.D.).
His research interests include 5G communication
systems, OFDM, Radar systems, and Reconfigurable
Intelligent Surface.
Dmitri Moltchanov received the M.Sc. and
Cand.Sc. degrees from the St. Petersburg State Uni-
versity of Telecommunications, Russia, in 2000 and
2003, respectively, and the Ph.D. degree from the
Tampere University of Technology in 2006. Cur-
rently he is University Lecturer in the Unit of Elec-
trical Engineering, Tampere University, Finland. He
has (co-)authored over 150 publications on wireless
communications, heterogeneous networking, IoT ap-
plications, applied queuing theory. In his career he
has taught more than 50 full courses on wireless and
wired networking technologies, P2P/IoT systems, network modeling, queuing
theory, etc. His current research interests include research and development
of 5G/5G+ systems, ultra-reliable low-latency service, industrial IoT applica-
tions, mission-critical V2V/V2X systems and blockchain technologies.
Alexander Pyattaev is the CTO of YL-Verkot Oy,
consulting in the area of wireless communication
system design. He has authored over 50 publications
on the subjects of medium access control in wireless
communications, simulation approaches for system
design, heterogeneous networking, and mobile com-
munication systems.
Bo Tan received the B.Sc and M.Sc degree in
communications engineering, Beijing University of
Posts and Telecommunications, in 2004 and 2008 re-
spectively. He received a PhD in Institute for Digital
Communications from the University of Edinburgh,
UK, in Nov 2013.
From 2012 to 2016, he carried out postdoc in
University College London and University of Bristol,
contributed to passive radar, pervasive sensing and
phased array radar for indoor robotic. He was a
lecturer in electronics engineering at Coventry Uni-
versity during 2017 and 2018. From 2019, he is a tenure track assistant
professor at Tampere University, Finland. His current research includes radio
signal processing for wireless communications and radar system, integration
of radio connectivity and sensing for intelligent machines. He is the member
of IEEE, active reviewer of multiple IEEE and IET journals in radar,
communications, wireless networks and machine learning.
This article has been accepted for publication in IEEE Transactions on Vehicular Technology. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/TVT.2022.3206863
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 17
Rui Dinis received the PhD degree from Instituto
Superior Técnico (IST), Technical University of
Lisbon, Portugal, in 2001 and the Habilitation in
Telecommunications from Faculdade de Ciência e
Tecnologia (FCT), Universidade Nova de Lisboa
(UNL), in 2010. He is an associate professor at FCT-
UNL and a researcher at Instituto de Telecomuni-
cações. During 2003 he was an invited professor at
Carleton University, Ottawa, Canada.
Rui Dinis is or was editor at IEEE Open Journal
on Communications, IEEE Transactions on Commu-
nications, IEEE Transactions on Vehicular Technology, IEEE Transactions
on Wireless Communications and Elsevier Physical Communication. He was
part of the Organizing Committee of several major IEEE ComSoc and VTS
conferences.
His main research interests are on signal processing techniques for wireless
communications, including modulations, MIMO systems, equalization and
multi-user detection, channel estimation and synchronization, and positioning
techniques.
Sergey Andreev is an associate professor of com-
munications engineering and Academy Research
Fellow at Tampere University, Finland. He has been
a Visiting Senior Research Fellow with King’s Col-
lege London, UK (2018-20) and a Visiting Postdoc
with University of California, Los Angeles, US
(2016-17). He received his Ph.D. (2012) from TUT
as well as his Specialist (2006), Cand.Sc. (2009),
and Dr.Habil. (2019) degrees from SUAI. He (co-
)authored more than 200 published research works
on intelligent IoT, mobile communications, and het-
erogeneous networking.
This article has been accepted for publication in IEEE Transactions on Vehicular Technology. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/TVT.2022.3206863
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/