# An IoT Architecture Leveraging Digital Twins: Compromised Node Detection
Scenario

Khaled Alanezi

Department of Computing,College of Basic Education, PAAET, Kuwait
<EMAIL_ADDRESS>Shivakant Mishra
This work has been submitted to the IEEE for possible publication. Copyright
may be transferred without notice, after which this version may no longer be
accessible. Computer Science Department,University of Colorado, Boulder, USA
<EMAIL_ADDRESS>
###### Abstract

Modern IoT (Internet of Things) environments with thousands of low-end and
diverse IoT nodes with complex interactions among them and often deployed in
remote and/or wild locations present some unique challenges that make
traditional node compromise detection services less effective. This paper
presents the design, implementation and evaluation of a fog-based architecture
that utilizes the concept of a digital-twin to detect compromised IoT nodes
exhibiting malicious behaviors by either producing erroneous data and/or being
used to launch network intrusion attacks to hijack other nodes eventually
causing service disruption. By defining a digital twin of an IoT
infrastructure at a fog server, the architecture is focused on monitoring
relevant information to save energy and storage space. The paper presents a
prototype implementation for the architecture utilizing malicious behavior
datasets to perform misbehaving node classification. An extensive accuracy and
system performance evaluation was conducted based on this prototype. Results
show good accuracy and negligible overhead especially when employing deep
learning techniques such as MLP (multilayer perceptron).

###### Index Terms:

Internet of Things, Digital-Twin, Fog Computing, Compromised Node Detection.

##  I Introduction

The Internet of Things (IoT) has brought increased convenience and
productivity to homes, factories, malls, hospitals, sidewalks, city squares
and more. Typically, an IoT application is a distributed system with
components deployed across the IoT-Fog-Cloud continuum. IoT components perform
data collection from the environment and feed the data to smart decision-
making systems running in the cloud with the fog layer playing a staging role
for data filtering and aggregation. Building applications on top of such
complex infrastructure is inherently difficult thereby leading to
interoperability issues [1]. Digital-Twins (henceforth DT) has been proposed
as a tool for managing these systems, predicting their behavior under
different scenarios and improving their performance. DT is defined as a
virtual replica of a physical entity such as people, assets, systems or
processes [2]. The concept of DT is not new, however, as it stems from
existing mature concepts such as IoT, AI and big data [3]. Despite showing
clear benefits for IoT, a systems implementation showing how to utilize DTs in
an IoT application and how the interplay of different components affects the
performance is still lacking. This work aims at filling this gap while
focusing on compromised node as an example scenario.

While IoT applications have enhanced our lifestyles in many areas, there is an
associated cost of potentially exposing user’s privacy and security.
Typically, IoT nodes embed wide array of sensors and are connected to the
network, thereby making them prime targets for attackers. Once an IoT node is
exploited, an attacker would typically couple the attack with payload codes
that can achieve certain objectives. First, an attacker can carry a Cyber-
Physical attack [4] to introduce data anomalies causing control system failure
thereby leading to physical damage [5, 6]. Second, once inside the network
(i.e. network intrusion), an attacker can utilize the node to launch large
scale botnet attacks such as the Mirai IoT Botnet [7]) which can lead to large
scale service disruption.

While there has been a plethora of research done in the area of preventing
and/or detecting node compromises over the last 30+ years, compromised node
detecting in an IoT environment presents some unique challenges. First,
typically only weak security measures are taken to protect IoT nodes, which
can be attributed to the focus on keeping the node cost low and ensuring a
plug-and-play operation, so that they can be deployed in large numbers.
Second, these nodes are often placed remotely in the wild with little or no
monitoring with many IoT vendors failing to provide proper measures or
automated-tools for timely security updates [8]. Third, the sheer number and
variety of IoT devices in an IoT infrastructure typically running into
hundreds and even thousands means an increased attack surface available to the
attackers and for the system administrators to monitor and maintain. Finally,
complex interplay among thousands of nodes makes it difficult to identify
faulty or anomalous behavior often confined to a small number of nodes under a
variety of different scenarios.

To address these challenges, we propose a fog-based architecture that utilizes
the concept of a digital-twin in which a virtual replica of the IoT
infrastructure is created in the fog to momentarily replicate IoT node state
changes where threat detection and mitigation can take place. Our proposed
architecture uses DT to employ detection techniques for both data anomaly and
network intrusion attacks for enhanced IoT network security. Our architecture
benefits from using DTs by utilizing two of its conceptual features [9].
First, by definition, the DT concept proposes to only mirror properties and
characteristics that are of importance to the application context.
Consequently, we only reflect status information represented by sensor values
and network activity summary information in the DT. Clearly, by focusing only
on important information our solution can save device energy, fog server space
and network resources. Second, creating DTs for all IoT nodes paves the way
for understanding the aggregate behavior of those nodes thereby leading to
better governance and control of the complex IoT system. In summary, the
contributions of this work are three fold:

  1. 1.

We provide a detailed design of a fog-based architecture utilizing the concept
of DTs for compromised node detection in an IoT environment.

  2. 2.

We show how this architecture can utilize various models for compromised IoT
node based on data anomaly and network intrusion detection. We also report the
accuracy and performance of those models.

  3. 3.

We provide a prototype implementation and extensive performance evaluation of
the architecture by utilizing open-source solutions such as Ditto [10] and
Docker [11].

The flow of the remaining sections of the paper is as follows. In Section II
we present the design of the architecture and introduce the details of the
datasets utilized to build the data anomaly and network intrusion models.
After that, Section III presents related works followed by Section IV which
provides technical details of the prototype implementation for the
architecture and the models. In Section V we present system performance
measurements for the prototype before concluding in Section VI.

##  II Design

###  II-A Architecture

Figure 1: Solution Architecture

As shown in Figure 1, the proposed architecture spans the edge-fog-cloud
continuum. The edge layer typically consists of battery-powered IoT devices
with limited resources. Those devices are meant to perform sensing and
actuation in the environment. At the other extreme end of the architecture is
the cloud layer, which typically has abundant storage and computing resources.
The architecture utilizes a cloud server to perform compute-intensive training
of malicious node detection models. In the middle of the architecture is the
fog layer providing low-latency access for IoT devices to the fog server. We
propose to utilize an edge server [12] installed in the fog to provide low-
latency access to trained malicious node detection models. These models will
be harnessed to monitor nodes activity at the edge of the network to detect
malicious behavior on spot.

We now turn into describing the functionality of each component in the
architecture. Starting from the edge layer, the IoT devices have the sensing
and actuation capabilities to aid various IoT applications. Those devices are
connected to the network using an IoT gateway. Devices at the edge layer have
one-network-hop access to a fog server running Ditto [10]. Ditto is an open
source framework for managing DTs. Through APIs exposed by Ditto, device DTs
receive status updates from IoT devices reflecting corresponding device status
change (i.e. sensor data changes). In addition, DTs receive status update from
the IoT gateway that are related to the network behavior of the device
(Detailed design of DTs is discussed in Section II-B).

DT status updates received from the IoT environment are used in two ways.
First, the sensory status and the network status are used as input for the
data anomaly model and network intrusion model respectively to discover any
anomalies in node behavior. The classification result is sent to the
corresponding DT, and only if the result shows that there is a possible
anomaly, a message is sent from the DT to the corresponding device to take the
needed action. Note that the actions themselves are defined by the system
administrators, e.g. quarantine the device or shut it down to avoid infecting
other nodes in the environment. The benefit from combining results from both
classifiers will lead to decreased false negatives thereby increasing
confidence in the overall system. The second usage of reported status updates
is to forward them via the Sensor/Network behavior monitoring components to
the Sensor/Network databases in the cloud. The latter will act as the ground
truth for the Data anomaly and the Network intrusion training done
periodically. Note that behavior monitoring should involve system
administrators utilizing malware analysis techniques for detecting IoT malware
[13]. Once a model is updated in the cloud by retraining, new parameters of
the model are pushed to the fog server to be used. The periodic updates ensure
that the architecture is adaptive to changing norms in the environment. We
discuss the design of the data anomaly model and network intrusion models in
sections II-C and II-D respectively.

###  II-B Digital Twin Design

Figure 2: Digital Twin Deployment Status

The concept of DTs has been around for almost two decades now. However, a
standard design and implementation guidelines for the concept is still lacking
[14]. Consequently, the design approach for the DT in this project will follow
the 5-steps guided approach for DT evolution [2] of mirroring, monitoring,
simulation, federation and autonomous. We begin by covering the first two
steps of mirroring and monitoring. The remaining three steps represent later
design stages that build on the understanding of the first two stages, which
we leave as a future work as described in Section VI.

TABLE I: Utilized Datasets for Data Anomaly and Network Intrusion Models Dataset Name |  Scenario |  No. of Records |  No. of Features |  Sample Features |  Labels
---|---|---|---|---|---
AnoML-IoT [15] |  Data Anomaly |  6,558 |  6 |  Timestamp, temperature reading in C and humidity percentage. |  Normal and Anomalous
DS2OS [16] |  Data Anomaly |  357,941 |  13 |  Timestamp, src ID, src type, dest. type, operation and value. |  Normal and Anomalous (Probing, DoS, Mal. Control, Mal. Operation, Scan, Spying and Wrong Setup.)
IoTID20 [17] |  Network Intrusion |  625,783 |  86 |  Timestamp, flow duration, min/max fwd packet size and flow bytes/s. |  Benign and Malicious (Mirai, DoS, Scan and MITM ARP Spoofing.)

As can be seen in Figure 2, the are two types of information mirrored about an
IoT device in the DT. First, the attributes of the device cover static
metadata such as the unique identifier of the device, the manufacturer and the
location coordinates if any. Second, the features contain dynamic information
that changes over time and are replicated to the DT momentarily. For data
anomaly monitoring we mirror changing sensors’ values as captured by the IoT
node micro-controller and the calls that the IoT node make to other nodes or
services. On the other hand, for network monitoring we mirror summary
information related to the exchanged network packets by the device. The exact
sensor values and network summary status that must be replicated to the DT
depends on the input parameters of the utilized data anomaly and network
intrusion models. Sections II-C and II-D describe three machine-learning
models that we will evaluate for use in the architecture. Whenever any of the
models is actually deployed on the fog server, its corresponding features must
be replicated to the DT in order to be used by the machine-learning model for
device behavior classification. We evaluate the performance of the models when
integrated with the DT in Section IV.

###  II-C Data Anomaly Models

Monitoring data anomaly involves inspecting data generated from sensors to be
consumed by an application or a service. Table I lists three example datasets
we used for the compromised node detection along with summary information for
each dataset. First, the AnoML-IoT dataset contains sensor readings captured
over two days for temperature, humidity, light, loudness and air quality
sensors. The authors of this dataset created data anomalies by subjecting the
sensors to an air dryer for some periods of time. Data coming during this time
is marked as an anomaly. Otherwise, sensor readings are marked as benign.
Second, DS2OS is a synthetic dataset created by the Distributed Smart Space
Orchestration System. The data is generated from a simulated setup including
four IoT sites each containing various services that can call each other.
Example services include thermostat and door lock controllers. A service can
read or write a value to or from another service depending on the required
action. Beside the normal traffic, the authors simulated communications for
various attacks including data probing, denial-of-service, malicious control,
malicious operation, scan, spying and wrong setup. In summary, we will use the
first two datasets as an example for an IoT deployment generating malicious
behavior at the perception layer (i.e. data anomalies).

###  II-D Network Intrusion Models

In addition to false data injection attacks to confuse an application, a
compromised node could be exploited by an attacker to launch network attacks
such as port scans, DDoS attacks or spoofing. These attacks often lead to data
theft, data corruption or system failures. In this part of the architecture we
focus on discovering and stopping network intrusion attacks. In order to
achieve this goal, we utilized the IoTID20 dataset also described in Table I.
This dataset is built using an actual IoT network consisting of two smart home
devices (AI Speaker and Security camera) and multiple laptops and smartphones
connected to an isolated LAN. Various attacks are then deployed or simulated
using this setup such as Mirai, Denial-of-Service (DoS), Scan and Man-In-The-
Middle Address Resolution Protocol (MITM ARP) spoofing attacks. Network packet
captures are then extracted and network packets containing summary features of
communication sessions are labeled as benign or malicious accordingly.

##  III Related Work

This work investigates integrating DTs in IoT systems. The application served
by the resultant architecture is compromised node detection by utilizing data
anomaly and network intrusion. We summarize in this section the recent works
in each of these areas.

###  III-A Digital Twins in IoT

Digital-Twins DTs, a concept popular in manufacturing, has been proposed
mainly for use in Industrial IoT (IIoT). With the aid of DT concept, an IIoT
controller collects massive data from devices to take smart environment-wide
decisions [18, 19]. To serve this purpose, a reference model of DTs in IIoT is
proposed [20] which involves mirroring the internal structure, runtime
environment, APIs of the physical objects as well as features such as
scalability, interoperability, security and privacy.

Also, the concept of DTs has been recently proposed in the IoT context for
staff safety management in cold warehouses’ hazardous environments [21]. Here,
a DT is created to synchronize the time/space information of the staff with
the controller. Consequently, the controller will run algorithms to detect
staff motionless status so as to alert first aid workers in a timely manner.
In addition to safety, the concept of DTs is utilized in IoT context for
elderly health [22] where DTs are used to mirror medical data obtained from
wearable devices to monitor and diagnose health issues.

Furthermore, the concept of DTs is utilized to enable smart buildings and
smart cities. For the former, DTs replicate static and dynamic building data
for enhanced building monitoring and management [23]. Whereas for the latter,
DUET [3] is proposed as a DT framework built for smart city applications. DUET
creates a cloud of integrated DT models that can be queried to perform smart
city planning (i.e. traffic, air pollution, or noise pollution) at the city
level.

DTs are also proposed in IoT for smart agriculture systems [24] where the goal
is to monitor farm information remotely thereby reducing manual efforts and to
simulate the effect of intervention techniques on farm productivity. Also,
battery energy storage systems BESS [25] are also shown to benefit from the DT
concept so as to prevent possible failures and cyberattacks.

Lastly, a survey paper by Minerva et al. [9] discussed DTs features and
architectures in the context of IoT.

###  III-B Data Anomaly Detection in IoT

IoT applications involve data collection to provide controlled services to
users. Consequently, an attacker can impact the accuracy of the controller
creating anomalies in sensory data [26]. There are several works aimed at
detection of data anomaly in IoT. AnoML-IoT [15] presents a pipeline for data
anomaly detection with the goal of masking heterogeneity in IoT systems. On
the other hand, a preliminary work by Hussain Et al. [27] focuses on utilizing
explainable AI (XAI) to understand the output of deep learning data anomaly
techniques for IoT. Lastly, a survey paper [28] presented a summary of
techniques to detect data anomalies in IoT sensory systems and the impact of
Cloud-Fog-Edge architectures on them.

###  III-C Network Intrusion Detection in IoT

Malicious node behavior other than producing data anomaly could manifest in
performing anomalous network activity. Researchers created datasets [17, 29,
30] containing the network traffic of benign and malicious nodes in order to
build models that can automatically detect malicious traffic. Based on such
datasets various techniques and architectures to detect malicious network
behavior are proposed. EDIMA [7] is a full architecture geared towards
detection of network intrusion activity during the scanning phase instead of
the attack phase. Diro Et Al. [31] proposed the use of deep learning models
over tradition ML in order to cope with newly surfacing small mutations of
malware. Also, Convolutional Neural Networks CNN were proposed [32] for
malicious traffic detection and classification. Finally, running network
traffic classification models on resource-limited IoT microcontrollers is also
investigated [33].

##  IV Experimental Work and Implementation

We propose a dynamic architecture to detect malicious IoT nodes. This requires
real-time monitoring of node behaviors and flagging of observed anomalies as
they occur. To achieve this objective, the architecture must support two
requirements. First, the ability to capture relevant node behavior. Second,
the availability of dynamically-trained machine-learning models for online
behavior classification. We begin this section by describing the hardware and
software components involved in building the architecture and how these
components are integrated. These details are described in Section IV-A. After
that, we describe the classification models and their accuracy based on
various machine-learning classifiers when applied to the chosen datasets. As
stated in Section II, we propose that the architecture must train two types of
models namely the data anomaly model and the network intrusion model. We
report in this section the design and accuracy for the two models when trained
with various classifiers. Note that the models along with the codes to build
them are made publicly available on
OSF111https://osf.io/mh6es/?view_only=f7dce520b1b64ce198ab039563c29e5f.

###  IV-A Architecture Implementation

TABLE II: Hardware and Software Components Used to Build the Architecture Prototype. Component Name |  Type |  Role
---|---|---
MacBook Air |  Hardware |  Fog server.
Arduino Uno R3 [34] |  Hardware |  IoT device Microcontroller.
Arduino Ethernet Shield [35] |  Hardware |  Connects microcontroller to the LAN.
Huawei Wireless Router |  Hardware |  Wireless LAN router.
Ditto [10] |  Software |  A framework for implementing Digital Twin Capabilities for IoT.
Docker [11] |  Software |  Container engine for building Ditto, data anomaly & network intrusion containers.
Data Anomaly Model Container |  Software |  Container running the data anomaly model.
Network Intrusion Model Container |  Software |  Container running the network intrusion model.
Postman [36] |  Software |  Software platform used to call Ditto to create digital twins.

We built a prototype for the architecture presented in Section II. The
prototype is a distributed solution spanning the edge of the network and the
fog layer as described earlier. The components utilized to build this
prototype are listed in Table II. Note that the code for this prototype is
also shared under the same OSF project below the Online Experiment component.

We utilized a MacBook Air laptop to resemble a fog server. The fog server is
typically a tethered (powered) machine with good computing capabilities that
is one-network-hop away from edge nodes. On the other hand, an Arduino Uno R3
board was used to resemble the IoT node. We stacked an Ethernet shield with
the Arduino Uno to provide it with Ethernet capability and connected it along
with the edge server to the same LAN using a Huawei wireless router.

The prototype relied on Eclipse Ditto [10] for implementing the needed DT
functionality. This functionality includes configuring DTs, online replication
of DT state from the physical IoT node to the virtualized replica and
observing DT state changes. To run Ditto, we deployed the pre-built ditto
docker images on the edge server.

We also used Docker [11] to dockerize and deploy python scripts for loading
the machine-learning models used for performing online classification. Each
script will load a pre-trained model that is stored on disk in a pickle file
(*.pkl) [37] and listen to a TCP socket to receive requests for record
classification. We evaluated the performance of the overall architecture using
the built prototype in Section V-C.

DTs must be configured on Ditto before the mirroring and monitoring processes
take place. Listing 1 demonstrates an example JSON configuration for creating
a new DT in Ditto. This configuration pertains to the case of monitoring data
anomalies based on the knowledge gained from the AnoML-IoT dataset as
described in Section II-C. Note that we only cover the AnoML-IoT scenario in
our online implementation which is sufficient to measure the system
performance of the architecture. Ditto requires to identify a definition
clause, which should contain a unique identifier for the DT. This identifier
will be used for later communication with the DT to update/observe its state
features values as they change. The attributes section of the JSON document
contains static information for the DT such as its logical location,
manufacturer, model and so on. Finally, the features section tracks the online
status of the DT. In the case of the AnoML-IoT scenario shown, it lists the
readings of the four sensors as captured by the IoT node that will be
monitored to detect anomalies in the environment.

Section V-C evaluates the systems performance of the architecture while
utilizing various datasets/ML classifiers combinations.

Listing 1: DT Configuration

⬇

{

”definition”:”kw.edu.paaet:arduino:1.0”,

”attributes”:{

”manufacturer”:”Arduino Inc”,

”location”:”CS Dept. Corridor”,

”serialno”:”1”,

”model”:”Arduino Uno”

},

”features”:{

”temperature”:{”properties”:{”value”: 0.0}},

”humidity”:{”properties”:{”value”: 0.0}},

”light”:{”properties”:{”value”: 0.0}},

”loudness”:{”properties”:{”value”: 0.0}}

}

}

###  IV-B Data Anomaly Models Implementation

We utilized two datasets for data anomaly detection. First, the AnoML-IoT
dataset represents a scenario where the attacker is deliberately producing
erroneous sensor values or data anomalies. Second, the DS2OS also included an
attacker controlling the application as it contains data traces produced at
the application level. However, instead of producing erroneous sensor values,
in this dataset the application is producing malicious calls for other
application level services in the same environment. For each dataset we ran
three types of classifiers namely Random Forest RF, Support Vector Machines
SVM and Multilayer Perceptron MLP. The accuracy results are shown in Table
III. Random forest was chosen due to its ability of visualising and studying
the classification results. We kept the number of estimators to 100, the
default number in Scikit Learn [38]. We also used SVM due to its efficiency
with numerical as well as categorical features since the datasets contained
both types of features. Finally, we used MLP as we wanted to also include a
deep learning classifier in the experimental design. MLP is known to perform
well with tabular data similar to the datasets we use. We have chosen to
implement MLP with 3 hidden layers and 11 neurons at each layer as a starting
point. We noticed that we were able to train the datasets efficiently with
this choice. Optimizing MLP is an iterative process that is out of the scope
of our work since our focus is to measure the system performance of the
architecture.

TABLE III: Accuracy for Data Anomaly Classifiers Based on Random Forest (RF), Support Vector Machines (SVM) and Multilayer Perceptron (MLP) | AnoML-IoT | DS2OS
---|---|---
| RF(n=100) | SVM | MLP | RF(n=100) | SVM | MLP
Accuracy | 0.989 | 0.938 | 0.966 | 0.993 | 0.993 | 0.993
Precision | 0.989 | 0.952 | 0.977 | 0.986 | 0.984 | 0.984
Recall | 0.983 | 0.899 | 0.942 | 0.893 | 0.887 | 0.894
F1-Score | 0.986 | 0.921 | 0.958 | 0.934 | 0.930 | 0.934

We now turn into comparing the accuracy results for the three classifiers
within each dataset as seen in Table III. For the AnoML-IoT dataset, a
relatively small dataset, we noticed that RF produced the best results in
terms of the four metrics (i.e. Accuracy, Precision, Recall and F1-Score).
However, the difference margin is small since for example the largest gap is
between RF and SVM at the recall metric. Recall reflects the ability of the
classifier to correctly flag all cases positive and negative. Note that this
measure was the most difficult for all the three classifiers.

For the DS2OS dataset, still Table III, a dataset that is larger than the
AnoML-IoT (refer to Section II-C for datasets description), all the three
classifiers produced the same accuracy of 99.3%. The accuracy is a common
metric that reflects the ability of the classifier to correctly flag positive
and negative instances. Also in this dataset, the recall achieved the worst
results with RF producing the lowest result. Conversely, RF achieved the best
result when it comes to precision.

###  IV-C Network Intrusion Models Implementation

For the network intrusion, we utilized the IoTID20 dataset which consists of
features extracted from packet capture (*.pcap) files containing packet
captures for attack scenarios as well as well as benign scenarios. This
dataset is a typical dataset to be used in intrusion detection solutions.
Detecting malicious network behavior for an IoT node requires capturing the
network packets produced by this IoT node and extracting features from those
packets to be used by the classifier.

TABLE IV: Accuracy for Network Intrusion Classifiers Based on Random Forest (RF), Support Vector Machines (SVM) and Multilayer Perceptron (MLP) | IoTID20
---|---
| RF(n=100) | SVM | MLP
Accuracy | 0.985 | 0.980 | 0.994
Precision | 0.992 | 0.970 | 0.993
Recall | 0.879 | 0.859 | 0.958
F1-Score | 0.927 | 0.906 | 0.975

Figure 3: IoT Node Implementation

Figure 4: Schematic Diagram

Figure 5: Software

Table IV reports the accuracy for the same three classifiers used with the
data anomaly models when applied to the network intrusion dataset. Notice that
MLP produced the best results across all the metrics, proving our design
choice of using it with tabular data that is large in size. When we compare
this result with data anomaly we see that RF produced the best results mostly
in all cases. This result can be attributed to the size of the IoTID20 dataset
which is larger than the other two datasets. We note that the choice of which
machine-learning classifier not only impacts the accuracy but also affects
important measures relevant to system efficiency such as model size, model
loading time and classification time. These measures are particularly
important due to the distributed nature of our system architecture. Hence, we
provide a complete system evaluation for the three datasets when utilizing the
three classifiers in Section V.

###  IV-D IoT Node Implementation

IoT nodes contain sensors and actuators to interact with the IoT environment.
In addition, a networking module must be present through which the node can
send and receive data and commands. We describe in this section an IoT node
that we built to cover these requirements. The node represents the data
anomaly in the AnoML-IoT scenario described in Section II. In this scenario,
data from four sensors must be captured and mirrored to the DT namely
temperature, humidity, loudness (i.e. microphone) and light sensors. Note that
we did not implement the air quality sensor sense we noticed that the values
of air quality in the dataset are not changing. By looking at Figure 5 we see
that to add Wi-Fi capability to the Arduino board, we stacked in Ethernet
shield (model: ESP13) on top of it. Afterwards, 5v, 3.3v, ground and analog
connections of the sensors were connected to the ESP13 shield by means of
jumper wires and a small breadboard. The schematic diagram for these
connections is shown in Figure 5. Notice from the figure that the light sensor
(model: Photoresistor LDR Light Sensor Module) and temperature and humidity
sensors (model: DHT11) needed to pull 5v current from the board. Whereas, the
audio sensor pulled 3.3v current from the board to minimise the noise. The
three sensor boards produced an analog output that was connected to the
Arduino to be read over Wi-Fi. As shown in Figure 5, we adapted the python
software and implementation from hackster.io [39] and changed it to display
our four sensor values. Once the python software is connected to the node it
can poll the sensor values periodically and push them to the DT via Ditto
APIs.

##  V Performance Evaluation

The overall performance of the architecture is impacted by how well the
individual components perform as well as the overhead resulting from
integrating those components. We begin in sections V-A and V-B by gauging the
performance of the individual machine-learning models. After that, in Section
V-C we measure the performance of the overall architecture when all the
components are put together.

###  V-A Data Anomaly Performance Evaluation

TABLE V: Time Performance for Data Anomaly Classifiers Based on Random Forest (RF), Support Vector Machines (SVM) and Multilayer Perceptron (MLP) ML Algorithms | AnoML-IoT | DS2OS
---|---|---
| Size | Loading (ms) | Fitting (ms) | Classification (ms) | Size | Loading (ms) | Fitting (S) | Classification (ms)
RF | 2.4 MB | 688.02 | 515.60 | 10.26 | 3.4 MB | 28.84 | 51.99 | 6.60
SVM | 41 KB | 1.16 | 126.12 | 0.34 | 20.60 MB | 25.19 | 284.58 | 2.76
MLP | 17 KB | 5.96 | 2,698.22 | 0.14 | 146 KB | 6.30 | 56.71 | 0.819

The choice of the dataset in terms of its size as well as the type of ML
classifier utilized will have a significant impact on the performance of the
architecture. The impact of these choices on the performance of the data
anomaly model is shown in Table V. We see from the table that the AnoML-IoT
produced smaller model sizes compared to the DS2OS for all classifiers. This
is normal since it is smaller in size with 6K records compared to 350K in the
case of the DS2OS dataset. Consequently, the bigger size of the DS2OS models
resulted a higher loading times compared to AnomML-IoT. Model loading time is
an important metric as we can not assume that the model will always be readily
available in memory when needed. Therefore, we cover the performance of both
loaded models and unloaded models for all scenarios when we measure the
overall architecture performance in Section V-C. Beside the loading time, we
report the fitting time for the two datasets across the three machine learning
models. We see that the fitting time is very high for the larger DS2OS
dataset. We also see that the machine-learning model producing the highest
fitting time for AnoML-IoT is MLP whereas the highest fitting time for the
DS2OS is produced by SVM. This unpredictable performance for the fitting time
is insignificant as the fitting process will take place offline. Finally, we
see that time results were consistent for the classification time across the
three machine-learning classifiers with RF having the highest classification
time and MLP having the lowest. Classification time is very low (<1ms) in the
case of MLP making it the most suitable for use in the distributed
architecture.

###  V-B Network Intrusion Performance Evaluation

TABLE VI: Time Performance for Network Intrusion Classifiers Based on Random Forest (RF), Support Vector Machines (SVM) and Multilayer Perceptron (MLP) ML Algorithms | IoTID20
---|---
| Size | Loading (ms) | Fitting (S) | Classification (ms)
RF | 26 MB | 69.83 | 44.77 | 5.92
SVM | 18.3 MB | 13.85 | 1489.21 | 14.27
MLP | 35 KB | 2.48 | 128.00 | 0.67
Figure 6: Time Elapsed Between DT State Change Until Receiving the
Classification Result for Different Combinations of Datasets/ML
Classifiers/Memory Loading Status

We report the model size and time performance for the network intrusion model
that is based on the IoTID20 dataset in Table IV. Notice that both RF and SVM
created large model sizes in the order of MBs leading to higher loading times.
Hence, these models must be carefully introduced to the architecture to ensure
that models are pre-loaded so as to avoid impacting the performance. In terms
of fitting time, the results where in harmony with the results achieved with
the DS2OS dataset. The lowest fitting time was achieved by RF and the highest
by SVM. Also, for classification time, MLP produced the lowest results making
it the most suitable for use in a distributed setting.

###  V-C Architectures Performance Evaluation

Finally, we conducted an experiment to measure the performance of the
architecture when different possibilities of individual components (i.e.
datasets and classifiers) are utilized. Figure 6 reports the total time for
detecting an anomaly when a change in the state of a DT is observed. Notice
that we measure the total time at the fog server level since it has the
administrative role in the environment in detecting malicious nodes and
blocking them. More specifically, the time reported in the figure is the time
elapsed between receiving a change in the state from the DT until the
classification result is received from data anomaly or network intrusion
container to the controller. Experiments cover both scenarios of a pre-loaded
models in memory waiting for classification queries (Loaded) versus only
loading a model when the request is received (unloaded). We report the average
time from 5 runs for each experiment with standard error bars. Notice from the
figure that in most of the cases, a loaded model achieved better time
performance when compared to the corresponding case of an unloaded model.
However, there are few exceptions (e.g. DS2OS/SVM and DS2OS/MLP scenarios)
where the time is comparable. We attribute such performance variability to two
reasons. First, Ditto’ unstable performance leading to variability form one
run to another. Second, Docker’s [11] cashing behavior as docker pre-loads
layers from previously loaded images to optimize the performance. Overall, we
noticed from Figure 6 that when models are loaded the total time to detect an
anomaly after observing a state changes is 500ms-600ms. This reasonable
additional time is justified by the added security layer to detect and block
malicious nodes in the environment.

##  VI Conclusion and Future Work

This paper demonstrated the design, implementation, and evaluation of an
architecture for compromised IoT node detection. The presented architecture
has three important features. First, the concept of DT is utilized to only
replicate relevant node information needed for malicious behavior detection.
Second, classification is performed in the fog layer for low latency access to
classifiers. Third, the architecture combines data anomaly and network
intrusion detection methods for better coverage of malicious behavior
detection leading to increased detection coverage. System evaluation of the
architecture and the used classifiers demonestrates good accuracy as well as
negligible overhead making it suitable for use in IoT solutions. In the
future, we plan to vary system components related to the
communication/application and study the impact on the performance. For
example, connectivity using BLE or LoRa can be explored where BLE is suitable
for body area networks and LoRa is suitable for smart agriculture. Also, we
plan to test the system scalability by simulating calls from large number of
IoT nodes and collecting larger volumes of data such as audio and video data.

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# Graph Koopman Autoencoder for Predictive Covert Communication Against UAV
Surveillance

Sivaram Krishnan1, Jihong Park1, Gregory Sherman2, Benjamin Campbell2, and
Jinho Choi1
1School of Information Technology, Deakin University, Australia
2Defense Science and Technology Group, Australia

###### Abstract

Low Probability of Detection (LPD) communication aims to obscure the very
presence of radio frequency (RF) signals, going beyond just hiding the content
of the communication. However, the use of Unmanned Aerial Vehicles (UAVs)
introduces a challenge, as UAVs can detect RF signals from the ground by
hovering over specific areas of interest. With the growing utilization of UAVs
in modern surveillance, there is a crucial need for a thorough understanding
of their unknown nonlinear dynamic trajectories to effectively implement LPD
communication. Unfortunately, this critical information is often not readily
available, posing a significant hurdle in LPD communication. To address this
issue, we consider a case-study for enabling terrestrial LPD communication in
the presence of multiple UAVs that are engaged in surveillance. We introduce a
novel framework that combines graph neural networks (GNN) with Koopman theory
to predict the trajectories of multiple fixed-wing UAVs over an extended
prediction horizon. Using the predicted UAV locations, we enable LPD
communication in a terrestrial ad-hoc network by controlling nodes’ transmit
powers to keep the received power at UAVs’ predicted locations minimized. Our
extensive simulations validate the efficacy of the proposed framework in
accurately predicting the trajectories of multiple UAVs, thereby effectively
establishing LPD communication.

###### Index Terms:

Koopman operator theory; Prediction of dynamical systems; Covert wireless
network; Dynamic power control

##  I Introduction

In the evergrowing landscape of mobile surveillance and digital warfare,
enabling covert communication is paramount [1]. While existing cryptography
and physical layer security (PLS) focus on concealing the content of
communication [2], covert communication aims to hide the existence of
communication links from untrustworthy entities or adversaries. In wireless
systems, this covert communication challenge is formulated as a problem of low
probability of detection (LPD) [3], which seeks to minimize transmit power to
evade signal detection while maintaining minimal connectivity.

Figure 1:  An illustration of covert communication against UAV surveillance
(top), wherein ground nodes (bottom) adjust transmit power for achieving low
probability of detection based on UAV trajectory prediction by their
associated central unit (left).

The LPD problem has been extensively studied in point-to-point communication
scenarios [4, 5], wherein Alice communicates with Bob under the surveillance
of Willie. Extending this to ad-hoc networks, LPD with multi-hop connectivity
constraints has been recast by the minimum-area spanning tree (MAST) problem
[6, 7]. This approach aims to minimize the network’s coverage area to minimize
the probability of signal detection by unknown eavesdroppers. Several
algorithms have been developed to solve the MAST problem, including branch-
and-cut algorithms [8], but their complexity increases with the number of
nodes. To address this scalability issue, deep learning has been employed to
solve the MAST problem with low latency, regardless of node quantity [9].
However, these existing works do not account for emerging mobile surveillance
technologies, such as unmanned aerial vehicle (UAV) assisted surveillance [1,
10], nor do they consider intelligent nodes capable of predicting surveillance
movements.

To address these gaps, in this article we introduce a novel LPD scenario where
a ground ad-hoc network aims to achieve LPD against a surveillance network of
mobile UAVs, as illustrated in Fig. 1. The ground users are coordinated by a
central unit (CU) that predicts UAV mobility and conveys this information to
ground users to optimize transmit power. This problem is non-trivial,
especially considering the nonlinear and complex mobility patterns of UAVs
[11].

To cope with this new LPD challenge, we first develop a novel multi-UAV
nonlinear dynamics prediction algorithm based on graph neural networks (GNNs)
[12, 13] and Koopman operator theory [14], coined graph-based Koopman
autoencoder (GKAE). In GKAE, the GNN spatially reduces a snapshot of multi-UAV
network topology into a single latent state, while the Koopman operator based
autoencoder linearizes and learns the temporal mobility pattern of these
latent states, enabling long-term and scalable multi-UAV movement prediction
with low latency. With these predicted UAV locations, we optimize transmit
power using a branch-and-cut algorithm. Our proposed GKAE successfully
predicts the trajectories of 4 UAVs over 80 future time slots with a mean-
squared error of $0.0025$. This enables achieving LPD with the UAV’s received
power being at least 18% lower than their signal detection threshold.

##  II Background: Koopman Operator Theory

Mobility prediction is severely challenged under nonlinear dynamics.
Traditional linearization techniques such as Jacobian approximation is
accurate within a short-term interval, hindering long-term prediction. Koopman
operator theory [14] offers an effective alternative, which linearizes not a
single point but the subspace of entire points. To be specific, consider a
state vector ${\bf x}(t)\in{\cal X}\subseteq{\mathbb{R}}^{N}$ of a node at a
discrete time $t\in{\mathbb{N}}$. The nonlinear temporal dynamics of ${\bf
x}(t)$ can be described as

${\bf x}(t+1)={\bf F}({\bf x}(t)),$ (1)

where ${\bf F}$ is a flow map. Consider that $g:{\cal X}\to{\mathbb{R}}$ is a
measurement function. Koopman operator theory states that there exists a
linear (infinite-dimensional) operator ${\cal K}$ that acts to advance all
$g$, i.e.,

$\displaystyle{\cal K}g=g\circ{\bf F},$ (2)

where $\circ$ represents the composition operator and ${\cal M}$ denotes a
smooth manifold. Applying (2) to (1), we have

$\displaystyle g({\bf x}(t+1))=g\circ{\bf F}({\bf x}(t))={\cal K}g({\bf
x}(t)),$ (3)

where $g({\bf x}(t))$ is an observable measured at time $t$. This can be
extended to the case with multiple observables. Precisely, let ${\bf
g}(t)=[g_{1}(t)\ \ldots\ g_{M}(t)]^{\rm T}$, where $g_{m}(t)=g_{m}({\bf
x}(t))$. Then, from (3), we have

${\bf g}(t+1)={\cal K}{\bf g}(t).$ (4)

If ${\bf g}(t)\in{\cal G}$ and ${\cal K}{\bf g}(t)\in{\cal G}$, where ${\cal
G}$ is a finite-dimensional space, ${\cal G}$ becomes a Koopman invariant
subspace. In this case, ${\cal K}$ becomes a finite-dimensional linear
operator and is represented by a matrix ${\bf K}\in{\mathbb{R}}^{M\times M}$,
which is called the Koopman matrix of dimension $M$. The eigenvalues and
eigenvectors of ${\bf K}$ describe the linear evolution of the dynamical
system in the Koopman invariant subspace. A prerequisite to discovering ${\bf
K}$ is to find a Koopman invariant subspace. While this has been tackled
traditionally using predefined kernel functions, recent frameworks rely on
training an encoder-decoder structured deep neural network (DNN) [15, 16],
hereafter referred to as Koopman autoencoder (KAE).

##  III System Model and Problem Formulation

In this section, we present our system model for achieving LPD communication
against UAV surveillance.

###  III-A Terrestrial Ad-hoc Network

We consider a terrestrial wireless ad-hoc network with $N$ ground nodes,
denoted by the set $\mathcal{N}=\\{1,2,\cdots,N\\}$ at known locations given
by $\\{{{\bf w}_{n}:(w_{n_{x}},w_{n_{y}},0)}\\}_{n\in\mathcal{N}}$. Here,
${\bf w}_{n}\in\mathbb{R}^{3}$ represents the three-dimensional (3D)
coordinates of the $n$-th ground node. Each ground node operates with an
adjustable transmit power, which is represented by $P_{n}(t)$ at time $t$,
$\forall n\in\mathcal{N}$. Then, the corresponding signal-to-noise ratio (SNR)
at receiver $j$, denoted by $\gamma_{i_{j}}$, becomes

$\gamma_{i_{j}}(t)=\frac{P_{i}(t)d_{i,j}^{-\eta}\nu_{i,j}(t)}{N_{0}},\forall
i\neq j\in\mathcal{N},$ (5)

where $d_{i,j}=||{\bf w}_{i}-{\bf w}_{j}||$ is the Euclidean norm denoting the
distance between the $i$-th and $j$-th nodes, $\nu_{i,j}(t)$ is the small-
scale fading term, and $\eta$ and $N_{0}$ represent the path-loss exponent and
noise variance, respectively.

To ensure a stable111Due to the presence of the small-scale fading term,
$\nu_{i,j}(t)$, in terrestrial communication, the SNR becomes time-variant.
Consequently, when the SNR undergoes deep fading, leading to low signal
strength, an outage event may occur. Thus, to maintain stable communication,
it is crucial to keep the outage probability low, even at the expense of
reducing the data-rate transmission. communication link between the ground
nodes, the received SNR must exceed a predefined SNR threshold, represented by
$\tilde{\gamma}$. Consequently, the set of communication links for node $i$ at
time $t$ can be formally expressed as:

$C_{i}(t)=\\{j:\gamma_{i_{j}}(t)\geq\tilde{\gamma}\\}_{i\neq
j\in\mathcal{N}}.$ (6)

###  III-B UAV Surveillance Network

We also consider the presence of $L$ UAVs, represented by the set
$\mathcal{L}=\\{1,2,\cdots,L\\}$ with time-variant locations $\\{{{\bf
u}_{l}(t):(u_{l_{x}}(t),u_{l_{y}}(t),h)}\\}_{l\in\mathcal{L}}$. These
locations indicate the 3D coordinates of the $l$-th UAV, which hovers at a
constant altitude denoted by $h$.

An air-ground channel is assumed to be dominated by line-of-sight (LoS). The
received signal strength at the $l$-th UAV from ground node $n$ at time $t$ is
given as

$P_{l,n}(t)=P_{n}(t)d_{l,n}(t)^{-\eta^{\prime}},$ (7)

where $\eta^{\prime}$ is the path-loss exponent for air-ground channel.

The presence of a group of multiple UAVs in a given area leads to spatial
dependencies, with UAVs situated near each other actively communicating. This
inter-UAV communication plays a crucial role in determining the dynamics of
these autonomous UAVs. The neighboring UAVs for UAV $k$, are defined by the
set $\alpha_{k}(t)$ which is represented as

$\alpha_{k}(t)=\\{l:||{\bf u}_{k}(t)-{\bf u}_{l}(t)||\leq\tilde{D}\\}_{k\neq
l\in\mathcal{L}},$ (8)

where $\tilde{D}$ is the minimum distance threshold. Assuming the UAVs are of
the fixed-wing type, the dynamics of UAV $l$ can be described as follows [17]:

$\displaystyle\frac{u_{l_{x}}(t)-u_{l_{x}}(t-1)}{\Delta t}$
$\displaystyle=v_{l}\cos(\phi_{l}(t-1))+v_{w}\cos(\theta_{w})$ (9)
$\displaystyle\frac{u_{l_{y}}(t)-u_{l_{y}}(t-1)}{\Delta t}$
$\displaystyle=v_{l}\sin(\phi_{l}(t-1))+v_{w}\sin(\theta_{w})$ (10)
$\displaystyle\phi_{l}(t)$
$\displaystyle=\phi_{l}(t-1)+0.1\phi_{\text{agg},l}(t-1)$ (11)

where $v_{l}$ is the forward velocity, $v_{w}$ is the wind velocity while
$\phi_{l}$ is the turning angle, and $\theta_{w}$ is the wind direction.
Furthermore, the adjustment of the turning angle for the UAV, is influenced by
its own rotational change, and the aggregated rotations of neighboring UAVs,
$\forall k\in\alpha_{l}(t)$. The aggregated turning angle for UAV $l$ at time
$t$ becomes

$\phi_{\text{agg},l}(t)=\frac{1}{|\alpha_{l}(t)|}\sum_{k\in\alpha_{l}(t)}\phi_{k}(t).$
(12)

Figure 2: Graph-based Koopman autoencoder (GKAE) architecture.

##  IV Mobility Prediction and Power Control for LPD

In this section, we present our optimization methodologies for addressing the
problems P1 and P2, which focus on multi-UAV trajectory prediction and LPD
optimization, respectively.

###  IV-A GNN-Aided Koopman Prediction of Multi-UAV Trajectories

We express the UAV network as a graph. Formally, a graph at time $t$ is
defined as $G(t)=(\mathcal{V},\mathcal{E}(t))$, where
$\mathcal{V}=\\{1,\cdots,L\\}$ is the set of the nodes representing UAVs,
$\mathcal{E}(t)$ is the set of edges encapsulating spatial dependencies among
the UAVs at time $t$ which is determined based on (8). Additionally, let ${\bf
u}_{k}$ be the node features for node $k\in\mathcal{V}$, corresponding to the
3D coordinates of the $k$-th UAV.

As illustrated in Fig. 2, the GKAE is divided into two major components: GNN-
based graph encoder-decoder and KAE encoder-decoder. First, the graph encoder-
decoder architecture follows from the sample and aggregate graph convolution
network (SAGE), which serves as an extension to the standard graph convolution
network (GCN) [12, 13]. At the $\ell$th layer with weights
$\boldsymbol{w}^{(\ell)}$, for the $k$-th node with a set $\alpha_{k}$ of
neighbours, a SAGE layer yields the output activation
$\boldsymbol{z}_{k}^{(\ell+1)}(t)$ as follows:

$\displaystyle\boldsymbol{z}_{k}^{(\ell+1)}(t)$
$\displaystyle=\sigma\left(\boldsymbol{w}^{(\ell)}\cdot\left[\boldsymbol{z}_{k}^{(\ell)}(t)\|\bigoplus_{l\in\alpha_{k}(t)}\left(\boldsymbol{z}_{k}^{(\ell)}(t),\boldsymbol{z}_{l}^{(\ell)}(t)\right)\right]\right)$
(13)

where $\sigma(\cdot)$ is the nonlinear activation function, $\bigoplus$ is an
permutation invariant aggregation function which could be mean or max pooling
and $\|$ is the concatenation operation. Using (13), the graph encoder
$\varphi$ reduces $G(t)$ to a single latent variable, denoted as ${\bf
z}(t)=[\boldsymbol{z}_{1}(t)^{\top}\cdots\boldsymbol{z}_{L}(t)^{\top}]^{\top}$.
Next, by receiving ${\bf z}(t)$ as its input, the KAE encoder $\phi$ produces
${\bf g}(t)$, and the KAE decoder $\phi^{-1}$ yields an one-step time lagged
output ${\bf z}(t+1)$. A Koopman matrix ${\bf K}$ connects $\phi$ and
$\phi^{-1}$, performing a one-step time lag ${\bf g}(t+1)={\bf K}{\bf g}(t)$
in the Koopman invariant subspace.

To train GKAE, we define loss function $L_{GKAE}$ as the following weighted
sum of two loss terms:

$\displaystyle\textbf{(P1)
:}\quad\min_{\boldsymbol{\varphi},\mathbf{K},\boldsymbol{\psi},\boldsymbol{\varphi}^{-1},\boldsymbol{\psi}^{-1}}\beta_{1}L_{\text{rec}}+\beta_{2}L_{\text{pred}},$
(14)

where $\beta_{1}$ and $\beta_{2}$ are hyperparameters. Here,

$\displaystyle L_{\text{rec}}$ $\displaystyle=\sum_{t=1}^{T}||\tilde{\bf
x}(t)||^{2}+||\tilde{\bf z}(t)||^{2}$ (15) $\displaystyle L_{\text{pred}}$
$\displaystyle=\sum_{t=2}^{S_{p}}\left\|\psi^{-1}(\mathbf{g}(t))-\psi^{-1}(\mathbf{K}^{(t-1)}\mathbf{g}(1))\right\|^{2}$
(16) $\displaystyle{\bf z}(t)$ $\displaystyle=\varphi({\bf x}(t),{\bf A}(t))$
(17) $\displaystyle{\bf g}(t)$ $\displaystyle=\phi({\bf z}(t)),{\bf
g}(t+1)={\bf K}{\bf g}(t).$ (18)

In (15), $\tilde{\bf x}(t)=\mathbf{x}(t)-\hat{\mathbf{x}}(t)$ is the graph
encoder-decoder’s reconstruction error, and $\tilde{\bf
z}(t)=\mathbf{z}(t)-\hat{\mathbf{z}}(t)$ is the KAE encoder-decoder’s
reconstruction error, where $\hat{\mathbf{x}}(t)$ and $\hat{\mathbf{z}}(t)$
represent the ground truth values. The term $S_{p}$ is a hyperparameter which
decides the linearity length, defined during the training. Here,
$L_{\text{pred}}$ in (16) denotes the forward prediction loss, which assesses
the accuracy of predicting future graph latent spaces and $L_{\text{rec}}$ in
(15) represents the reconstruction loss, which is utilized to evaluate the
error of reconstructing the graph node features, $\tilde{{\bf x}}(t)$, and
error of reconstructing the graph latent spaces, $\tilde{{\bf z}}(t)$.

TABLE I: Simulation Parameters for UAV Dynamics. Parameter | Value
---|---
Area of operation | $5000\times 5000\ \text{m}^{2}$
Time step ($\Delta t$) | $0.1\ \text{s}$
Num. of UAVs (L) | 4
Constant velocity ($\\{v_{1},v_{2},v_{3},v_{4}\\}$) | $\\{20,20,20,20\\}\ \text{m/s}$
Turning radius ($\\{\phi_{1},\phi_{2},\phi_{3},\phi_{4}\\}$) | $\\{0.25,0.25,0.25,0.25\\}\ \text{rad.}$
Wind direction ($\theta_{w}$) | $10^{-8}\ \text{rad.}$
Wind speed ($v_{w}$) | $10^{-3}\ \text{m/s}$
Distance threshold ($\tilde{D}$) | $10^{4}\ \text{m}$
TABLE II: Simulation Parameters for LPD Problem. Parameter | Value
---|---
Number of Ground Nodes ($N$) | 25
Maximum Transmit Power ($P_{\text{max}}$) | 0.1 W
Minimum Required Number of Communication Links ($\tilde{C}$) | 5
Target SNR ($\tilde{\gamma}$) | 10 dB
Threshold for Received Power ($\tilde{P}_{\text{det}}$) | 0.5 $\mu\text{W}$
Path-loss constant ($\eta$) | $5$
Path-loss constant for air-ground channel ($\eta^{\prime}$) | $2$
Noise variance ($N_{0}$) | -174 dBm/Hz

###  IV-B Transmit Power Optimization for LPD

We aim to minimize the received power for the ground nodes in the terrestrial
ad-hoc network at the predicted surveillance locations of UAVs. The
optimization problem where we aim to minimize the maximum received power with
the predicted locations of the $L$ UAVs is given by

$\displaystyle\textbf{(P2) :}\quad\min_{P_{n}(t)}\max_{l}\ $ $\displaystyle
P_{n}(t)d_{l,n}^{-\eta}(t)$ (19) $\displaystyle\text{subject to}\quad 0\leq
P_{n}(t)$ $\displaystyle\leq P_{\text{max}},\quad\forall n\in\mathcal{N}$ (20)
$\displaystyle|C_{n}(t)|$ $\displaystyle\geq\tilde{C},\quad\forall
n\in\mathcal{N}$ (21) $\displaystyle P_{l,n}(t)$
$\displaystyle\leq\tilde{P}_{\text{det}},\quad\forall n\in{\cal N}.$ (22)

In (19), the transmit power of the ground nodes are to be optimized with the
power constraint in (20). To avoid any isolated clusters, each ground node
should have at least $\tilde{C}$ communication links, as seen in (21). More
importantly, in (22), we enforce that the transmit power should be optimized
such that the received power at the UAV is always less than a threshold,
denoted by, $\tilde{P}_{\text{det}}$. This problem is NP-hard due to the
constraints. To reduce complexity, we assume that the same transmit power is
used uniformly across all the nodes, meaning $P_{n}(t)=P(t),\forall n$,
resulting in the simplified problem below:

$\displaystyle(\textbf{P2'}):\min_{P(t)}\max_{l}\ P(t)d_{l,n}^{-\eta}(t)$ (23)
$\displaystyle\text{subject to}\quad\eqref{subeq:pp},\eqref{subeq:3},\text{
and }\eqref{subeq:4}.$

##  V Numerical Results

In this section, we present numerical results for LPD with 25 ground nodes and
4 surveillance UAVs based on our proposed GKAE. Unless otherwise specified,
simulation parameters follow Tables I and LABEL:tab:SP2 for UAV dynamics and
LPD optimization, respectively.

Trajectory Prediction: For predicting the trajectory of UAVs, we first train
the GKAE architecture which consists of 3 SAGE layers and 6 fully-connected
layers. The exponential linear unit (elu) and tangent hyperbolic (tanh)
activation functions have been used after SAGE layers and fully-connected
layers, respectively. The encoder-decoder architectures are connected through
a linear fully-connected layer, i.e. a Koopman matrix. The GKAE is trained
over 500 epochs using the Adam optimizer, given the loss function (14) with
$\beta_{1}=\beta_{2}=1$ and $S_{p}=20$. The GKAE performance depends
significantly on the dimension of the Koopman matrix, which determines the
number of eigenvalues in the Koopman invariant subspace. In Fig. 3(a), $M=b$
represents the chosen values for the dimension of the Koopman matrix. It is
seen that the GKAE converges for various $b$ values but a very small value for
$b$ decreases convergence speed. After training completes, Fig. 3(b) displays
the prediction error $\epsilon_{\text{pred}}$, measured using the mean-squared
error averaged over a maximum prediction $p=40$ time steps, i.e.,
$\epsilon_{\text{pred}}=\sum_{t=2}^{p}||{\bf x}(t)-\varphi^{-1}(\psi^{-1}({\bf
K}^{(t-1)}{\bf g}(1)))||^{2}$. Here, the prediction input observation is fixed
as ${\bf g}(1))$ at the first time step. The results show that there $b=10$
achieves the lowest prediction error. Furthermore, with $b=10$, we extend the
maximum prediction time steps to $p=80$, and obtain
$\epsilon_{\text{pred}}=0.0025$. The resulting predicted trajectories are
close to the ground-truth values as visualized in Fig. 4.

(a) Train convergence

(b) Prediction error

Figure 3: Training convergence and prediction errors of GKAE with respect to
different Koopman matrix of dimension $b$. Figure 4: Predicted 4 UAV
trajectories for $p=80$ time steps.

(a) Received power at UAVs over varying time steps

(b) Mean transmit power over a varying number $N$ of ground nodes.

(c) Mean transmit power over a varying minimum number of required links.

Figure 5: Received power at UAVs, transmit power with respect to the number
$N$ of ground nodes, and to the minimum number $\tilde{C}$ of required
communication links.

Optimal Transmit Power: Fig. 5(a) visualizes the received power at UAVs over
time when ground node transmit power is optimized as $P(t)^{\ast}$ by solving
P2’. The result shows that the proposed solution ensures that a maximum
received power remains below the UAV’s detection threshold
$\tilde{P_{\text{det}}}$ (dashed black line). This effectively ensures that
UAVs conducting surveillance are unable to detect any unusual activity, as the
received power is maintained at a very low level. To show the impact of the
number $N$ of ground nodes, Fig. 5(b) demonstrates the mean optimal transmit
power $\mathbb{E}[P(t)^{\ast}]$ averaged over the maximum prediction time
steps $p$. For different values of SNR threshold $\tilde{\gamma}$, the result
consistently indicates that the mean optimal transmit power decreases rapidly
with $N$ as the network density increases.

Network Connectivity: Fig. 5(c) shows that the mean optimal transmit power
increases not only with the SNR treshold $\tilde{\gamma}$ but also with the
minimum number $\tilde{C}$ of required communication links. Note that our
connectivity constraint imposes the minimum number of links per node, which
may not always guarantee the network’s full-connectivity without any isolated
node clusters. To study this, we visualize the entire network topology in Fig.
6. With $\tilde{C}=5$, Fig. 6(a) and Fig. 6(b) show that the ground network
become fully connected for both $N=10$ and $N=25$.

(a) $N=10$

(b) $N=25$

Figure 6: LPD achieved network topology, given a minimum number of neighbors
for each node with $\tilde{C}=5$ and a target SNR of $\tilde{\gamma}=10$ dB.

##  VI Conclusions

Our study has tackled the challenge of enabling LPD communication for
terrestrial ad-hoc networks under UAV surveillance. To gain a full knowledge
of the UAV mobility pattern, we aimed to predict the trajectory of the UAV
surveillance based on a novel data-driven approach that integrates graph
learning with Koopman theory. By leveraging GNN architecture, it was possible
to learn the intricate spatial interactions in the UAV network and linearize
the dynamics of multiple UAVs using the same architecture. Using these
predicted locations, we conducted a case study for optimizing nodes’ transmit
power in a terrestrial ad-hoc network for minimizing detectability of RF
signals. Extensive simulations have demonstrated accurate long-term
predictions of fixed-wing UAV trajectories, which, in turn, hold promise for
enabling low-latency LPD covert operations.

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