Trajectory Optimization for UAV-Aided IoT Secure Communication Against Multiple Eavesdroppers ^†

Abstract

This study concentrates on physical layer security (PLS) in UAV-aided Internet of Things (IoT) networks and proposes an innovative approach to enhance security by optimizing the trajectory of unmanned aerial vehicles (UAVs). In an IoT system with multiple eavesdroppers, formulating the optimal UAV trajectory poses a non-convex and non-differentiable optimization challenge. The paper utilizes the successive convex approximation (SCA) method in conjunction with hypograph theory to address this challenge. First, a set of trajectory increment variables is introduced to replace the original UAV trajectory coordinates, thereby converting the original non-convex problem into a sequence of convex subproblems. Subsequently, hypograph theory is employed to convert these non-differentiable subproblems into standard convex forms, which can be solved using the CVX toolbox. Simulation results demonstrate the UAV’s trajectory fluctuations under different parameters, affirming that trajectory optimization significantly improves PLS performance in IoT systems.

1. Introduction

In recent years, the rapid advance of the Internet of Things (IoT) has led to ubiquitous connectivity among a vast number of smart devices, posing significant challenges to both the reliability and real-time performance of IoT communications. Unmanned aerial vehicles (UAVs), due to their flexible maneuverability and fast deployment capabilities, are progressively emerging as a pivotal enabler of IoT communication networks [1,2].

In IoT applications, UAVs may swiftly access target locations and establish solid line-of-sight (LoS) connections with ground terminals, significantly enhancing signal quality and data transmission efficacy. Furthermore, optimizing UAV trajectories enables IoT networks to attain superior energy efficiency and broader coverage. In [3,4], UAVs serve as airborne base stations, facilitating swift 3D deployment to ensure ubiquitous air-to-ground connection. In [5], UAV functions as a mobile relay, maintaining robust wireless connectivity for ground users in environments where line-of-sight (LoS) is hindered by physical obstructions such as buildings or trees. To address the resource allocation issue, Ref. [6] proposes enhancing the energy efficiency of beamforming in IoT systems by optimizing UAV trajectories. To address suboptimal channel state information (CSI), leveraging the inherent advantages of LoS connections established by UAVs is beneficial. In a reconfigurable intelligent surface (RIS)-assisted UAV communication environment, a three-dimensional geometric dynamic channel model and a deep-learning-based channel tracking method are developed, leading to a significant improvement in channel estimation precision [7]. The swift progression of IoT has led to UAVs becoming vital nodes for collecting, transferring, and relaying data, hence broadening their applications and enhancing their significance in interconnected systems. Nonetheless, UAVs encounter substantial communication security issues despite their considerable potential.

Specifically, UAV communication networks face several critical security challenges. Firstly, when a UAV functions as a lawful broadcaster, its air-to-ground LoS communication links, although advantageous for authorized receivers, simultaneously increase the risk of potential eavesdropping. Secondly, the elevated mobility of UAVs creates dynamic communication environments, allowing eavesdroppers to capitalize on channel fluctuations for malicious activities. Furthermore, the extensive utilization of UAVs in IoT communication services forces UAV networks to address not only traditional threats but also new risks stemming from device heterogeneity and network scalability, driven by the extensive interconnection of IoT devices and the continuous transmission of real-time data. The increased threat of eavesdropping exacerbates security weaknesses, highlighting the need for secure UAV network communications [8,9]. Existing research has provided numerous strategies to solve these challenges. For example, to address security risks in UAV networks, researchers have created a security protocol tailored for UAV-to-ground communication, exhibiting markedly improved security compared to conventional protocols [10]. Furthermore, to address the need for resource-efficient and lightweight solutions, a mutual authentication system utilizing physical unclonable functions (PUFs) has been implemented. This technique facilitates mutual authentication and user anonymity while maintaining comparatively low computing costs [11]. Additionally, to address the robustness deficiencies of existing lightweight encryption techniques, a lightweight symmetric encryption algorithm and key agreement mechanism based on SM4 have been presented, improving data transmission security [12]. Notwithstanding these developments, current lightweight encryption systems continue to demonstrate constraints regarding flexibility and authentication. Due to the inherent resource limitations of UAVs, proper resource usage is essential. Consequently, researchers have developed a blockchain-based distributed security solution specifically built for UAV computing networks. This system allows UAVs to independently manage authentication, attribute administration, and access control, while adaptively modifying access policies according to real-time network conditions, thereby enhancing both security and resource efficiency [13]. Although data encryption remains a pivotal focus in communication security research, its high cost, computational complexity, and reliance on stable channels make it challenging to ensure adequate security in resource-constrained and dynamic IoT environments. In contrast, as a supplementary approach to traditional encryption methods, physical layer security (PLS) techniques, founded upon information-theoretic security principles, provide significant advantages. With low computational overhead and no need for complex encryption or decryption operations, PLS is well-suited for resource-limited scenarios. By preventing eavesdroppers from extracting meaningful information while ensuring reliable communication, PLS has emerged as a critical approach for countering ground-based eavesdroppers and safeguarding UAV communication systems [14,15,16].

Investigating how to secure information transmission for UAVs in IoT environments is of critical importance. The introduction of PLS technology not only provides essential safeguards for data sharing in UAV networks, but also enhances communication reliability and security in the context of large-scale IoT device interconnectivity. In UAV secure communications, secrecy rate is recognized as the principal metric for assessing the effectiveness of physical layer security (PLS) systems. Secure UAV communication is deemed feasible when the received signal quality at the legitimate link exceeds that at all eavesdropping nodes [17]. Generally, studies on UAV-assisted secure communication can be categorized into two main directions: UAV-enabled secure communication [18,19] and UAV-aided secure cooperation [20,21]. Due to their ability to dynamically reposition in response to changing radio propagation environments, UAVs can establish highly efficient LoS communication links for legitimate users, making their deployment and trajectory optimization fundamental to PLS design. For instance, one study proposed a buffer-aided UAV secure communication system, where optimized UAV trajectories significantly improved the overall secrecy rate [22]. In UAV-assisted relay communication systems, the joint optimization of the base station’s transmit power and the UAV’s flight trajectory can significantly improve the secrecy rate of communications [23]. Short-packet communication and UAVs play pivotal roles in 5G and future wireless networks, particularly in scenarios with stringent latency requirements and security challenges. Accordingly, researchers have developed a secure SPC-IoT system leveraging UAVs as mobile decode-and-forward relays. By exploiting their agile 3D mobility, UAVs periodically receive and forward short packets from remote IoT devices in a two-hop manner, ensuring end-to-end secure and reliable transmission. This approach not only mitigates risks posed by ground-based eavesdroppers in uncertain locations, but also enhances the secrecy and reliability of SPC networks [24]. Multi-UAV cooperative PLS has also attracted significant attention. For example, a secure communication system assisted by two UAVs has been proposed to support the mobility of ground devices. By leveraging reinforcement learning to jointly optimize the UAVs’ trajectories and transmission rates, the system enables secure bidirectional communication [25]. Unlike conventional methods limited to unidirectional security with static devices, this work innovatively supports device mobility while ensuring mutual security between UAVs and ground nodes. PLS can be further strengthened by integrating interference injection and beamforming techniques. One study demonstrated that co-designing UAV jammer trajectories and transmit power can maximize the average achievable secrecy rate [26]. Energy efficiency is another critical consideration. A UAV-assisted amplify and forward relay network has been proposed, combining wireless energy harvesting with cooperative friendly jamming [27]. Here, a cluster of hovering UAVs not only relays information from ground sources to distant destinations, but also actively transmits jamming signals to eavesdroppers. Additionally, UAVs can form virtual antenna arrays to enable secure communication with ground terminals via beamforming, thereby improving secrecy rates [28]. In summary, PLS technology, when combined with UAVs’ flexible mobility and cost-effective deployment, offers robust support for securing large-scale IoT wireless networks. It also presents novel solutions to overcome the limitations of traditional encryption in resource-constrained environments.

However, research is still scarce for scenarios with multiple eavesdroppers in IoT systems, with insufficient exploration of effective countermeasures to address the security challenges presented by such multi-eavesdropper configurations. Most existing studies focus exclusively on single-eavesdropper scenarios, whereas real-world IoT deployments often involve multiple eavesdroppers distributed across different locations, significantly increasing the complexity of ensurting secure communication. Moreover, coordinated eavesdropping among multiple malicious nodes can substantially increase the risk of information leakage. To tackle these critical challenges, we expand upon our earlier work presented at the 2022 International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery [29]. In this paper, we introduce an innovative and efficient trajectory optimization algorithm tailored for multi-eavesdropper scenarios, aimed at strengthening UAV communication security within IoT networks. The main contributions of this study are summarized as follows:

• A secure communication framework for IoT systems is introduced, incorporating UAVs alongside multiple eavesdropping entities. Through the optimization of UAV flight trajectories, we improve the worst-case secrecy rate, thereby augmenting physical layer security in environments with multiple eavesdropping nodes.
• To mitigate the computational complexity of continuous trajectory optimization, we discretize the UAV trajectory into a limited collection of coordinate points and develop an optimization model based on these discrete coordinate variables.
• To address the challenge of maximizing secrecy rates under the worst-case scenario, where the optimization problem is inherently non-convex and non-differentiable, we utilize SCA techniques and hypograph theory. By implementing a novel set of trajectory increment variables to replace the original UAV trajectory coordinates, we reformulate the initial non-convex problem into a set of convex subproblems. Moreover, by utilizing hypograph theory, we equivalently convert the non-differentiable subproblems into standard convex optimization formats, facilitating rapid resolution.
• Simulation results indicate that under varied parameter conditions, the proposed method can efficiently evade multiple eavesdroppers with a low computational complexity while significantly improving the system’s physical layer security (PLS) performance. This validates the substantial impact of UAV trajectory optimization on improving PLS effectiveness.

The remainder of this article is organized as follows. Section 2 presents the system model and problem formulation. Section 3 introduces a novel and efficient trajectory optimization algorithm. Section 4 presents and analyzes the simulation results. Section 5 provides the conclusion. Finally, Section 6 discusses the future work.

2. System Model and Problem Formulation

This study investigates a secure UAV communication system within an Internet of Things environment, consisting of a communication destination and K potential eavesdroppers (Eves). The UAV initiates its mission at a designated starting point, transmits sensitive information to the communication destination during its flight, and ultimately reaches a specified endpoint. We assume that any of the K potential passive eavesdroppers may intercept the information intended for the communication destination. Therefore, UAV flight trajectories must be optimized to guarantee the security of UAV communication downlinks. Specifically, in this UAV-aided IoT communication system, the objective is to maximize the system’s achievable secrecy rate and ensure the security of the information received by the legitimate ground node.

2.1. System Model

Without loss of generality, the positions of all eavesdroppers, the communication destination, and the UAV are represented within a three-dimensional (3D) Cartesian coordinate system. As illustrated in Figure 1, in this UAV-aided IoT communication system, we assume that all K eavesdroppers (Eves) and the communication destination are located on the horizontal ground plane. Specifically, the set of eavesdroppers is defined as $k\in \mathcal{K}\triangleq \{1,\dots ,K\}$. The fixed horizontal positions of the $k^{th}$ eavesdropper and the communication destination are denoted by ${\mathbf{W}}_k={[x_k,y_k]}^T$ and ${\mathbf{W}}_g={[x_g,y_g]}^T$, respectively.

The UAV is assumed to maintain a constant flight altitude, denoted by H, throughout the entire flight duration T. The UAV’s instantaneous horizontal position at time t is denoted by ${\mathbf{U}}_q\left[t\right]=[x_q\left(t\right),y_q\left(t\right)]$, where $0\le t\le T$. To simplify the trajectory design, the continuous flight time T is uniformly divided into N time slots of equal duration, each with a length of ${\delta }_t=T/N$. The number of time slots N is chosen to be sufficiently large so that the UAV’s position can be approximated as constant within each interval. Consequently, the UAV’s trajectory is discretized into N anchor points, each representing its horizontal position at the corresponding time slot. The resulting discrete trajectory is denoted as ${\mathbf{U}}_q\left[n\right]={[x_q\left(n\right),y_q\left(n\right)]}^T$, where $n\in \mathcal{N}\triangleq \{1,2,\dots ,N\}$.

The UAV’s horizontal positions at the initial and final time instances of the total flight duration T are denoted by ${\mathbf{U}}_q\left[I\right]={[x_q\left(I\right),y_q\left(I\right),H]}^T$ and ${\mathbf{U}}_q\left[F\right]={[x_q\left(F\right),y_q\left(F\right),H]}^T$, respectively. Accordingly, the Euclidean distance between the UAV and the communication destination at time slot n is given by

$$d_{ug}\left(n\right)=\sqrt{{∥{\mathbf{U}}_q\left[n\right]-{\mathbf{W}}_g∥}^2+H^2},\forall n\in \mathcal{N},$$

(1)

Here, $\parallel ·\parallel$ represents the Euclidean norm. Likewise, the Euclidean distance between the UAV and the $k^{th}$ eavesdropper at time slot n is expressed as

$$d_{uk}\left(n\right)=\sqrt{{∥{\mathbf{U}}_q\left[n\right]-{\mathbf{W}}_k∥}^2+H^2},\forall k\in \mathcal{K},\forall n\in \mathcal{N}.$$

(2)

When the UAV operates at a higher altitude in environments with minimal obstructions, the wireless channels between the UAV and both the communication destination and the eavesdroppers are predominantly LoS, and the widely adopted free-space path loss model is employed. Accordingly, the channel power gain between the UAV and the communication destination at time slot n can be expressed as

$$h_{ug}\left(n\right)={\rho }_0{d}_{ug}^{-2}\left(n\right)={\displaystyle \frac{{\rho }_0}{{∥{\mathbf{U}}_q\left[n\right]-{\mathbf{W}}_g∥}^2+H^2}},\forall n\in \mathcal{N},$$

(3)

Likewise, the channel power gain between the UAV and the $k^{th}$ eavesdropper at time slot n is expressed as

$$h_{uk}\left(n\right)={\rho }_0{d}_{uk}^{-2}\left(n\right)={\displaystyle \frac{{\rho }_0}{{∥{\mathbf{U}}_q\left[n\right]-{\mathbf{W}}_k∥}^2+H^2}},\forall k\in \mathcal{K},\forall n\in \mathcal{N}.$$

(4)

where ${\rho }_0$ denotes the reference channel power gain measured at a distance of 1 m.

Furthermore, let $v_{max}$ (m/s) denote the UAV’s maximum allowable speed during any time slot. Accordingly, the maximum permissible flight distance within a single time slot is expressed as $L_{max}={\delta }_t{v}_{max}$. Moreover, to regulate velocity transitions between consecutive time slots, the UAV has a maximum allowable acceleration, denoted as $a_{max}$. Therefore, the UAV’s mobility constraints can be formulated as follows:

$${∥{\mathbf{U}}_q\left[n\right]-{\mathbf{U}}_q[n-1]∥}^2\le L_{max}^2,n=2,\dots ,N,$$

(5)

$${∥{\mathbf{U}}_q\left[1\right]-{\mathbf{U}}_q\left[I\right]∥}^2\le L_{max}^2,$$

(6)

$${∥{\mathbf{U}}_q\left[F\right]-{\mathbf{U}}_q\left[N\right]∥}^2\le L_{max}^2,$$

(7)

$${∥{\mathbf{U}}_q(n+1)-2{\mathbf{U}}_q\left(n\right)+{\mathbf{U}}_q(n-1)∥}_2\le a_{max}{\delta }_t^2,n=2,\dots ,N-1.$$

(8)

Accordingly, the instantaneous data transmission rate between the UAV and the communication destination at time slot n is expressed as

$$R_g\left(n\right)={log}_2\left(1+{\displaystyle \frac{h_{ug}\left(n\right)p}{{\sigma }^2}}\right),$$

(9)

where ${\sigma }^2$ denotes the noise power of the additive white Gaussian noise (AWGN) at the ground communication destination, and p denotes the UAV’s instantaneous transmit power.

Likewise, the instantaneous information leakage rate to the $k^{th}$ eavesdropper at time slot n is given by

$$R_k\left(n\right)={log}_2\left(1+{\displaystyle \frac{h_{uk}\left(n\right)p}{{\sigma }^2}}\right).$$

(10)

Consequently, the achievable secrecy rate at the communication destination during the $n^{th}$ time slot is defined as

$$R_g^{\sec }\left(n\right)={\left[R_g\left(n\right)-R_k\left(n\right)\right]}^{+},$$

(11)

where ${\left[x\right]}^{+}\triangleq max\{0,x\}$.

2.2. Problem Formulation

The study aims to enhance physical layer security in an IoT communication system with multiple eavesdroppers by optimizing the UAV’s flight trajectory. Considering the worst-case scenario in confidential transmission, our objective is to maximize the minimum security rate at the communication destination. Accordingly, the original optimization problem is formulated as follows:

$$\begin{array}{cc}\hfill \mathbf{P}\mathbf{0}:& \underset{\{x_q\left(n\right),y_q\left(n\right)\}}{max}\underset{k}{min}\sum _{n=1}^N{R}_g^{\sec }\left(n\right)\hfill \\ \hfill & \mathrm{s}.\mathrm{t}.\left(5\right)–\left(8\right).\hfill \end{array}$$

(12)

It is noteworthy that, due to Equation (12), problem $P0$ is an inherently non-convex optimization problem. Thus, directly solving this problem poses great computational challenges. To simplify this, the original problem will be transformed and reformulated in the following section, enabling an optimal solution to be derived using convex optimization techniques.

3. Trajectory Optimization

In this section, we introduce a new set of auxiliary variables to reformulate the original optimization problem. Subsequently, we derive the lower bounds for Equations (9) and (10). However, the reformulated problem remains non-differentiable and, thus, intractable using standard convex optimization methods. To overcome this problem, we apply hypograph theory to further transform the problem into a standard convex form, which can be solved easily.

3.1. Change of Variables

To overcome the non-convexity associated with direct UAV trajectory optimization, we reformulate the problem by discarding the direct treatment of the coordinate ${\mathbf{U}}_q\left[n\right]$ as an independent variable. Instead, we iteratively refine the trajectory through incremental updates, representing each coordinate as a correction to the previous iteration’s position $(x_q^{i-1}\left(n\right),y_q^{i-1}\left(n\right))$. Consequently, in the $n^{th}$ time slot, the updated trajectory coordinate in the $i^{th}$ iteration are given by

$$x_q^i\left(n\right)=x_q^{i-1}\left(n\right)+\Delta x^{i-1}\left(n\right),$$

(13)

$$y_q^i\left(n\right)=y_q^{i-1}\left(n\right)+\Delta y^{i-1}\left(n\right).$$

(14)

Let $(\Delta x^i\left(n\right),\Delta y^i\left(n\right))$ denote the trajectory displacement increments at the $n^{th}$ point during the $i-1^{th}$ iteration in the positive x and y directions. For notational clarity, we define $x_q^0=x_q^{i-1}\left(n\right)$, $y_q^0=y_q^{i-1}\left(n\right)$, and introduce auxiliary rate variables ${\tilde{R}}_g^i\left(n\right)$ and ${\tilde{R}}_k^i\left(n\right)$. By applying a lower bound approximation of the legitimate receiver’s rate around $(x_q^0,y_q^0)$, the transmission rate is approximated as

$$\begin{array}{cc}\hfill {\tilde{R}}_g^i\left(n\right)\triangleq & R_g^{i-1}\left(n\right)-f_g^{i-1}\left(n\right)\left[{\left(\Delta x^{i-1}\left(n\right)\right)}^2+{\left(\Delta y^{i-1}\left(n\right)\right)}^2\right]\hfill \\ \hfill & -2(x_q^0-x_g)f_g^{i-1}\left(n\right)\Delta x^{i-1}\left(n\right)\hfill \\ \hfill & -2(y_q^0-y_g)f_g^{i-1}\left(n\right)\Delta y^{i-1}\left(n\right),\hfill \end{array}$$

(15a)

where

$$f_g^{i-1}\left(n\right)={\displaystyle \frac{p}{ln2\left({\rho }_0^{-1}{\sigma }^2{d}_{ug}^{i-1}{\left(n\right)}^4+p{d}_{ug}^{i-1}{\left(n\right)}^2\right)}}\ge 0.$$

(15b)

Similarly, the concave lower bound approximation of the $k^{th}$ eavesdropper’s rate can be formulated as follows:

$$\begin{array}{cc}\hfill {\tilde{R}}_k^i\left(n\right)\triangleq & R_k^{i-1}\left(n\right)-f_k^{i-1}\left(n\right)\left[{\left(\Delta x^{i-1}\left(n\right)\right)}^2+{\left(\Delta y^{i-1}\left(n\right)\right)}^2\right]\hfill \\ \hfill & -2(x_q^0-x_k)f_k^{i-1}\left(n\right)\Delta x^{i-1}\left(n\right)\hfill \\ \hfill & -2(y_q^0-y_k)f_k^{i-1}\left(n\right)\Delta y^{i-1}\left(n\right),\hfill \end{array}$$

(16a)

where

$$f_k^{i-1}\left(n\right)={\displaystyle \frac{p}{ln2\left({\rho }_0^{-1}{\sigma }^2{d}_{uk}^{i-1}{\left(n\right)}^4+p{d}_{uk}^{i-1}{\left(n\right)}^2\right)}}\ge 0.$$

(16b)

Furthermore, the UAV’s mobility constraints are re-expressed as quadratic norm inequalities, as follows:

$${∥{\mathbf{U}}_q\left[n\right]+Q\left(n\right)-{\mathbf{U}}_q[n-1]-Q(n-1)∥}^2\le {\left(L_{max}\right)}^2,n=2,\dots ,N,$$

(17)

$${∥{\mathbf{U}}_q\left[1\right]+Q\left(1\right)-{\mathbf{U}}_q\left[I\right]∥}^2\le {\left(L_{max}\right)}^2,$$

(18)

$${∥{\mathbf{U}}_q\left[F\right]-Q\left(N\right)-{\mathbf{U}}_q\left[N\right]∥}^2\le {\left(L_{max}\right)}^2,$$

(19)

$$\begin{array}{cc}\hfill & ∥{\mathbf{U}}_q(n+1)+Q(n+1)-2{\mathbf{U}}_q\left(n\right)-2Q\left(n\right)+{\mathbf{U}}_q(n-1)\hfill \\ \hfill & {+Q(n-1)∥}_2\le a_{max}·{\delta }_t^2,n=2,\dots ,N-1.\hfill \end{array}$$

(20)

where $Q\left(n\right)=(\Delta x(n),\Delta y(n\left)\right)$. Accordingly, in the $i^{\mathrm{th}}$ iteration, the lower bound of problem $P0$ is reformulated as follows:

$$\mathbf{P}{\mathbf{0}}^{\left(\mathbf{i}\right)}:\underset{\begin{array}{c}\{\Delta x(n),\Delta y(n\left)\right\},\\ \{R_g^i\left(n\right),R_k^i\left(n\right)\}\end{array}}{max}\underset{k}{min}\sum _{n=1}^N{R}_g^{sec}\left(n\right)$$

(21)

$$\mathrm{s}.\mathrm{t}.R_g^i\left(n\right)\le {\tilde{R}}_g^i\left(n\right),n=1,\dots ,N,$$

(22)

$$R_k^i\left(n\right)\le {\tilde{R}}_k^i\left(n\right),k=1,\dots ,K,n=1,\dots ,N,$$

(23)

$$\mathrm{s}.\mathrm{t}.\left(17\right)–\left(20\right).$$

The lower bounds ${\tilde{R}}_g^i\left(n\right)$ and ${\tilde{R}}_k^i\left(n\right)$, derived in Equations (15a) and (16a) are concave quadratic functions of the trajectory increment variables $(\Delta x,\Delta y)$. Consequently, under the increment-variable framework, the reformulated problem ${\mathbf{P}\mathbf{0}}^{\left(\mathbf{i}\right)}$ satisfies the convexity requirements. Once expressed in a differentiable form, it can be efficiently solved using standard convex optimization techniques. In the subsequent section, hypograph theory is employed to transform ${\mathbf{P}\mathbf{0}}^{\left(\mathbf{i}\right)}$ into a standard convex optimization problem.

3.2. Hypograph

Defining $f\triangleq {\sum }_{n=1}^N{R}_g^{sec,i}\left(n\right)$, the hypograph of Equation (21) is defined as

$$\mathbf{hypo}f=\begin{array}{c}\hfill \left\{\left(\{\Delta x\left(n\right),\Delta y\left(n\right),R_g^i\left(n\right),R_k^i\left(n\right)\},R^{*}\right)|f\ge R^{*}\right\}.\end{array}$$

(24)

We know that hypo f is a convex set, as ${\sum }_{n=1}^N{R}_g^{sec,i}\left(n\right)$ is a linear function. Then, we can form the hypograph problem as follows:

$$\mathbf{P}{\mathbf{1}}^{\left(\mathbf{i}\right)}:\underset{\begin{array}{c}\{(\Delta x\left(n\right),\Delta y\left(n\right)),R^{*}\left(n\right)\},\\ \{R_g^i\left(n\right),R_k^i\left(n\right)\}\end{array}}{max}{R}^{*}$$

(25)

$$\mathrm{s}.\mathrm{t}.\left(17\right)–\left(20\right),\left(22\right)–\left(23\right)$$

The reformulated problem ${\mathbf{P}\mathbf{1}}^{\left(\mathbf{i}\right)}$ constitutes a standard convex quadratic program, and can be efficiently solved using existing solvers such as CVX (version 2.2), a MATLAB (R2024a) toolbox specifically designed for convex optimization.

4. Simulation Results

The simulation results presented in this section demonstrate the effectiveness of UAV trajectory optimization in enhancing the secrecy rate of the UAV-aided IoT secure communication system. The simulation consists of two parts. First, we present several UAV trajectories under different $v_{max}$ and show how the UAV’s instantaneous speed changes over time. In the second part, we analyze the impact of UAV mobility constraints on the secrecy rate and validate the convergence of the secrecy rate.

In the simulation, the UAV’s transmit power is set to $p=20\mathrm{dBm}$ and the power spectral density of the AWGN is fixed at $-174\mathrm{dBm}/\mathrm{Hz}$. The communication bandwidth is defined as $1\mathrm{MHz}$. The UAV operates at a constant altitude of $100\mathrm{m}$ throughout a total flight duration of $100\mathrm{s}$. Additionally, the UAV’s acceleration is assumed to be $2\mathrm{m}/{\mathrm{s}}^2$. The horizontal coordinates of the three eavesdroppers are fixed at ${\mathbf{W}}_1={[300,50]}^T$, ${\mathbf{W}}_2={[50,100]}^T$, and ${\mathbf{W}}_3={[20,250]}^T$, respectively. The communication destination is fixed at ${\mathbf{W}}_g={[200,200]}^T$, and UAV’s initial and final horizontal positions are specified as ${\mathbf{U}}_q\left[I\right]={[0,0]}^T$ and ${\mathbf{U}}_q\left[F\right]={[400,0]}^T$, respectively.

4.1. UAV Trajectories

Figure 2 illustrates the optimal UAV trajectories obtained under various speed constraints, with the objective of maximizing the secrecy rate. During the initial phase of flight, the UAV rapidly approaches the communication destination, as closer proximity enhances the secrecy rate. However, after passing the node, the UAV exhibits different trajectory behaviors depending on the speed constraints. To enhance secrecy performance, the UAV dynamically adjusts its trajectory to reduce its exposure to eavesdroppers while maintaining effective communication with the intended destination. Ultimately, within the constraints of the total mission duration, the UAV completes its transmission task and proceeds to the designated endpoint.

As shown in Figure 3, the UAV initially flies toward the communication destination at its maximum speed. Then, the speed decreases significantly, as proximity to the communication destination facilitates more secure transmission. Subsequently, the UAV undergoes two acceleration phases to reach positions favorable for secure communication, interspersed with brief periods of deceleration. After reaching the farthest location that still supports secure transmission, the UAV proceeds to the endpoint at a relatively high speed.

4.2. Secrecy Rate Versus Iteration Number and UAV Speed

As shown in Figure 4, the secrecy rate of the secure communication system converges rapidly as the number of iterations of ${\mathbf{P}\mathbf{1}}^{\left(\mathbf{i}\right)}$ increases. The secrecy rate of the secure communication system converges rapidly, typically within about two to three iterations. In addition, the UAV’s maximum speed $v_{max}$ has an impact on the secure transmission performance. Specifically, a higher maximum UAV speed results in a greater achievable secrecy rate. This is because a higher UAV speed allows for increased trajectory design flexibility, thereby improving its capability to evade potential eavesdropping threats.

Finally, we observed whether the secrecy rate reaches a saturation point as the UAV’s speed increases. In Figure 5, we find that when the UAV speed increases to a relatively large value, the secrecy rate gradually stops increasing. Therefore, when the UAV speed is large, it is not necessary to keep increasing the speed of UAV to secure transmission.

5. Conclusions

In this paper, we investigate trajectory optimization to enhance physical layer security in a UAV-aided IoT communication system. We formulated the problem of optimizing the UAV’s trajectory to ensure secure transmission in the presence of multiple eavesdroppers. A novel set of trajectory increment variables was introduced to replace the discretized UAV trajectory coordinates, thereby transforming the original non-convex problem into a sequence of convex subproblems. These non-differentiable sub-problems were then equivalently converted into standard convex forms using hypograph theory. Finally, we solved these problems using the CVX toolbox. The simulation results show how the UAV adjusts its trajectory to approach the communication destination while avoiding eavesdroppers under different system parameters. The significant impact of trajectory optimization on enhancing physical layer security performance is clearly verified. Moreover, we found that the achievable secrecy rate converges rapidly, and a higher maximum UAV speed benefits the UAV-aided IoT secure communication system.

6. Future Work

This study focuses on addressing the theoretical problem of maximizing physical-layer security through UAV trajectory optimization in the presence of multiple eavesdroppers. The primary contribution of this work lies in the design of the optimization algorithm. In future work, we plan to extend the proposed algorithm to real-world scenarios, where we will consider the design of the UAV security system’s network architecture, the integration of hardware and software, and the deployment of the algorithm within this system.