Max-Min Secrecy Rate for UAV-Assisted Energy Harvesting IoT Networks

Abstract

The future Internet of Things (IoT) will consist of energy harvesting devices and Unmanned Aerial Vehicles (UAVs) to support applications in remote areas. However, as UAVs communicate with IoT devices using broadcast channels, information leakage emerges as a critical security threat. This paper considers the problem of maximizing the minimum secrecy rate in an energy harvesting IoT network supported by two UAVs, where one acts as a server to collect data from devices, and the other is an eavesdropper to intercept data transmission. It presents a novel Mixed-Integer Nonlinear Program (MINLP), which we then linearize into a Mixed-Integer Linear Program (MILP) problem. It also proposes a heuristic solution called Fly Nearest Location (FNL). Both solutions determine (i) the UAV server’s flight routing, flight time, and computation time, as well as (ii) the energy usage and operation mode of IoT devices. Our results show that FNL achieves on average 78.15% of MILP’s performance.

1. Introduction

The Internet of Things (IoT) is an emerging technology to connect a myriad of devices to a data fusion center. It has led to significant advancements across various fields such as smart cities [1], agriculture [2], and industrial networks [3]. In general, these applications consist of massive geo-distributed IoT devices. These devices collect data from their surrounding environment and transmit these data to data fusion for further processing. Thus, the amount of data received by the data fusion directly impacts the quality of data processing. For example, AI applications, such as Virtual Reality (VR) [4] and disaster relief [5], collect a huge amount of data from IoT devices for training or inference, resulting in significant energy consumption by these devices. However, these IoT devices are usually deployed in remote geographical areas, leading to these devices not accessing the main electricity. This energy constraint severely limits the data collection performance of these devices. To this end, powering these devices becomes a key challenge in IoT networks. To address this challenge, energy harvesting (EH) provides a sustainable solution for powering IoT devices [6]. In general, IoT devices harvest energy from various renewable energy sources, particularly through solar panels, to extend network operation lifetime and mitigate environmental concerns such as carbon emissions.

Recently, Unmanned Aerial Vehicles (UAVs) have been widely adopted to assist IoT networks. For instance, in [7], UAVs act as mobile base stations. They fly and hover over some locations to collect data from geo-distributed IoT devices, extending IoT network coverage. This UAV-assisted IoT network provides several advantages, including flexible deployment, improved line-of-sight connectivity, and rapid response to network failures reliability [8]. To fully leverage these benefits, several studies have explored UAV trajectory optimization [9], adaptive power control [10], and data scheduling strategies [11], aiming to enhance communication efficiency. Given these advantages, UAV-assisted IoT networks, with their flexibility in deployment and high mobility, have the potential to become the fundamental infrastructure of future IoT networks [12].

Information leakage is one of the security threats in UAV-assisted IoT systems. Specifically, UAVs rely on wireless channels to collect data from ground IoT devices [13]. As the broadcast nature of wireless channels, attackers, also known as eavesdroppers, intercept sensitive data, including private user information, device authentication keys, and operational commands [14]. To evaluate the security of such systems, the secrecy rate of each device is a critical performance metric to measure the confidentiality of communication. The secrecy rate of a device is defined as the difference between the legitimate channel capacity and the eavesdropper’s channel capacity [15].

In this paper, we consider fair and secure communication between IoT devices. Our aim is to address the problem of maximizing the minimum secrecy rate of solar-powered devices. Specifically, this problem jointly optimizes (i) the energy usage of devices, (ii) jammer selection among devices, (iii) data offloading decisions at devices, (iv) time used by the UAV server to travel and collect data, and (v) the UAV server’s trajectory. As shown in Figure 1. Server UAV-S flies to location A, B and C to collect data from device a, b, c, and d. UAV-E, an eavesdropper, flies over a given trajectory, and aims to intercept data sent from devices to UAV-S. In this respect, to reduce information leakage to UAV-E or lower its secrecy rate, some devices can act as a jammer that sends a jamming signal to prevent the eavesdropper UAV when other devices upload data to UAV-S.

There are a number of issues to be addressed. First, the solar energy arrival of devices and wireless channels have spatiotemporal properties, meaning that the energy level of devices to vary over time. It has a direct impact on the amount of data uploaded by each device and whether they have the energy to send a jamming signal. The second issue is that the UAV server needs to plan its trajectory, which is constrained by its maximum velocity, flight time, energy level of devices and wireless channel quality. The next issue is fairness between IoT devices, where we ensure the fairness data collection under secure communication. The last issue is to decide which devices act as jammers in each time frame. Jammer selection has an impact on wireless interference on devices and eavesdroppers.

Henceforth, we make the following contributions:

• As we discuss in Section 2, no prior works have considered the max-min average secrecy rate in a novel solar-powered IoT network including a UAV server and a UAV eavesdropper.

• We present the first Mixed-Integer Nonlinear Program (MINLP) to compute the optimal max-min average secrecy rate in the said IoT networks. The MINLP is transformed into a Mixed-Integer Linear Program (MILP). Both formulations jointly optimize (i) the energy usage of devices, (ii) jammer selection among devices, (iii) data offloading decisions at devices, (iv) time used by the UAV server to flight and collect data, and (v) the UAV server’s trajectory.

• We outline the first heuristic algorithm called Fly Nearest Location (FNL) for solving the proposed problem. In the FNL, the UAV server always selects the nearest location. Devices determine their operation modes based on their energy usage.

• We present a number of theoretical properties. First, we prove the hardness of our problem. Second, we present the computation complexity of our MILP and FNL.

• Our result shows that the max-min secrecy rate of FNL achieves 78.15% of that of MILP. Further, more locations, more frames, and higher energy harvesting efficiency increase the max-min secrecy rate while more devices in the networks decrease the result. When the transmit power of devices increases, the result increases and then decreases. The increase in network bandwidth has no effect on the max-min secrecy rate.

The rest of this research is organized as follows. Section 2 reviews existing works. Section 3 outlines our network model and constraints. Section 4 formulates our optimization problem as aMINLP and then linearizes it to a MILP problem. Section 5 presents our solution for the problem. Section 6 lists the properties of the problem and solution. Section 7 reports the results of our simulations. Finally, Section 8 summarizes the research.

2. Related Work

Past works have considered secure communication in UAV-assisted networks. For example, in [16], a UAV acts as a based station and a jammer to transmit information to devices and prevent a ground eavesdropper, respectively. Its aim is to maximize the secrecy energy efficiency (SEE) of the system. In [17], a UAV relays data from a source to a destination with the presence of a ground eavesdropper. The authors propose maximizing the SEE of the system by jointly optimizing the transmit power of the UAV and the source, the UAV trajectory, and the time allocation at the UAV. In [18], a UAV server collects data from devices and sends a jamming signal to prevent a ground eavesdropper. It proposes to maximize the SEE of the system by jointly controlling the transmit power of devices, the jamming power of the UAV, and the UAV trajectory. The authors of [19] propose to maximize the secrecy rate of users’ underground eavesdroppers, where a UAV emits an RF signal to an intelligent reflecting surface for Backscatter Communications. In [20], the authors aim to maximize the secrecy rate of devices and minimize the energy consumption of the network, where a UAV receives data from devices and sends a jamming signal to an eavesdropper. Qian et al. [21] design a jammer selection solution to prevent a ground eavesdropper when a UAV collects data from sensors. Their aim is to maximize the secrecy throughput of sensors. In [22], a UAV works for relaying data from a base station to multiple IoT terminals with the presence of a ground eavesdropper. The authors propose to maximize the minimum average secrecy rate among IoT devices by jointly optimizing the UAV trajectory, device upload scheduling and transmit power of devices. The authors of [23] consider a UAV eavesdropper when users offload their tasks to a UAV server. Their aim is to maximize the minimum secrecy rate of users by jointly controlling the user offloading scheduling, the transmit power of users, and the trajectory of UAVs. In [24], the authors propose minimizing the maximum energy consumption of the ground devices in a UAV-assisted wireless sensor network with the presence of a ground eavesdropper. A block coordinate descent (BCD) method is used to optimize the schedule of devices and the trajectory of UAVs. However, these aforementioned works do not consider energy harvesting IoT devices.

Recently, some works have integrated energy harvesting into UAV-assisted secure communication. For example, the authors of [25] consider energy harvesting IoT devices. They present the close-form expression of the secure output possibility (SOP) and the information leakage probability of the network when a jamming UAV prevents a ground eavesdropper and a malicious jammer. In [26], devices harvest RF energy from a base station and send data to a UAV in the presence of a ground eavesdropper. The authors analyze the SEE and SOP of the system. In [27], IoT devices harvest energy from a power beacon and communicate with other devices through a relay UAV in the presence of a ground eavesdropper. The authors analyze the SOP of the system. In [28], a device decodes information and harvests energy from a UAV server and a UAV jammer by simultaneous wireless information and power transfer (SWIPT) technique. The authors optimize the UAVs’ transmit power, trajectory, and power splitting ratio at the device, where their aim is to maximize the average secrecy rate at the device. In [29], a device simultaneously decodes information and harvests energy from the signal relied on by a UAV. However, the presence of a ground eavesdropper introduces a potential threat to the communication. A successive convex approximation (SCA) based solution is proposed to maximize the SEE of the system, where it optimizes the transmit power of the signal source and the UAV, the power-splitting ratio at the device, and the trajectory of UAVs.

In summary, we compare the aforementioned works in Table 1. Specifically, the works in [16,17,18,19,21,24,25,26,27,29] does not consider the max-min secrecy rate between devices, wherein these solutions cannot ensure the fairness of secrecy rate between devices. Further, references [17,18,19,20,22,23,24,25,26,27,28,29] do not select jammer from devices. All works except [21] consider ground eavesdropper. Works in [25,26,27,28,29,30] do not optimize the trajectory of UAV. Further, works in [18,19,20,21,22,23,24] neglect the time allocation between hovering and data collection in a frame when they optimize the trajectory of UAV. Lastly, works in [16,17,18,19,20,21,22,23,24] neglect the spatiotemporal energy arrival at devices. To the best of our knowledge, no prior study has jointly optimized a UAV trajectory, time allocation within a frame, data offloading decisions, and jammer selection in an energy harvesting IoT network.

3. Preliminaries

We first formalize our network model before formulating our problem. Table 2 lists our notations. We denote $\mathcal{V}$ as a set of solar-powered devices. We consider two UAVs: one UAV, referred to as a server, is responsible for data collection and is denoted by s, while the other UAV, denoted by e, acts as an eavesdropper. There is a set of locations recorded in $\mathcal{M}$, and the optimization spans a set of time frames, denoted as $\mathcal{T}$, which is also referred to as the planning horizon. Each frame, indexed by $t\in \mathcal{T}$, has a fixed length of $\tau$. To model UAV s and UAV e, we use Vertical Take-off and Landing (VTOL) UAVs in [31], which operate in hover-fly-hover mode. Specifically, as shown in Figure 2, each frame contains a flight slot during which UAV s travels among locations, and a data slot used by UAV s to receive data from devices. Devices upload data over the whole data slot. Let ${\tau }_F^t$ and ${\tau }_D^t$ denote the length of the flight slot and data slot in frame t, respectively. Formally, we have

(1)$\begin{array}{cc}\hfill {\tau }_F^t+{\tau }_D^t=\tau ,& \forall t\in \mathcal{T}.\end{array}$

In each frame t, UAV s travels with a velocity v during the flight slot and hovers on a location in $\mathcal{M}$ during the data slot to facilitate communication with devices. We use the trajectory estimation methods presented in [32] to obtain the position of UAV e in each frame.

Figure 2

Frame structure: each frame includes a flight slot and a data slot.

[Figure omitted. See PDF]

Table 2

Common notations.

1. Sets
$\mathcal{M}$	Set of locations.
$\mathcal{T}$	Set of discrete time frames.
$\mathcal{V}$	Set of solar-powered devices.
2. Constants
$g_{iu}^t$	Channel gain of device i and UAV u in frame t.
$C_{im}^t$	Link capacity between device i and location m in frame t.
$C_{ie}^t$	Link capacity between device i and UAV e in frame t.
$C_{is}^t$	Total capacity received by UAV s in frame t.
$D_{mn}$	Distance between location m and n.
$D_{iu}^t$	Distance between device i and UAV u in frame t.
$E_i^t$	Solar energy arrival at device i in frame t.
$P_0$	Transmit power of a device.
${\beta }_0$	Channel power gain at a reference distance of one meter.
${\sigma }^2$	Noise power in the channel.
$\tau$	Length of a frame.
3. Variables
$b_i^t$	Energy available at device i in frame t.
$f_{mn}^t$	Indicate whether UAV s flies from m to n in frame t.
$l_m^t$	Indicate whether UAV s is located at point m in frame t.
$x_i^t$	Indicate whether device i operates in Tx-mode in frame t.
$y_i^t$	Indicate whether device i operates in Jam-Mode in frame t.
${\tau }_F^t$	The length of flight slot in frame t.
${\tau }_D^t$	The length of data slot in frame t.
${\omega }_i^t$	Energy stored by device i in frame t.

3.1. UAV Server Trajectory

UAV s hovers over specific locations to collect information, with these locations being densely populated with devices to enhance data transfer and collection efficiency [33]. Denote $D_{mn}$ as the Euclidean distance between location m and n. Let $f_{mn}^t\in \{0,1\}$ represent whether UAV s flies from location m to n during frame t. Specifically, $f_{mn}^t=1$ if UAV s travels from m to n; otherwise, it is set to zero. The flying distance of UAV s within a frame is constrained by (i) the duration of the flight slot and (ii) its velocity. Hence, the maximum flying distance in a frame is limited to ${\tau }_F^{t}v$. Formally,

(2)$\begin{array}{cc}\hfill f_{mn}^t{D}_{mn}\le {\tau }_F^{t}v,& \forall m,n\in \mathcal{V},\forall t\in \mathcal{T}.\end{array}$

Next, we model the movement of UAV s between locations in $\mathcal{M}$. Let $l_m^t$ denote whether UAV s is at location m during frame t. If UAV s is at location m, then $l_m^t=1$; otherwise, $l_m^t=0$. Assume $l_m^t=1$, indicating that UAV s is located at m during frame t. To reach m, UAV s must have traveled from a neighboring location u to m during frame t, which implies $f_{um}^t=1$. Formally, we have

(3)$\begin{array}{cc}\hfill \sum _{u\in \mathcal{M}}{f}_{um}^t=l_m^t,& \forall m\in \mathcal{M},\forall t\in \mathcal{T}.\end{array}$

Similarly, if UAV s is located at m, it flies to another location at the start of frame $t+1$. Thus, we have

(4)$\begin{array}{cc}\hfill l_m^t=\sum _{v\in \mathcal{M}}{f}_{mv}^{t+1},& \forall m\in \mathcal{M},\forall t\in \mathcal{T}.\end{array}$

Lastly, UAV s only visits one point in $\mathcal{M}$ in each frame. Mathematically, we have

(5)$\begin{array}{cc}\hfill \sum _{m\in \mathcal{M}}{l}_m^t=1,& \forall t\in \mathcal{T}.\end{array}$

3.2. Devices

Each device is equipped with a solar panel and a rechargeable battery with a capacity of $B_{max}$. The solar energy arrivals at each device are modeled using the hidden Markov model from [34], which defines four energy arrival states: excellent, good, fair, and poor. Each state is characterized by a probability distribution with a specific mean and variance, and transitions between states are governed by state transition probabilities; see Section 7.

Let $E_i^t$ represent the solar energy arriving at device i during frame t. Device i stores ${\omega }_i^t$ units of energy in its rechargeable battery, which becomes available for use at the start of frame $t+1$. The available energy at device i during frame t is denoted by $b_i^t$. To constrain the amount of harvested energy, we have

(6)$\begin{array}{cc}\hfill b_i^{t-1}+{\omega }_i^{t-1}\le B_{max},& \forall i\in \mathcal{V},t\in \mathcal{T},\end{array}$

(7)$\begin{array}{cc}\hfill {\omega }_i^t\le E_i^t,& \forall i\in \mathcal{V},t\in \mathcal{T},\end{array}$

where (6) and (7) indicate the amount of energy that device i stores in slot t and is bounded by (i) its available battery space and (ii) solar energy arrival, respectively.

Each device is assigned an orthogonal channel and has a transmit power of $P_0$ [35]. Each device consumes energy either to (i) transmit data or (ii) broadcast a jamming signal. Thus, each device operates in one of two modes: (i) Tx-mode and (ii) Jam-mode. In particular, when device i transmits data to UAV s, it operates in Tx-mode. Conversely, when device i functions as a jammer, it operates in Jam-mode. The mode of each device is denoted as follows: $x_i^t\in \{0,1\}$, where $x_i^t=1$ indicates that device i is in Tx-mode during frame t to transmit data to UAV s. Otherwise, it is zero. Similarly, let $y_i^t$ denote whether device i is in Jam-mode during frame t, where $y_i^t=1$ indicates that device i is acting as a jammer in frame t. Otherwise, we have $y_i^t=0$. As each device only runs one mode in a frame, we have

(8)$\begin{array}{cc}\hfill x_i^t+y_i^t\le 1,& \forall i\in \mathcal{V},\forall t\in \mathcal{T}.\end{array}$

Lastly, the energy level of devices evolves between two adjacent slots as follows:

(9)$\begin{array}{cc}\hfill b_i^t=b_i^{t-1}+{\omega }_i^{t-1}-P_0{\tau }_D^t(x_i^t+y_i^t),& \forall i\in \mathcal{V},t\in \mathcal{T}.\end{array}$

3.3. Link Capacity

There is a LoS channel between a UAV and a device. We assume a block-fading channel, where the channel gain remains constant within a frame but varies across frames. This model reflects the fact that while the channel conditions might fluctuate over time, they stay stable during each frame, providing a realistic approximation of the wireless communication environment in which UAVs and devices interact. Further, we use the channel model in [36], where the channel power gain between two nodes in frame t is given by

(10)$\begin{array}{c}\hfill g_{ij}^t={\displaystyle \frac{{\beta }_0}{{\left(D_{ij}^t\right)}^2}},\end{array}$

where $D_{ij}^t$ denotes their distance and ${\beta }_0$ is channel power gain at a reference distance of one meter.

We now define the secrecy rate between devices and UAV s. Let $C_{im}^t$ denote the theoretical link capacity between device i and location m in frame t, which is calculated using the Shannon–Hartley formula. For each device $i\in \mathcal{V}$, its capacity to UAV s at location m in frame t is given by

(11)$\begin{array}{c}\hfill C_{im}^t=W{log}_2\left(1+{\displaystyle \frac{P_0{x}_i^t{g}_{im}^t}{{\sigma }^2+{\sum }_{u\in \mathcal{V}/\left\{i\right\}}{P}_0{g}_{um}^t(x_u^t+y_u^t)}}\right),\end{array}$

where W is the bandwidth and ${\sigma }^2$ is the noise power.

We emphasize that a link has nonzero capacity only when UAV s is located at m. To model this, we have

(12)$\begin{array}{cc}\hfill C_{is}^t=\sum _{m\in \mathcal{M}}{l}_m^t{C}_{im}^t,& \forall i\in \mathcal{V},\forall t\in \mathcal{T}.\end{array}$

Let $C_{ie}^t$ be the link capacity between device i and UAV e (eavesdropper) in frame t. Thus, for each device $i\in \mathcal{V}$ in each frame $t\in \mathcal{T}$, we have

(13)$\begin{array}{c}\hfill C_{ie}^t=W{log}_2\left(1+{\displaystyle \frac{P_0{x}_i^t{g}_{ie}^t}{{\sigma }^2+{\sum }_{u\in \mathcal{V}/\left\{i\right\}}{P}_0{g}_{ue}^t(x_u^t+y_u^t)}}\right).\end{array}$

As per [37], the secrecy rate of device i in frame t is

(14)$\begin{array}{cc}\hfill R_i^t=C_{is}^t-C_{ie}^t,& \forall i\in \mathcal{V},\forall t\in \mathcal{T}.\end{array}$

4. Problem Formulation

Our aim is to maximize the minimum average secrecy rate of devices over multiple frames by optimizing several factors: (i) the allocation of frame time, represented by the length of the flight slot and data slot in frame t i.e., ${\tau }_F^t$ and ${\tau }_D^t$, (ii) the UAV trajectory, including the travel decisions $f_{mn}^t$ and the location $l_m^t$, (iii) the harvested energy ${\omega }_i^t$ for each device, and (iv) the operation mode of each device, denoted by $x_i^t$ for Tx-mode and $y_i^t$ for Jam-mode. For convenience, define $\mathit{\pi }=[{\tau }_F^t,{\tau }_D^t,f_{mn}^t,l_m^t,{\omega }_i^t,x_i^t,y_i^t]$. The problem is formulated as follows:

(15)$\begin{array}{ll}\underset{\mathit{\pi }}{\max }& {\min \left\{{\displaystyle \sum _{t=1}^{\left|\mathcal{T}\right|}},\frac{R_i^t{\tau }_D^t}{\left|\mathcal{T}\right|}\right\}}_{\forall i\in \mathcal{V},\forall m\in \mathcal{M}}\\ \mathrm{s}.\mathrm{t}.& \left(1\right)–\left(9\right).\end{array}$

Note that Equations (9), (11) and (13) contain nonlinear terms. Thus, the problem is modeled as an MINLP, that is difficult to solve. To take advantage of efficient algorithms used by commercial solvers, we will now proceed to linearize these nonlinear terms; i.e., convert problem (15) into an MILP.

We first consider Equation (9), where the terms ${\tau }_D^t{x}_i^t$ and ${\tau }_D^t{y}_i^t$ are nonlinear due to the multiplication of a continuous variable by a binary variable. To linearize Equation (9), we use Binary-Continuous Multiplication Linearization similar to [38] by introducing auxiliary variables to replace the product of the binary and continuous variables, thus converting the nonlinear terms into linear ones.

Specifically, we define $X_i^t={\tau }_D^t{x}_i^t$ as an auxiliary variable. This substitution helps to remove the nonlinearity and allows us to express the relationship linearly. For each $t\in \mathcal{T}$ and $i\in \mathcal{V}$, we bound $X_i^t$ as follows:

(16)$\begin{array}{cc}\hfill X_i^t\ge 0,& \forall t\in \mathcal{T},\forall i\in \mathcal{V},\end{array}$

(17)$\begin{array}{cc}\hfill X_i^t\le x_i^t,& \forall t\in \mathcal{T},\forall i\in \mathcal{V},\end{array}$

(18)$\begin{array}{cc}\hfill X_i^t\le {\tau }_D^t,& \forall t\in \mathcal{T},\forall i\in \mathcal{V},\end{array}$

(19)$\begin{array}{cc}\hfill X_i^t\ge {\tau }_D^t-(1-x_i^t).& \forall t\in \mathcal{T},\forall i\in \mathcal{V}.\end{array}$

When $x_i^t$ is set to zero, the value of $X_i^t$ is forced to zero. However, if $x_i^t$ is set to one, then $X_i^t$ equals ${\tau }_D^t$.

As for ${\tau }_D^t{y}_i^t$ in Equation (9), we assume $Y_i^t={\tau }_D^t{y}_i^t$ and use Binary-Continuous Multiplication Linearization to constrain the value of $Y_i^t$. We then rewrite Equation (9) as follows:

(20)$\begin{array}{cc}\hfill b_i^t=b_i^{t-1}+{\omega }_i^{t-1}-P_0{X}_i^t-P_0{Y}_i^t& \forall i\in \mathcal{V},t\in \mathcal{T}.\end{array}$

We now move to the nonlinear terms in Equations (11) and (13). Specifically, we approximate the ${log}_2(.)$ function using line segments, where for a given input or signal-to-noise-plus-interference ratio (SINR) value, we estimate its value using a corresponding line segment. As ${log}_2(.)$ is a concave function, by definition, the values on line segments or chords are always less than or equal to the value of the log2(.) function. More line segments result in more precise approximations but higher computational complexity.

Denote $[Z_{min},Z_{max}]$ as the range of SINR values. This range is discretized into $\left|\mathcal{Z}\right|$ levels that are recorded in set $\mathcal{Z}$. Each level $z\in \mathcal{Z}$ corresponds to a specific SINR value, and we approximate the ${log}_2(.)$ of the SINR using a linear function over the range of z. Let ${\varphi }_z$ be the z-th SINR value with corresponding data rate

(21)$\begin{array}{cc}\hfill R_z=W{log}_2\left(1+{\varphi }_z\right),& \forall z\in \mathcal{Z}.\end{array}$

We first consider Equation (11). We denote ${\beta }_{im}^{tz}\in \{0,1\}$ as a binary variable, where ${\beta }_{im}^{tz}=1$ indicates that device i uploads data to location m using a data rate $R_z$ in frame t. Otherwise, we have ${\beta }_{im}^{tz}=0$. Further, if UAV s stops at location m, then location m has a nonnegative data rate. Formally,

(22)$\begin{array}{cc}\hfill \sum _{z=1}^{\left|\mathcal{Z}\right|}{\beta }_{im}^{tz}=l_m^t,& \forall i\in \mathcal{V},\forall m\in \mathcal{M},\forall t\in \mathcal{T}.\end{array}$

The next constraint selects a data rate; equivalently, the resulting SINR must exceed a given value. To determine ${\beta }_{im}^{tz}$, we rewrite Equation (11) for each SINR ${\varphi }_z$ value. In particular, to decode the received information, device m must ensure that its received power overcomes its interference from other devices, i.e., $\forall u\in \mathcal{V}/\left\{i\right\}$. Thus, for each frame $t\in \mathcal{T}$, each device $i\in \mathcal{V}$, each location $m\in \mathcal{M}$, and each SINR level $z\in \mathcal{Z}$, we have

(23)$\begin{array}{c}\hfill P_0{x}_i^t{g}_{im}^t-{\varphi }_z\left({\sigma }^2+\sum _{u\in \mathcal{V}/\left\{i\right\}}{P}_0(x_u^t+y_u^t)g_{um}^t\right)\\ \hfill \ge ({\beta }_{im}^{tz}-1)\Phi ,\forall t\in \mathcal{T},\forall i\in \mathcal{V},\forall m\in \mathcal{M},\forall z\in \mathcal{Z},\end{array}$

where $\Phi$ is a large positive number. Observe that if the received power of device m is smaller than its total received interference, the value of ${\beta }_{im}^{ty}$ is forced to zero. In other words, Equation (23) is disabled for data rate z.

Next, we focus on the nonlinear terms in Equation (13). Let ${\gamma }_{ie}^{tz}\in \{0,1\}$ be a binary variable that is set to one when the link capacity of $(i,e)$ is set to $R_z$ in frame t. Further, as each device only has one data rate to UAV e, we have

(24)$\begin{array}{ccc}\hfill \sum _{z=1}^{\left|\mathcal{Z}\right|}{\gamma }_{ie}^{tz}=1,& \forall i\in \mathcal{V},& \forall t\in \mathcal{T}.\hfill \end{array}$

We now select a data rate from device i to UAV e; i.e., we determine which SINR threshold can be satisfied by link $(i,e)$ aiming to ensure that the received power from device i is larger than the interference from other devices. Thus, we rewrite Equation (13) to determine the value of ${\gamma }_{ie}^{tz}$. For each frame $t\in \mathcal{T}$, each device $i\in \mathcal{V}$ and each SINR level $z\in \mathcal{Z}$, we have

(25)$\begin{array}{c}\hfill P_0{x}_i^t{g}_{ie}^t-{\varphi }_z\left({\sigma }^2+\sum _{u\in \mathcal{V}/\left\{i\right\}}{P}_0(x_u^t+y_u^t)g_{ue}^t\right)\\ \hfill \ge ({\gamma }_{ie}^{tz}-1)\Phi ,\forall t\in \mathcal{T},\forall i\in \mathcal{V},\forall z\in \mathcal{Z},\end{array}$

where Equation (25) becomes disable (${\gamma }_{ie}^{tz}=0$) if the SINR is less than ${\varphi }_z$.

Lastly, we rewrite Equation (14). For each frame t in $\mathcal{T}$, each device i in $\mathcal{V}$, and each location m in $\mathcal{M}$, we have

(26)$\begin{array}{cc}\hfill R_i^t=\sum _{\forall z\in \mathcal{Z}}\left(\sum _{\forall m\in \mathcal{M}}{\beta }_{im}^{tz}-{\gamma }_{ie}^{tz}\right)R_z,& \forall z\in \mathcal{Z}.\end{array}$

Next, we consider the nonlinear terms ${\beta }_{im}^{tz}{\tau }_D^t$ and ${\gamma }_{ie}^{tz}{\tau }_D^t$ in Equation (15). The nonlinear terms are a multiplication of a binary variable and a continuous variable. We use Binary-Continuous Multiplication Linearization again. Denote ${\zeta }_{im}^{tz}\in [0,1]$ and ${\eta }_{ie}^{tz}\in [0,1]$ as two auxiliary variables. Respectively, ${\zeta }_{im}^{tz}={\beta }_{im}^{tz}{\tau }_D^t$ and ${\eta }_{ie}^{tz}={\gamma }_{ie}^{tz}{\tau }_D^t$.

Lastly, we rewrite our problem as a MILP:

(27)$\begin{array}{ll}\underset{\pi }{\max }& {\min \left\{{\displaystyle \sum _{t=1}^{\left|\mathcal{T}\right|}},\frac{R_i^t{\tau }_D^t}{\left|\mathcal{T}\right|}\right\}}_{\forall i\in \mathcal{V},\forall m\in \mathcal{M}}\\ \mathrm{s}.\mathrm{t}.& \left(1\right)–\left(8\right),\left(20\right),\\ & \left(22\right)–\left(25\right)\end{array}$

Our problem is computationally hard due to the combinatorial explosion of possible UAV server trajectories as the number of destinations and time frames increases. Specifically, the UAV server’s decision space grows exponentially with $\left|\mathcal{M}\right|$ and $\left|\mathcal{T}\right|$. At the start of a frame t, if the UAV server is at location m, it has two actions to consider: (i) flying to a new location or (ii) staying at the current location. If it chooses to fly, it has up to $\left|\mathcal{M}\right|-1$ potential destinations. Alternatively, staying at the current location adds another option, resulting in $\left|\mathcal{M}\right|$ possible locations at each frame. Over $\left|\mathcal{T}\right|$ frames, the UAV server must determine a sequence of decisions, leading to a total of ${\left|\mathcal{M}\right|}^{\left|\mathcal{T}\right|}$ possible trajectories. This exponential growth quickly becomes intractable as the number of destinations or frames increases.

5. Heuristic Solution: FNL

To solve our problem in large-scale networks, we design a heuristic solution called FNL. Briefly, the main idea of the FNL algorithm is to have UAV s select the nearest location in each frame, aiming to reduce travel time and maintain efficient communication with devices. By focusing on proximity, this strategy minimizes the length of flight slot while maximizing the length of data slot. More data transmission time is important for energy-constrained devices, as it helps reduce their transmit power and enhances communication efficiency. FNL consists of the following phases in each frame t: (i) Path selection, which determines the next location of UAV s in frame t, (ii) Time calculation, which estimates the length of the data slot in frame t, and (iii) Mode selection, which selects the operation mode for each device.

Algorithm 1 presents the details of FNL. We assume that UAV s is initially located at m at the start of frame t. In the Path selection phase, the goal is to determine the next destination of UAV s for the upcoming frame. Let $n^{\ast }$ denote the destination location of UAV s at the end of frame t. FNL sends UAV s to the next nearest location in each frame t; see line 2. Formally, the value of $n^{\ast }$ is calculated as follows:

(28)$\begin{array}{c}\hfill n^{\ast }=\underset{n\in \mathcal{M}-\left\{m\right\}}{argmin}{D}_{mn}.\end{array}$

Next, FNL enters the Time calculation phase. The flying time is ${\displaystyle \frac{D_{m{n}^{\ast }}}{V}}$. Thus, the data slot duration in frame t is

(29)$\begin{array}{c}\hfill {\tau }_D^t=\tau -{\displaystyle \frac{D_{m{n}^{\ast }}}{V}}.\end{array}$

where Equation (29) estimates the length of data slot in frame t.

In the Mode selection phase, each device i first checks its energy level to ensure that it has sufficient energy to either upload data or send a jamming signal in frame t. Specifically, if the energy constraint is satisfied, i.e., $b_i^t\ge P_0{\tau }_D^t$, the device proceeds to select its operation mode, as detailed in lines 4–12.

If the distance between device i and the UAV server s is shorter than the distance between device i and the eavesdropper UAV e, device i enters the Tx-mode ($x_i^t=1$), as shown in lines 6–7. This decision allows device i to upload data efficiently to the UAV server. On the other hand, if the distance between device i and UAV s is longer than that to UAV e, device i enters the Jam-mode ($y_i^t=1$), as outlined in lines 8–9. In this mode, device i intentionally sends a jamming signal to disrupt the eavesdropper, protecting the transmitted data from interception.

Algorithm 1: Pseudocode of FNL

6. Analysis

In this section, we present the following propositions related to the MILP model and FNL solution.

Proposition 1.

MILP (27) has $\left|\mathcal{T}\right|\left(\right|\mathcal{M}{|}^2+\left|\mathcal{M}\right|+3\left|\mathcal{V}\right|)$ decision variables and $\left|\mathcal{T}\right|\left(\right|\mathcal{V}\left|\right(5\left|\mathcal{Z}\right|\left(\right|\mathcal{M}|+1)+\left|\mathcal{V}\right|+\left|\mathcal{M}\right|+14)+2(\left|\mathcal{M}\right|+1\left)\right)$ constraints.

Proof. 

We first consider the number of decision variables. As per (27), we have seven types of decision variables, i.e., ${\tau }_F^t,{\tau }_D^t,f_{mn}^t,l_m^t,{\omega }_i^t,x_i^t,$ and $y_i^t$. In particular, for UAV s, it flies in each frame t. Thus, the numbers of ${\tau }_F^t$ and ${\tau }_D^t$ are $\left|\mathcal{T}\right|$, respectively. For $f_{mn}^t$, UAV s flies from one location to another in a frame. Thus, we have ${\left|\mathcal{T}\right|\left|\mathcal{M}\right|}^2$ such variables. Next, each device harvests solar energy in each frame. Thus, we have $\left|\mathcal{T}\right|\left|\mathcal{V}\right|$ of ${\omega }_i^t$. Lastly, a device operates in one mode in a frame. Thus, we have $\left|\mathcal{T}\right|\left|\mathcal{V}\right|$ of $x_i^t$ and $y_i^t$. Consequently, we have $\left|\mathcal{T}\right|\left(\right|\mathcal{M}{|}^2+\left|\mathcal{M}\right|+3\left|\mathcal{V}\right|)$ decision variables.

We now count the number of constraints. For UAV s, we have one constraint of type (1)–(5). Thus, we have $\left|\mathcal{T}\right|\left(\right|\mathcal{V}{|}^2+2\left|\mathcal{M}\right|+2)$ such constraints. Further, a device has one constraint of type (6)–(8). Hence, we have $4\left|\mathcal{T}\right|\left|\mathcal{V}\right|$ such constraints. Lastly, we count the constraints in linearization. When using Binary-Continuous Multiplication Linearization, we need four types of constraints to linearize one nonlinear term. The number of constraints depends on the number of auxiliary variables. For example, to linearize ${\tau }_D^t{x}_i^t$, we introduce $X_i^t$ as an auxiliary variable. The number of $X_i^t$ is $\left|\mathcal{T}\right|\left|\mathcal{V}\right|$. We have one constraint of type (16)–(19). Thus, we need $4\left|\mathcal{T}\right|\left|\mathcal{V}\right|$ constraints to linearize ${\tau }_D^t{x}_i^t$. Similarly, there are $4\left|\mathcal{T}\right|\left|\mathcal{V}\right|$ constraints to linearize ${\tau }_F^t{y}_i^t$. Each device has one type of (20). Thus, we have $\left|\mathcal{T}\right|\left|\mathcal{V}\right|$ such constraints. UAV s has one constraint of type (22) and (23). Hence, we have $\left|\mathcal{T}\right|\left|\mathcal{M}\right|\left|\mathcal{V}\right|(1+|\mathcal{Z}\left|\right)$ such constraints. UAV e has one constraint of type (24) and (25). Thus, we have $\left|\mathcal{T}\right|\left|\mathcal{V}\right|(1+|\mathcal{Z}\left|\right)$ such constraints. To linearize ${\beta }_{im}^{tz}{\tau }_D^t$ and ${\gamma }_{ie}^{tz}{\tau }_D^t$. We introduce two auxiliary variables ${\zeta }_{im}^{tz}$ and ${\eta }_{ie}^{tz}$. The number of ${\zeta }_{im}^{tz}$ is $\left|\mathcal{T}\right|\left|\mathcal{M}\right|\left|\mathcal{V}\right|\left|\mathcal{Z}\right|$ and the number of ${\eta }_{ie}^{tz}$ is $\left|\mathcal{T}\right|\left|\mathcal{V}\right|\left|\mathcal{Z}\right|$. Thus, we have $4\left|\mathcal{T}\right|\left|\mathcal{V}\right|\left|\mathcal{Z}\right|(1+|\mathcal{M}\left|\right)$ constraints when using Binary-Continuous Multiplication Linearization.

In conclusion, the proposed MILP has $\left|\mathcal{T}\right|\left(\right|\mathcal{V}\left|\right(5\left|\mathcal{Z}\right|\left(\right|\mathcal{M}|+1)+\left|\mathcal{V}\right|+\left|\mathcal{M}\right|+14)+2(\left|\mathcal{M}\right|+1\left)\right)$ constraints. □

Proposition 2.

MILP (27) is an NP-hard problem.

Proof. 

The NP-hard prize collecting traveling salesman problem (PC-TSP) [39] is a special case of our problem. Briefly, given cities, each with a prize, a salesman’s goal is to visit a subset of cities to collect a required prize amount at minimum cost, which is a function of traveling costs and penalties from unvisited cities. Consider the case when IoT devices have ample energy, and an operator or server-UAV wishes to collect a given prize or data amount. Note that the prize of a city is equivalent to the collected data at a location. Note, a key difference from PC-TSP is that in our case, the server-UAV can visit a location/city several times instead of once. We can, however, duplicate locations visited multiple times to yield the same setup required by PC-TSP. Thus, PC-TSP is a special case of our problem. In fact, our problem is at least as hard as PC-TSP because we also have to consider the energy budget and the mode of devices. In conclusion, our MILP problem is an NP-hard problem. □

Proposition 3.

Heuristic solution FNL has a time complexity of $\mathcal{O}\left(\right|\mathcal{V}\left|\right|\mathcal{T}\left|\right)$.

Proof. 

To analyze the time complexity of FNL, we evaluate the number of operations performed during its execution. The primary factor affecting the time complexity of the FNL algorithm is the presence of nested for-loops. First, FNL iterates through all time frames $t\in \mathcal{T}$. This means the outer loop runs $\left|\mathcal{T}\right|$ times. Further, in each time frame, the algorithm iterates over all devices in the set $\mathcal{V}$. As a result, the operations in line 4 and the condition in line 6 are executed $\left|\mathcal{V}\right|$ times for each time frame. In conclusion, since the outer and inner loops are nested, the total number of iterations is the product of the size of $\mathcal{T}$ and $\mathcal{V}$. This makes the overall time complexity of the FNL algorithm $\mathcal{O}\left(\right|\mathcal{V}\left|\right|\mathcal{T}\left|\right)$. □

7. Evaluation

We solve problem (27) and study FNL using Python 3.12.3 with Gurobi 12.0. The experiments are conducted on a PC equipped with a 12th Gen Intel(R) Core(TM) i7-12700 CPU running at 2.10 GHz and 16 GB of RAM, ensuring the computations are performed within a reasonable timeframe. We use two DJI Matrice 300 RTK UAVs manufactured by DJI Innovations, Shenzhen, China as UAV s and UAV e [31] in our simulation experiments. UAVs, devices, and locations in $\mathcal{M}$ are randomly deployed over a 100 × 100 m² area, simulating practical network configurations. The maximum velocity of UAVs is set to 50 m/s [40]. The trajectory of the eavesdropper is generated randomly, introducing variability to test the system’s performance under diverse conditions. Each device is equipped with a $63\times 63$ mm² solar panel [41]. Each device has a battery with a capacity of 100 mJ. As per [42], the values of ${\beta }_0$ and ${\sigma }^2$ are −60 dBm and −110 dBm, respectively. Solar energy arrives at devices as per [34], where the Markov model has four states with a corresponding mean of 94.6, 76.0, 45.6, and 17.9 mW/cm². Variances of the four states are 0.31, 1.55, 1.48 and 0.71. Table 3 shows the means and variances of each energy arrival state. Table 4 demonstrates the state transition probability between states.

We have five SINR levels, whose data rate is 0, 1, 10, 100, 1000 kb/s. Table 5 lists parameter values. Table 5 lists parameter values.

We propose two benchmark solutions, named BENC and NO-EAV, for comparison purposes. Specifically, in BENC, the UAV’s next location is randomly selected at each time frame. This approach does not use any optimization for the UAV’s movement, providing a simple baseline to compare with other more complex strategies. For NO-EAV, we remove eavesdroppers from the system, focusing on maximizing the minimum data rate. This setup allows us to investigate the effect of eavesdroppers on system performance and provides insight into how the presence of eavesdropping impacts the achievable secrecy rate.

To study the factors that impact the max-min secrecy rate, we consider six parameters, i.e., $\left|\mathcal{M}\right|$, $\left|\mathcal{V}\right|$, $\left|\mathcal{T}\right|$, $P_0$, W and the energy harvesting efficiency. Each result is an average of 30 runs; each run uses a different eavesdropper trajectory, arrived solar energy, and channel gains.

In the first experiment, we set $\left|\mathcal{V}\right|$ and $\left|\mathcal{T}\right|$ to 10, with the transmit power of each device set to 1 mW. The bandwidth of the network is 20 kHz and the energy harvesting efficiency is 20%. As shown in Figure 3, the max-min secrecy rate increases when the value of $\left|\mathcal{M}\right|$ rises from five to 25. For example, the max-min secrecy rate of MILP increases by 35.31% from 48.15 kbits/s. The reason is because UAV s selects a better location in high $\left|\mathcal{M}\right|$ case, where more locations provide shorter data transmission distance between devices in Tx-mode and the UAV server. Further, as per Equation (10), these devices use a higher-quality channel when they upload data.

Next, we set $\left|\mathcal{M}\right|$, $\left|\mathcal{T}\right|$, $P_0$, W and energy harvesting efficiency to 10, 10, 1 mW, 20 kHz, and 20%, respectively, and study the impact of $\left|\mathcal{V}\right|$. As shown in Figure 4, the max-min secrecy rate decreases as $\left|\mathcal{V}\right|$ increases. Specifically, for MILP, the value decreases from 75.53 kbit/s to 20.50 kbit/s as $\left|\mathcal{V}\right|$ increases from five to 25. The reason is as follows. Since $\left|\mathcal{T}\right|$ is fixed, more devices upload data or send a jamming signal in a frame. Thus, a device in Tx-mode faces high wireless interference from other devices, which reduces their wireless link capacity to the UAV server.

In the third experiment, the values of $\left|\mathcal{M}\right|$ and $\left|\mathcal{V}\right|$ are set to 10, and each device transmits data using a fixed power of 1 mW. The system has a 20 kHz bandwidth and the efficiency of energy harvesting is 20%. We increase $\left|\mathcal{T}\right|$ from five to 25 with an interval of five. According to Figure 5, the value of MILP increases from 39.70 kbit/s to 73.01 kbit/s. This is because when there are more frames, a device is more likely to select a frame with good channel conditions, which allows it to upload more data. In addition, we observe the value of MILP increases by 76.60% from 39.70 kbit/s when $\left|\mathcal{T}\right|$ increases from 5 to 20. However, as $\left|\mathcal{T}\right|$ increases to 25, the value of MILP increases from 70.11 kbit/s to 73.01 kbit/s. The reason is because when $\left|\mathcal{T}\right|$ increases, the max-min secrecy rate is restricted by the limited resources in the network.

In the fourth experiment, we study $P_0=\{0.01,0.1,1,10,100\}$ mW in a network with 10 devices, 10 locations, and 10 frames. We set the value of W to 20 kHz and each device harvests energy with an efficiency of 20%. Referring to Figure 6, when $P_0$ increases from $0.01$ mW to 1 mW, the result of the MILP increases from 32.31 kbit/s to 57.54 kbit/s. The reason is because a device in Tx-mode transmits more data when $P_0$ increases from $0.01$ mW to 1 mW; see Equation (11). Further, devices in Jam-mode transmit more power jamming signal to the eavesdropper, reducing $C_{ie}^t$. In addition, we observe that when $P_0$ increases from 1 mW to 100 mW, the result has a 23.83% decrease from 57.54 kbit/s to 43.83 kbit/s. This is because some devices may not harvest sufficient energy over $\left|\mathcal{T}\right|$ frames when $P_0$ continues increases. Thus, it cannot upload data, leading to a decrease in max-min secrecy rate.

In the fifth experiment, we consider 10 devices and 10 locations. Each device transmits data using a fixed power of 1mW and has a 20% energy harvesting rate. We increase the network bandwidth from 20 kHz to 100 kHz with an interval of 20 kHz. As shown in Figure 7, the result of MILP ranges from 55.05 kbit/s to 57.79 kbit/s. This is because the increase in network bandwidth leads to an increase in $C_{im}^t$ and $C_{ie}^t$; see (14).

In the last experiment, we investigate various energy harvesting efficiencies, ranging from 20% to 100% in a 10-device network over 10 frames. The transmit power of each device is 1 mW. The value of $\left|M\right|$ and W is 10 and 20 kHz. The results in Figure 8 show that MILP increases from 57.54 kbit/s to 68.75 kbit/s when energy harvesting efficiency increases from 20% to 100%. The reason is because devices harvest more energy with higher energy harvesting efficiency. For each device, it has sufficient energy to upload data to UAV s. As a result, the value of $C_{im}^t$ increases. Further, we observe that when energy harvesting efficiency increases from 20% to 40%, the result of MILP increases 16.09% from 57.54 kbit/s to 66.80 kbit/s. But the result increases from 66.80 kbit/s to 68.75 kbit/s when energy harvesting efficiency increases from 40% to 100%. This is because all devices have sufficient energy to operate in either Tx-mode or Jam-mode when energy harvesting efficiency is high.

Lastly, we observe that the performance of FNL and BENC achieves 78.15% and 49.39% that of MILP, respectively. The reason is because MILP has all information about solar arrivals at devices and channel gain over $\left|\mathcal{T}\right|$ frames. As a comparison, FNL and BENC only have information in one frame. In addition, FNL and BENC neglect the remaining energy of devices when they determine the trajectory of UAV s. Further, they only use $D_{is}^t$ and $D_{ie}^t$ to determine the mode of devices. For not considering an eavesdropper, the NO-EAV result is 129.83% of MILP.

8. Conclusions

This paper has studied a novel problem in a UAV-assisted energy harvesting IoT network. Its aim is to maximize the minimum secrecy rate among devices. It presented the first MILP for the problem and designed a heuristic solution called FNL. Simulation results show that FNL achieved an average of 78.15% of the secrecy rate obtained by MILP. Further, more locations, time frames, and energy harvesting efficiency improve the max-min secrecy rate. By contrast, more devices reduce the max-min secrecy rate. The transmit power of devices and network bandwidth has a limited impact on the max-min secrecy rate.

There are a number of possible future directions. The first direction is to explore the application of reinforcement learning to dynamically plan the trajectory of server-UAVs, leveraging real-time environmental data to further improve system performance. Second, a promising direction is the integration of sensing and communication (ISAC) technologies, allowing UAVs or IoT devices to utilize communication signals for localizing eavesdroppers. The third direction is to consider uncertain positions of the rogue UAV in future time frames.

Author Contributions

Writing—original draft preparation, M.Z. and T.H.; writing—review and editing, M.Z. and T.F. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.

Conflicts of Interest

Author Tianrui Feng is employed by CAAC Central and South Airport Design Research Institute Ltd., Guangzhou 510420, China. The remaining author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. An example UAV-assisted IoT network with solar-powered devices. The hovering locations of UAV-S are labeled as A, B, and C. The red dotted line indicates a possible trajectory for UAV-S, and the green dotted lines indicate jamming transmissions. Blue solid lines represent data transmissions.

Figure 3. Impact of number of locations [Forumla omitted. See PDF.] on max-min secrecy rate.

Figure 4. Impact of number of devices [Forumla omitted. See PDF.] on max-min secrecy rate.

Figure 5. Impact of number of locations [Forumla omitted. See PDF.] on max-min secrecy rate.

Figure 6. Impact of transmit power of devices [Forumla omitted. See PDF.] on max-min secrecy rate.

Figure 7. Impact of network bandwidth W on max-min secrecy rate.

Figure 8. Impact of energy harvesting efficiency on max-min secrecy rate.

Table 1

A comparison between works.

Studies	Max-Min Secrecy Rate	Jammer Selection	UAV Eavesdropper	UAV Trajectory	Time Allocation	EH
[16]	◯	⬤	◯	◯	⬤	◯
[17]	◯	◯	◯	⬤	⬤	◯
[18]	◯	◯	◯	⬤	◯	◯
[19]	⬤	◯	◯	⬤	◯	◯
[20]	⬤	◯	◯	⬤	◯	◯
[21]	◯	⬤	⬤	⬤	◯	◯
[22]	⬤	◯	◯	⬤	◯	◯
[23]	⬤	◯	◯	⬤	◯	◯
[24]	◯	◯	◯	⬤	◯	◯
[25]	◯	◯	◯	◯	◯	⬤
[26]	◯	◯	◯	◯	◯	⬤
[27]	◯	◯	◯	◯	◯	⬤
[28]	⬤	◯	◯	⬤	◯	⬤
[29]	◯	◯	◯	⬤	◯	⬤
Our work	⬤	⬤	⬤	⬤	⬤	⬤

⬤ Considered, ◯ Not considered.

Table 3

Energy harvesting profile [34].

State	Poor	Fair	Good	Excellent
$\mu$ (mW/cm2)	94.6	76.0	45.6	17.9
$\rho$	0.31	1.55	1.48	0.71

Table 4

State transition probability [34].

State	Poor	Fair	Good	Excellent
Poor	0.979	0.015	0.006	0
Fair	0.005	0.988	0.007	0
Good	0.006	0.009	0,975	0.010
Excellent	0	0	0.007	0.993

Table 5

Simulation Parameters.

Parameter	Value
Area size	$100\times 100$ m2
UAV flying altitude	30 m
maximum velocity of UAVs v [40]	50 m/s
Area of solar panels of devices [41]	$63\times 63$ mm2
Device battery capacity	100 mJ
Channel power gain at one meter ${\beta }_0$ [42]	−60 dBm
Noise power ${\sigma }_0$ [42]	−110 dBm

References

1. Abadía, J.J.P.; Walther, C.; Osman, A.; Smarsly, K. A systematic survey of Internet of Things frameworks for smart city applications. Sustain. Cities Soc.; 2022; 83, 103949. [DOI: https://dx.doi.org/10.1016/j.scs.2022.103949]

2. Xu, J.; Gu, B.; Tian, G. Review of agricultural IoT technology. Artif. Intell. Agric.; 2022; 6, pp. 10-22. [DOI: https://dx.doi.org/10.1016/j.aiia.2022.01.001]

3. Song, F.; Ma, Y.; You, I.; Zhang, H. Smart collaborative evolvement for virtual group creation in customized industrial IoT. IEEE Trans. Netw. Sci. Eng.; 2022; 10, pp. 2514-2524. [DOI: https://dx.doi.org/10.1109/TNSE.2022.3203790]

4. Raman, R.; Kaul, M.; Meenakshi, R.; Jayaprakash, S.; Devi, D.R.; Murugan, S. IoT Applications in Sports and Fitness: Enhancing Performance Monitoring and Training. Proceedings of the 2023 Second International Conference on Smart Technologies for Smart Nation (SmartTechCon); Singapore, 18–19 August 2023; pp. 137-141.

5. Renugadevi, R.; Medida, L.H. Artificial Intelligence and IoT-Based Disaster Management System. Predicting Natural Disasters with AI and Machine Learning; IGI Global: Hershey, PA, USA, 2024; pp. 135-146.

6. He, T.; Chin, K.W.; Zhang, Z.; Liu, T.; Wen, J. Optimizing information freshness in RF-powered multi-hop wireless networks. IEEE Trans. Wirel. Commun.; 2022; 21, pp. 7135-7147. [DOI: https://dx.doi.org/10.1109/TWC.2022.3155168]

7. Yang, C.; Liu, Y.; Chin, K.W.; He, T.; Zheng, Z. Maximizing Computed Data in In-Band Full-Duplex UAV-Assisted IIoT Networks. IEEE Trans. Ind. Inform.; 2024; 21, pp. 1379-1388. [DOI: https://dx.doi.org/10.1109/TII.2024.3477550]

8. Pandey, G.K.; Gurjar, D.S.; Yadav, S.; Jiang, Y.; Yuen, C. UAV-assisted communications with RF energy harvesting: A comprehensive survey. IEEE Commun. Surv. Tutor.; 2024; [DOI: https://dx.doi.org/10.1109/COMST.2024.3425597]

9. Zhang, L.; Celik, A.; Dang, S.; Shihada, B. Energy-efficient trajectory optimization for UAV-assisted IoT networks. IEEE Trans. Mob. Comput.; 2021; 21, pp. 4323-4337. [DOI: https://dx.doi.org/10.1109/TMC.2021.3075083]

10. Kazim, M.; Azar, A.T.; Koubaa, A.; Zaidi, A. Disturbance-rejection-based optimized robust adaptive controllers for UAVs. IEEE Syst. J.; 2021; 15, pp. 3097-3108. [DOI: https://dx.doi.org/10.1109/JSYST.2020.3006059]

11. Long, Y.; Zhang, W.; Gong, S.; Luo, X.; Niyato, D. AoI-aware scheduling and trajectory optimization for multi-UAV-assisted wireless networks. Proceedings of the GLOBECOM 2022—2022 IEEE Global Communications Conference; Rio de Janeiro, Brazil, 4–8 December 2022; pp. 2163-2168.

12. Shahzadi, R.; Ali, M.; Khan, H.Z.; Naeem, M. UAV assisted 5G and beyond wireless networks: A survey. J. Netw. Comput. Appl.; 2021; 189, 103114. [DOI: https://dx.doi.org/10.1016/j.jnca.2021.103114]

13. Nour, B.; Mastorakis, S.; Ullah, R.; Stergiou, N. Information-centric networking in wireless environments: Security risks and challenges. IEEE Wirel. Commun.; 2021; 28, pp. 121-127. [DOI: https://dx.doi.org/10.1109/MWC.001.2000245]

14. Michailidis, E.T.; Maliatsos, K.; Skoutas, D.N.; Vouyioukas, D.; Skianis, C. Secure UAV-aided mobile edge computing for IoT: A review. IEEE Access; 2022; 10, pp. 86353-86383. [DOI: https://dx.doi.org/10.1109/ACCESS.2022.3199408]

15. Illi, E.; Qaraqe, M.; Althunibat, S.; Alhasanat, A.; Alsafasfeh, M.; de Ree, M.; Mantas, G.; Rodriguez, J.; Aman, W.; Al-Kuwari, S. Physical layer security for authentication, confidentiality, and malicious node detection: A paradigm shift in securing IoT networks. IEEE Commun. Surv. Tutor.; 2023; 26, pp. 347-388. [DOI: https://dx.doi.org/10.1109/COMST.2023.3327327]

16. Bastami, H.; Moradikia, M.; Abdelhadi, A.; Behroozi, H.; Clerckx, B.; Hanzo, L. Maximizing the secrecy energy efficiency of the cooperative rate-splitting aided downlink in multi-carrier UAV networks. IEEE Trans. Veh. Technol.; 2022; 71, pp. 11803-11819. [DOI: https://dx.doi.org/10.1109/TVT.2022.3192298]

17. Xiao, L.; Xu, Y.; Yang, D.; Zeng, Y. Secrecy energy efficiency maximization for UAV-enabled mobile relaying. IEEE Trans. Green Commun. Netw.; 2019; 4, pp. 180-193. [DOI: https://dx.doi.org/10.1109/TGCN.2019.2949802]

18. Duo, B.; Wu, Q.; Yuan, X.; Zhang, R. Energy efficiency maximization for full-duplex UAV secrecy communication. IEEE Trans. Veh. Technol.; 2020; 69, pp. 4590-4595. [DOI: https://dx.doi.org/10.1109/TVT.2020.2977948]

19. Han, S.; Wang, J.; Xiao, L.; Li, C. Broadcast secrecy rate maximization in UAV-empowered IRS backscatter communications. IEEE Trans. Wirel. Commun.; 2023; 22, pp. 6445-6458. [DOI: https://dx.doi.org/10.1109/TWC.2023.3243270]

20. Li, W.; Hu, Z.; Wen, X.; Lu, Z.; Zhang, Y. Trade-off between secrecy rate and energy consumption in a secure UAV-MEC system. Proceedings of the 2022 IEEE/CIC International Conference on Communications in China (ICCC); Foshan, China, 11–13 August 2022; pp. 862-867.

21. Qian, L.P.; Zhang, W.; Wang, Q.; Wu, Y.; Yang, X. Alternative optimization for secrecy throughput maximization in UAV-aided NOMA networks. IEEE Wirel. Commun. Lett.; 2022; 11, pp. 2580-2584. [DOI: https://dx.doi.org/10.1109/LWC.2022.3210144]

22. Na, Z.; Ji, C.; Lin, B.; Zhang, N. Joint optimization of trajectory and resource allocation in secure UAV relaying communications for Internet of Things. IEEE Internet Things J.; 2022; 9, pp. 16284-16296. [DOI: https://dx.doi.org/10.1109/JIOT.2022.3151105]

23. Lu, W.; Ding, Y.; Gao, Y.; Hu, S.; Wu, Y.; Zhao, N.; Gong, Y. Resource and trajectory optimization for secure communications in dual unmanned aerial vehicle mobile edge computing systems. IEEE Trans. Ind. Inform.; 2021; 18, pp. 2704-2713. [DOI: https://dx.doi.org/10.1109/TII.2021.3087726]

24. Ding, X.; Tian, W.; Liu, G.; Ji, X. Energy Consumption Minimization in Unmanned Aerial Vehicle-Enabled Secure Wireless Sensor Networks. Sensors; 2023; 23, 9411. [DOI: https://dx.doi.org/10.3390/s23239411]

25. Vo, V.N.; So-In, C.; Tran, H.; Tran, D.D.; Huu, T.P. Performance analysis of an energy-harvesting IoT system using a UAV friendly jammer and NOMA under cooperative attack. IEEE Access; 2020; 8, pp. 221986-222000. [DOI: https://dx.doi.org/10.1109/ACCESS.2020.3044760]

26. Ji, B.; Li, Y.; Cao, D.; Li, C.; Mumtaz, S.; Wang, D. Secrecy performance analysis of UAV assisted relay transmission for cognitive network with energy harvesting. IEEE Trans. Veh. Technol.; 2020; 69, pp. 7404-7415. [DOI: https://dx.doi.org/10.1109/TVT.2020.2989297]

27. Pandey, G.K.; Gurjar, D.S.; Yadav, S.; Krstic, D.; Jiang, Y. Enabling Secure UAV-Assisted IoT Communications with RF Energy Harvesting in the Presence of Eavesdropper. Proceedings of the 2023 IEEE International Conference on Advanced Networks and Telecommunications Systems (ANTS); Jaipur, India, 17–20 December 2023; pp. 732-737.

28. Mamaghani, M.T.; Hong, Y. Improving PHY-security of UAV-enabled transmission with wireless energy harvesting: Robust trajectory design and communications resource allocation. IEEE Trans. Veh. Technol.; 2020; 69, pp. 8586-8600. [DOI: https://dx.doi.org/10.1109/TVT.2020.2998060]

29. Ha, D.; Jeong, S.; Kang, J.; Kang, J. Secrecy Energy Efficiency Maximization for Secure Unmanned-Aerial-Vehicle-Assisted Simultaneous Wireless Information and Power Transfer Systems. Drones; 2023; 7, 672. [DOI: https://dx.doi.org/10.3390/drones7110672]

30. Pandey, G.K.; Gurjar, D.S.; Nguyen, H.H.; Yadav, S. Security threats and mitigation techniques in UAV communications: A comprehensive survey. IEEE Access; 2022; 10, pp. 112858-112897. [DOI: https://dx.doi.org/10.1109/ACCESS.2022.3215975]

31. Gil-Castilla, M.; Caballero, A.; Maza, I.; Ollero, A. Integration of Customized Commercial UAV s with Open-Source Tools in a Heterogeneous Multi-UAV System for Power-Lines Inspection. Proceedings of the 2024 International Conference on Unmanned Aircraft Systems (ICUAS); Chania, Greece, 4–7 June 2024; pp. 1362-1369.

32. Güvenç, I.; Ozdemir, O.; Yapici, Y.; Mehrpouyan, H.; Matolak, D. Detection, localization, and tracking of unauthorized UAS and jammers. Proceedings of the 2017 IEEE/AIAA 36th Digital Avionics Systems Conference (DASC); St. Petersburg, FL, USA, 17–21 September 2017; pp. 1-10.

33. Chen, J.; Tang, J. UAV-assisted data collection for dynamic and heterogeneous wireless sensor networks. IEEE Wirel. Commun. Lett.; 2022; 11, pp. 1288-1292. [DOI: https://dx.doi.org/10.1109/LWC.2022.3164784]

34. Ku, M.L.; Chen, Y.; Liu, K.R. Data-driven stochastic models and policies for energy harvesting sensor communications. IEEE J. Sel. Areas Commun.; 2015; 33, pp. 1505-1520. [DOI: https://dx.doi.org/10.1109/JSAC.2015.2391651]

35. Zhan, J.; Wu, J.; He, T.; Chin, K.W. Task Offloading and Approximate Computing in Solar Powered IoT Networks. IEEE Netw. Lett.; 2023; 6, pp. 26-30. [DOI: https://dx.doi.org/10.1109/LNET.2023.3328893]

36. Wang, H.; Ren, G.; Chen, J.; Ding, G.; Yang, Y. Unmanned aerial vehicle-aided communications: Joint transmit power and trajectory optimization. IEEE Wirel. Commun. Lett.; 2018; 7, pp. 522-525. [DOI: https://dx.doi.org/10.1109/LWC.2018.2792435]

37. Tedeschi, P.; Sciancalepore, S.; Di Pietro, R. Security in energy harvesting networks: A survey of current solutions and research challenges. IEEE Commun. Surv. Tutor.; 2020; 22, pp. 2658-2693. [DOI: https://dx.doi.org/10.1109/COMST.2020.3017665]

38. Yang, G.Y.; Hovland, G.; Majumder, R.; Dong, Z.Y. TCSC allocation based on line flow based equations via mixed-integer programming. IEEE Trans. Power Syst.; 2007; 22, pp. 2262-2269. [DOI: https://dx.doi.org/10.1109/TPWRS.2007.907928]

39. Balas, E. The prize collecting traveling salesman problem. Networks; 1989; 19, pp. 621-636. [DOI: https://dx.doi.org/10.1002/net.3230190602]

40. Wu, Q.; Zeng, Y.; Zhang, R. Joint trajectory and communication design for multi-UAV enabled wireless networks. IEEE Trans. Wirel. Commun.; 2018; 17, pp. 2109-2121. [DOI: https://dx.doi.org/10.1109/TWC.2017.2789293]

41. Kjellby, R.A.; Cenkeramaddi, L.R.; Johnsrud, T.E.; Løtveit, S.E.; Jevne, G.; Beferull-Lozano, B.; Soumya, J. Self-powered IoT device based on energy harvesting for remote applications. Proceedings of the 2018 IEEE International Conference on Advanced Networks and Telecommunications Systems (ANTS); Indore, India, 16–19 December 2018; pp. 1-4.

42. Ji, J.; Zhu, K.; Niyato, D.; Wang, R. Joint trajectory design and resource allocation for secure transmission in cache-enabled UAV-relaying networks with D2D communications. IEEE Internet Things J.; 2020; 8, pp. 1557-1571. [DOI: https://dx.doi.org/10.1109/JIOT.2020.3013647]