# A Secure Downlink Transmission Scheme for a UAV-Assisted Edge Network

Authors: Xinmei Gao; Yan Huo; Qinghe Gao; Hongjun Zhao; Long Ma
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

As an extension of centralized cloud services in a space-air-ground integrated network, an unmanned aerial vehicle (UAV-)-enabled edge network brings computation as close ground terminals of need as possible. In this scenario, the UAV is considered a mobile base station (MBS) to achieve data forwarding and processing from cloud servers to terminals. Note that downlink signals from the MBS to ground terminals are vulnerable to passive wiretapping by a malicious node. We formulate an average secrecy rate maximization problem to tackle the wiretapping issue by simultaneously transmitting confidential information and artificial noise (AN). We decompose the problem into two subproblems, including the UAV transmit power allocation subproblem and the UAV trajectory subproblem. Then, we adopt the successive convex approximation scheme and the alternating optimization method to develop our iterative algorithm to achieve secure transmission. Simulation results demonstrate that the proposed scheme is significantly better than other benchmarks in UAV-enabled downlink communication secrecy performance.


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## Body

## 1. Introduction

Data-intensive applications such as video streaming are experiencing an unprecedented surge as digital savvy generation rises. In conjunction with the rapid development of mobile computing and the Internet of Things (IoT), large volumes of data have been moving within edge networking [1]. As an extension of backbone networks, edge computing enables terminals with limited resources to upload computing-intensive tasks to edge servers for execution by deploying servers near edge users. It can greatly reduce computational load and communication costs of terminals and cloud servers [2]. However, complex environments may introduce high infrastructure deployment costs, especially for remote areas and emergency relief applications.Unmanned aerial vehicles (UAVs-)-enabled wireless network is considered a promising paradigm to provide beyond line-of-sight (LOS) signal transmission. Due to high maneuverability, flexible deployment, low cost, and strong hover ability, it is expected to be one of the critical steps in a space-air-ground integrated network (SAGIN). Many works on UAVs-enabled communications include air-to-ground (A2G) channel modeling, optimal throughput-based deployment, and multi-UAV cooperative communication [3]. These technologies may be conveniently introduced into most scenarios and applications, e.g., surveillance missions, weather monitoring, emergency search, and recognition missions [4].With the gradual maturity of UAV technology, UAVs with flexible operation, good scalability, and adaptability to various harsh environments bring more possibilities for network construction, route inspection, and other scenarios. Combining UAVs with a mobile edge computing (MEC) network and assuming UAVs as MEC servers, we can realize rapid deployment and flexible unloading of computing tasks. At the same time, UAVs limited by endurance time and detection range need to plan resources and paths during application.Note that data in UAV-enabled edge networks contain sensitive and private information [5]. The security of data transmission in the open wireless environment is of critical importance for the wide deployment and acceptance of edge services in the future [6, 7]. Traditional methods to address wireless communication security are based on cryptography. It may cause high key management costs and computational complexity. The idea of physical layer security is to use channel information to enhance transmission security, which is an effective supplement to the upper layer security. Some scholars devoted to UAV-aided secure cooperation research [8, 9]. They considered a UAV a mobile relay or a friendly jammer to achieve secure transmission. This scenario is similar to a relay network with cooperative jamming. Essentially, the more general model in UAV-enabled secure communication includes a UAV aerial base station (ABS) and numerous mobile users [10]. A UAV can actively send signals instead of just forwarding information. In this case, an enabled mobile base station leads to changeable channel states, which may complex cooperative jamming design. Thus, it is a crux to design a feasible cooperative jamming scheme for secure communication in a mobile UAV-ABS scenario.For secure communication of UAV-ABS scenarios, several techniques have been introduced to achieve positive secrecy rates or low secrecy outage probability [11]. In [12], the authors intended to jointly optimize the UAV’s trajectory, transmit power, and power allocation of jamming signals to achieve the maximum average secrecy rate (ASR) for a UAV-enabled communication system. For a multi-UAV scenario, the authors in [13] used the orthogonal frequency division multiple access (OFDMA) technology to assign idle UAVs to send artificial noise (AN) to achieve secure transmission.Motivated by the existing works, we discuss secure downlink transmission for a multiantenna UAV-ABS in this paper. In addition, inspired by [14], our system model adopts a hybrid probability channel, including a LOS link and a non-line-of-sight (NLOS) link. In this scenario, we intend to find the ASR. The main contributions of the paper are summarized as follows.
(i)
Considering a UAV-ABS edge network with the random subcarrier selection-orthogonal frequency division multiplexing-direction modulation (RSCS-OFDM-DM) technology, we propose an ASR maximization problem to jointly optimize a feasible three-dimensional (3D) trajectory and power allocation(ii)
We exploit the successive convex approximation (SCA) scheme and the alternating optimization (AO) method to design our iterative algorithm to solve the initial nonconvex problem(iii)
We provide numerous simulation results, including the optimal flight trajectory, ASR, and average transmit power to evaluate our secure transmission methodThe rest of the paper is organized as follows. The related work is presented in the next section. Next, we provide the system model and problem formulation and following propose an efficient iteration algorithm to solve our average secrecy rate maximization problem. Finally, we discuss and evaluate the performance of our method and conclude the article in the last two sections.


## 2. Related Work

### 2.1. Secure Transmit for a UAV Network

Due to the flexibility of UAV-enabled networking, many scholars have studied secure data transmission methods as shown in Table1. In [15], Wu et al. studied energy-saving secure communication for a downlink A2G link. They discussed the impact of a jitter UAV on secure performance and formulated a power minimization and allocation problem with security constraints. Then, they further used secrecy coverage probability (SCP) and ergodic secrecy capacity (ESC) to investigate how to exploit the UAV jitter feature to enhance secrecy in [16]. Considering various service requirements, the authors in [17] proposed an achievable minimum secrecy rate maximization problem and designed a joint optimization method based on user scheduling, power allocation, and trajectory. In addition, [18] considered UAVs networks with downlink millimeter-wave direction modulation simultaneous wireless information and power transfer under nonorthogonal multiple access (NOMA) and orthogonal multiple access schemes. The authors derived secure outage probability (SOP) and effective secure throughput (EST) to measure security and reliability. In [19], Shengnan et al. proposed a secure transmission scheme of UAVs relay-assisted cognitive radio network (CRN), which optimized UAV relay’s flight trajectory and transmit power to maximize secrecy rate. In [20], the authors considered a scenario of GPS interference and Eve covert operation. They proposed a robust joint optimization problem of UAV jamming power and trajectory to maximize the average security rate without completed information of UAV receiver and Eve.Table 1
Secure transmission for a UAV-enabled network.
ReferencesMetricsContributions[15]Secrecy rateDesign a joint optimization to transmit confidential signals and artificial noise to achieve secrecy requirements.[16]SCP and ESCPropose a UAV-jitter-based method to enhanced secrecy performance for an A2G wiretapping scenario.[17]Secrecy rateUse a UAV-ABS with the NOMA technology to develop a secure multiuser data transmit scheme.[18]SOP and ESTDesign a direction modulation (DM) scheme for a mmWave UAV network with the simultaneous wireless information and power transfer (SWIPT) technical.[19]Secrecy ratePropose a secure data transmission scheme for a UAV relay-assisted CRN to improve spectrum utilization and communication secrecy rate.[20]ASRUse a block coordinate descent method to jointly optimize jamming power and trajectory to maximize ASR.However, the above work does not discuss the misuse of friendly jamming signals due to variable flight altitudes and unreasonable jammer configurations. In [21, 22], the authors introduced a RSCS-OFDM-DM technology to efficiently utilize multiple antennas to reduce unnecessary resource deployment. The use of the technology can reduce the impact on system secrecy performance when the eavesdropper and the legitimate user are in the same beam direction and reduce the complexity of the receiver through fast Fourier transformation.


### 2.2. Optimization in MEC Networks

There are rich literatures on MEC resource management that aims at optimizing system latency [23, 24], energy consumption [25, 26], and overall cost of system latency and/or energy consumption [27, 28]. In [23], Ren et al. investigated the joint communication and computation resource allocation problem under the cooperation of cloud computing and edge computing to minimize system delay of all mobile devices. Park et al. in [24] proposed a Cloud-Ran architecture for cloud computing and local edge node collaborative computing. They intend to minimize end-to-end delay by jointly optimizing computing and communication resources. Zhang et al. [25] studied the problem of task unloading and resource allocation in dense network Cloud-Ran architecture to optimize network energy efficiency. Then, Zhou et al. designed a double deep Q network (DDQN-)-based method to joint optimize computation offloading and resource allocation in a dynamic multiuser MEC system in [26]. Their objective is to minimize the energy consumption of the entire MEC system by considering the delay constraint and the uncertain resource requirements of heterogeneous computation tasks. In [27], we studied the joint task unloading and resource allocation of MEC in NOMA-based HetNets. And Dai et al. designed an optimized computing offload and resource allocation strategy using DRL based on 5G beyond terminal edge cloud coordination network to minimize system energy consumption in [28].Considering the flexible deployment of UAVs, some works introduced UAVs into MEC networks and discussed optimization issues for a UAV-enabled MEC network. In [29], the authors proposed a secure communication scheme for a dual UAV-MEC system. They optimized the resource and trajectories of UAV servers to maximize secure computing power. In [30], the authors studied a secure transmission problem for dual UAV-assisted MEC systems. One UAV is called to help ground terminals (GTs) calculate unloading tasks, and the other UAV acts as a jammer to suppress malicious eavesdroppers. By jointly optimizing the communication resources, computing resources, and UAV’s trajectories, they discussed the maximization problem of the minimum secure capacity in time division multiple access and NOMA scenarios. In addition, [31] proposed an innovative UAV-MEC system that involved an interaction between IoT devices, UAVs, and edge clouds. UAVs and edge clouds in the system cooperate in providing MEC services for a group of IoT devices. By jointly optimizing UAV location, communication, computing resource allocation, and task segmentation decision, the weighted sum of service delay of IoT devices and UAV energy consumption is minimized.Note that these studies assumed wired or dedicated wireless links with sufficient bandwidth among edge nodes deployed in a fixed paradigm. Yet, the assumption is not suitable for data secure transmit in the existing MEC, especially in massive edge users or sparse distribution of network facilities scenarios [32]. Accordingly, we intend to study secure data transmission during task offloading in a UAV-assisted edge network.


## 2.1. Secure Transmit for a UAV Network

Due to the flexibility of UAV-enabled networking, many scholars have studied secure data transmission methods as shown in Table1. In [15], Wu et al. studied energy-saving secure communication for a downlink A2G link. They discussed the impact of a jitter UAV on secure performance and formulated a power minimization and allocation problem with security constraints. Then, they further used secrecy coverage probability (SCP) and ergodic secrecy capacity (ESC) to investigate how to exploit the UAV jitter feature to enhance secrecy in [16]. Considering various service requirements, the authors in [17] proposed an achievable minimum secrecy rate maximization problem and designed a joint optimization method based on user scheduling, power allocation, and trajectory. In addition, [18] considered UAVs networks with downlink millimeter-wave direction modulation simultaneous wireless information and power transfer under nonorthogonal multiple access (NOMA) and orthogonal multiple access schemes. The authors derived secure outage probability (SOP) and effective secure throughput (EST) to measure security and reliability. In [19], Shengnan et al. proposed a secure transmission scheme of UAVs relay-assisted cognitive radio network (CRN), which optimized UAV relay’s flight trajectory and transmit power to maximize secrecy rate. In [20], the authors considered a scenario of GPS interference and Eve covert operation. They proposed a robust joint optimization problem of UAV jamming power and trajectory to maximize the average security rate without completed information of UAV receiver and Eve.Table 1
Secure transmission for a UAV-enabled network.
ReferencesMetricsContributions[15]Secrecy rateDesign a joint optimization to transmit confidential signals and artificial noise to achieve secrecy requirements.[16]SCP and ESCPropose a UAV-jitter-based method to enhanced secrecy performance for an A2G wiretapping scenario.[17]Secrecy rateUse a UAV-ABS with the NOMA technology to develop a secure multiuser data transmit scheme.[18]SOP and ESTDesign a direction modulation (DM) scheme for a mmWave UAV network with the simultaneous wireless information and power transfer (SWIPT) technical.[19]Secrecy ratePropose a secure data transmission scheme for a UAV relay-assisted CRN to improve spectrum utilization and communication secrecy rate.[20]ASRUse a block coordinate descent method to jointly optimize jamming power and trajectory to maximize ASR.However, the above work does not discuss the misuse of friendly jamming signals due to variable flight altitudes and unreasonable jammer configurations. In [21, 22], the authors introduced a RSCS-OFDM-DM technology to efficiently utilize multiple antennas to reduce unnecessary resource deployment. The use of the technology can reduce the impact on system secrecy performance when the eavesdropper and the legitimate user are in the same beam direction and reduce the complexity of the receiver through fast Fourier transformation.


## 2.2. Optimization in MEC Networks

There are rich literatures on MEC resource management that aims at optimizing system latency [23, 24], energy consumption [25, 26], and overall cost of system latency and/or energy consumption [27, 28]. In [23], Ren et al. investigated the joint communication and computation resource allocation problem under the cooperation of cloud computing and edge computing to minimize system delay of all mobile devices. Park et al. in [24] proposed a Cloud-Ran architecture for cloud computing and local edge node collaborative computing. They intend to minimize end-to-end delay by jointly optimizing computing and communication resources. Zhang et al. [25] studied the problem of task unloading and resource allocation in dense network Cloud-Ran architecture to optimize network energy efficiency. Then, Zhou et al. designed a double deep Q network (DDQN-)-based method to joint optimize computation offloading and resource allocation in a dynamic multiuser MEC system in [26]. Their objective is to minimize the energy consumption of the entire MEC system by considering the delay constraint and the uncertain resource requirements of heterogeneous computation tasks. In [27], we studied the joint task unloading and resource allocation of MEC in NOMA-based HetNets. And Dai et al. designed an optimized computing offload and resource allocation strategy using DRL based on 5G beyond terminal edge cloud coordination network to minimize system energy consumption in [28].Considering the flexible deployment of UAVs, some works introduced UAVs into MEC networks and discussed optimization issues for a UAV-enabled MEC network. In [29], the authors proposed a secure communication scheme for a dual UAV-MEC system. They optimized the resource and trajectories of UAV servers to maximize secure computing power. In [30], the authors studied a secure transmission problem for dual UAV-assisted MEC systems. One UAV is called to help ground terminals (GTs) calculate unloading tasks, and the other UAV acts as a jammer to suppress malicious eavesdroppers. By jointly optimizing the communication resources, computing resources, and UAV’s trajectories, they discussed the maximization problem of the minimum secure capacity in time division multiple access and NOMA scenarios. In addition, [31] proposed an innovative UAV-MEC system that involved an interaction between IoT devices, UAVs, and edge clouds. UAVs and edge clouds in the system cooperate in providing MEC services for a group of IoT devices. By jointly optimizing UAV location, communication, computing resource allocation, and task segmentation decision, the weighted sum of service delay of IoT devices and UAV energy consumption is minimized.Note that these studies assumed wired or dedicated wireless links with sufficient bandwidth among edge nodes deployed in a fixed paradigm. Yet, the assumption is not suitable for data secure transmit in the existing MEC, especially in massive edge users or sparse distribution of network facilities scenarios [32]. Accordingly, we intend to study secure data transmission during task offloading in a UAV-assisted edge network.


## 3. System Model

Considering flexibility and low-cost features of UAVs, they are very suitable as edge servers to provide signal coverage and information forward for edge terminals. In an UAV-ABS edge network, a UAV can be regarded as an edge server, and ground terminals are edge nodes, as shown in Figure1. When communicating with a UAV, the edge node is vulnerable to wiretapping by an eavesdropper. This may cause private information disclosure and reduce the secure level of an edge network. In order to ensure secure data transmission, we intend to design a novel scheme to solve the security issue in this scenario.Figure 1
A downlink UAV-ABS model.


### 3.1. A UAV-ABS Network Model

According to Figure1, a typical UAV-ABS network model includes a UAV source with a NT-element linear antenna array, a legitimate ground terminal (GT) with a single antenna, and a ground eavesdropper (Eve) with a single antenna. We assume that positions of GTs and the eavesdropper are known and static, which are defined as U=xU,yU,0 and E=xE,yE,0, respectively. To simplify the optimization problem, the UAV flight duration from the initial position to the final position is T time, and it can discretize into N time slots, where T=Nδt and δt is the fixed length of a transmission time slot. Assuming δt is small enough, the flight in each time slot can be regarded as a uniform motion. Therefore, in time slot nn≜1,2,⋯,N, the coordinates of a UAV can be denoted as Ln≜xn,yn,hn. The UAV can exploit its multiple antennas to broadcast confidential signals and sends AN directly to the eavesdropper via the RSCS-OFDM-DM technology [21].In the system, the UAV uses its linear antenna array to send OFDM symbols to the target GTs by randomly selecting multiple subcarriers from the subcarrier set. Supposing that there areNs orthogonal subcarriers [21], the set is defined as follows:
(1)Ss=fmfm=fc+mΔf,m=0,⋯,Ns−1,where m is the number of subcarriers and Δf is the bandwidth of a subchannel. In this paper, we assume that the total bandwidth of subcarriers is much less than the center carrier frequency, i.e., NsΔf≪fc. The signals transmitted by the kth k=1,⋯,NT antenna at time slot n can be defined as follows:
(2)Skn=α1nPsxejϕk+α2nPswk,where x is confidential signals with Ex∗x=1, ϕk is the initial vector of the kth antenna, and wk is the artificial noise. The transmit power at time slot n is Ps, and α1n and α2n are the distribution ratio of transmit power to confidential signals and AN, respectively.The above signals with AN are emitted to the open wireless channel. We assume that the wireless channel experiences a small-scale Rayleigh fading and a large-scale path loss. This channel consists of a LOS link and a NLOS one, wherePL+PN=1. The probability of the LOS link is related to the elevation angle θ and that of time slot n is defined as follows:
(3)PLθn=11+aexp−b180∘/πθn−a,where a and b are two constants, depending only on the wireless environment, which are provided in work [33]. Similarly, the probability of the NLOS link is denoted as follows:
(4)PNθn=1−PLθn.By combining these two links, the expected channel power gain can be computed as follows:(5)ρθn2=β0ηLPLθnRnαL+β0ηNPNθnRnαN,where β0≜20log10C/4πd0fc is the path loss at a reference distance d0=1 meter. Rn is the distance of the first antenna of the UAV and the target receiver in time slot n. αL and αN denote the pass loss exponents for the LOS and NLOS links. ηL and ηN are the excessive path loss coefficients for the LOS and NLOS links.ConsideringRn, we further define the distance between the kth antenna of the UAV, and the receiver is Rkn=Rn−k−1dcosθn, where d=C/2fc is the distance between the antennas. Thus, the reference phase of Rn is φ0Rn=2πfcRn/C, and the phase shifting of the kth antenna is computed as follows:
(6)ψkθn,Rkn=2πfc+knΔfRknC−φ0Rn,where kn is the serial number of the randomly selected subcarrier, corresponding to m.In Figure1, we assume that the elevation angle of the legitimate GT and the distance between the first reference antenna of the UAV and the GT are θUn,RUn. Similarly, these parameters of eavesdropper are θEn,REn. For the GT, the received signals synthesized by all array antennas can be expressed as follows:
(7)yθUn,RUn=ρθUnα1nPsx+ρθUnα2nPshHw+∑k=1NTn0,where h is a channel vector from UAV to the GT; i.e.,
(8)h=1NTejψ1θUn,RUn,⋯,ejψNTθUn,RUnT.Andn0~CN0,σ2 is the additive white Gaussian noise. w is the artificial noise that is designed in the zero space of h, i.e., w=INT−hhHz.Here, z is a vector composed of NT independent and identically distributed (i.i.d.) circular symmetric complex Gaussian random variables with zero mean and unit variance. It satisfies the distribution of z~CN0,INT. Thus, hHw=0 holds. The received signals of the GT can be rewritten as follows:
(9)yθUn,RUn=ρθUnα1nPsx+∑k=1NTn0.Similarly, the received signals of the eavesdropper is defined as follows:(10)yθEn,REn=ρθEnα1nPsx+ρθEnα2nPshEHw+∑k=1NTn0,where hE is a channel steering vector from the UAV to the eavesdropper. Then, we can derive the signal to interference plus noise ratio of the GT and eavesdropper as follows:
(11)γUn=ρθUn2α1nPsNTσ2,(12)γEn=ρθEn2α1nPsρθEn2α2nPs∥hEHw∥2+NTσ2.


### 3.2. UAV Models

In the system, we consider the mobile UAV can fly in 3D space. And the distance of the flight in thenth time slot, Dn, satisfies the following constraints:
(13)∥Dn∥=∥Ln−Ln−1∥≤vmaxδt,n=1,⋯,N,where vmax is the maximum flying speed of a UAV and ∥·∥ denotes the Euclidean norm of a vector. In addition, to avoid collisions with buildings and ensure effective communication links during flight, the flying height of a UAV should meet a height constraint, i.e.,
(14)hmin≤hn≤hmax,n=1,⋯,N,where hmin and hmax are the lowest and the highest height of a UAV.For the mobile UAV, we introduce an AN projection matrix to the null space of a channel steering vector of confidential signals. In this case, signals received by the eavesdropper will have a phase offset. Thus, the eavesdropping correctness will be decreased. During the flight, if the total power of a UAV isPtot, the transmit power at time slot n is computed as follows:
(15)Ps≜Ptot/N.And the power allocation of confidential signals and AN is as follows:(16)α1n+α2n=1,α1n,α2n≥0,∀n∈N.In the next section, we expect to find the optimal power distribution ratio by changing transmit power.


### 3.3. Problem Formulation

In order to realize secure communication of a UAV-ABS network, we exploit the RSCS-OFDM-DM technology to maximize the average secrecy rate by jointly optimizing UAV trajectory and the UAV power allocation ratio. The maximization problem is as follows:(17)maxQ,PSRs.t.13,14,and16,where Q≜Ln∈ℝ3×1∀n represents the position set of a UAV, P≜αin∈ℝi∈1,2,∀n is the set of power allocation coefficients, and the objective function is defined as follows:
(18)SR=1N∑n=1Nlog21+γUn−log21+γEn+,where a+=maxa,0; when the secrecy rates are favorable, UAVs and legitimate ground nodes can communicate normally.


## 3.1. A UAV-ABS Network Model

According to Figure1, a typical UAV-ABS network model includes a UAV source with a NT-element linear antenna array, a legitimate ground terminal (GT) with a single antenna, and a ground eavesdropper (Eve) with a single antenna. We assume that positions of GTs and the eavesdropper are known and static, which are defined as U=xU,yU,0 and E=xE,yE,0, respectively. To simplify the optimization problem, the UAV flight duration from the initial position to the final position is T time, and it can discretize into N time slots, where T=Nδt and δt is the fixed length of a transmission time slot. Assuming δt is small enough, the flight in each time slot can be regarded as a uniform motion. Therefore, in time slot nn≜1,2,⋯,N, the coordinates of a UAV can be denoted as Ln≜xn,yn,hn. The UAV can exploit its multiple antennas to broadcast confidential signals and sends AN directly to the eavesdropper via the RSCS-OFDM-DM technology [21].In the system, the UAV uses its linear antenna array to send OFDM symbols to the target GTs by randomly selecting multiple subcarriers from the subcarrier set. Supposing that there areNs orthogonal subcarriers [21], the set is defined as follows:
(1)Ss=fmfm=fc+mΔf,m=0,⋯,Ns−1,where m is the number of subcarriers and Δf is the bandwidth of a subchannel. In this paper, we assume that the total bandwidth of subcarriers is much less than the center carrier frequency, i.e., NsΔf≪fc. The signals transmitted by the kth k=1,⋯,NT antenna at time slot n can be defined as follows:
(2)Skn=α1nPsxejϕk+α2nPswk,where x is confidential signals with Ex∗x=1, ϕk is the initial vector of the kth antenna, and wk is the artificial noise. The transmit power at time slot n is Ps, and α1n and α2n are the distribution ratio of transmit power to confidential signals and AN, respectively.The above signals with AN are emitted to the open wireless channel. We assume that the wireless channel experiences a small-scale Rayleigh fading and a large-scale path loss. This channel consists of a LOS link and a NLOS one, wherePL+PN=1. The probability of the LOS link is related to the elevation angle θ and that of time slot n is defined as follows:
(3)PLθn=11+aexp−b180∘/πθn−a,where a and b are two constants, depending only on the wireless environment, which are provided in work [33]. Similarly, the probability of the NLOS link is denoted as follows:
(4)PNθn=1−PLθn.By combining these two links, the expected channel power gain can be computed as follows:(5)ρθn2=β0ηLPLθnRnαL+β0ηNPNθnRnαN,where β0≜20log10C/4πd0fc is the path loss at a reference distance d0=1 meter. Rn is the distance of the first antenna of the UAV and the target receiver in time slot n. αL and αN denote the pass loss exponents for the LOS and NLOS links. ηL and ηN are the excessive path loss coefficients for the LOS and NLOS links.ConsideringRn, we further define the distance between the kth antenna of the UAV, and the receiver is Rkn=Rn−k−1dcosθn, where d=C/2fc is the distance between the antennas. Thus, the reference phase of Rn is φ0Rn=2πfcRn/C, and the phase shifting of the kth antenna is computed as follows:
(6)ψkθn,Rkn=2πfc+knΔfRknC−φ0Rn,where kn is the serial number of the randomly selected subcarrier, corresponding to m.In Figure1, we assume that the elevation angle of the legitimate GT and the distance between the first reference antenna of the UAV and the GT are θUn,RUn. Similarly, these parameters of eavesdropper are θEn,REn. For the GT, the received signals synthesized by all array antennas can be expressed as follows:
(7)yθUn,RUn=ρθUnα1nPsx+ρθUnα2nPshHw+∑k=1NTn0,where h is a channel vector from UAV to the GT; i.e.,
(8)h=1NTejψ1θUn,RUn,⋯,ejψNTθUn,RUnT.Andn0~CN0,σ2 is the additive white Gaussian noise. w is the artificial noise that is designed in the zero space of h, i.e., w=INT−hhHz.Here, z is a vector composed of NT independent and identically distributed (i.i.d.) circular symmetric complex Gaussian random variables with zero mean and unit variance. It satisfies the distribution of z~CN0,INT. Thus, hHw=0 holds. The received signals of the GT can be rewritten as follows:
(9)yθUn,RUn=ρθUnα1nPsx+∑k=1NTn0.Similarly, the received signals of the eavesdropper is defined as follows:(10)yθEn,REn=ρθEnα1nPsx+ρθEnα2nPshEHw+∑k=1NTn0,where hE is a channel steering vector from the UAV to the eavesdropper. Then, we can derive the signal to interference plus noise ratio of the GT and eavesdropper as follows:
(11)γUn=ρθUn2α1nPsNTσ2,(12)γEn=ρθEn2α1nPsρθEn2α2nPs∥hEHw∥2+NTσ2.


## 3.2. UAV Models

In the system, we consider the mobile UAV can fly in 3D space. And the distance of the flight in thenth time slot, Dn, satisfies the following constraints:
(13)∥Dn∥=∥Ln−Ln−1∥≤vmaxδt,n=1,⋯,N,where vmax is the maximum flying speed of a UAV and ∥·∥ denotes the Euclidean norm of a vector. In addition, to avoid collisions with buildings and ensure effective communication links during flight, the flying height of a UAV should meet a height constraint, i.e.,
(14)hmin≤hn≤hmax,n=1,⋯,N,where hmin and hmax are the lowest and the highest height of a UAV.For the mobile UAV, we introduce an AN projection matrix to the null space of a channel steering vector of confidential signals. In this case, signals received by the eavesdropper will have a phase offset. Thus, the eavesdropping correctness will be decreased. During the flight, if the total power of a UAV isPtot, the transmit power at time slot n is computed as follows:
(15)Ps≜Ptot/N.And the power allocation of confidential signals and AN is as follows:(16)α1n+α2n=1,α1n,α2n≥0,∀n∈N.In the next section, we expect to find the optimal power distribution ratio by changing transmit power.


## 3.3. Problem Formulation

In order to realize secure communication of a UAV-ABS network, we exploit the RSCS-OFDM-DM technology to maximize the average secrecy rate by jointly optimizing UAV trajectory and the UAV power allocation ratio. The maximization problem is as follows:(17)maxQ,PSRs.t.13,14,and16,where Q≜Ln∈ℝ3×1∀n represents the position set of a UAV, P≜αin∈ℝi∈1,2,∀n is the set of power allocation coefficients, and the objective function is defined as follows:
(18)SR=1N∑n=1Nlog21+γUn−log21+γEn+,where a+=maxa,0; when the secrecy rates are favorable, UAVs and legitimate ground nodes can communicate normally.


## 4. Maximal ASR Scheme Design

Solving problem (17) directly is challenging due to its nonconvexity. We use AO and SCA methods to find the approximate optimal solution of (17). In particular, we study the optimization problem from two perspectives, i.e., UAV transmit power allocation and UAV 3D trajectory design during each flight time slot.


### 4.1. Power Allocation Subproblem

In this subproblem, we assume that the UAV source 3D trajectory is predefined. We introduce two slack variables,τ and u, into (17). Then, the UAV transmit power allocation subproblem is formulated as follows:
(19a)maxP,τ,uτ(19b)s.t.1N∑n=1Nlog21+A1nα1n−μn≥τ,(19c)log21+A2nα1nA3n1−α1n+1≤μn,and16,where u≜μn∈ℝn∈N is the upper boundary of eavesdropper’s transmit rate, A1n=ρθUn2Ps/NTσ2, A2n=ρθEn2Ps/NTσ2, and A3n=ρθEn2PshEHw2/NTσ2. Because the UAV trajectory is predefined, A1n, A2n, and A3n can be regarded as constants. Yet, the constraint (19c) is still nonconvex. Then, we further transform it based on the first-order Taylor approximation method; i.e., gx=gx∗+g′x∗x−x∗, where x∗ is the result of the previous iteration x. Then, (19c) can be rewritten as follows:
(20)maxP,τ,uτgα1n≤μn,s.t.16and19b.We can exploit CVX toolbox to solve the subproblem since it satisfies the convex optimization requirements.


### 4.2. UAV 3D Trajectory Subproblem

When the power allocation coefficients are known, we still introduce two slack variables,ζU and ζE, to simplify the original problem to the UAV 3D trajectory subproblem as follows:
(21a)maxQ,ζU,ζE1N∑n=1NSRn,(21b)s.t.ξUn≥Ln−U2,(21c)ξEn≤Ln−E2,(21d)ξUn≥hmin2,where SRn=log21+D1nρθUn2−log21+D1nρθEn2/D2nρθEn2+1, ζU≜ξUn∀n, ζE≜ξEn∀n, D1n=α1nPs/NTσ2, and D2n=α2nPshEHw2/NTσ2. Because the flight time slot of the UAV is tiny, we assume that the elevation change before and after trajectory iteration is small. The channel power gains of the legitimate GT and the eavesdropper can be rewritten as follows:
(22)ρUn2=ηLPLθU∗nβ0ξUnαL/2+ηNPNθU∗nβ0ξUnαN/2,(23)ρEn2=ηLPLθE∗nβ0ξEnαL/2+ηNPNθE∗nβ0ξEnαN/2.Then, the objective function can be rewritten as follows:(24)SR~n=log21+D1nρUn2−log21+D1nρEn2D2nρEn2+1.Note that the constraint (21c) is still a nonconvex constraint on Ln, which causes the subproblem to be nonconvex. We use the SCA method to transform this nonconvex subproblem into a convex one. We assume that the coordinate of the previous iteration is L∗n. Since the first-order Taylor expansion of a convex function at one point is its lower bound, the constraints (21c) and SR~n can be approximates as follows:
(25)ξEn≤2L∗n−ETLn−L∗n+∥L∗n−E∥2,(26)SR~n≥S^R∗n=gξUn−log21+D1nρEn2D2nρEn2+1,where gξUn is also the first-order Taylor expansion of the first term in (24). Accordingly, the subproblem (21a) is approximately equivalent to the following convex problem:
(27)maxQ,ζU,ζE1N∑n=1NS^R∗ns.t.13,14,21b,21d,and25.


### 4.3. Hybrid Iteration Algorithm

We design a hybrid iteration algorithm to solve the problem (17). In the ith iteration, we obtain the optimal transmit allocation ratio Pi with a given UAV 3D trajectory Qi−1 by solving subproblem (20). Next, the optimal UAV 3D trajectory is Qi with a given transmit allocation ratio of Pi by solving the subproblem (27). The details of our algorithm are summarized in Algorithm1.Algorithm 1: The proposed hybrid iteration algorithm.
1: InputP0: the initial power allocation coefficients.Q0: the initial UAV 3D trajectory.ξU0: a slack variable.2:Set: iteration index i=1, the maximum iteration step L=20, and the threshold ω=10−33:repeat4: Compute the optimalPi by solving (20) with Qi−1.5: Compute the optimalQi by solving (27) with Pi6: Obtain the current optimal objective functionRi7: Update iteration indexi=i+18:untilR−Rold/Rold≤ω or i>L9:Output the objective value Rold=RiIn each iteration of Algorithm1, two convex subproblems (20) and (27) are solved by SCA algorithm. We define that the number of UAVs is K, the number of GTs is M, and the number of time slots is N. The number of optimization variables in (20) is only related to K and N. If the number of iterations is assumed to be L1, the computational complexity of (20) can be calculated as OL1K3N3 [34]. Similarly, the number of optimization variables in (27) is related to K, M, and N. And the computational complexity of (27) is OL2K3M3N3 when the number of iterations is L2. Therefore, the computational complexity of Algorithm1 is OLL1K3N3+L2K3M3N3, where L is the iteration number of Algorithm 1.


## 4.1. Power Allocation Subproblem

In this subproblem, we assume that the UAV source 3D trajectory is predefined. We introduce two slack variables,τ and u, into (17). Then, the UAV transmit power allocation subproblem is formulated as follows:
(19a)maxP,τ,uτ(19b)s.t.1N∑n=1Nlog21+A1nα1n−μn≥τ,(19c)log21+A2nα1nA3n1−α1n+1≤μn,and16,where u≜μn∈ℝn∈N is the upper boundary of eavesdropper’s transmit rate, A1n=ρθUn2Ps/NTσ2, A2n=ρθEn2Ps/NTσ2, and A3n=ρθEn2PshEHw2/NTσ2. Because the UAV trajectory is predefined, A1n, A2n, and A3n can be regarded as constants. Yet, the constraint (19c) is still nonconvex. Then, we further transform it based on the first-order Taylor approximation method; i.e., gx=gx∗+g′x∗x−x∗, where x∗ is the result of the previous iteration x. Then, (19c) can be rewritten as follows:
(20)maxP,τ,uτgα1n≤μn,s.t.16and19b.We can exploit CVX toolbox to solve the subproblem since it satisfies the convex optimization requirements.


## 4.2. UAV 3D Trajectory Subproblem

When the power allocation coefficients are known, we still introduce two slack variables,ζU and ζE, to simplify the original problem to the UAV 3D trajectory subproblem as follows:
(21a)maxQ,ζU,ζE1N∑n=1NSRn,(21b)s.t.ξUn≥Ln−U2,(21c)ξEn≤Ln−E2,(21d)ξUn≥hmin2,where SRn=log21+D1nρθUn2−log21+D1nρθEn2/D2nρθEn2+1, ζU≜ξUn∀n, ζE≜ξEn∀n, D1n=α1nPs/NTσ2, and D2n=α2nPshEHw2/NTσ2. Because the flight time slot of the UAV is tiny, we assume that the elevation change before and after trajectory iteration is small. The channel power gains of the legitimate GT and the eavesdropper can be rewritten as follows:
(22)ρUn2=ηLPLθU∗nβ0ξUnαL/2+ηNPNθU∗nβ0ξUnαN/2,(23)ρEn2=ηLPLθE∗nβ0ξEnαL/2+ηNPNθE∗nβ0ξEnαN/2.Then, the objective function can be rewritten as follows:(24)SR~n=log21+D1nρUn2−log21+D1nρEn2D2nρEn2+1.Note that the constraint (21c) is still a nonconvex constraint on Ln, which causes the subproblem to be nonconvex. We use the SCA method to transform this nonconvex subproblem into a convex one. We assume that the coordinate of the previous iteration is L∗n. Since the first-order Taylor expansion of a convex function at one point is its lower bound, the constraints (21c) and SR~n can be approximates as follows:
(25)ξEn≤2L∗n−ETLn−L∗n+∥L∗n−E∥2,(26)SR~n≥S^R∗n=gξUn−log21+D1nρEn2D2nρEn2+1,where gξUn is also the first-order Taylor expansion of the first term in (24). Accordingly, the subproblem (21a) is approximately equivalent to the following convex problem:
(27)maxQ,ζU,ζE1N∑n=1NS^R∗ns.t.13,14,21b,21d,and25.


## 4.3. Hybrid Iteration Algorithm

We design a hybrid iteration algorithm to solve the problem (17). In the ith iteration, we obtain the optimal transmit allocation ratio Pi with a given UAV 3D trajectory Qi−1 by solving subproblem (20). Next, the optimal UAV 3D trajectory is Qi with a given transmit allocation ratio of Pi by solving the subproblem (27). The details of our algorithm are summarized in Algorithm1.Algorithm 1: The proposed hybrid iteration algorithm.
1: InputP0: the initial power allocation coefficients.Q0: the initial UAV 3D trajectory.ξU0: a slack variable.2:Set: iteration index i=1, the maximum iteration step L=20, and the threshold ω=10−33:repeat4: Compute the optimalPi by solving (20) with Qi−1.5: Compute the optimalQi by solving (27) with Pi6: Obtain the current optimal objective functionRi7: Update iteration indexi=i+18:untilR−Rold/Rold≤ω or i>L9:Output the objective value Rold=RiIn each iteration of Algorithm1, two convex subproblems (20) and (27) are solved by SCA algorithm. We define that the number of UAVs is K, the number of GTs is M, and the number of time slots is N. The number of optimization variables in (20) is only related to K and N. If the number of iterations is assumed to be L1, the computational complexity of (20) can be calculated as OL1K3N3 [34]. Similarly, the number of optimization variables in (27) is related to K, M, and N. And the computational complexity of (27) is OL2K3M3N3 when the number of iterations is L2. Therefore, the computational complexity of Algorithm1 is OLL1K3N3+L2K3M3N3, where L is the iteration number of Algorithm 1.


## 5. Simulation and Discussion

In this section, we evaluate the performance of our proposed scheme through numerical simulation. Unless otherwise specified, simulation parameters are shown in Table2.Table 2
Simulation parameters.
ParametersValuesNumber of antennas,NT4Carrier frequency,fc3GHz [21]Bandwidth of subchannel,Δf50kHzChannel gain,β0−42dBDuration of each time slot,δt0.5s [29]UAV maximum velocity,vmax20.6m/s [17, 35]UAV minimum flight altitude,hmin100 mUAV maximum flight altitude,hmax200 mUAV maximum average transmit power,Ps30dBM [29]Noise power,σ2−110dBm [29]Channel environment coefficients,a,b20,0.2 [33]LOS link excess path loss coefficient,ηL−2.14dB [15]NLOS link excess path loss coefficient,ηN−3.14dB [15]LOS link path loss exponent,αL2NLOS link path loss exponent,αN3In Figure2, we first discuss the optimal trajectory of the UAV and the corresponding interference temperature. According to Algorithm 1, we find the optimal horizontal trajectory of the UAV under flight time T=35s, 40s, and 60s, as shown in Figure 2(a) It is found that as flight time increased, the UAV preferred to stay closer to the GT and away from the eavesdropper to increase the ASR. In particular, the UAV will hover over the legitimate GT as long as possible to increase the ASR when T=60s. Figures 2(b)–2(d) demonstrate that the ground eavesdropper is subject to intense interference temperature at three different positions of UAV’s flight trajectory. In Figure 2(c), α2=0.26, the transmitted AN is relatively small, so the order of magnitude of the interference temperature is smaller than Figures 2(b) and 2(d). Compared with Figure 2(d), the eavesdropper in Figures 2(c) and 2(d) is located at the edge of the interference temperature mass. The interference temperature is constrained by the AN power and the distance between the UAV and the ground eavesdropper. In addition, we find that the interference temperature radiates to the eavesdropper with the UAV as the center in Figure 2(b). Yet, the center of the interference temperature in Figures 2(c) and 2(d) Figure appears between the UAV and the eavesdropper’s position with a slight offset. The reason is that AN signals sent by the UAV is affected by GT’s positions.Figure 2
Horizontal trajectories analysis and jamming temperatures at different positions withT=40s.
(a)
UAV trajectories(b)
t=13s,α2=0.66(c)
[t=21s,α2=0.26(d)
t=26.5s,α2=0.58In Figure3, we discuss the convergence of the proposed algorithm at flight time T=40s, 60s, and 80s. The ASR of the first two iterations is almost zero because the trajectory optimization of the UAV at the beginning of the iteration is similar to the initial trajectory. Then, the ASR increases sharply as the increasing number of iterations and gradually converges to a fixed value after four or five iterations. It shows that the proposed algorithm can effectively converge to the optimal solution. Also, the longer the flight time, the higher ASR after convergence. The reason is that the hovering time of the UAV becomes longer as the flight time increases.Figure 3
Convergence analysis.In order to verify the effectiveness of our iterative algorithm, we next compare the ASR performance of different schemes in Figure4. In the figure, we know that the ASR performances of either two-dimensional (2D) or 3D trajectory optimization are greater than that of static UAV and nonoptimized trajectory schemes. This explains the impact of trajectory optimization on the system secrecy performance. The reason is that the UAV trajectory design can help to obtain a better channel between a UAV and a GT. In addition, the RSCS-OFDM-DM technology has a better jamming effect on an eavesdropper via comparing with OFDM-DM and broadcast AN schemes. Overall, the proposed algorithm can jointly optimize the 3D flight trajectory and transmit signal power to improve physical layer security of the UAV-enabled network. Then, we compare the average transmit AN power of different schemes in Figure 5. It shows that the scheme using both random subcarrier selection and mobile UAV has higher energy efficiency. In the case of the same total transmit power, our scheme can send the smallest average transmit AN power to achieve the same secrecy performance.Figure 4
ASRvs transmit power.Figure 5
Average AN power.Figure6 provides the impact of the UAV’s flight altitude h on power distribution ratio of confidential signals when the flight durition is T=40s and T=60s, respectively. It can be seen that h is inversely proportional to α1. When the UAV is closer to the eavesdropper and farther from the GT, α1=0. This means that all transmit power is used to emit artificial noise. As the UAV approaches the GT and the eavesdropper, α1 increases, while the UAV’s altitude decreases. It can improve the quality of the channel between the UAV and the legitimate ground node to ensure secure communication. For the T=60s case, the UAV hovers over the GT during the period of 22s to 39s. In this period, the quality of the legitimate channel is the best. All power is used to transmit confidential signals.Figure 6
The altitude and power allocation coefficient.
(a)
T=40s(b)
T=60s


## 6. Conclusion

In this paper, we study how to improve security of data transmission for a UAV-enabled edge network by jointly optimizing the 3D flight trajectory and power allocation design. First, we formulate an optimization problem by establishing a UAV communication system model based on the RSCS-OFDM-DM technology. Next, we divide the optimization problem into two subproblems for discussion, i.e., UAV transmit power allocation and UAV 3D trajectory design, and then present a hybrid iterative algorithm to find the optimal solution of the optimization problem. Finally, we compare the secrecy performance of the proposed scheme with other five schemes. Also, we verify that the mobile UAV and random subcarrier selection can improve the secrecy energy efficiency.



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*Source: 5390771-2022-04-21.xml*