# Secure Transmission of mmWave NOMA UAV-Assisted Relay System against Randomly Located Eavesdroppers

Authors: Danyu Diao; Buhong Wang; Kunrui Cao; Runze Dong; Tianhao Cheng
Journal: Security and Communication Networks
 (2022)

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## Abstract

UAV wireless communication has been regarded as a promising technology in the fifth-generation (5G) networks. In this paper, we consider the security of the mmWave NOMA UAV-assisted relay system, where a ground source transmits messages to two types of authorized users assisted by a UAV relay in the presence of multiple eavesdroppers. A practical probabilistic line-of-sight (LoS) channel model with Nakagami-m small-scale fading and three-dimensional (3D) antenna gain is established to describe the mmWave air-to-ground channel. In addition, to improve the security of the system, cooperative jamming and protected zone strategies are introduced. The analytical expressions of connection outage probability (COP), secrecy outage probability (SOP), and effective secrecy throughput (EST) under the NOMA scheme and cooperative jamming NOMA scheme are derived. Also, the asymptotic SOP and EST are analyzed to gain further insights. The theoretic analysis and simulation results show the effectiveness of the proposed schemes. As the transmitting power of the source and UAV relay increases, the SOP depends only on the location distribution and density of eavesdroppers and the ESTs under different schemes converge to the same floor.


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## Body

## 1. Introduction

To support long-range connectivity, massive access, and explosive traffic growth in 5G networks, unmanned aerial vehicles (UAVs) have rekindled strong interest of both industry and academia in wireless connectivity owing to enhanced channel quality and flexible dynamic deployment [1–3]. In emergencies such as natural disasters or military activities, UAVs can be deployed as temporary base stations, mobile relays, and cooperative jammers. For example, the urgent deployment of Wing Loong UAV provided stable access to residents affected by the storm that disrupted communications. There has been numerous research on UAV wireless communication systems recently [4–25]. In order to improve the reliability of UAV communications, the trajectory and transmitting power of UAV relay were jointly optimized to minimize the connection outage probability (COP) in [4]. By considering the propulsion energy limitations of UAVs, the authors of [5] investigated the maximization of energy efficiency and transmission rate, where the UAV was deployed to support uplink communications. To further solve the problem, energy harvesting technology was applied in the UAV-assisted relay communication networks to enhance the flight endurance in [6].Nevertheless, owing to the strong line-of-sight (LoS) components over air-to-ground (A2G) links, it is extremely arduous to investigate the security of UAV communication systems. Physical layer security technology can exploit the randomness of wireless fading channels to secure wireless communications from the perspective of information theory, which is a good complement to conventional cryptography technology [26–28]. The authors of [7] employed UAVs as an aerial base station and cooperative jammer to defend against eavesdropping exploiting the controllable mobility. By designing neural networks, [8] proposed a dynamic beamforming technique to maximize the average secrecy rate in the UAV wireless communication system. Considering the scenario of full-duplex active eavesdropping, [9] maximized the secrecy rate of the system by optimizing the trajectory and transmitting power. Unlike [7–13] focused on the performance analysis of secure UAV communications. Reference [10] studied the secrecy performance of a UAV-assisted relay system. Ji et al. and coauthor proposed a novel UAV cognitive network to achieve higher-spectrum efficiency [11]. Artificial noise (AN) was used to improve the secrecy performance of the UAV system in [12]. The authors of [13] investigated the secrecy performance of UAV systems from the perspective of three-dimensional (3D) space.Due to its widely available spectrum resources, integrating millimeter wave (mmWave) technique into UAV networks has been a potential solution to address the spectrum crunch [14–18]. The 3D mmWave antenna gain from UAV to ground nodes is first proposed in [16]. The authors of [17] investigated the secrecy performance of mmWave communications assisted by multiple UAV-enabled relays and jammers. Furthermore, the on–off transmission strategy was designed in [18] to evaluate the performance under the effect of beam alignment error.Meanwhile, with the explosive growth of traffic demand, nonorthogonal multiple access (NOMA) has been viewed as a promising candidate for 5G networks [29–31]. It is noteworthy investigating the transmission scheme of UAV-assisted NOMA systems to obtain important insights on performance improvement [19–21, 32]. A UAV-assisted NOMA network was proposed in [22] to achieve secure simultaneous wireless information and power transfer (SWIPT) transmission, while the inherent mobility of UAV was not considered. As a further advance, the authors of [23] proposed an aerial cooperative jamming strategy to secure terrestrial NOMA communications and optimized the position of the UAV. Moreover, the authors of [24] achieved secure transmission by jointly designing user scheduling, trajectory, and power allocation from the perspective of secure users. Pang et al. [25] considered the energy-constrained UAV mmWave NOMA network and maximized the energy efficiency. Introducing NOMA into UAV mmWave communication system can further improve system performance and satisfy the different communication needs of users. Despite such research progress, none of them considered the security topic of UAV-assisted relay mmWave NOMA system, and corresponding secrecy transmission scheme designing and the impact of key system parameters are not reported yet, which motivates this work.In this work, we consider the physical layer security of a mmWave NOMA UAV-assisted relay system, where a UAV is deployed as a relay to enhance the communication quality of the system while another UAV is deployed as a friendly jammer to send AN for enhancing the security of the system. This is in stark contrast to the existing work which is without taking into account the security [33], OMA transmission mode [17, 34], and simplified LoS channel [35]. The contributions of the work are summarized as follows: We model a mmWave NOMA UAV-assisted relay network in the presence of randomly distributed eavesdroppers. Due to the blockage or long distance, a UAV relay is employed to decode-and-forward (DF) signals from the terrestrial source to NOMA users. Based on different service requirements, the authorized users are classified into high-security required users and common users. The distribution of users and eavesdroppers is modeled as homogeneous Poisson point processes (HPPPs). We take into account a practical probabilistic line-of-sight (LoS) and nonline-of-sight (NLoS) A2G channel model based on the elevation. Moreover, the 3D antenna gain model is established to characterize the mmWave transmission:In order to study the reliability and security of the system and reveal the effects of key parameters on the system, we derive the closed-form expressions of connection outage probability (COP), secrecy outage probability (SOP), and effective secrecy throughput (EST) under the NOMA scheme. To further improve the secrecy performance of the system, the cooperative aerial jamming scheme is proposed to degrade the quality of wiretapping. Based on the proposed scheme, the COP, SOP, and EST are obtained by utilizing Gauss–Chebyshev quadrature. Furthermore, the asymptotic SOP and EST are derived to gain valuable insights.The numerical results show that (1) the proposed NOMA scheme with cooperative jamming outperforms benchmark schemes. (2) Increasing the number of antennas equipped at each node can improve the security of the system due to the increased main lobe gain. The improvement is more obvious when the jamming power is relatively large. (3) The asymptotic SOP is independent of the transmitting power of the source and UAV relay, while it is influenced by the size of protected zone and the density of eavesdroppers. (4) With the increase of jamming power, the EST of cooperative jamming scheme converges to a performance floor, which is independent of the size of the protected zone.The remainder of the paper is organized as follows: In Section2, we describe the system and channel models. The COP, SOP, and EST of UAV-assisted mmWave relay system are investigated in Section 3. With cooperative jamming, the expressions are derived in Section 4. In Section 5, numerical results are presented to validate the theoretical analysis. Finally, the conclusions are provided in Section 6.


## 2. System Model

We consider a secure mmWave NOMA UAV-assisted communication system as illustrated in Figure1, where a source S sends the confidential message to two NOMA users (D1 and D2) via a UAV-based relay U in the presence of randomly distributed eavesdroppers E. Since NOMA users use the same frequency and spread spectrum coding at the same time, the interference between users will be relatively strong. In general, it is impractical for all users to jointly perform NOMA due to high complexity and high decoding latency [36]. A promising alternative is to split the user into multiple orthogonal pairs and perform NOMA in each pair [37]. In our work, a NOMA pair is taken as an example. (Since NOMA users use the same frequency and spread spectrum coding at the same time, the interference between users will be relatively strong. In general, it is impractical for all users to jointly perform NOMA due to high-complexity and high-decoding latency [36]. A promising alternative is to split the user into multiple orthogonal pairs and perform NOMA in each pair [37]. In our work, a NOMA pair is taken as an example) The communication can be divided into two time slots. In the first slot, S sends a superimposed signal to U, and in the second slot, U decodes the signal and sends it to the users on the ground. Due to the obstruction on the ground, the source and the users cannot communicate directly. Without loss of generality, one of the users D2 is high-security required user and the other user D1 is a common user with only rate requirements. This makes sense in many practical applications for the Internet of Things (IoT) era [24], such as the transmission of private information or military secrets may require a higher-security priority, while information such as weather forecasts has low or no security requirements. Eavesdroppers denoted by Φe follow HPPPs with density λe. A sector protected zone method is introduced to enhance security. Particularly, we model the finite range around U as the sector protected zone with radius rE and central angle θs considering the sector-protected zone in a sector beam. D2 is randomly located in a circle with center O and radius rmin. D1 is randomly located at the external sector ring spanning the radius from rmin to rmax. We denote ni∈CN0,σi2 as the additive white Gaussian noise (AWGN) at the receiver i, i∈U,D1,D2,E.Figure 1
System model.


### 2.1. Directional Beamforming

In order to compensate for the loss of mmWave, each node is equipped with multiple pint-sized antennas. 3D antenna gain model is established, whereGM and Gm represent the main-lobe gain and side-lobe gain. θa and θd are denoted as the beamwidth in azimuth and depression/elevation directions, respectively. The 3D beamforming’s horizontal projection shows the range of azimuth angle is −π,π. The worst-case scenario is considered as [16] that the range of depression/elevation angle is θd/2,π−θd/2 for the node l, l∈S,D1,D2,E and −π,0 for the UAV. Thus, the directional antenna gain and the corresponding probability in the system can be written as follows: (1)Gil=GMl,pMl=θal2π⋅θdlπ−θdl,Gml,pml=1−θal2π⋅θdlπ−θdl,GiU=GMU,pMU=θaU2π⋅θdUπ,GmU,pmU=1−θaU2π⋅θdUπ.In the training phase, we consider perfect beam alignment for A2G legitimate communication links. In addition, lack of training information makes it difficult for eavesdroppers to align to aerial nodes. Specifically, the antenna gain between legitimate nodes can be given byGSU=GMSGMU, GUD1=GMUGMD1, GUD2=GMUGMD2. Since the transmitting beam of S is aligned with U, the gain of the terrestrial eavesdropping link can be obtained as GSE=GmSGiE, where i∈m,M. The gain of U−E link can be formulated as follows:(2)GUE=GmUGmE,p1=pmUpmE,GmUGME,p2=pmUpME,GMUGmE,p3=pMUpmE,GmUGmE,p4=pMUpME.


### 2.2. Channel Model

#### 2.2.1. Line-of-Sight (LoS) Probability

For the A2G link betweenU and l, we model it as a channel with a given LoS probability, which is determined by the environment and elevation angle [38]. The LoS probability is given by(3)PLrUl=11+φexp−ωarctanH/rUl−φ,where rUl denotes the horizontal distance between U and l. H is the minimum flying height of U without colliding with obstacles on the ground. φ and ω are constants associated with the environment. Then the NLoS probability of the A2G channel can be formulated as PNrUl=1−PLrUl.


#### 2.2.2. Path Loss

Similar to [39], the path loss for the A2G channel with distance dUl under LoS and NLoS links can be expressed as follows:(4)LdUl=dUl−τηL,LoS links,dUl−τηN,NLoS links,where dUl=rUl2+H2 and τ denotes the path loss factor. ηL and ηN depend on environment. For the ground-to-ground (G2G) channel, the path loss is calculated as LdSE=dSE−τηN.


#### 2.2.3. Small-Scale Fading

We assume all communication links experience independent Nakagami-m fading [11, 34], where different parameters represent LoS and NLoS links, respectively. To be specific, the small-scale fading between i and j satisfies hij∼ΓNL,1/NL for the LoS links and hij∼ΓNN,1/NL for the NLoS links, i,j∈S,U,D1,D2,E. Denoting Gamma random variable Z=hij2, the probability density function (PDF) and cumulative distribution function (CDF) are, respectively, denoted as follows:(5)fZz=NkNkzNk−1ΓNke−Nkz,FZz=1−∑n=0Nk−1Nkzn1n!e−Nkz,where k∈L,N.


## 2.1. Directional Beamforming

In order to compensate for the loss of mmWave, each node is equipped with multiple pint-sized antennas. 3D antenna gain model is established, whereGM and Gm represent the main-lobe gain and side-lobe gain. θa and θd are denoted as the beamwidth in azimuth and depression/elevation directions, respectively. The 3D beamforming’s horizontal projection shows the range of azimuth angle is −π,π. The worst-case scenario is considered as [16] that the range of depression/elevation angle is θd/2,π−θd/2 for the node l, l∈S,D1,D2,E and −π,0 for the UAV. Thus, the directional antenna gain and the corresponding probability in the system can be written as follows: (1)Gil=GMl,pMl=θal2π⋅θdlπ−θdl,Gml,pml=1−θal2π⋅θdlπ−θdl,GiU=GMU,pMU=θaU2π⋅θdUπ,GmU,pmU=1−θaU2π⋅θdUπ.In the training phase, we consider perfect beam alignment for A2G legitimate communication links. In addition, lack of training information makes it difficult for eavesdroppers to align to aerial nodes. Specifically, the antenna gain between legitimate nodes can be given byGSU=GMSGMU, GUD1=GMUGMD1, GUD2=GMUGMD2. Since the transmitting beam of S is aligned with U, the gain of the terrestrial eavesdropping link can be obtained as GSE=GmSGiE, where i∈m,M. The gain of U−E link can be formulated as follows:(2)GUE=GmUGmE,p1=pmUpmE,GmUGME,p2=pmUpME,GMUGmE,p3=pMUpmE,GmUGmE,p4=pMUpME.


## 2.2. Channel Model

### 2.2.1. Line-of-Sight (LoS) Probability

For the A2G link betweenU and l, we model it as a channel with a given LoS probability, which is determined by the environment and elevation angle [38]. The LoS probability is given by(3)PLrUl=11+φexp−ωarctanH/rUl−φ,where rUl denotes the horizontal distance between U and l. H is the minimum flying height of U without colliding with obstacles on the ground. φ and ω are constants associated with the environment. Then the NLoS probability of the A2G channel can be formulated as PNrUl=1−PLrUl.


### 2.2.2. Path Loss

Similar to [39], the path loss for the A2G channel with distance dUl under LoS and NLoS links can be expressed as follows:(4)LdUl=dUl−τηL,LoS links,dUl−τηN,NLoS links,where dUl=rUl2+H2 and τ denotes the path loss factor. ηL and ηN depend on environment. For the ground-to-ground (G2G) channel, the path loss is calculated as LdSE=dSE−τηN.


### 2.2.3. Small-Scale Fading

We assume all communication links experience independent Nakagami-m fading [11, 34], where different parameters represent LoS and NLoS links, respectively. To be specific, the small-scale fading between i and j satisfies hij∼ΓNL,1/NL for the LoS links and hij∼ΓNN,1/NL for the NLoS links, i,j∈S,U,D1,D2,E. Denoting Gamma random variable Z=hij2, the probability density function (PDF) and cumulative distribution function (CDF) are, respectively, denoted as follows:(5)fZz=NkNkzNk−1ΓNke−Nkz,FZz=1−∑n=0Nk−1Nkzn1n!e−Nkz,where k∈L,N.


## 2.2.1. Line-of-Sight (LoS) Probability

For the A2G link betweenU and l, we model it as a channel with a given LoS probability, which is determined by the environment and elevation angle [38]. The LoS probability is given by(3)PLrUl=11+φexp−ωarctanH/rUl−φ,where rUl denotes the horizontal distance between U and l. H is the minimum flying height of U without colliding with obstacles on the ground. φ and ω are constants associated with the environment. Then the NLoS probability of the A2G channel can be formulated as PNrUl=1−PLrUl.


## 2.2.2. Path Loss

Similar to [39], the path loss for the A2G channel with distance dUl under LoS and NLoS links can be expressed as follows:(4)LdUl=dUl−τηL,LoS links,dUl−τηN,NLoS links,where dUl=rUl2+H2 and τ denotes the path loss factor. ηL and ηN depend on environment. For the ground-to-ground (G2G) channel, the path loss is calculated as LdSE=dSE−τηN.


## 2.2.3. Small-Scale Fading

We assume all communication links experience independent Nakagami-m fading [11, 34], where different parameters represent LoS and NLoS links, respectively. To be specific, the small-scale fading between i and j satisfies hij∼ΓNL,1/NL for the LoS links and hij∼ΓNN,1/NL for the NLoS links, i,j∈S,U,D1,D2,E. Denoting Gamma random variable Z=hij2, the probability density function (PDF) and cumulative distribution function (CDF) are, respectively, denoted as follows:(5)fZz=NkNkzNk−1ΓNke−Nkz,FZz=1−∑n=0Nk−1Nkzn1n!e−Nkz,where k∈L,N.


## 3. Performance Analysis Without Jamming

In this section, we consider the reliability and security performance of the mmWave NOMA UAV-assisted relay system in terms of COP, SOP, and EST.In the first time slot,S transmits superimposed signal x=α1Psx1+α2Psx2 to U, where Ps denotes the transmitting power. αjj∈1,2 denotes the power allocation factor for the user Dj, α1≥α2 and α1+α2=1. Following the principle of downlink NOMA, U first decodes x1, then removes x1 from the signal, and decodes x2 without interference. Hence, the signal-to-interference-plus-noise ratio (SINR) and signal-to-noise ratio (SNR) for x1 and x2 at U can be, respectively, expressed as follows: (6)γSUx1=α1GSUPshSU2LdSUα2GSUPshSU2LdSU+σU2,γSUx2=α2GSUPshSU2LdSUσU2.The worst-case scenario is considered where the eavesdropper owns the multiuser detection capacity to detect signals of users with high-security requirements [40]. Besides, we consider noncolluding eavesdroppers, which mean the instantaneous SNR for eavesdropping on the information of D2 is determined by the most detrimental eavesdropper. Therefore, the SNR for eavesdroppers to decode x2 from S can be calculated as follows: (7)γSE=maxE∈Φeα2GSEPshSE2LdSEσE2.In the second time slot,U works in DF mode to decode and reforward the signal. After receiving the signal from U, D1 decodes x1 by interpreting x2 as interference. The SINR at D1 can be written as follows: (8)γUD1x1=α1GUD1PuhUD12LdUD1α2GUD1PuhUD12LdUD1+σD12,where Pu denotes the transmitting power of U. The user D2 utilizes successive interference cancellation (SIC) to decode the message x1 before decoding its own message. The SINR at D2 to decode x1 can be written as follows: (9)γUD2x1=α1GUD2PuhUD22LdUD2α2GUD2PuhUD22LdUD2+σD22.After subtracting the signalx1, D2 decodes its own message and the SNR can be expressed as follows:(10)γUD2x2=α2GUD2PuhUD22LdUD2σD22.In the second time slot, the SNR for eavesdroppingx2 from U at the most detrimental eavesdropper is given by(11)γUE=maxE∈Φeα2GUEPuhUE2LdUEσE2.


### 3.1. COP ofD1 and D2 for NOMA Scheme

The connection outage probability (COP) is defined as the probability that the system will be interrupted when the instantaneous transmission rate of the system is less than a given target rate. As such, we present the COP ofD1 in the following theorem.Theorem 1.
For the reliable communication ofD1, S-U, and U-D1 links must satisfy the target rate R1 simultaneously. The COP of D1 can be derived as (15), where rvl=rmaxvl+1/2, vl=cos2l−1/2Lπ, rvt=rminvt+1/2, vt=cos2t−1/2Lπ, and L denotes the number of Gauss–Chebyshev nodes.(12)PcopD1=1−∑k1=L,NPk1rSU∑n=0Nk1−1Nk1ϵ1σU2rSU2+H2τ/2ηkα1−ϵ1α2GSUPsn1n!e−Nkϵ1σU2rSU2+H2−τ/2ηk/α1−ϵ1α2GSUPs∑k2=L,N2rmax2−rmin2×rmaxπ2L∑l=1L∑n=0Nk2−11−vl2Pk2rvlNk2ϵ1σD12rvl2+H2τ/2ηkα1−ϵ1α2GUD1Punrvln!e−Nk2ϵ1σD12rvl2+H2τ/2ηk/α1−ϵ1α2GUD1Pu−rminπ2T∑t=1T∑n=0Nk2−11−vt2Pk2rvtNk2ϵ1σD12rvt2+H2τ/2ηkα1−ϵ1α2GUD1Punrvtn!e−Nk2ϵ1σD12rvt2+H2τ/2ηk/α1−ϵ1α2GUD1Pu,Proof.
According to the definition of COP, we have(13)PcopD1=1−Pr12log21+γSUx1>R1,12log21+γUD1x1>R1=1−PrγSUx1>22R1−1,γUD1x1>22R1−1=1−PrhSU2>ϵ1σU2α1−ϵ1α2GSUPsLdSU︸K1×PrhUD12>ϵ1σD12α1−ϵ1α2GUD1PuLdUD1︸K2,where ϵ1=22R1−1. According to (5), K1 can be given by(14)K1=∑k=L,NPkrSU∑n=0Nk−1Nkξ1n1n!e−Nkξ1,wheredSU=rSU2+H2 and ξ1=ϵ1σU2rSU2+H2τ/2ηk/α1−ϵ1α2GSUPs. By applying the polar coordinates and the probability generating functional (PGFL) of PPP, K2 can be derived as follows:(15)K2=PrhUD12>ϵ1σD12α1−ϵ1α2GUD1PuLdUD1=∑k=L,N2rmax2−rmin2∫rminrmaxPkr×PrhUD12>ξ2rdr=∑k=L,N2rmax2−rmin2∫0rmaxPkr×PrhUD12>ξ2rdr−∫0rminPkr×PrhUD12>ξ2rdr=∑k=L,N2rmax2−rmin2∫0rmaxPkr×∑n=0Nk−1Nkξ2n1n!e−Nkξ2rdr−∫0rminPkr×∑n=0Nk−1Nkξ2n1n!e−Nkξ2rdr,where ξ2=ϵ1σD12r2+H2τ/2ηk/α1−ϵ1α2GUD1Pu. It is difficult to obtain the closed-form expression of (15), so the Gaussian–Chebyshev quadrature is applied to yield a close approximation with rvl=rmaxvl+1/2, vl=cos2l−1/2Lπ, rvt=rminvt+1/2, and vt=cos2t−1/2Lπ. By substituting (14) and (15) into (13), the closed-form expression can be obtained as (12).
In the following, we investigate the reliable transmission ofD2 for the NOMA scheme.Theorem 2.
SinceD2 decodes x1 first and then decodes its own information x2, γSUx1>2R1−1, γSUx2>2R2−1, γUD2x1>2R1−1 and γUD2x2>2R2−1 must be satisfied simultaneously for the reliable communications. The closed-form expression of COP can be derived as (19).(16)PcopD2=1−∑k1=L,NPk1rSU∑n=0Nk1−1Nkξ3rSU2+H2τ/2n1n!e−Nkξ3rSU2+H2τ/2∑k2=L,N2rmin2×∑l=1L∑n=0Nk2−11−gl2Pk2rglNkξ4rgl2+H2τ/2nn!e−Nkξ4rgl2+H2τ/2rgl.Proof.
The COP ofD2 can be given by(17)PcopD2=1−PrγSUx1>22R1−1,γSUx2>22R2−1×PrγUD2x1>22R1−1,γUD2x2>22R2−1=1−PrhSU2>ξ3rSU2+H2τ/2︸K3×PrhUD22>ξ4rUD22+H2τ/2︸K4,where ξ3=maxϵ2σU2ηk/α2GSUPs,ϵ1σU2ηk/α1−ϵ1α2GSUPs, ξ4=maxϵ2σD22ηk/α2GUD2Pu,ϵ1σD22ηk/α1−ϵ1α2GUD2Pu and ϵ2=22R2−1. Similar to (17), K3 can be obtained as follows:(18)K3=∑k=L,NPkrSU∑n=0Nk−1Nkξ3rSU2+H2τ/2n×1n!e−Nkξ3rSU2+H2τ/2.
SinceD2 is randomly located in a circle of radius rmin, K4 can be obtained as follows: (19)K4=PrhUD22>ξ4rUD22+H2τ/2=∑k=L,N2rmin2∫0rminPkr×PrhUD12>ξ4rUD22+H2τ/2rdr=∑k=L,N2rmin2∫0rminPkr×∑n=0Nk−1Nkξ4r2+H2τ/2nn!e−Nkξ4r2+H2τ/2rdr.
By exploiting the Gaussian–Chebyshev quadrature and substitutingrgl=rmingl+1/2, gl=cos2l−1/2Lπ, K4 can be rewritten as follows: (20)K4=∑k=L,NπrminL∑l=1L∑n=0Nk−11−gl2Pkrgl×Nkξ4rgl2+H2τ/2nn!e−Nkξ4rgl2+H2τ/2rgl.
According to (18) and (20), the COP of D2 can be derived as (16).Remark 1.
It can be observed from Theorems1 and 2 that the COPs of D1 and D2 decrease with the increase of source transmitting power Ps and Pu. Besides, reducing the zone radius of external sector ring rmax and rmin can decrease the COPs of D1 and D2, which implies a smaller user area or one closer to the UAV relay can improve the reliability of the system.Proposition 1.
The asymptotic COPs ofD1 and D2 can be respectively expressed as follows: (21)Pcop,asyD1=1−2rmax2−rmin2∑k1=L,N∑k2=L,NPk1rSU×∫rminrmaxPk2rrdr,and(22)Pcop,asyD2=1−2rmin2∑k1=L,N∑k2=L,NPk1rSU×∫0rminPk2rrdr.Proof.
As the transmitting powerPs and Pu approach infinity, by exploiting e−x=1−x for small x, we have(23)∑n=0Nk−1Nkξ1n1n!e−Nkξ1≈∑n=0Nk−1Nkξ1n1n!1−Nkξ1≈∑n=0Nk−1Nkξ1n1n!.
In (23), the term corresponding to n=0 is larger than the summation of other terms owing to the presence of ξ1n and ξ2n when Ps and Pu go to infinity. Hence, Pcop,asyD1 can be approximated as the term corresponding to n=0. After some mathematical manipulation, Pcop,asyD1 can be rewritten as (21). Similarly, the expression of Pcop,asyD2 can be obtained as (22). The proof is completed.


### 3.2. SOP ofD2 for NOMA Scheme

SinceD2 is a high-security required user, we analyze the secrecy performance of D2 in terms of SOP. According to Wyner’s wiretap code theory, the SOP is defined as the probability which the wiretap channel capacity is larger than the redundancy rate of wiretap code [26]. For the proposed protected zone method, we consider the case that the eavesdroppers are located inside the circle of radius (rE, rmax) with angle θs. Particularly, by denoting r as the horizontal distance between U and E, the distance dSE can be expressed as dSE=r2+rSU2−2rrSUcosπ−θ with rE≤r≤rmax and θ∈−θs/2,θs/2.Lemma 1.
DenotingRs as the target secrecy rate of D2, we define the function F1r,θ and F2r in polar coordinates to describe the probability PrγSE>22R2−Rs−1 and PrγUE>22R2−Rs−1. By considering S−E channel as the NLoS link, while U−E channel is composed of NLoS link and LoS link, and F1r,θ and F2r can be expressed as follows: (24)F1r,θ=PrγSE>22R2−Rs−1=PrhSE2>εsσE2α2GSEPsLdSE=∑i∈m,MpiEPrhSE2>ξ5r2+rSU2−2rrSUcosπ−θτ/2,and(25)F2r=PrγUE>2R2−Rs−1=PrhUE2>ϵsσE2α2GUEPsLdUE=∑w=L,N∑i,j∈m,MpiUpjEPwrPrhUE2>ξ6r2+H2τ/2,where ϵs=22R2−Rs−1, ξ5=ϵsσE2/α2GSmGEiPs and ξ6=ϵsσE2ηw/α2GUiGEjPu.
Based on Lemma1, the SOP of D2 is given in the following theorem:Theorem 3.
In light of the HPPPs distribution forE, the SOP of D2 under protected zone method is given by(26)PsopD2=PrmaxmaxE∈ΦeγSE,maxE∈ΦeγUE>ϵs=1−E∏E∈ΦePrγSE<ϵs︸K5E∏E∈ΦePrγUE<ϵs︸K6,where K5 and K6 are given in (27) and (28(27)K5=exp−θs3λE64TL∑i∈m,M∑l=1L∑t=1T∑n=0NN−1piEn!1−al21−bt2rmax−rE2bt+rmax+rE2×NNϵsσE2α2GSmGEiPsrmax−rE2bt+rmax+rE22+rSU2+2rmax−rE2bt+rmax+rE2rSUcosθτ/2n×e−NNϵsσE2/α2GSmGEiPsrmax−rE/2bt+rmax+rE/22+rSU2+2rmax−rE/2bt+rmax+rE/2rSUcosθτ/2,(28)K6=exp−λEθs∑i,j∈m,MpiUpjEπrmaxrcl2L∑w=L,N∑l=1L∑n=0Nw−11−cl2Pwrcln!NwϵsσE2r2cl+H2τ/2α2GUiGEjPun×e−NwϵsσE2r2cl+H2τ/2/α2GUiGEjPu−πrErdt2L∑w=L,N∑l=1L∑n=0Nw−11−dt2Pwrdtn!NwϵsσE2r2dt+H2τ/2α2GUiGEjPune−NwϵsσE2r2dt+H2τ/2/α2GUiGEjPu.Proof.
Following the PGFL of PPP, we can obtain(29)K5=exp−λE∫−θs/2θs/2∫rErmaxPrγSE>ϵsrdrdθ=exp−2λE∫0θs/2∫rErmaxF1r,θrdrdθ≈aexp−θs3λE64∑l=1L∑t=1T1−al21−bt2×1TLrmax−rE2bt+rmax+rE2×F1rmax−rE2bt+rmax+rE2,θs4al+1,K6=exp−λEθs∫rErmaxPrγUE>ϵsrdr=exp−λEθs∫rErmaxF2rrdr≈bexp−λEθsπrmax2L∑l=1L1−cl2F2rclrcl−πrE2T∑t=1T1−dt2F2rdtrdt.
Step (a) is computed by a two-layer Gauss–Chebyshev integration related tor and θ, where al=cos2l−1/2Lπ and bt=cos2t−1/2Tπ. Step (b) is calculated through the similar procedure of deriving K2 with cl=cos2l−1/2Lπ, dt=cos2t−1/2Tπ, rcl=rmaxcl+1/2 and rdt=rEdt+1/2. Substituting (5) into (24) and (25), equation K5 and K6 are expressed as (27) and (28), respectively. The proof is completed.Remark 2.
From Theorem3, we can observe that the SOP of D2 is influenced by the transmitting power Ps and Pu, the target codeword rate R2, the confidential codeword rate Rs, the power allocation factor α2, and the distribution of eavesdroppers Φe. To be specific, the SOP decreases with the reduction of eavesdroppers’ density λE and the increase of rE. The SOP increases with the enlargement of Ps and Pu, which means the enhancement of reliability leads to more information at the risk of eavesdropping.
To proceed forward, we derive the asymptotic expression of the SOP to gain more insights. When the transmitting powerPs and Pu are sufficiently large, the asymptotic SOP under the NOMA scheme is shown in the following:Proposition 2.
The asymptotic SOP under the NOMA scheme can be calculated as follows:(30)Psop−asyD2=1−exp−θsλErmax2−rE2.Proof.
For sufficiently largePs, K5 can be calculated as follows: (31)K5=exp−λE∫−θs/2θs/2∫rErmaxPrγSE>ϵsrdrdθ=exp−λE∫−θs/2θs/2∫rErmax∑i∈m,MpiE×∑n=0NN−1NNΩPsn1n!e−NNΩ/Psrdrdθ,where Ω=ϵsσE2r2+rSU2−2rrSUcosπ−θτ/2/α2GSmGEi. When Ps⟶∞, by utilizing the approximation of e−x≈1−x for small x, we have(32)∑n=0NN−1NNΩPsn1n!e−NNΩ/Ps≈∑n=0NN−1NNΩPsn1n!1−NNΩPs≈∑n=0NN−1NNΩPsn1n!.
In (32), the term corresponding to n=0 is larger than the summation of other terms owing to the presence of Ω/Psn when Ps goes to infinity. Hence, K5 can be approximated as the term corresponding to n=0, and it can be rewritten as follows: (33)K5=exp−θsλE2rmax2−rE2.
Similarly, we can deriveK6=K5. After some calculations, the proof of Psop−asyD2 is completed.Remark 3.
It can be observed from Proposition2 that the asymptotic SOP is influenced by the density of eavesdroppers and the size of the protected zone when Ps and Pu are considerably large.


### 3.3. EST ofD2 for NOMA Scheme

The reliability and security of the system are investigated above. However, it is necessary to use a unified framework to integrate security and reliability considerations. To holistically characterize the performance of the system, we derive the effective secrecy throughput (EST) of the system, which is defined as the secrecy rate multiplied by the reliable-and-secure probability ofD2.Theorem 4.
The EST ofD2 for NOMA scheme can be written as follows: (34)TESTD2=Rs1−PcopD21−PsopD2,where PcopD2 and PsopD2 are shown in (16) and (26), respectively.Proof.
Due to the independence of the channels,PcopD2 and PsopD2 are independent of each other. As a result, we can derive(35)TESTD2=RsPrγSUx2>ϵ2,γUD2x1>ϵ1,γUD2x2>ϵ2,maxmaxE∈ΦeγSE,maxE∈ΦeγUE<ϵs=Rs1−PcopD21−PsopD2.
The proof is completed.Remark 4.
From Theorem4, we can observe that the reliability is improved while the security is degraded with the increase of Ps and Pu. It means there exists a trade-off between reliability and security. By selecting the optimal transmitting power, the system’s reliability-security performance index can be maximized.
Next, we analyze the system performance for the OMA transmission scheme to make a fair comparison. By considering one of the OMA transmissions, that is, the TDMA scheme, the communication progress is evenly divided into four time slots. In the first time slot,S sends signal x1 to U. U decodes and forwards x1 to D1 at the next time slots. Similarly, S sends signal x2 to D2 by relay U in the next two time slots.
The COPs ofD1 and D2 for OMA scheme can be expressed as follows: (36)PcopOMAD1=1−PrγSUx1>24R1−1,γUD1x1>24R1−1=1−PrhSU2>ϵ1′σu2LdSUPs×PrhUD12>ϵ1′σD12LdUD1Pu,PcopOMAD2=1−PrγSUx2>24R2−1,γUD1x2>24R2−1=1−PrhSU2>ϵ2′σu2LdSUPs×PrhUD22>ϵ2′σD22LdUD2Pu,where ϵ1′=24R1−1 and ϵ2′=24R2−1. The SOP of D2 for OMA scheme can be expressed as follows:(37)PsopOMAD2=1−PrmaxE∈ΦeγSE<24R2−Rs−1×PrmaxE∈ΦeγUE<24R2−Rs−1=1−E∏E∈ΦePrhSE2<ϵs′σE2PsLdSE×E∏E∈ΦePrhUE2<ϵs′σE2PuLdUE,where ϵs′=24R2−Rs−1.


## 3.1. COP ofD1 and D2 for NOMA Scheme

The connection outage probability (COP) is defined as the probability that the system will be interrupted when the instantaneous transmission rate of the system is less than a given target rate. As such, we present the COP ofD1 in the following theorem.Theorem 1.
For the reliable communication ofD1, S-U, and U-D1 links must satisfy the target rate R1 simultaneously. The COP of D1 can be derived as (15), where rvl=rmaxvl+1/2, vl=cos2l−1/2Lπ, rvt=rminvt+1/2, vt=cos2t−1/2Lπ, and L denotes the number of Gauss–Chebyshev nodes.(12)PcopD1=1−∑k1=L,NPk1rSU∑n=0Nk1−1Nk1ϵ1σU2rSU2+H2τ/2ηkα1−ϵ1α2GSUPsn1n!e−Nkϵ1σU2rSU2+H2−τ/2ηk/α1−ϵ1α2GSUPs∑k2=L,N2rmax2−rmin2×rmaxπ2L∑l=1L∑n=0Nk2−11−vl2Pk2rvlNk2ϵ1σD12rvl2+H2τ/2ηkα1−ϵ1α2GUD1Punrvln!e−Nk2ϵ1σD12rvl2+H2τ/2ηk/α1−ϵ1α2GUD1Pu−rminπ2T∑t=1T∑n=0Nk2−11−vt2Pk2rvtNk2ϵ1σD12rvt2+H2τ/2ηkα1−ϵ1α2GUD1Punrvtn!e−Nk2ϵ1σD12rvt2+H2τ/2ηk/α1−ϵ1α2GUD1Pu,Proof.
According to the definition of COP, we have(13)PcopD1=1−Pr12log21+γSUx1>R1,12log21+γUD1x1>R1=1−PrγSUx1>22R1−1,γUD1x1>22R1−1=1−PrhSU2>ϵ1σU2α1−ϵ1α2GSUPsLdSU︸K1×PrhUD12>ϵ1σD12α1−ϵ1α2GUD1PuLdUD1︸K2,where ϵ1=22R1−1. According to (5), K1 can be given by(14)K1=∑k=L,NPkrSU∑n=0Nk−1Nkξ1n1n!e−Nkξ1,wheredSU=rSU2+H2 and ξ1=ϵ1σU2rSU2+H2τ/2ηk/α1−ϵ1α2GSUPs. By applying the polar coordinates and the probability generating functional (PGFL) of PPP, K2 can be derived as follows:(15)K2=PrhUD12>ϵ1σD12α1−ϵ1α2GUD1PuLdUD1=∑k=L,N2rmax2−rmin2∫rminrmaxPkr×PrhUD12>ξ2rdr=∑k=L,N2rmax2−rmin2∫0rmaxPkr×PrhUD12>ξ2rdr−∫0rminPkr×PrhUD12>ξ2rdr=∑k=L,N2rmax2−rmin2∫0rmaxPkr×∑n=0Nk−1Nkξ2n1n!e−Nkξ2rdr−∫0rminPkr×∑n=0Nk−1Nkξ2n1n!e−Nkξ2rdr,where ξ2=ϵ1σD12r2+H2τ/2ηk/α1−ϵ1α2GUD1Pu. It is difficult to obtain the closed-form expression of (15), so the Gaussian–Chebyshev quadrature is applied to yield a close approximation with rvl=rmaxvl+1/2, vl=cos2l−1/2Lπ, rvt=rminvt+1/2, and vt=cos2t−1/2Lπ. By substituting (14) and (15) into (13), the closed-form expression can be obtained as (12).
In the following, we investigate the reliable transmission ofD2 for the NOMA scheme.Theorem 2.
SinceD2 decodes x1 first and then decodes its own information x2, γSUx1>2R1−1, γSUx2>2R2−1, γUD2x1>2R1−1 and γUD2x2>2R2−1 must be satisfied simultaneously for the reliable communications. The closed-form expression of COP can be derived as (19).(16)PcopD2=1−∑k1=L,NPk1rSU∑n=0Nk1−1Nkξ3rSU2+H2τ/2n1n!e−Nkξ3rSU2+H2τ/2∑k2=L,N2rmin2×∑l=1L∑n=0Nk2−11−gl2Pk2rglNkξ4rgl2+H2τ/2nn!e−Nkξ4rgl2+H2τ/2rgl.Proof.
The COP ofD2 can be given by(17)PcopD2=1−PrγSUx1>22R1−1,γSUx2>22R2−1×PrγUD2x1>22R1−1,γUD2x2>22R2−1=1−PrhSU2>ξ3rSU2+H2τ/2︸K3×PrhUD22>ξ4rUD22+H2τ/2︸K4,where ξ3=maxϵ2σU2ηk/α2GSUPs,ϵ1σU2ηk/α1−ϵ1α2GSUPs, ξ4=maxϵ2σD22ηk/α2GUD2Pu,ϵ1σD22ηk/α1−ϵ1α2GUD2Pu and ϵ2=22R2−1. Similar to (17), K3 can be obtained as follows:(18)K3=∑k=L,NPkrSU∑n=0Nk−1Nkξ3rSU2+H2τ/2n×1n!e−Nkξ3rSU2+H2τ/2.
SinceD2 is randomly located in a circle of radius rmin, K4 can be obtained as follows: (19)K4=PrhUD22>ξ4rUD22+H2τ/2=∑k=L,N2rmin2∫0rminPkr×PrhUD12>ξ4rUD22+H2τ/2rdr=∑k=L,N2rmin2∫0rminPkr×∑n=0Nk−1Nkξ4r2+H2τ/2nn!e−Nkξ4r2+H2τ/2rdr.
By exploiting the Gaussian–Chebyshev quadrature and substitutingrgl=rmingl+1/2, gl=cos2l−1/2Lπ, K4 can be rewritten as follows: (20)K4=∑k=L,NπrminL∑l=1L∑n=0Nk−11−gl2Pkrgl×Nkξ4rgl2+H2τ/2nn!e−Nkξ4rgl2+H2τ/2rgl.
According to (18) and (20), the COP of D2 can be derived as (16).Remark 1.
It can be observed from Theorems1 and 2 that the COPs of D1 and D2 decrease with the increase of source transmitting power Ps and Pu. Besides, reducing the zone radius of external sector ring rmax and rmin can decrease the COPs of D1 and D2, which implies a smaller user area or one closer to the UAV relay can improve the reliability of the system.Proposition 1.
The asymptotic COPs ofD1 and D2 can be respectively expressed as follows: (21)Pcop,asyD1=1−2rmax2−rmin2∑k1=L,N∑k2=L,NPk1rSU×∫rminrmaxPk2rrdr,and(22)Pcop,asyD2=1−2rmin2∑k1=L,N∑k2=L,NPk1rSU×∫0rminPk2rrdr.Proof.
As the transmitting powerPs and Pu approach infinity, by exploiting e−x=1−x for small x, we have(23)∑n=0Nk−1Nkξ1n1n!e−Nkξ1≈∑n=0Nk−1Nkξ1n1n!1−Nkξ1≈∑n=0Nk−1Nkξ1n1n!.
In (23), the term corresponding to n=0 is larger than the summation of other terms owing to the presence of ξ1n and ξ2n when Ps and Pu go to infinity. Hence, Pcop,asyD1 can be approximated as the term corresponding to n=0. After some mathematical manipulation, Pcop,asyD1 can be rewritten as (21). Similarly, the expression of Pcop,asyD2 can be obtained as (22). The proof is completed.


## 3.2. SOP ofD2 for NOMA Scheme

SinceD2 is a high-security required user, we analyze the secrecy performance of D2 in terms of SOP. According to Wyner’s wiretap code theory, the SOP is defined as the probability which the wiretap channel capacity is larger than the redundancy rate of wiretap code [26]. For the proposed protected zone method, we consider the case that the eavesdroppers are located inside the circle of radius (rE, rmax) with angle θs. Particularly, by denoting r as the horizontal distance between U and E, the distance dSE can be expressed as dSE=r2+rSU2−2rrSUcosπ−θ with rE≤r≤rmax and θ∈−θs/2,θs/2.Lemma 1.
DenotingRs as the target secrecy rate of D2, we define the function F1r,θ and F2r in polar coordinates to describe the probability PrγSE>22R2−Rs−1 and PrγUE>22R2−Rs−1. By considering S−E channel as the NLoS link, while U−E channel is composed of NLoS link and LoS link, and F1r,θ and F2r can be expressed as follows: (24)F1r,θ=PrγSE>22R2−Rs−1=PrhSE2>εsσE2α2GSEPsLdSE=∑i∈m,MpiEPrhSE2>ξ5r2+rSU2−2rrSUcosπ−θτ/2,and(25)F2r=PrγUE>2R2−Rs−1=PrhUE2>ϵsσE2α2GUEPsLdUE=∑w=L,N∑i,j∈m,MpiUpjEPwrPrhUE2>ξ6r2+H2τ/2,where ϵs=22R2−Rs−1, ξ5=ϵsσE2/α2GSmGEiPs and ξ6=ϵsσE2ηw/α2GUiGEjPu.
Based on Lemma1, the SOP of D2 is given in the following theorem:Theorem 3.
In light of the HPPPs distribution forE, the SOP of D2 under protected zone method is given by(26)PsopD2=PrmaxmaxE∈ΦeγSE,maxE∈ΦeγUE>ϵs=1−E∏E∈ΦePrγSE<ϵs︸K5E∏E∈ΦePrγUE<ϵs︸K6,where K5 and K6 are given in (27) and (28(27)K5=exp−θs3λE64TL∑i∈m,M∑l=1L∑t=1T∑n=0NN−1piEn!1−al21−bt2rmax−rE2bt+rmax+rE2×NNϵsσE2α2GSmGEiPsrmax−rE2bt+rmax+rE22+rSU2+2rmax−rE2bt+rmax+rE2rSUcosθτ/2n×e−NNϵsσE2/α2GSmGEiPsrmax−rE/2bt+rmax+rE/22+rSU2+2rmax−rE/2bt+rmax+rE/2rSUcosθτ/2,(28)K6=exp−λEθs∑i,j∈m,MpiUpjEπrmaxrcl2L∑w=L,N∑l=1L∑n=0Nw−11−cl2Pwrcln!NwϵsσE2r2cl+H2τ/2α2GUiGEjPun×e−NwϵsσE2r2cl+H2τ/2/α2GUiGEjPu−πrErdt2L∑w=L,N∑l=1L∑n=0Nw−11−dt2Pwrdtn!NwϵsσE2r2dt+H2τ/2α2GUiGEjPune−NwϵsσE2r2dt+H2τ/2/α2GUiGEjPu.Proof.
Following the PGFL of PPP, we can obtain(29)K5=exp−λE∫−θs/2θs/2∫rErmaxPrγSE>ϵsrdrdθ=exp−2λE∫0θs/2∫rErmaxF1r,θrdrdθ≈aexp−θs3λE64∑l=1L∑t=1T1−al21−bt2×1TLrmax−rE2bt+rmax+rE2×F1rmax−rE2bt+rmax+rE2,θs4al+1,K6=exp−λEθs∫rErmaxPrγUE>ϵsrdr=exp−λEθs∫rErmaxF2rrdr≈bexp−λEθsπrmax2L∑l=1L1−cl2F2rclrcl−πrE2T∑t=1T1−dt2F2rdtrdt.
Step (a) is computed by a two-layer Gauss–Chebyshev integration related tor and θ, where al=cos2l−1/2Lπ and bt=cos2t−1/2Tπ. Step (b) is calculated through the similar procedure of deriving K2 with cl=cos2l−1/2Lπ, dt=cos2t−1/2Tπ, rcl=rmaxcl+1/2 and rdt=rEdt+1/2. Substituting (5) into (24) and (25), equation K5 and K6 are expressed as (27) and (28), respectively. The proof is completed.Remark 2.
From Theorem3, we can observe that the SOP of D2 is influenced by the transmitting power Ps and Pu, the target codeword rate R2, the confidential codeword rate Rs, the power allocation factor α2, and the distribution of eavesdroppers Φe. To be specific, the SOP decreases with the reduction of eavesdroppers’ density λE and the increase of rE. The SOP increases with the enlargement of Ps and Pu, which means the enhancement of reliability leads to more information at the risk of eavesdropping.
To proceed forward, we derive the asymptotic expression of the SOP to gain more insights. When the transmitting powerPs and Pu are sufficiently large, the asymptotic SOP under the NOMA scheme is shown in the following:Proposition 2.
The asymptotic SOP under the NOMA scheme can be calculated as follows:(30)Psop−asyD2=1−exp−θsλErmax2−rE2.Proof.
For sufficiently largePs, K5 can be calculated as follows: (31)K5=exp−λE∫−θs/2θs/2∫rErmaxPrγSE>ϵsrdrdθ=exp−λE∫−θs/2θs/2∫rErmax∑i∈m,MpiE×∑n=0NN−1NNΩPsn1n!e−NNΩ/Psrdrdθ,where Ω=ϵsσE2r2+rSU2−2rrSUcosπ−θτ/2/α2GSmGEi. When Ps⟶∞, by utilizing the approximation of e−x≈1−x for small x, we have(32)∑n=0NN−1NNΩPsn1n!e−NNΩ/Ps≈∑n=0NN−1NNΩPsn1n!1−NNΩPs≈∑n=0NN−1NNΩPsn1n!.
In (32), the term corresponding to n=0 is larger than the summation of other terms owing to the presence of Ω/Psn when Ps goes to infinity. Hence, K5 can be approximated as the term corresponding to n=0, and it can be rewritten as follows: (33)K5=exp−θsλE2rmax2−rE2.
Similarly, we can deriveK6=K5. After some calculations, the proof of Psop−asyD2 is completed.Remark 3.
It can be observed from Proposition2 that the asymptotic SOP is influenced by the density of eavesdroppers and the size of the protected zone when Ps and Pu are considerably large.


## 3.3. EST ofD2 for NOMA Scheme

The reliability and security of the system are investigated above. However, it is necessary to use a unified framework to integrate security and reliability considerations. To holistically characterize the performance of the system, we derive the effective secrecy throughput (EST) of the system, which is defined as the secrecy rate multiplied by the reliable-and-secure probability ofD2.Theorem 4.
The EST ofD2 for NOMA scheme can be written as follows: (34)TESTD2=Rs1−PcopD21−PsopD2,where PcopD2 and PsopD2 are shown in (16) and (26), respectively.Proof.
Due to the independence of the channels,PcopD2 and PsopD2 are independent of each other. As a result, we can derive(35)TESTD2=RsPrγSUx2>ϵ2,γUD2x1>ϵ1,γUD2x2>ϵ2,maxmaxE∈ΦeγSE,maxE∈ΦeγUE<ϵs=Rs1−PcopD21−PsopD2.
The proof is completed.Remark 4.
From Theorem4, we can observe that the reliability is improved while the security is degraded with the increase of Ps and Pu. It means there exists a trade-off between reliability and security. By selecting the optimal transmitting power, the system’s reliability-security performance index can be maximized.
Next, we analyze the system performance for the OMA transmission scheme to make a fair comparison. By considering one of the OMA transmissions, that is, the TDMA scheme, the communication progress is evenly divided into four time slots. In the first time slot,S sends signal x1 to U. U decodes and forwards x1 to D1 at the next time slots. Similarly, S sends signal x2 to D2 by relay U in the next two time slots.
The COPs ofD1 and D2 for OMA scheme can be expressed as follows: (36)PcopOMAD1=1−PrγSUx1>24R1−1,γUD1x1>24R1−1=1−PrhSU2>ϵ1′σu2LdSUPs×PrhUD12>ϵ1′σD12LdUD1Pu,PcopOMAD2=1−PrγSUx2>24R2−1,γUD1x2>24R2−1=1−PrhSU2>ϵ2′σu2LdSUPs×PrhUD22>ϵ2′σD22LdUD2Pu,where ϵ1′=24R1−1 and ϵ2′=24R2−1. The SOP of D2 for OMA scheme can be expressed as follows:(37)PsopOMAD2=1−PrmaxE∈ΦeγSE<24R2−Rs−1×PrmaxE∈ΦeγUE<24R2−Rs−1=1−E∏E∈ΦePrhSE2<ϵs′σE2PsLdSE×E∏E∈ΦePrhUE2<ϵs′σE2PuLdUE,where ϵs′=24R2−Rs−1.


## 4. Performance Analysis with Jamming

In this section, we propose a cooperative jamming strategy to improve the secrecy performance of the system. Specifically, a friendly aerial jammerJ is introduced to interfere with the eavesdroppers by sending AN. As illustrated in [41], the AN is designed by the pseudorandom sequence method, which is known to legitimate nodes but unknown to eavesdroppers. Therefore, the AN can be canceled at the legitimate nodes and only deteriorate the channel quality of the eavesdroppers. It is worth noting that the pseudorandom sequence can be realized by channel estimation-assisted physical layer key generation and agreement without presharing as in traditional cryptography [42–44]. Without loss of generality, we assume the jammer UAV is hovering at the same altitude as the relay UAV. Under this method, the COP of D1 and D2 is the same as (12) and (16). In the following, we analyze the SOP and EST of the cooperative jamming strategy.


### 4.1. SOP ofD2 for NOMA Scheme with Cooperative Jamming

The SINR for eavesdroppers to decodex2 from S and U can be calculated as follows:(38)γSEJ=maxE∈Φeα2GSEPshSE2LdSEσE2+GJEPjhJE2LdJE,γUEJ=maxE∈Φeα2GUEPuhUE2LdUEσE2+GJEPjhJE2LdJE.Lemma 2.
For the NOMA scheme with cooperative jamming, we set the polar functionF3r,θ and F4r,θ to denote PrγSEJ>22R2−Rs−1 and PrγUEJ>22R2−Rs−1. F3r,θ and F4r,θ are, respectively, written as (40) and (41).Proof.
By denotingz=hJE2, F3r,θ can be derived as(39)F3r,θ=Prα2GSEPshSE2LdSEσE2+GJEPjhJE2LdJE>ϵs=PrhSE2>ϵsσE2+GJEPjhJE2LdJEα2GSEPsLdSE=∑w=L,N∑i,j∈m,MpiSEpjJEPwrJE×PrhSE2>ϵsσE2+GJMGEjPjhJE2LdJEα2GSmGEiPsLdSE=∑w=L,N∑i,j∈m,MpiSEpjJEPwrJE×∫0∞1−FhSE2ϵsσE2+zGJMGEjPjLdJEα2GSmGEiPsLdSEfZzdz.
Utilizing (6) and (7), F3r,θ can be further derived as (40) according to Eq. (3.381.4) in [45], where rJE=r2+rUJ2−2rrUJcosθ, dJE=H2+rJE2 and rUJ denotes the horizontal distance between U and J. Similarly, F4r,θ can be calculated as (41). Lemma 2 is proved.(40)F3r,θ=∑w=L,N∑i,j∈m,Me−NNϵsσE2/α2GSmGEiPsLdSEpiSEpjJpeEPwrJENwNwΓNw∑n=0NN−11n!NNϵsα2GSmGEiPsLdSEn×∑k=0nσE2n−kGJjGEePjLdJEkk+Nw−1!NNϵsGJjGEePjLdJEα2GSmGEiPsLdSE+Nw−k−Nw,(41)F4r,θ=∑w,q=L,N∑i,j∈m,MpiUpjEPqrPwrJEe−NqϵsσE2/α2GUiGEjPuLdUENwNwΓNw∑n=0Nq−11n!Nqϵsα2GUiGEjPuLdUEn×∑k=0nσE2n−kGJjGEePjLdJEkk+Nw−1!NNϵsGJjGEePjLdJEα2GUiGEjPsLdUE+Nw−k−Nw.Theorem 5.
Similar to the above section, the SOP ofD2 under the proposed cooperative jamming scheme can be expressed as follows: (42)PsopJ=1−E∏E∈ΦePrγSEJ<ϵs︸K7E∏E∈ΦePrγUEJ<ϵs︸K8,where(43)K7≈exp−θs3λE64∑l=1L∑t=1T1−al21−bt2×1TLrmax−rE2bt+rmax+rE2×F3rmax−rE2bt+rmax+rE2,θs4al+1,K8≈exp−θs3λE64∑l=1L∑t=1T1−al21−bt2×1TLrmax−rE2bt+rmax+rE2×F4rmax−rE2bt+rmax+rE2,θs4al+1.Proof.
Following similar steps as in the proof of Theorem3, then Theorem 5 can be proved by exploiting a two-layer Gauss–Chebyshev quadrature equation.Remark 5.
As can be seen from Theorem5, the SOP of D2 under the proposed cooperative jamming scheme is affected by many factors, among which jamming power plays an important role. By designing AN, the noise will not affect the SNR of legitimate users and the SOP monotonically decreases with the increase of Pj.


### 4.2. EST ofD2 for NOMA Scheme with Cooperative Jamming

Similar to the previous process of proving Theorem4, the EST of D2 under cooperative jamming scheme can be expressed as follows: (44)TESTJ=Rs1−PcopD21−PsopJ,where PcopD2 and PsopJ are shown in (16) and (42). To gain more insights, we analyze the performance when Pj is sufficiently large.Proposition 3.
The asymptotic EST achieved by the cooperative jamming scheme can be calculated as follows:(45)TEST−asyJ=Rs1−PcopD2.Proof.
AsPj goes to infinity, K7 and K8 approximately equals 1. Hence, the asymptotic EST under the cooperative jamming scheme can be rewritten as equation (45). The proof is completed.Remark 6.
As can be observed from Proposition3, in the case of high SNR of Pj, the EST of D2 is mainly determined by COP and the influence of SOP on the system can be ignored. It is noted that the increase of power allocation factor α2 improves the performance of the system in the high-SNR region. It can also be found that the asymptotic EST is independent of the jamming power, which means that the EST of the proposed cooperative jamming scheme converges to a floor with the increasing Pj.


## 4.1. SOP ofD2 for NOMA Scheme with Cooperative Jamming

The SINR for eavesdroppers to decodex2 from S and U can be calculated as follows:(38)γSEJ=maxE∈Φeα2GSEPshSE2LdSEσE2+GJEPjhJE2LdJE,γUEJ=maxE∈Φeα2GUEPuhUE2LdUEσE2+GJEPjhJE2LdJE.Lemma 2.
For the NOMA scheme with cooperative jamming, we set the polar functionF3r,θ and F4r,θ to denote PrγSEJ>22R2−Rs−1 and PrγUEJ>22R2−Rs−1. F3r,θ and F4r,θ are, respectively, written as (40) and (41).Proof.
By denotingz=hJE2, F3r,θ can be derived as(39)F3r,θ=Prα2GSEPshSE2LdSEσE2+GJEPjhJE2LdJE>ϵs=PrhSE2>ϵsσE2+GJEPjhJE2LdJEα2GSEPsLdSE=∑w=L,N∑i,j∈m,MpiSEpjJEPwrJE×PrhSE2>ϵsσE2+GJMGEjPjhJE2LdJEα2GSmGEiPsLdSE=∑w=L,N∑i,j∈m,MpiSEpjJEPwrJE×∫0∞1−FhSE2ϵsσE2+zGJMGEjPjLdJEα2GSmGEiPsLdSEfZzdz.
Utilizing (6) and (7), F3r,θ can be further derived as (40) according to Eq. (3.381.4) in [45], where rJE=r2+rUJ2−2rrUJcosθ, dJE=H2+rJE2 and rUJ denotes the horizontal distance between U and J. Similarly, F4r,θ can be calculated as (41). Lemma 2 is proved.(40)F3r,θ=∑w=L,N∑i,j∈m,Me−NNϵsσE2/α2GSmGEiPsLdSEpiSEpjJpeEPwrJENwNwΓNw∑n=0NN−11n!NNϵsα2GSmGEiPsLdSEn×∑k=0nσE2n−kGJjGEePjLdJEkk+Nw−1!NNϵsGJjGEePjLdJEα2GSmGEiPsLdSE+Nw−k−Nw,(41)F4r,θ=∑w,q=L,N∑i,j∈m,MpiUpjEPqrPwrJEe−NqϵsσE2/α2GUiGEjPuLdUENwNwΓNw∑n=0Nq−11n!Nqϵsα2GUiGEjPuLdUEn×∑k=0nσE2n−kGJjGEePjLdJEkk+Nw−1!NNϵsGJjGEePjLdJEα2GUiGEjPsLdUE+Nw−k−Nw.Theorem 5.
Similar to the above section, the SOP ofD2 under the proposed cooperative jamming scheme can be expressed as follows: (42)PsopJ=1−E∏E∈ΦePrγSEJ<ϵs︸K7E∏E∈ΦePrγUEJ<ϵs︸K8,where(43)K7≈exp−θs3λE64∑l=1L∑t=1T1−al21−bt2×1TLrmax−rE2bt+rmax+rE2×F3rmax−rE2bt+rmax+rE2,θs4al+1,K8≈exp−θs3λE64∑l=1L∑t=1T1−al21−bt2×1TLrmax−rE2bt+rmax+rE2×F4rmax−rE2bt+rmax+rE2,θs4al+1.Proof.
Following similar steps as in the proof of Theorem3, then Theorem 5 can be proved by exploiting a two-layer Gauss–Chebyshev quadrature equation.Remark 5.
As can be seen from Theorem5, the SOP of D2 under the proposed cooperative jamming scheme is affected by many factors, among which jamming power plays an important role. By designing AN, the noise will not affect the SNR of legitimate users and the SOP monotonically decreases with the increase of Pj.


## 4.2. EST ofD2 for NOMA Scheme with Cooperative Jamming

Similar to the previous process of proving Theorem4, the EST of D2 under cooperative jamming scheme can be expressed as follows: (44)TESTJ=Rs1−PcopD21−PsopJ,where PcopD2 and PsopJ are shown in (16) and (42). To gain more insights, we analyze the performance when Pj is sufficiently large.Proposition 3.
The asymptotic EST achieved by the cooperative jamming scheme can be calculated as follows:(45)TEST−asyJ=Rs1−PcopD2.Proof.
AsPj goes to infinity, K7 and K8 approximately equals 1. Hence, the asymptotic EST under the cooperative jamming scheme can be rewritten as equation (45). The proof is completed.Remark 6.
As can be observed from Proposition3, in the case of high SNR of Pj, the EST of D2 is mainly determined by COP and the influence of SOP on the system can be ignored. It is noted that the increase of power allocation factor α2 improves the performance of the system in the high-SNR region. It can also be found that the asymptotic EST is independent of the jamming power, which means that the EST of the proposed cooperative jamming scheme converges to a floor with the increasing Pj.


## 5. Simulation Results and Discussions

In this section, numerical results are presented to illustrate the reliable and secure performance of the mmWave NOMA UAV-assisted relay system. Without loss of generality, the parameters are set as shown in Table1. We assume that all nodes are equipped with N antennas. The transmitting power from the source and relay satisfies Ps=Pu=P. The unit of transmission rate is BPCU. The simulation results are obtained through 106 different Monte Carlo simulations.Table 1
Simulation parameters.
Number of antennasN=16Environment parametersφ=9.6, ω=0.28Half-power beamwidthθa=θd=3/NMain-lobe gainGM=NSide-lobe gainGm=N−3/2πNsin3/2N/N−3/2πsin3/2NThe distance between ground nodesrmin=20 m, rmax=80 m, rE=30 mPath loss parametersτ=2, ηL=1 dB, ηN=20 dBNoise power−174+10lgBW+NF dBmThe number of Gauss–Chebyshev nodesL=T=20Nakagami-m fading parametersNN=2, NL=3The angle of protected zoneθs=π/3The flight altitude of UAVsH=50 mThe density of eavesdroppers0.0005/m2Transmission bandwidthBW=1 GHzNoise parametersNF=10 dBThe horizontal distance betweenS and UrSU=50 mThe horizontal distance betweenU and JrUJ=30 mIn Figure2, we investigate the reliability of D1 versus R1 under NOMA scheme for different parameters α1 and N. It can be observed that the theoretical analysis agrees well with the simulation, which verifies the correctness of the theoretical derivation. Furthermore, the COP of D1 increases with the target transmission rate R1. It can also be found that the COP of D1 decreases with the increase of P and α1 because more power assigned to D1 results in higher reliability of D1. At the same time, more antennas deployed on UAVs can lead to greater main-lobe gain and thus improve the reliability, which encourages us to equip UAV with more antennas.Figure 2
The COP ofD1 versus R1 under NOMA scheme.Figure3 illustrates the COP of D1 versus H for different target transmission rate R1 and user zone. The analytical curves precisely match the simulations and the correctness of the derivation can be verified. As shown in Figure 3, the COP increases with the increase of flight height H, which demonstrates that longer distance leads to more path loss and impairs the reception quality of the signal. However, the higher LoS link probability caused by the increase of H is relatively negligible. In addition, the OMA scheme outperforms the NOMA scheme when α1=0.7 because the interference from the message of D2 weakens the performance of D1. The NOMA scheme performs better when α1 continues to increase. Furthermore, reducing COP can be achieved by decreasing the user zone. It is due to the fact that in the case of random distribution, there are closer users in a smaller user area, which reduces the path loss.Figure 3
The COP ofD1 versus H under NOMA and OMA scheme for user zone radius and α1, where P=−20 dBm and R1=0.6.Figure4 shows the effect of P and R2 on the reliability of D2 under OMA and NOMA schemes. Observations can be drawn that the COP is reduced by increasing P. In addition, the asymptotic COP is in good agreement with the simulated value, which verifies the correctness of the analysis. For the COP of D2, we note that the transmitting power demanded a small target rate R2 is also small and vice versa. By comparing the COP under NOMA and OMA schemes, it is easy to find that the NOMA scheme outperforms the OMA scheme when R2 is large. It is due to the fact that D2 is difficult to achieve reliable transmission under the OMA scheme in half the time of the NOMA scheme. However, transmission in OMA mode is better for the system performance when R2 is small, which encourages us to select the appropriate transmission mode according to different target transmission rates.Figure 4
The COP ofD2 versus P under the NOMA and OMA scheme, where R1=0.6, Rs=1 and α1=0.6.In Figure5, we plot the SOP of D2 as the function of λE under the NOMA scheme for different Pj and the number of antennas N. We can find that the secrecy performance can be improved by adopting the aerial cooperative jamming strategy. It can be explained that the channel quality of eavesdroppers can be deteriorated by jamming, while the channel quality of the legitimate user remains unchanged. Furthermore, it is obvious that the SOP of D2 increases with the increase of λE. This is because the more the eavesdroppers distributed around S and U, the better the channel quality of the eavesdropper with the best eavesdropping SINR. It can also be seen that increasing the number of antennas can improve the security of the system, and it is more obvious when the jamming power increases. This is because increasing the number of antennas will suppress side-lobe gain and increase the main-lobe gain. It is noted that employing a large number of antennas is useful for the practical secure UAV system.Figure 5
The SOP ofD2 versus λE under NOMA scheme, where R1=0.6,R2=1.5,Rs=1,α1=0.6,P=−30 dBm.Figure6 compares the EST of D2 versus P under three schemes. It can be observed that the EST of D2 increases to a peak value with the increase of P and then decreases to a stable value. There exists an optimal P to maximize EST. It is because the reliability is dominant when P is small, and the security is dominant when P is large. Increasing P reduces the probability of connection outage while making the signal more susceptible to eavesdropping, which is consistent with Figure 4. When P is considerably large, the SO is a dominant factor affecting the EST because COP tends to zero in that case. Note that the NOMA scheme with cooperative jamming outperforms the other two schemes. This is because the reliability of the NOMA scheme is better than the OMA scheme and the cooperative jamming strategy improves the security of the system.Figure 6
The EST ofD2 versus P under different schemes, where R1=0.6,R2=2,Rs=1,α1=0.6,Pj=−20 dBm.Figure7 plots the EST of D2 versus Pj under three schemes. As shown in the figure, the EST of D2 increases with the increase of Pj under the NOMA scheme with cooperative jamming. It can be explained by the fact that increasing Pj results in more interference on the channel of eavesdroppers, which deteriorates the quality of wiretapping. The smaller the location distribution of eavesdroppers, the higher the EST of D2 is. When Pj goes to infinity, the ESTs of D2 with different protected zones converge to the same value, which verifies the result of Proposition 3. Note that, increasing the jamming power within a reasonable range is meaningful for the practical system design. Meanwhile, the EST of the system without cooperative jamming strategy does not change with Pj. Obviously, the NOMA scheme outperforms the OMA scheme owing to the improvement of reliability under the NOMA scheme. As a result, it shows the superiority of the proposed NOMA scheme with cooperative jamming.Figure 7
The EST ofD2 versus Pj under different schemes, where R1=0.6,R2=2,Rs=1,α1=0.6,P=0 dBm.Figure8 shows the EST of D2 versus different P and Pj under the NOMA scheme with cooperative jamming. It is observed that the higher jamming power is beneficial to the EST of the system. When the transmitting power of P increases, the EST of D2 increases initially and decreases afterward. However, when Pj is fairly large or fairly small, the EST remains constant after enlargement as P increases. The figure also shows that there is an optimal P,Pj point, which can minimize the consumption of resources and obtain good reliability and security performance. It provides the theoretical basis and reference for the practical design of the UAV mmWave NOMA system.Figure 8
The EST ofD2 versus P and Pj under NOMA scheme with cooperative jamming, where R1=0.6,R2=2,Rs=1,α1=0.6.


## 6. Conclusion

In this paper, we have studied the downlink mmWave NOMA UAV-assisted relay system in the presence of randomly distributed eavesdroppers and users with different levels of security requirements. The distribution of users and eavesdroppers was characterized as independent HPPPs. Two transmission schemes without or with cooperative jamming were proposed. Based on the two schemes, the COP, SOP, and EST expressions of the users were derived to measure the reliability and security. The simulation results show that the reliability and security performance of NOMA scheme with cooperative jamming outperforms other schemes. However, when the transmitting power of the source and UAV relay is large, SOP depends on the shape of the protected zone and the density of eavesdroppers. With the increase of jamming power, the EST of the cooperative jamming scheme converges to a performance floor, which is independent of the size of the protected zone. In the future, it is worth investigating the performance of the system by exploiting the mobility of UAVs.



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*Source: 7452014-2022-10-10.xml*