# On the Power-Splitting Relaying Protocol for SWIPT with Multiple UAVs in Downlink NOMA-IoT Networks

Authors: Huu Q. Tran; Ca V. Phan; Quoc-Tuan Vien
Journal: Wireless Communications and Mobile Computing
 (2022)

---

## Abstract

Unmanned aerial vehicle (UAV) communication and non-orthogonal multiple access (NOMA) are two promising technologies for wireless 5G networks and beyond. The UAVs can be used as flying base stations to form line-of-sight communication links to the Internet of things devices (IDs) and to enhance the performance of usual terrestrial cellular networks. Moreover, the UAVs can also be deployed as flying relay nodes for forwarding data from a base station (BS) to the IDs. On the other hand, non-orthogonal resource sharing for many concurrent users is exploited in NOMA, thus improving spectrum efficiency (SE) and supporting massive connections. The NOMA combined with energy harvesting (EH) in an amplify-and-forward (AF) with cooperative UAV systems is researched. Specifically, the UAVs act as rotary-wing relays to forward data from the BSs to two IDs. This paper focuses on the analysis of outage probabilities (OPs), system throughput, and energy efficiency (EE) for two IDs. Besides, we also do the asymptotic analysis of OPs at high signal-to-noise ratios (SNRs). Furthermore, this paper also inspects the impacts of the UAV-based relaying on the OP, system throughput, and EE of the proposed NOMA scheme. The derived asymptotic expansions show that the suggested model can enhance user fairness and the analytical results match the simulation results.


---

## Body

## 1. Introduction

Unmanned aerial vehicles (UAVs) communications and non-orthogonal multiple access (NOMA) are envisioned as two key technologies for unlocking the potential of the fifth-generation (5G) and future networks[1, 2]. In particular, the use of UAVs for 5G and beyond-5G networks has received much attention over the past few years [3]. Owning to distinctive characteristics, UAVs have been adopted for a variety of wireless networks and communication applications, for example, UAV-carried flying base stations (BSs) for capacity and coverage improvement, public safety scenarios, information dissemination, UAV-based wireless backhaul, and cellular connected UAVs as mobile users [4]. The NOMA technique exhibits benefits such as increased user data rate, massive connectivity, reduced end-to-end latency, improved fairness among users, high spectral efficiency (SE), and more energy efficiency (EE) than that of traditional orthogonal multiple access (OMA) [5–11]. The NOMA exploited two mechanisms including superposition coding (SC) and successive interference cancellation (SIC) [12, 13]. Some recent studies have showed that the integration of NOMA into UAV networks can enhance the network performance in terms of max-min rate [14], sum rate [15], and mission completion time [16], over conventional OMA schemes. Two protocols are exploited for energy harvesting (EH) at relays including power splitting relay and time switching relay in the decode-and-forward (DF) cooperative communication network [17, 18]. NOMA in UAV-enabled cooperative amplify-and-forward (AF) with the outdated relay selection algorithm is investigated [19].


### 1.1. Related Works

In this section, we review the novel study works on NOMA and UAV networks. UAV-assisted communication has become a potential application in industry and academic fields. NOMA is one of the important candidates to integrate UAV into 5G and future networks due to its overwhelming characteristics, such as superior spectral efficiency, low latency, and massive connectivity [2]. UAVs have also been recently studied as a promising solution to proven their potential in civil applications such as aerial photography, enhanced freight distribution, and wildfire management and disasters [4, 20]. A resource allocation scheme was proposed in NOMA UAV communication to enhance the user transmission rate with worse channel state information (CSI) [21]. UAVs can act as moving BSs or relays to facilitate reliable and efficient communication with multiple users [22, 23]. In [24], the authors discussed NOMA-based UAV-aided communications such as UAV-BS-enabled NOMA and NOMA-assisted cellular-connected UAVs. In [25], the authors conducted the complete performance analysis of a NOMA-aided UAV communication system, including selection combining double diversity receivers on UAVs, communicating over bivariate Rician shadowed fading channels. The work in [26] investigated the impact of residual hardware impairments on the performance of UAV-aided NOMA multiway relay networks by deriving the approximate analytical expressions for the achievable sum rate. Specifically, the asymptotic analysis in the high signal-to-noise-ratio (SNR) regions is carried out by invoking a high SNR slope and high SNR power offset. In [27], the authors investigated the impact of residual hardware impairments on the performance of UAV-aided NOMA multiway relay networks by deriving the approximate analytical expressions for the achievable sum rate. Specifically, the asymptotic analysis in the high signal-to-noise-ratio (SNR) regions is carried out by invoking a high SNR slope and high SNR power offset. In [28], the authors studied a 5G-based IoT to access the 5G spectrum to transfer 5G and IoT information simultaneously. The 5G network can be used at the IoT nodes to transmit voice and video information while using the IoT network for forwarding sensing data.The work presented in [29] investigated a novel UAV relay-assisted IoT model with the emergency communication system that takes into account the latency requirement of Internet of Things (IoT) devices and the limited storage capacity of the UAV. A novel joint content caching and EH scheme is studied to improve UAV communications in the IoT NOMA network wherein a UAV acts like an aerial relay for serving users on demand [30]. In [31], the authors studied the throughput maximization problem with a focus on UAV-assisted wireless communication, considering a communication system with one couple of source and destination, where a UAV serves like an aerial relay based on an AF scheme and EH using a PS protocol. Performance of the IoT system with an EH UAV-enabled relay with downlink NOMA under Nakagami-m fading using the DF and AF schemes is investigated, where the time switching and adaptive power splitting protocols are utilized for the UAV [32].Based on the above review, in this paper, we focus on power-switching relaying (PSR) for an RF EH and AF-based multiple-UAV NOMA in a SWIPT IoT system.


### 1.2. Motivation and Contribution

This paper researched the engagement of EH and AF-based multiple-UAV NOMA in a SWIPT IoT system wherein a UAV serves as a rotary-wing relay to communicate with two IoT devices (IDs). We also look at the UAV option (UAVO) scheme because it requires CSI knowledge of one-hop links. Hence, the use of rotary-wing relay AF in the UAVO model is greatly desirable in practice when complicated problems occur as the main anxiety. According to the depicted system model, the outage probabilities (OPs), the system throughput, and EE of the NOMA schemes in AF transition systems with UAVO were studied. The major contributions of this paper are outlined as follows:(i)
We exploit NOMA access technology in a dual-hop network to improve the SE of the network(ii)
A system model is studied in this work that consists of a BS and n types of UAVs and two IDs(iii)
The use of one SWIPT based EH and information processing (IP) protocol, specifically BS-based PSR, is exploited at a UAV that serves as a rotary-wing relay in this model(iv)
We derive closed-form expressions of OPs, system throughput, and EE at two IDs to assess the performance of the PRS scheme in SWIPT based on multiple-UAV cooperative NOMA systems


### 1.3. Organization

The remainder of the paper is arranged as below: Section2 shows the proposed system model and assumptions. Section 3 analyzes the performance parameters with OP, throughput, and EE of the system. Section 4 discusses the simulation results. Ultimately, Section 5 is the main conclusion.


## 1.1. Related Works

In this section, we review the novel study works on NOMA and UAV networks. UAV-assisted communication has become a potential application in industry and academic fields. NOMA is one of the important candidates to integrate UAV into 5G and future networks due to its overwhelming characteristics, such as superior spectral efficiency, low latency, and massive connectivity [2]. UAVs have also been recently studied as a promising solution to proven their potential in civil applications such as aerial photography, enhanced freight distribution, and wildfire management and disasters [4, 20]. A resource allocation scheme was proposed in NOMA UAV communication to enhance the user transmission rate with worse channel state information (CSI) [21]. UAVs can act as moving BSs or relays to facilitate reliable and efficient communication with multiple users [22, 23]. In [24], the authors discussed NOMA-based UAV-aided communications such as UAV-BS-enabled NOMA and NOMA-assisted cellular-connected UAVs. In [25], the authors conducted the complete performance analysis of a NOMA-aided UAV communication system, including selection combining double diversity receivers on UAVs, communicating over bivariate Rician shadowed fading channels. The work in [26] investigated the impact of residual hardware impairments on the performance of UAV-aided NOMA multiway relay networks by deriving the approximate analytical expressions for the achievable sum rate. Specifically, the asymptotic analysis in the high signal-to-noise-ratio (SNR) regions is carried out by invoking a high SNR slope and high SNR power offset. In [27], the authors investigated the impact of residual hardware impairments on the performance of UAV-aided NOMA multiway relay networks by deriving the approximate analytical expressions for the achievable sum rate. Specifically, the asymptotic analysis in the high signal-to-noise-ratio (SNR) regions is carried out by invoking a high SNR slope and high SNR power offset. In [28], the authors studied a 5G-based IoT to access the 5G spectrum to transfer 5G and IoT information simultaneously. The 5G network can be used at the IoT nodes to transmit voice and video information while using the IoT network for forwarding sensing data.The work presented in [29] investigated a novel UAV relay-assisted IoT model with the emergency communication system that takes into account the latency requirement of Internet of Things (IoT) devices and the limited storage capacity of the UAV. A novel joint content caching and EH scheme is studied to improve UAV communications in the IoT NOMA network wherein a UAV acts like an aerial relay for serving users on demand [30]. In [31], the authors studied the throughput maximization problem with a focus on UAV-assisted wireless communication, considering a communication system with one couple of source and destination, where a UAV serves like an aerial relay based on an AF scheme and EH using a PS protocol. Performance of the IoT system with an EH UAV-enabled relay with downlink NOMA under Nakagami-m fading using the DF and AF schemes is investigated, where the time switching and adaptive power splitting protocols are utilized for the UAV [32].Based on the above review, in this paper, we focus on power-switching relaying (PSR) for an RF EH and AF-based multiple-UAV NOMA in a SWIPT IoT system.


## 1.2. Motivation and Contribution

This paper researched the engagement of EH and AF-based multiple-UAV NOMA in a SWIPT IoT system wherein a UAV serves as a rotary-wing relay to communicate with two IoT devices (IDs). We also look at the UAV option (UAVO) scheme because it requires CSI knowledge of one-hop links. Hence, the use of rotary-wing relay AF in the UAVO model is greatly desirable in practice when complicated problems occur as the main anxiety. According to the depicted system model, the outage probabilities (OPs), the system throughput, and EE of the NOMA schemes in AF transition systems with UAVO were studied. The major contributions of this paper are outlined as follows:(i)
We exploit NOMA access technology in a dual-hop network to improve the SE of the network(ii)
A system model is studied in this work that consists of a BS and n types of UAVs and two IDs(iii)
The use of one SWIPT based EH and information processing (IP) protocol, specifically BS-based PSR, is exploited at a UAV that serves as a rotary-wing relay in this model(iv)
We derive closed-form expressions of OPs, system throughput, and EE at two IDs to assess the performance of the PRS scheme in SWIPT based on multiple-UAV cooperative NOMA systems


## 1.3. Organization

The remainder of the paper is arranged as below: Section2 shows the proposed system model and assumptions. Section 3 analyzes the performance parameters with OP, throughput, and EE of the system. Section 4 discusses the simulation results. Ultimately, Section 5 is the main conclusion.


## 2. System Model

We investigate a downlink cooperative two-hop rotary-wing relay system in which a base station (BS) aims to send the signal to two IDs, i.e.,D1 and D2 with the support of one out of N AF UAVs UAV1,UAV2,⋯,UAVN with N>1, as shown in Figure 1. It is assumed that there is no communication between the UAVs. We mainly focus our attention on a homogeneous network topology in which all wireless links show non-selective Rayleigh block fading and additive white Gaussian noise (AWGN).Figure 1
System model.As shown in Figure1, without loss of generality, we assume that the channels of two IDs have been ordered as hSD1≤hSD2. We also investigate that D1 and D2 are coupled together to implement NOMA downlink cooperative system. Hence, two successive phases are implicated for completing the information transmission that can be combined by selection combining. Selection combining (SC): Out of the N signal received, the strongest signal is selected. When signal N is independent and distributes Rayleigh, the increase is shown in the power ratio as follows ∑n=1N1/n.Table1 below lists the parameters used throughout the paper, unless otherwise stated.Table 1
Notation description.
NotationDescriptionhSUAVn~CN0,ΩSUAVnThe complex flat coefficient between BS andUAVnnUAVn~CN0,N0Additive white Gaussian noise (AWGN) atUAVnhUAVnDi~CN0,ΩUAVnDiThe complex flat coefficient betweenUAVn and Di, i∈0,1nUAVnDi~CN0,N0Additive white Gaussian noise (AWGN) atDi indirect link between BS and DihSDi~CN0,ΩSDiThe complex flat coefficient with direct link between BS andDinDi~CN0,N0Additive white Gaussian noise (AWGN) atDi with direct link between BS and DiPSTransmission power at theBSβ0<β<1The power splitting ratio at theUAVnE.Expectation operationEnUAVnDi2=N0Expectation operation of AWGN atUAVnmThe path-loss of channel modelxii∈0,1The transmitted signals fromBS⟶UAVn⟶Di indirect link between BS and Di and BS⟶Di with direct link between BS and DiExi2=1.Expectation operation ofxiTThe total time blocka1Power allocation coefficient for signalx1a2Power allocation coefficient for signalx2η0<η≤1The energy conversion efficiency at theUAVn


### 2.1. BS-Based PSR Protocol of EH atUAVn

At theUAVn, we consider the EH mechanism BS-based PSR protocol.Figure2 depicts a diagram illustration of BS-based PSR scheme for EH at UAVn in the block time of T.Figure 2
Diagram illustration of PSR-basedUAVn.For direct link: In the whole time,T, BS transmits information directly to two IDs D1 and D2, with transmission powers PS1=PS2=PS.For indirect link: The collected signal power atUAVn is indicated by P. Assuming that the BS transmits the information to UAVn in the half-block of T, while the information is sent from UAVn to two IDs D1 and D2 in the remaining time of T (i.e., T/2). BS concurrently sends the superposed coding signal to Rn. Therefore, the sent signal at BS can be given by
(1)xBS=a1PSx1+a2PSx2,Based on the employment of superposition of the sent signals at BS like in the NOMA scheme, the surveillance atUAVn can be given by
(2)yUAVn=hSUAVnxBS+nUAVn=hSUAVna1PSx1+a2PSx2+nUAVn.The signals received at two IDsD1 and D2, respectively, are given by
(3)yD1=hSD1a1PSx1+a2PSx2+nD1,(4)yD2=hSD2a1PSx1+a2PSx2+nD2.SinceD1 is further to UAVn than D2, the power is allocated for D1 more than that for D2 to ensure the user fairness.With no generality losses,0<a2<a1 satisfies a1+a2=1. Based on PSR protocol, UAVn divides the collected power into two portions consisting of collected energy and IP energy. The energy harvested at UAVn is obtained by
(5)EH=PShSRn2ηβT2,whereη relies on the rectifier and the EH circuitry at UAVn. The total energy harvested in the EH phase is consumed at UAVn while forwarding the decoded signal to Di, i∈1,2. The transmission power at UAVn depends on EH and is determined by
(6)PRn=EHT/2=PShSRn2ηβ=PS.GE,whereGE=hSRn2ηβ indicates the EH coefficient in the PSR protocol.


### 2.2. Information Processing atUAVn and Di

In the first phase, BS transmits signalsx1 and x2 for all UAVs and two IDs as in Equation (1).During the second phase,UAVn transmits the signal xRn=GnyRn to two IDs D1 and D2, where Gn denotes the amplifying gain at UAVn, i.e.,
(7)Gn2=PUAVnPShSUAVn2+N0=ρGEYn+1,whereρΔ=PS/N0 depicts the sent SNR and the random variables (RVs) Ai=ρhSDi2, Bn=ρhSUAVn2, and Cin=ρhUAVnDi2 describe the instantaneous SNRs of the links BS⟶Di, BS⟶Rn, Rn⟶Di, respectively. Thus, the signals at D1 and D2 are forwarded by UAVn and can be given by as follows:
(8)yUAVnD1=hUAVnD1xUAVn+nUAVnD1=GnhUAVnD1hSUAVna1PSx1+GnhUAVnD1hSUAVna2PSx2+GnhUAVnD1nUAVn+nUAVnD1,(9)yUAVnD2=hUAVnD2xUAVn+nUAVnD2=GnhUAVnD2hSUAVna1PSx1+GnhUAVnD2hSUAVna2PSx2+GnhUAVnD2nUAVn+nUAVnD2.During the first phase, considerx2 like interference in yD1. The immediate SINR at D1 is provided by
(10)γ1,D1=a1ρhSD12a2ρhSD12+1=a1A1a2A1+1.In the same way, the instantaneous SINR atD2 is provided by
(11)γ1,D2=a1ρhSD22a2ρhSD22+1=a1A2a2A2+1.By following the NOMA scheme,D2 decrypts the message specified for D1 first and deletes it with SIC; then, it decrypts itself without interfering. Hence, the immediate SNR at D2 is provided by
(12)γ2,D2=a2A2.During the second phase, the instantaneous SINR calculation is same as the first phase. Therefore, the immediate SINR atD1 relative to the link is expressed as
(13)γUAVnD1=a1GEBnC1na2GEBnC1n+GEC1n+Bn+1,(14)γUAVnD12=a1GEBnC2na2GEBnC2n+GEC2n+Bn+1,(15)γUAVnD2=a2GEBnC2nGEC2n+Bn+1.Finally, by using (10)-(15), it is assumed that the signals from the forward link and the direct link are associated by selection combining (SC). The instantaneous SINR per ID can be written as
(16)γD1=maxγ1,D1,γUAVnD1,(17)γD2=maxγ1,D2,γUAVnD2.In the next, we will compute the OPs of two IDs assuming a UAVO method [33]. Therefore, the transition index is chosen and its corresponding SNR is given by
(18)n∗=argmaxn=1,⋯,NγBSUAVn,Bn∗=maxn=1,⋯,NBn,in which the instantaneous SNR atUAVn is denoted by γBSUAVn=Bn.


## 2.1. BS-Based PSR Protocol of EH atUAVn

At theUAVn, we consider the EH mechanism BS-based PSR protocol.Figure2 depicts a diagram illustration of BS-based PSR scheme for EH at UAVn in the block time of T.Figure 2
Diagram illustration of PSR-basedUAVn.For direct link: In the whole time,T, BS transmits information directly to two IDs D1 and D2, with transmission powers PS1=PS2=PS.For indirect link: The collected signal power atUAVn is indicated by P. Assuming that the BS transmits the information to UAVn in the half-block of T, while the information is sent from UAVn to two IDs D1 and D2 in the remaining time of T (i.e., T/2). BS concurrently sends the superposed coding signal to Rn. Therefore, the sent signal at BS can be given by
(1)xBS=a1PSx1+a2PSx2,Based on the employment of superposition of the sent signals at BS like in the NOMA scheme, the surveillance atUAVn can be given by
(2)yUAVn=hSUAVnxBS+nUAVn=hSUAVna1PSx1+a2PSx2+nUAVn.The signals received at two IDsD1 and D2, respectively, are given by
(3)yD1=hSD1a1PSx1+a2PSx2+nD1,(4)yD2=hSD2a1PSx1+a2PSx2+nD2.SinceD1 is further to UAVn than D2, the power is allocated for D1 more than that for D2 to ensure the user fairness.With no generality losses,0<a2<a1 satisfies a1+a2=1. Based on PSR protocol, UAVn divides the collected power into two portions consisting of collected energy and IP energy. The energy harvested at UAVn is obtained by
(5)EH=PShSRn2ηβT2,whereη relies on the rectifier and the EH circuitry at UAVn. The total energy harvested in the EH phase is consumed at UAVn while forwarding the decoded signal to Di, i∈1,2. The transmission power at UAVn depends on EH and is determined by
(6)PRn=EHT/2=PShSRn2ηβ=PS.GE,whereGE=hSRn2ηβ indicates the EH coefficient in the PSR protocol.


## 2.2. Information Processing atUAVn and Di

In the first phase, BS transmits signalsx1 and x2 for all UAVs and two IDs as in Equation (1).During the second phase,UAVn transmits the signal xRn=GnyRn to two IDs D1 and D2, where Gn denotes the amplifying gain at UAVn, i.e.,
(7)Gn2=PUAVnPShSUAVn2+N0=ρGEYn+1,whereρΔ=PS/N0 depicts the sent SNR and the random variables (RVs) Ai=ρhSDi2, Bn=ρhSUAVn2, and Cin=ρhUAVnDi2 describe the instantaneous SNRs of the links BS⟶Di, BS⟶Rn, Rn⟶Di, respectively. Thus, the signals at D1 and D2 are forwarded by UAVn and can be given by as follows:
(8)yUAVnD1=hUAVnD1xUAVn+nUAVnD1=GnhUAVnD1hSUAVna1PSx1+GnhUAVnD1hSUAVna2PSx2+GnhUAVnD1nUAVn+nUAVnD1,(9)yUAVnD2=hUAVnD2xUAVn+nUAVnD2=GnhUAVnD2hSUAVna1PSx1+GnhUAVnD2hSUAVna2PSx2+GnhUAVnD2nUAVn+nUAVnD2.During the first phase, considerx2 like interference in yD1. The immediate SINR at D1 is provided by
(10)γ1,D1=a1ρhSD12a2ρhSD12+1=a1A1a2A1+1.In the same way, the instantaneous SINR atD2 is provided by
(11)γ1,D2=a1ρhSD22a2ρhSD22+1=a1A2a2A2+1.By following the NOMA scheme,D2 decrypts the message specified for D1 first and deletes it with SIC; then, it decrypts itself without interfering. Hence, the immediate SNR at D2 is provided by
(12)γ2,D2=a2A2.During the second phase, the instantaneous SINR calculation is same as the first phase. Therefore, the immediate SINR atD1 relative to the link is expressed as
(13)γUAVnD1=a1GEBnC1na2GEBnC1n+GEC1n+Bn+1,(14)γUAVnD12=a1GEBnC2na2GEBnC2n+GEC2n+Bn+1,(15)γUAVnD2=a2GEBnC2nGEC2n+Bn+1.Finally, by using (10)-(15), it is assumed that the signals from the forward link and the direct link are associated by selection combining (SC). The instantaneous SINR per ID can be written as
(16)γD1=maxγ1,D1,γUAVnD1,(17)γD2=maxγ1,D2,γUAVnD2.In the next, we will compute the OPs of two IDs assuming a UAVO method [33]. Therefore, the transition index is chosen and its corresponding SNR is given by
(18)n∗=argmaxn=1,⋯,NγBSUAVn,Bn∗=maxn=1,⋯,NBn,in which the instantaneous SNR atUAVn is denoted by γBSUAVn=Bn.


## 3. Performance Analysis

### 3.1. Outage Performance

The target SINR of two IDs is determined by the ID’s request for the quality of service (QoS). Hence, each ID has a target SINR,γthi=22Ri−1,i∈1,2 [3, 5].


#### 3.1.1. Outage Probability atD1

Based on [4], the RVs’ cumulative distribution functions (CDF) and, correspondingly, can be expressed by
(19)FAiγthi=1−exp−γthiΩAi,(20)FBn∗γthi=1−exp−γthiΩBnN=1−∑n=1NnN−1n−1exp−γthiΩBn,(21)FCin∗γthi=1−exp−γthiΩCin,whereΩAi=ρΩ1,Di,ΩBn=ρΩBSUAVn∗,ΩCin=ρΩUAVn∗Di represent the average SNR of the links, respectively. According to the NOMA principle, one outage event happens if there is indirect transmission or no successful forward sending. Hence, the OP at D1 is given by
(22)PD1=PrγD1<γth1=Prmaxγ1,D1,γUAVnD1<γth1=Prγ1,D1<γth1,γUAVnD1<γth1=Fγ1,D1γth1⏟I1FγUAVn∗D1γth1.⏟I2Theorem 1 The OP atD1 can be derived as (see (23)).
(23)PD1=1−exp−γ~th1ΩA11−∑n=1NNn−1n−1exp−σnGEΩBn+1ΩC1n2αK12α,
whereK1. denotes the first-order modified Bessel function of the second kind ([34], Eq.(3.324.1)), α=nσ1+σGE/ΩBnΩC1n, σ=γth1/a1GE−a2GEγth1, and σ=γth1/a1GE−a2GEγth1 with a1>a2γth1.Proof.
See AppendixA.


#### 3.1.2. Outage Probability atD2

BecauseD2 needs to decode the signal of the first D1, D2 will be outage if both the first and the second stage are outages. Therefore, OP at D2 can be formatted as
(24)PD2=Fγ1,D2γth2FγUAVn∗D2γth2.Theorem 2 The OP atD2 can be derived as (see (25)).
(25)PD2=1−exp−θΩA21−∑n=1NNn−1n−1exp−ωnGEΩBn+1ΩBn2βK12δ,
whereK1. denotes the first-order modified Bessel function of the second kind ([34], Eq.(3.324.1)), δ=nω1+ωGE/ΩBnΩC2n, λ1=γth2/a1GE−a2GEγth2, λ2=γth2/a2GE, and ω=maxλ1,λ2 with a1>a2γth1.Proof.
See AppendixB.


#### 3.1.3. Asymptotic Outage Probability atD1

Applying the McLaurin expression, we get thatex≃1+x and K1x≃x−1 for small x. Hence, it turns out that
(26)2αK12α≃1.An expression for the asymptotic OP forPD1, whose exact analysis is presented in (23), is simplified as follows:
(27)1−exp−γth1a1−a2γth1ΩA1=γ~th1ΩA1,(28)exp−σnGEΩBn+1ΩC1n≃1−σkGEΩBn+1ΩC1n.Hence, we can obtain a fraction of the asymptotic approximation forPD1 in (24) as follows:
(29)M1~≃1−∑n=1NNn−1n−11−σkGEΩBn+1ΩC1n=1−∑n=1NNn−1n−1+∑k=1NNn−1n−1×σnGEΩBn+1ΩC1n.With∑n=1NNn−1n−1=1.We have(30)M1≃∑n=1NNn−1n−1σnΩBn+1ΩC1n.Ultimately, from (31) and (34), an asymptotic OP expression for PD1 in (25), we obtain
(31)PD1∞=γth1~ΩA1M1.


#### 3.1.4. Asymptotic Outage Probability atD2

The asymptotic OP forPD2 is expressed the same as PD1, whose exact analysis is portrayed in (27); we have
(32)1−exp−γth2a1−a2γth2ΩA2=γ~th2ΩA2,(33)exp−ωnGEΩBn+1ΩC2n≃1−ωnGEΩBn+1ΩC2n.Thus, we can obtain a portion of the asymptotic approximation forPD2 in (28) as follows:
(34)M2~≃1−∑n=1NnN−1n−11−ωnGEΩBn+1ΩC2n=1−∑n=1NnN−1n−1+∑n=1NnN−1n−1×ωnGEΩBn+1ΩC2n.With∑n=1NNn−1n−1=1, we have,
(35)M2≃∑n=1NNn−1n−1ωnGEΩBn+1ΩC2n.Ultimately, from (36) and (39), an asymptotic OP expression for PD2 in (29), we have
(36)PD2∞=θΩA2M2.


### 3.2. System Throughput

In this case, the BS sends information at a constant target rate, rely on the performance of the OP because of the wireless fading channel. The system throughput of the NOMA indirect link is shown by as follows.


### 3.3. The System Throughput atD1

(37)τD1=1−PD1R1,wherePD1 is given in (23).


### 3.4. The System Throughput atD2

(38)τD2=1−PD2R2,wherePD2 is given in (25).


### 3.5. Energy Efficiency

EE is known as the ratio of sum throughput to total power consumed in the whole network system.


#### 3.5.1. Energy Efficiency atD1

(39)EED1=2τD1ρ1+GEΩYn,whereτD1 is calculated by using (37).


#### 3.5.2. Energy Efficiency atD2

(40)EED2=2τD2ρ1+GEΩYn,whereτD2 is calculated by using (38).


## 3.1. Outage Performance

The target SINR of two IDs is determined by the ID’s request for the quality of service (QoS). Hence, each ID has a target SINR,γthi=22Ri−1,i∈1,2 [3, 5].


### 3.1.1. Outage Probability atD1

Based on [4], the RVs’ cumulative distribution functions (CDF) and, correspondingly, can be expressed by
(19)FAiγthi=1−exp−γthiΩAi,(20)FBn∗γthi=1−exp−γthiΩBnN=1−∑n=1NnN−1n−1exp−γthiΩBn,(21)FCin∗γthi=1−exp−γthiΩCin,whereΩAi=ρΩ1,Di,ΩBn=ρΩBSUAVn∗,ΩCin=ρΩUAVn∗Di represent the average SNR of the links, respectively. According to the NOMA principle, one outage event happens if there is indirect transmission or no successful forward sending. Hence, the OP at D1 is given by
(22)PD1=PrγD1<γth1=Prmaxγ1,D1,γUAVnD1<γth1=Prγ1,D1<γth1,γUAVnD1<γth1=Fγ1,D1γth1⏟I1FγUAVn∗D1γth1.⏟I2Theorem 1 The OP atD1 can be derived as (see (23)).
(23)PD1=1−exp−γ~th1ΩA11−∑n=1NNn−1n−1exp−σnGEΩBn+1ΩC1n2αK12α,
whereK1. denotes the first-order modified Bessel function of the second kind ([34], Eq.(3.324.1)), α=nσ1+σGE/ΩBnΩC1n, σ=γth1/a1GE−a2GEγth1, and σ=γth1/a1GE−a2GEγth1 with a1>a2γth1.Proof.
See AppendixA.


### 3.1.2. Outage Probability atD2

BecauseD2 needs to decode the signal of the first D1, D2 will be outage if both the first and the second stage are outages. Therefore, OP at D2 can be formatted as
(24)PD2=Fγ1,D2γth2FγUAVn∗D2γth2.Theorem 2 The OP atD2 can be derived as (see (25)).
(25)PD2=1−exp−θΩA21−∑n=1NNn−1n−1exp−ωnGEΩBn+1ΩBn2βK12δ,
whereK1. denotes the first-order modified Bessel function of the second kind ([34], Eq.(3.324.1)), δ=nω1+ωGE/ΩBnΩC2n, λ1=γth2/a1GE−a2GEγth2, λ2=γth2/a2GE, and ω=maxλ1,λ2 with a1>a2γth1.Proof.
See AppendixB.


### 3.1.3. Asymptotic Outage Probability atD1

Applying the McLaurin expression, we get thatex≃1+x and K1x≃x−1 for small x. Hence, it turns out that
(26)2αK12α≃1.An expression for the asymptotic OP forPD1, whose exact analysis is presented in (23), is simplified as follows:
(27)1−exp−γth1a1−a2γth1ΩA1=γ~th1ΩA1,(28)exp−σnGEΩBn+1ΩC1n≃1−σkGEΩBn+1ΩC1n.Hence, we can obtain a fraction of the asymptotic approximation forPD1 in (24) as follows:
(29)M1~≃1−∑n=1NNn−1n−11−σkGEΩBn+1ΩC1n=1−∑n=1NNn−1n−1+∑k=1NNn−1n−1×σnGEΩBn+1ΩC1n.With∑n=1NNn−1n−1=1.We have(30)M1≃∑n=1NNn−1n−1σnΩBn+1ΩC1n.Ultimately, from (31) and (34), an asymptotic OP expression for PD1 in (25), we obtain
(31)PD1∞=γth1~ΩA1M1.


### 3.1.4. Asymptotic Outage Probability atD2

The asymptotic OP forPD2 is expressed the same as PD1, whose exact analysis is portrayed in (27); we have
(32)1−exp−γth2a1−a2γth2ΩA2=γ~th2ΩA2,(33)exp−ωnGEΩBn+1ΩC2n≃1−ωnGEΩBn+1ΩC2n.Thus, we can obtain a portion of the asymptotic approximation forPD2 in (28) as follows:
(34)M2~≃1−∑n=1NnN−1n−11−ωnGEΩBn+1ΩC2n=1−∑n=1NnN−1n−1+∑n=1NnN−1n−1×ωnGEΩBn+1ΩC2n.With∑n=1NNn−1n−1=1, we have,
(35)M2≃∑n=1NNn−1n−1ωnGEΩBn+1ΩC2n.Ultimately, from (36) and (39), an asymptotic OP expression for PD2 in (29), we have
(36)PD2∞=θΩA2M2.


## 3.1.1. Outage Probability atD1

Based on [4], the RVs’ cumulative distribution functions (CDF) and, correspondingly, can be expressed by
(19)FAiγthi=1−exp−γthiΩAi,(20)FBn∗γthi=1−exp−γthiΩBnN=1−∑n=1NnN−1n−1exp−γthiΩBn,(21)FCin∗γthi=1−exp−γthiΩCin,whereΩAi=ρΩ1,Di,ΩBn=ρΩBSUAVn∗,ΩCin=ρΩUAVn∗Di represent the average SNR of the links, respectively. According to the NOMA principle, one outage event happens if there is indirect transmission or no successful forward sending. Hence, the OP at D1 is given by
(22)PD1=PrγD1<γth1=Prmaxγ1,D1,γUAVnD1<γth1=Prγ1,D1<γth1,γUAVnD1<γth1=Fγ1,D1γth1⏟I1FγUAVn∗D1γth1.⏟I2Theorem 1 The OP atD1 can be derived as (see (23)).
(23)PD1=1−exp−γ~th1ΩA11−∑n=1NNn−1n−1exp−σnGEΩBn+1ΩC1n2αK12α,
whereK1. denotes the first-order modified Bessel function of the second kind ([34], Eq.(3.324.1)), α=nσ1+σGE/ΩBnΩC1n, σ=γth1/a1GE−a2GEγth1, and σ=γth1/a1GE−a2GEγth1 with a1>a2γth1.Proof.
See AppendixA.


## 3.1.2. Outage Probability atD2

BecauseD2 needs to decode the signal of the first D1, D2 will be outage if both the first and the second stage are outages. Therefore, OP at D2 can be formatted as
(24)PD2=Fγ1,D2γth2FγUAVn∗D2γth2.Theorem 2 The OP atD2 can be derived as (see (25)).
(25)PD2=1−exp−θΩA21−∑n=1NNn−1n−1exp−ωnGEΩBn+1ΩBn2βK12δ,
whereK1. denotes the first-order modified Bessel function of the second kind ([34], Eq.(3.324.1)), δ=nω1+ωGE/ΩBnΩC2n, λ1=γth2/a1GE−a2GEγth2, λ2=γth2/a2GE, and ω=maxλ1,λ2 with a1>a2γth1.Proof.
See AppendixB.


## 3.1.3. Asymptotic Outage Probability atD1

Applying the McLaurin expression, we get thatex≃1+x and K1x≃x−1 for small x. Hence, it turns out that
(26)2αK12α≃1.An expression for the asymptotic OP forPD1, whose exact analysis is presented in (23), is simplified as follows:
(27)1−exp−γth1a1−a2γth1ΩA1=γ~th1ΩA1,(28)exp−σnGEΩBn+1ΩC1n≃1−σkGEΩBn+1ΩC1n.Hence, we can obtain a fraction of the asymptotic approximation forPD1 in (24) as follows:
(29)M1~≃1−∑n=1NNn−1n−11−σkGEΩBn+1ΩC1n=1−∑n=1NNn−1n−1+∑k=1NNn−1n−1×σnGEΩBn+1ΩC1n.With∑n=1NNn−1n−1=1.We have(30)M1≃∑n=1NNn−1n−1σnΩBn+1ΩC1n.Ultimately, from (31) and (34), an asymptotic OP expression for PD1 in (25), we obtain
(31)PD1∞=γth1~ΩA1M1.


## 3.1.4. Asymptotic Outage Probability atD2

The asymptotic OP forPD2 is expressed the same as PD1, whose exact analysis is portrayed in (27); we have
(32)1−exp−γth2a1−a2γth2ΩA2=γ~th2ΩA2,(33)exp−ωnGEΩBn+1ΩC2n≃1−ωnGEΩBn+1ΩC2n.Thus, we can obtain a portion of the asymptotic approximation forPD2 in (28) as follows:
(34)M2~≃1−∑n=1NnN−1n−11−ωnGEΩBn+1ΩC2n=1−∑n=1NnN−1n−1+∑n=1NnN−1n−1×ωnGEΩBn+1ΩC2n.With∑n=1NNn−1n−1=1, we have,
(35)M2≃∑n=1NNn−1n−1ωnGEΩBn+1ΩC2n.Ultimately, from (36) and (39), an asymptotic OP expression for PD2 in (29), we have
(36)PD2∞=θΩA2M2.


## 3.2. System Throughput

In this case, the BS sends information at a constant target rate, rely on the performance of the OP because of the wireless fading channel. The system throughput of the NOMA indirect link is shown by as follows.


## 3.3. The System Throughput atD1

(37)τD1=1−PD1R1,wherePD1 is given in (23).


## 3.4. The System Throughput atD2

(38)τD2=1−PD2R2,wherePD2 is given in (25).


## 3.5. Energy Efficiency

EE is known as the ratio of sum throughput to total power consumed in the whole network system.


### 3.5.1. Energy Efficiency atD1

(39)EED1=2τD1ρ1+GEΩYn,whereτD1 is calculated by using (37).


### 3.5.2. Energy Efficiency atD2

(40)EED2=2τD2ρ1+GEΩYn,whereτD2 is calculated by using (38).


## 3.5.1. Energy Efficiency atD1

(39)EED1=2τD1ρ1+GEΩYn,whereτD1 is calculated by using (37).


## 3.5.2. Energy Efficiency atD2

(40)EED2=2τD2ρ1+GEΩYn,whereτD2 is calculated by using (38).


## 4. Simulation Results

This section confirms the derived analytical results shown by the previous sections. The distance between BS and IDs is standardized to unity, i.e.,ΩBS−>Di≈1, ΩBS−>Rn≈d−m, and ΩRn−>Di≈1−d−m. Table 2 lists the simulation parameters for assessment circumstances of the SWIPT based on multi-UAV cooperative NOMA systems.Table 2
Simulation parameters.
ParametersValueThe standardized distance between the BS andUAVnd=0.3The path-loss factorm=2The target rateR1=0.5,R2=0.25Energy harvesting efficiencyη=0.8Power splitting ratioβ=0.7Power allocation coefficient for signala1=0.8, a2=0.2Figure3 describes the OP at D1 with PSR protocol versus SNR without a direct link. Theoretically correct curves for the OP at D1 for NOMA are plotted according to the corresponding points (3.24) and (3.27). Exact probability curves are consistent with Monte-Carlo simulation results. The value ID1 is assumed to be N=1,2,10, and ΩSD1=0.Figure 3
Outage probability atD1 of PSR versus N=1,2,10 without a direct link.Figure4 shows the OP at D1 with PSR protocol versus SNR with direct link. Theoretically correct curves for the OP at ID1 for NOMA are plotted according to the corresponding points (3.24), (3.27), and (3.37). Assume that the value ID1 is N=1 and ΩSD1=1.Figure 4
Outage probability atD1 of PSR versus N=1 with direct link.Figure5 describes the OP at D2 with PSR protocol versus SNR indirect link. Theoretically correct curves for the OP of D2 for NOMA are plotted according to the corresponding points (3.24) and (3.27). Exact probability curves are consistent with Monte-Carlo simulation results. The value ID2 is assumed to be N=1,2,10, and ΩSD1=0.Figure 5
Outage probability atD2 of PSR versus N=1,2,10 without a direct link.Figure6 shows the OP at D2 with PSR protocol versus SNR with direct link. Theoretically correct curves for the OP at ID2 for NOMA are plotted according to the corresponding Equations (3.24), (3.27), and (3.37). Assume that the value ID2 is N=1 and ΩSD1=1.Figure 6
Outage probability atD2 of PSR versus N=1 with direct link.Figure7 shows the OP at D1 and D2 with PSR protocol versus SNR indirect link. Theoretically correct curves for the OPs at D1 and D2 for NOMA are plotted according to the Equations (3.24), (3.27), (3.28), and (3.30), respectively. The values at D1 and D2 are assumed N=3, and Ω1=Ω1=0.Figure 7
Outage probability at two IDsD1 and D2 of PSR versus N=3 without direct link.Figure8 depicts the OP at D1 and D2 of PSR protocol versus SNR indirect link. Assume that the values at D1 and D2 are N=3 and ΩSD1=ΩSD2=1.Figure 8
Outage probability at two IDsD1 and D2 of PSR versus N=3 with direct link.Figure9 shows the throughput at D1 and D2 of PSR protocol versus SNR with direct link. Theoretically correct curves for the throughput at D1 and D2 for NOMA are plotted according to the Equations (3.43) and (3.44). Throughput curves are consistent with the results of the Monte-Carlo simulation. The values at D1 and D2 are assumed N=3, and ΩSD1=ΩSD2=1.Figure 9
Throughput of two IDsD1 and D2 versus N=3 with direct link.Figure10 shows the energy efficiency at D1 and D2 of PSR protocol versus SNR with direct link. The theoretically correct curves for the energy efficiency at D1 and D2 for NOMA are plotted according to the points (3.45) and (3.46). Energy efficiency curves consistent with Monte-Carlo simulation results. Assume that the values at D1 and D2 are N=3 and ΩSD1=ΩSD2=1.Figure 10
Energy efficiency of two IDsD1 and D2 versus N=3 with direct link.


## 5. Conclusion

This paper has investigated the BS-based PSR protocol for the NOMA system. We used an AF rotary-wing relay network with cooperative UAV systems with UAV options. Closed-form expressions of OP for the two IDs were derived. Based on a simulation of the OP, throughput, EE, the results indicated that NOMA with the UAV option improves the efficiency increase by increasing the number of UAVs, but hardly any outage performance when the number of UAVs increases from 2 to 10 in the high SNR region. The indicates that the NOMA protocol with the UAVO will not need to use more than two UAVs. Numerical results confirm that our derived analytical results matched precisely with the Monte-Carlo simulation results in connection with all possible system parameters. Furthermore, we also can deploy the multiple antennas system at two IDs along with the investigation of Rayleigh Rician fading channel for enhancing the system performance that would be in our future works.



---

*Source: 3018225-2022-09-05.xml*