# NOMA-Based Overlay Cognitive Satellite-UAV-Terrestrial Networks with Multiple Primary Users

Authors: Rui Liu; Kefeng Guo; Kang An; Shibing Zhu; Haifeng Shuai
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

Satellite communication is becoming more and more significant in present and future communication systems for its unique advantages of strong survivability and seamless coverage, which can offset the defects of terrestrial communication such as being restricted by terrain and little coverage. Moreover, unmanned aerial vehicle (UAV)-assisted communication is considered as a promising development direction due to its flexibility and expansibility in the integrated satellite-terrestrial networks (ISTN). In addition, to overcome the spectrum shortage and low spectrum utilization problems, cognitive radio and nonorthogonal multiple access (NOMA) has been widely utilized to enhance spectrum efficiency, which is considered as the key technologies of the next generation communication. In this regard, our paper investigates the performance of cognitive satellite-UAV-terrestrial networks with NOMA scheme and multiple primary users. Specifically, the exact expressions of outage probability (OP) and ergodic capacity for both primary network and secondary network are derived. To gain further views, the asymptotic expression of OP and diversity orders for the two networks are provided. Finally, through numerical simulations, the correctness of the theoretical derivations is verified and the influences of critical variables on system indexes are also analyzed.


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## Body

## 1. Introduction

For the next generation wireless communication system, large coverage, high speed, low energy consumption, and high spectrum utilization are considered to be its main characteristics. Satellite communication (SatCom) is considered as an indispensable part, which can help realize the seamless connection of global communication and deal with emergencies in disaster areas or remote areas [1, 2]. Consequently, integrated satellite-terrestrial network (ISTN) is becoming a hot research direction over recent years, which can realize the complementarity of SatCom and terrestrial wireless communication [3]. Moreover, unmanned aerial vehicle (UAV)-assisted communication has attracted the interests of many experts, which can be rapidly deployed and adjusted in time [4]. Hence, the UAV-assisted ISTN, namely, integrated satellite-UAV-terrestrial network (ISUAVTN) has many practical applications in the situation of the surge of wireless terminals [5]. However, limited spectrum resources will restrict the development of ISUAVTN. In this regard, cognitive radio (CR) and nonorthogonal multiple access (NOMA) are utilized to solve the above problem by enhancing spectral efficiency (SE) [6–8].


### 1.1. Related Works

As a promising network architecture for the future communications, ISTN has momentous practical significance, which is able to overcome obstacles and geographical constraints [9–11]. In [10], the authors utilized auction mechanism to reduce the system consumption of ISTN, and Hungarian algorithm was applied to solve the optimization problem. An integrated multibeam method was designed to maximize aggregated rate of ISTN in [11]. The authors of [12] discussed the outage performance of an unlink ISTN with co-channel interference (CCI) and inherent hardware impairments (HIs), which utilized partial relay selection scheme to choose the optimal relay. In [13], the distinct adaptive transmission schemes were developed to serve ISTN with actual applications. A new dual-hop ISTN with HIs was investigated in [14], where a land mobile satellite (LMS) was regarded as the relay. The authors of [15] investigated the physical layer security of ISTN with multiple relays, users, and eavesdroppers, where opportunistic user relay selection scheme was adopted to enhance secrecy performance. In [16], the best-user and user-fairness scheduling schemes were proposed to enhance the outage performance of ISTN by utilizing the optimal beam-forming (BF) weight vectors of relay.Meeting the characteristics of low energy consumption and high efficiency for future communications, UAV communication can be quickly established and adjusted at low cost, which has been applied to ensure the communication of large-scale activities and disaster areas [17–19]. Considering the above advantages, many scientists and engineers have focused on the research of ISUAVTN. The authors of [20] discussed the energy efficient (EE) transmission of ISUAVTN, where total power constraint-based BF and per-antenna power constraint-based BF schemes were designed to maximize EE. In [21], a penalty function-based algorithm was designed to maximize the sum rate of ISUAVTN with rate-splitting multiple access (RSMA), which can satisfy large-scale transmission. The authors of [22] considered a cache-enabled ISUAVTN, which can decrease transmission delay and accelerate the updates of documents. Liu et al. [23] established an uplink ISUAVTN with multiple users, and a BF scheme was designed to improve the system performance. The authors of [24] discussed the uplink massive access of ISUAVTN, where a space division multiple access (SDMA) scheme was proposed to optimize the ergodic sum rate.Moreover, CR has been fully discussed in terrestrial wireless communication and has become a hot topic in ISTN. It can improve spectrum utilization by allowing secondary network (SN) to share the spectrum of primary network (PN), which is of great significance to the establishment of highly efficient network [25–27]. An EE-SE tradeoff index was designed to measure the performance of cognitive integrated satellite-vehicular networks in [27]; based on this, a power allocation scheme was developed. In [28], the authors investigated the performance of the cognitive ISTN with decode-and-forward (DF) protocol, in which the exact and asymptotic expressions of outage probability (OP) were derived. The authors of [29] established an overlay cognitive ISTN with multiple SNs, in which partial and opportunistic SN selection schemes were proposed to minimize the OP of PN. In [30], the authors investigated the outage performance of an underlay cognitive ISTN, where multiple primary users and HIs were considered. In [31], a BF scheme was developed to improve the security performance of a cognitive ISTN, where there existed multiple unknown eavesdroppers. The authors of [32] investigated the performance of an overlay cognitive ISTN with considering HIs, where an adaptive relay scheme was proposed to reduce OP.In addition, the NOMA scheme can also be adopted to overcome spectrum shortage, especially in the scenario of large-scale ends, which can economize access resources. In ISTN, the utilization of NOMA is able to save valuable time/frequency/code resources by sacrificing a little complexity of the receivers [33–35]. In [35], the authors applied bandwidth compression (BC) in NOMA-based ISTN to enhance spectrum utilization. The authors of [36] proposed a BF scheme based on an iterative algorithm to maximize the sum rate of NOMA-based ISTN, which considered the transmission quality of both satellite and terrestrial nodes. In [37], the authors discussed ergodic capacity (EC) of the uplink NOMA-based ISTN, but the exact closed-form expression of EC for the system was not provided. The authors of [38] considered a NOMA-based ISTN with multiple relays and HIs, in which secrecy outage probability (SOP) was derived to reveal the secrecy performance of two eavesdropping cases, namely, colluding case and noncolluding case. In [39], the authors investigated the performance of an underlay cognitive ISTN with NOMA scheme, in which the OP and EC were derived. The authors of [40] considered a NOMA-based cognitive ISTN with multiple SNs; the system performance was enhanced by adopting the partial SN selection scheme.


### 1.2. Main Contributions

Inspired by the abovementioned works, this paper considers a cognitive integrated satellite-UAV-terrestrial network (CISUAVTN) with NOMA scheme and multiple primary users, while all users are equipped with multiple antennas. Specifically, the major contributions of this paper are summarized as below:(1)
Firstly, a novel structure of overlay CISUAVTN with NOMA scheme and multiple primary users is built, where the communication of ISTN is assisted by secondary UAV. Besides, the satellite and UAV use the same frequency to enhance the SE.(2)
Secondly, considering the practical effects in signal propagation, such as rain attenuation and free path loss, the statistical properties of channels are provided. On this foundation, the exact expressions of OP and EC for both PN and SN are obtained.(3)
Thirdly, the asymptotic expression of OP for the two networks in high signal-to-noise ratio (SNR) regime is derived to obtain deeper opinions, based on which the diversity orders (DOs) for the two networks are also provided.(4)
Finally, to further comprehend the performance of our considered system, numerical results are provided. In addition, some observation results are also highlighted and analyzed.


### 1.3. Paper Organization

The composition of the remainder of the paper is shown as follows. Section2 provides the system model, channel model, and problem formulation, while Section 3 investigates the statistical properties of channels and performance of our considered system. Besides, numerical results are given in Section 4, which analyzes the effects of critical parameters on system performance. Finally, the whole paper is summed up in Section 5.Remark 1.
Jn· denotes the n-order first-kind Bessel function. · is absolute values of complex number scalars, and the Frobenius-norm of vectors are denoted as ·F. E· stands for the expectation operator and ·H represents conjugate transpose. ·n denotes the Pochhammer symbol (equation notation of [41]). IN×M is identity matrix with N rows and M columns and diag·,·,…,· is diagonal matrix. Gp,qm,nt|apbq is Meijer-G function (equation 9.301 of [41]).


## 1.1. Related Works

As a promising network architecture for the future communications, ISTN has momentous practical significance, which is able to overcome obstacles and geographical constraints [9–11]. In [10], the authors utilized auction mechanism to reduce the system consumption of ISTN, and Hungarian algorithm was applied to solve the optimization problem. An integrated multibeam method was designed to maximize aggregated rate of ISTN in [11]. The authors of [12] discussed the outage performance of an unlink ISTN with co-channel interference (CCI) and inherent hardware impairments (HIs), which utilized partial relay selection scheme to choose the optimal relay. In [13], the distinct adaptive transmission schemes were developed to serve ISTN with actual applications. A new dual-hop ISTN with HIs was investigated in [14], where a land mobile satellite (LMS) was regarded as the relay. The authors of [15] investigated the physical layer security of ISTN with multiple relays, users, and eavesdroppers, where opportunistic user relay selection scheme was adopted to enhance secrecy performance. In [16], the best-user and user-fairness scheduling schemes were proposed to enhance the outage performance of ISTN by utilizing the optimal beam-forming (BF) weight vectors of relay.Meeting the characteristics of low energy consumption and high efficiency for future communications, UAV communication can be quickly established and adjusted at low cost, which has been applied to ensure the communication of large-scale activities and disaster areas [17–19]. Considering the above advantages, many scientists and engineers have focused on the research of ISUAVTN. The authors of [20] discussed the energy efficient (EE) transmission of ISUAVTN, where total power constraint-based BF and per-antenna power constraint-based BF schemes were designed to maximize EE. In [21], a penalty function-based algorithm was designed to maximize the sum rate of ISUAVTN with rate-splitting multiple access (RSMA), which can satisfy large-scale transmission. The authors of [22] considered a cache-enabled ISUAVTN, which can decrease transmission delay and accelerate the updates of documents. Liu et al. [23] established an uplink ISUAVTN with multiple users, and a BF scheme was designed to improve the system performance. The authors of [24] discussed the uplink massive access of ISUAVTN, where a space division multiple access (SDMA) scheme was proposed to optimize the ergodic sum rate.Moreover, CR has been fully discussed in terrestrial wireless communication and has become a hot topic in ISTN. It can improve spectrum utilization by allowing secondary network (SN) to share the spectrum of primary network (PN), which is of great significance to the establishment of highly efficient network [25–27]. An EE-SE tradeoff index was designed to measure the performance of cognitive integrated satellite-vehicular networks in [27]; based on this, a power allocation scheme was developed. In [28], the authors investigated the performance of the cognitive ISTN with decode-and-forward (DF) protocol, in which the exact and asymptotic expressions of outage probability (OP) were derived. The authors of [29] established an overlay cognitive ISTN with multiple SNs, in which partial and opportunistic SN selection schemes were proposed to minimize the OP of PN. In [30], the authors investigated the outage performance of an underlay cognitive ISTN, where multiple primary users and HIs were considered. In [31], a BF scheme was developed to improve the security performance of a cognitive ISTN, where there existed multiple unknown eavesdroppers. The authors of [32] investigated the performance of an overlay cognitive ISTN with considering HIs, where an adaptive relay scheme was proposed to reduce OP.In addition, the NOMA scheme can also be adopted to overcome spectrum shortage, especially in the scenario of large-scale ends, which can economize access resources. In ISTN, the utilization of NOMA is able to save valuable time/frequency/code resources by sacrificing a little complexity of the receivers [33–35]. In [35], the authors applied bandwidth compression (BC) in NOMA-based ISTN to enhance spectrum utilization. The authors of [36] proposed a BF scheme based on an iterative algorithm to maximize the sum rate of NOMA-based ISTN, which considered the transmission quality of both satellite and terrestrial nodes. In [37], the authors discussed ergodic capacity (EC) of the uplink NOMA-based ISTN, but the exact closed-form expression of EC for the system was not provided. The authors of [38] considered a NOMA-based ISTN with multiple relays and HIs, in which secrecy outage probability (SOP) was derived to reveal the secrecy performance of two eavesdropping cases, namely, colluding case and noncolluding case. In [39], the authors investigated the performance of an underlay cognitive ISTN with NOMA scheme, in which the OP and EC were derived. The authors of [40] considered a NOMA-based cognitive ISTN with multiple SNs; the system performance was enhanced by adopting the partial SN selection scheme.


## 1.2. Main Contributions

Inspired by the abovementioned works, this paper considers a cognitive integrated satellite-UAV-terrestrial network (CISUAVTN) with NOMA scheme and multiple primary users, while all users are equipped with multiple antennas. Specifically, the major contributions of this paper are summarized as below:(1)
Firstly, a novel structure of overlay CISUAVTN with NOMA scheme and multiple primary users is built, where the communication of ISTN is assisted by secondary UAV. Besides, the satellite and UAV use the same frequency to enhance the SE.(2)
Secondly, considering the practical effects in signal propagation, such as rain attenuation and free path loss, the statistical properties of channels are provided. On this foundation, the exact expressions of OP and EC for both PN and SN are obtained.(3)
Thirdly, the asymptotic expression of OP for the two networks in high signal-to-noise ratio (SNR) regime is derived to obtain deeper opinions, based on which the diversity orders (DOs) for the two networks are also provided.(4)
Finally, to further comprehend the performance of our considered system, numerical results are provided. In addition, some observation results are also highlighted and analyzed.


## 1.3. Paper Organization

The composition of the remainder of the paper is shown as follows. Section2 provides the system model, channel model, and problem formulation, while Section 3 investigates the statistical properties of channels and performance of our considered system. Besides, numerical results are given in Section 4, which analyzes the effects of critical parameters on system performance. Finally, the whole paper is summed up in Section 5.Remark 1.
Jn· denotes the n-order first-kind Bessel function. · is absolute values of complex number scalars, and the Frobenius-norm of vectors are denoted as ·F. E· stands for the expectation operator and ·H represents conjugate transpose. ·n denotes the Pochhammer symbol (equation notation of [41]). IN×M is identity matrix with N rows and M columns and diag·,·,…,· is diagonal matrix. Gp,qm,nt|apbq is Meijer-G function (equation 9.301 of [41]).


## 2. System Model and Problem Formulation

As shown in Figure1, an overlay CISUAVTN framework with NOMA scheme is established, where a PN and a SN exist. In the PN, there are a source satellite A and K primary users Cin=1K, while the SN includes a UAV transmitter B and a terrestrial secondary user D. Considering some severe shadowing fading, it is assumed that A cannot communicate with Ci directly. Hence, overlay mode is adopted in our considered system, in which B forwards the signals of PN and transmits the expected signals of D simultaneously with DF protocol. Besides, each node works in half-duplex mode. In addition, both satellite and terrestrial nodes apply multiple antennas and all terrestrial nodes are located in the same satellite beam, while omnidirectional antenna is equipped at B due to power constraint (it is assumed that perfect CSI can be achieved through feedback and training, and it has been adopted in DVE-S2). Moreover, the K primary users are divided into K/2 two-user pairs, which have been adopted in many former works [33, 40] (too many users will lead to heavy interference or high receiver complexity, so this paper adopts two-user pair scheme to balance performance gain and communication cost). Thus, we assume C1 and C2 are assigned to the same pair.Figure 1
System model.In general, it is assumed that the satellite-aerial link is modeled by Shadowed-Rician (SR) fading and aerial-terrestrial links experience Rayleigh fading.


### 2.1. Channel Model

To get closer to the actual transmission scenario, the impacts of rain attenuation, free space loss, and satellite antenna gain are considered in our system; thus, the channel coefficient betweenA and B is given by(1)hab=Vabgab,where gab is the random channel coefficient of SR fading, Vab=ωabℓabεab/ζab, and ζab is the rain attenuation coefficient distributed as CNϑζ,σζ2, which undergoes lognormal random distribution.Besides,ωab represents the influence of free space loss with(2)ωab=vabfab21dab2+dc2,where vab=c/4π with c denoting the speed of light, fab represents the carrier frequency, dab≈35786km, and dc denotes the distance between the center of the satellite beam and the UAV.Moreover,(3)ℓab≃ℓmax−2.5×10−3dbθη2,0°<θ<θ1,2+15logdbη,θ1<θ<θ2,32−25logθ,θ2<θ<48°,−10,48°<θ<180°,denotes the antenna gain of UAV, where ℓmax is the maximum of ℓab, db represents antenna diameter of B, η is the signal wavelength, θ denotes the off-boresight angle, θ1=20η/dbℓmax−2+15logdb/η, and θ2=15.85db/η−0.6.In addition, the antenna gain of satellite is given by(4)εab=εmaxJ1t2t+36J3tt32,where εmax is the maximum of εab and t=2.70123sinϖ/sinϖ3dB with ϖ being the angle between UAV and satellite beam center and ϖ3dB denoting the 3 dB angle of ϖ.Furthermore, theNe×1 channel vectors between UAV and terrestrial nodes are given by(5)hbe=Tbegbe,where the subscript e=c1,c2,d represents destinations C1, C2, and D, Ne is the number of antennas for user e, and gbe denotes the channel complex vector of Rayleigh fading. Tbe can be represented as(6)Tbe=1220lgλ−10ℐlgdbe−20lg4π,where λ is the center wavelength of the signal carrier, ℐ is the path loss factor which ranges from 2 to 4, and dbe is the distance between UAV and terrestrial nodes.


### 2.2. Signal Model

Because the system realizes communication with the help of UAV, the whole transmission process includes two time periods. In the first time period,A transmits the integrated signal to B by utilizing superposition coding technique (SCT), which is expected for terrestrial primary users and given by(7)xa=αPax1+1−αPax2,where α is the power allocation coefficient of primary signal, Pa denotes the transmit power of satellite, and x1 and x2 represent the target signal of C1 and C2, respectively, whose expectations are equal to 1. Consequently, the received signal at B can be expressed as (to simplify the analysis, hardware impairments and decoding errors have not been considered in this paper, which will be considered in our future work)(8)yb=habxa+nb,where nb is the additive white Gaussian noise (AWGN) with CN0,σb2.In the second time period,B transmits the desired signal of D and the decoded signal from A to all terrestrial users simultaneously; the combined signal is given by(9)sb=βPbαx1+1−αx2+1−βPbxb,where β is the power split coefficient of B, Pb is the transmit power of the UAV, and xb is the signal D expected with Exb2=1. Thus, we can obtain the received signal at terrestrial nodes as(10)ybe=wbeHhbesb+wbeHne,where wbe=hbe/hbeF is the Ne×1 receive BF weight vector and ne∼CN0,σeINe×1 stands for the Ne×1 AWGN vector. In this study, we assume that hbc1F<hbc2F; thus, α∈0.5,1.


### 2.3. Problem Formulation

According to the above illustration, the end-to-end signal-to-interference plus noise ratio (SINR) can be obtained.Firstly,B decodes x1 with treating x2 as interference; then, we can get the SINR of x1 at B as(11)γab1R=αγab1−αγab+1,where γab=γ¯abhab2 and γ¯ab=Pa/σb2 is the average SNR of A−B link.After that,x1 is eliminated by B and x2 is decoded; thus, the SINR of x2 at B is given by(12)γab2R=1−αγab.In the users’ end,C1 decodes its expected signal as regarding other signal as in-band interference; then, we can get the SINR by detecting x1 at C1 as(13)γbc1R=αβγbc1μ1γbc1+1,where μ1=1−αβ+1−β, γbc1=γ¯bc1hbc1F2, and γ¯bc1=Pb/σc12.Recalling the NOMA scheme adopted in our proposed system, successive interference cancellation (SIC) is utilized inC2; thus, C2 decodes x1 at first, and x2 is treated as CCI. Therefore, the SINR of x1 at C2 can be represented as(14)γbc1⟶2R=αβγbc2μ1γbc2+1,where γbc2=γ¯bc2hbc2F2 and γ¯bc2=Pb/σc22.Then,x1 is cleared up by C2 from ybc2 and x2 is decoded; we can derive the SINR by discovering x2 at C2 as(15)γbc2R=1−αβγbc2μ2γbc2+1,where μ2=1−β.In addition, the SINR ofxb at D is given by(16)γbdR=1−βγbdβγbd+1,where γbd=γ¯bdhbdF2 and γ¯bd=Pb/σd2.


## 2.1. Channel Model

To get closer to the actual transmission scenario, the impacts of rain attenuation, free space loss, and satellite antenna gain are considered in our system; thus, the channel coefficient betweenA and B is given by(1)hab=Vabgab,where gab is the random channel coefficient of SR fading, Vab=ωabℓabεab/ζab, and ζab is the rain attenuation coefficient distributed as CNϑζ,σζ2, which undergoes lognormal random distribution.Besides,ωab represents the influence of free space loss with(2)ωab=vabfab21dab2+dc2,where vab=c/4π with c denoting the speed of light, fab represents the carrier frequency, dab≈35786km, and dc denotes the distance between the center of the satellite beam and the UAV.Moreover,(3)ℓab≃ℓmax−2.5×10−3dbθη2,0°<θ<θ1,2+15logdbη,θ1<θ<θ2,32−25logθ,θ2<θ<48°,−10,48°<θ<180°,denotes the antenna gain of UAV, where ℓmax is the maximum of ℓab, db represents antenna diameter of B, η is the signal wavelength, θ denotes the off-boresight angle, θ1=20η/dbℓmax−2+15logdb/η, and θ2=15.85db/η−0.6.In addition, the antenna gain of satellite is given by(4)εab=εmaxJ1t2t+36J3tt32,where εmax is the maximum of εab and t=2.70123sinϖ/sinϖ3dB with ϖ being the angle between UAV and satellite beam center and ϖ3dB denoting the 3 dB angle of ϖ.Furthermore, theNe×1 channel vectors between UAV and terrestrial nodes are given by(5)hbe=Tbegbe,where the subscript e=c1,c2,d represents destinations C1, C2, and D, Ne is the number of antennas for user e, and gbe denotes the channel complex vector of Rayleigh fading. Tbe can be represented as(6)Tbe=1220lgλ−10ℐlgdbe−20lg4π,where λ is the center wavelength of the signal carrier, ℐ is the path loss factor which ranges from 2 to 4, and dbe is the distance between UAV and terrestrial nodes.


## 2.2. Signal Model

Because the system realizes communication with the help of UAV, the whole transmission process includes two time periods. In the first time period,A transmits the integrated signal to B by utilizing superposition coding technique (SCT), which is expected for terrestrial primary users and given by(7)xa=αPax1+1−αPax2,where α is the power allocation coefficient of primary signal, Pa denotes the transmit power of satellite, and x1 and x2 represent the target signal of C1 and C2, respectively, whose expectations are equal to 1. Consequently, the received signal at B can be expressed as (to simplify the analysis, hardware impairments and decoding errors have not been considered in this paper, which will be considered in our future work)(8)yb=habxa+nb,where nb is the additive white Gaussian noise (AWGN) with CN0,σb2.In the second time period,B transmits the desired signal of D and the decoded signal from A to all terrestrial users simultaneously; the combined signal is given by(9)sb=βPbαx1+1−αx2+1−βPbxb,where β is the power split coefficient of B, Pb is the transmit power of the UAV, and xb is the signal D expected with Exb2=1. Thus, we can obtain the received signal at terrestrial nodes as(10)ybe=wbeHhbesb+wbeHne,where wbe=hbe/hbeF is the Ne×1 receive BF weight vector and ne∼CN0,σeINe×1 stands for the Ne×1 AWGN vector. In this study, we assume that hbc1F<hbc2F; thus, α∈0.5,1.


## 2.3. Problem Formulation

According to the above illustration, the end-to-end signal-to-interference plus noise ratio (SINR) can be obtained.Firstly,B decodes x1 with treating x2 as interference; then, we can get the SINR of x1 at B as(11)γab1R=αγab1−αγab+1,where γab=γ¯abhab2 and γ¯ab=Pa/σb2 is the average SNR of A−B link.After that,x1 is eliminated by B and x2 is decoded; thus, the SINR of x2 at B is given by(12)γab2R=1−αγab.In the users’ end,C1 decodes its expected signal as regarding other signal as in-band interference; then, we can get the SINR by detecting x1 at C1 as(13)γbc1R=αβγbc1μ1γbc1+1,where μ1=1−αβ+1−β, γbc1=γ¯bc1hbc1F2, and γ¯bc1=Pb/σc12.Recalling the NOMA scheme adopted in our proposed system, successive interference cancellation (SIC) is utilized inC2; thus, C2 decodes x1 at first, and x2 is treated as CCI. Therefore, the SINR of x1 at C2 can be represented as(14)γbc1⟶2R=αβγbc2μ1γbc2+1,where γbc2=γ¯bc2hbc2F2 and γ¯bc2=Pb/σc22.Then,x1 is cleared up by C2 from ybc2 and x2 is decoded; we can derive the SINR by discovering x2 at C2 as(15)γbc2R=1−αβγbc2μ2γbc2+1,where μ2=1−β.In addition, the SINR ofxb at D is given by(16)γbdR=1−βγbdβγbd+1,where γbd=γ¯bdhbdF2 and γ¯bd=Pb/σd2.


## 3. Performance Analysis

In this section, the statistical properties of SR fading and Rayleigh fading are provided. On this basis, the exact expressions of OP for both primary network and secondary network are derived. Besides, we derive the asymptotic OP of the two networks in high SNR regime to obtain further insights. Finally, the exact ECs of the two networks are obtained.


### 3.1. Statistical Properties of Channels

Firstly, the probability distribution function (PDF) and cumulative distribution function (CDF) of SR fading and Rayleigh fading are obtained. From [42], the PDF of gab is given by(17)fgab2x=αabe1−βabxF1mab;1;δabx,where αab≜1/2bab2babmab/2babmab+Ωabmab, βab≜1/2bab, and δab≜Ωab/2bab2babmab+Ωab. mab represents the Nakagami-m parameter which is always greater than 0, and 2bab is the average power of the multi-path part, while Ωab is that of line of sight (LOS) part.Under the situation thatmab is an integer, by using equation 07.20.03.009.01 of [43] and equation 07.02.03.0014.01 of [43], F11mab;1;δabx is represented as(18)F11mab;1;δabx=e−δabx∑n=0mab−1−δabn1−mabnn!2xn.According to (17) and (18), the PDF of gab can be rewritten as(19)fgab2x=αabe−βab−δabx∑n=0mab−1−δabn1−mabnn!2xn.From (1) and γab=γ¯abhab2, we can get the PDF of γab as(20)fγabx=αab∑n=0mab−1ξnxne−Δabx,where Δab=βab−δab/γ¯ab and(21)ξn=−δabn1−mabnn!2Vab2γ¯abn+1.By utilizing equation 3.351.2 of [41], the CDF of γab is given by(22)Fγabx=1−αab∑n=0mab−1∑t=0nn!ξnt!Δabn−t+1xte−Δabx.From [39, 44], the PDF and CDF of γbe can be expressed as, respectively,(23)fγbex=∑i=1ρΛbe∑j=1δiΛbeΞi,jΛbeλi−jj−1!xj−1e−x/λi,(24)Fγbex=1−∑i=1ρΛbe∑j=1δiΛbe∑t=0j−1Ξi,jΛbet!xλite−x/λi,where λii=1Ne is the average SNR of aerial-terrestrial links, Λbe=diagλ1,λ2,…,λNe, ρΛbe denotes the amount of different diagonal elements of Λbe, λρΛbe<⋯<λ2<λ1 are the different diagonal elements in ascending sequence, δiΛbe is the multiplicity of λi, and Ξi,jΛbe represents the i,jth characteristic coefficient of Λbe.


### 3.2. OP

OP can well evaluate the performance of the system, and in this paper, we define the OP as the probability of the instantaneous capacity for any nodes lower than its excepted capacity.


#### 3.2.1. OP of PN

From the definition of OP, the OP of PN can be expressed as(25)Poutp=1−Pr12log21+γab1R≥R1,12log21+γab2R≥R2Pr12log21+γbc1R≥R1,12log21+γbc1⟶2R≥R1×Pr12log21+γbc2R≥R2.Then, by lettingγ1=22R1−1 and γ2=22R2−1, (25) can be rewritten as(26)Poutp=1−Prγab1R≥γ1,γab2R≥γ2Prγbc1R≥γ1,γbc1⟶2R≥γ1,γbc2R≥γ2.By substituting (11)–(15) into (26), we can obtain(27)Poutp=1−1−Fγabτmax1−Fγbc1φ11−Fγbc2φmax,where τmax=maxτ1,τ2, τ1=γ1/α−γ11−α, τ2=γ2/1−α, φmax=maxφ1,φ2, φ1=γ1/αβ−μ1γ1, and φ2=γ2/1−αβ−μ2γ2.At last, by taking (22) and (24) into (27), the final expression of OP for PN is obtained as(28)Poutp=1−αab∑n=0mab−1∑t=0nn!ξnt!Δabn−t+1τmaxte−Δabτmax∑i1=1ρΛbc1∑j1=1δi1Λbc1∑t1=0j1−1Ξi1,j1Λbc1t1!φ1λi1t1e−φ1/λi1×∑i2=1ρΛbc2∑j2=1δi2Λbc1∑t2=0j2−1Ξi2,j2Λbc1t2!φmaxλi2t2e−φmax/λi2.


#### 3.2.2. OP of SN

Similar to the derivation of OP for PN, the OP for SN is given by(29)Pouts=1−Pr12log21+γab1R≥R1,12log21+γab2R≥R2Pr12log21+γbdR≥Rd=1−1−Fγabτmax1−Fγbdφd,where φd=γd/1−β−βγd and γd=22Rd−1. By utilizing (22) and (24) into (29), we can obtain(30)Pouts=1−αab∑n=0mab−1∑t=0nn!ξnt!Δabn−t+1τmaxte−Δabτmax×∑i=1ρΛbd∑j=1δiΛbd∑t1=0j−1Ξi,jΛbdt1!φdλit1e−φd/λi.


### 3.3. Asymptotic OP

To achieve deeper insights, we discuss the asymptotic OP in high SNR regime.


#### 3.3.1. Asymptotic OP of PN

Firstly, in high SNR regime, the CDF ofγab and γbe are approximately represented as(31)Fγabx≜αabxγ¯a,(32)Fγbex≜1Ne!xγ¯bNe.By substituting (31) and (32) into (27), the asymptotic expression of OP for PN is derived as(33)Poutp⟶∞=αabτmaxγ¯a,Nc1>1,Nc2>1,αabτmaxγ¯a+1Nc1!φ1γ¯bNc1,Nc1=1,Nc2>1,αabτmaxγ¯a+1Nc2!φmaxγ¯bNc2,Nc1>1,Nc2=1,αabτmaxγ¯a+1Nc1!φ1γ¯bNc1+1Nc2!φmaxγ¯bNc2,Nc1=1,Nc2>1.From (33), the DO of PN can be clearly obtained as DOp=min1,Nc1,Nc2.


#### 3.3.2. Asymptotic OP of SN

With the similar method to derive asymptotic OP of PN, we can get the asymptotic expression of OP for SN as(34)Pouts⟶∞=αabτmaxγ¯a,Nd>1,αabτmaxγ¯a+1Nc1!φ1γ¯bNc1,Nd=1.Besides, the DO of SN isDOs=min1,Nd.


### 3.4. EC

EC is also a momentous index in transmission system, which is defined as the time average of the maximal transmission capacity from the transmitter to the receiver under all fading conditions.


#### 3.4.1. EC of PN

The EC of PN is defined as the minimal EC of the satellite-aerial link and aerial-terrestrial links (equation 19 of [45]), which can be expressed as(35)EC=minECab,ECbc,where ECab and ECbc are the EC of satellite-aerial link and aerial-terrestrial links, respectively. To get the final expression of EC for PN, we should derive ECab and ECbc at first.Theorem 1.
The exact expression ofECab can be expressed as(36)ECab=12ln2αab∑n=0mab−1ξnΔabn+1G2,33,1Δab|0,11+n,1,1.Proof.
See AppendixA.Theorem 2.
The exact expression ofECbc can be expressed as(37)ECbc=12ln2∑i1=1ρΛbc1∑j1=1δi1Λbc1Ξi1,j1Λbc11j1−1!G2,33,11λi1|0,1j1,0,0−G2,33,11μ1λi1|0,1j1,0,0+∑i2=1ρΛbc2∑j2=1δi2Λbc2Ξi2,j2Λbc21j2−1!G2,33,11λi2|0,1j2,0,0−G2,33,11μ2λi2|0,1j2,0,0.Proof.
See AppendixB.Finally, by taking (36) and (37) into (35), we can obtain the final EC of PN.


#### 3.4.2. EC of SN

Theorem 3.
The exact expression of EC for SN can be represented as(38)ECSN=12ln2∑id=1ρΛbd∑jd=1δidΛbdΞid,jdΛbd1jd−1!G2,33,11λid|0,1jd,0,0−G2,33,11βλid|0,1jd,0,0.Proof.
The proof is similar to AppendixB, and the detailed process is omitted here.


## 3.1. Statistical Properties of Channels

Firstly, the probability distribution function (PDF) and cumulative distribution function (CDF) of SR fading and Rayleigh fading are obtained. From [42], the PDF of gab is given by(17)fgab2x=αabe1−βabxF1mab;1;δabx,where αab≜1/2bab2babmab/2babmab+Ωabmab, βab≜1/2bab, and δab≜Ωab/2bab2babmab+Ωab. mab represents the Nakagami-m parameter which is always greater than 0, and 2bab is the average power of the multi-path part, while Ωab is that of line of sight (LOS) part.Under the situation thatmab is an integer, by using equation 07.20.03.009.01 of [43] and equation 07.02.03.0014.01 of [43], F11mab;1;δabx is represented as(18)F11mab;1;δabx=e−δabx∑n=0mab−1−δabn1−mabnn!2xn.According to (17) and (18), the PDF of gab can be rewritten as(19)fgab2x=αabe−βab−δabx∑n=0mab−1−δabn1−mabnn!2xn.From (1) and γab=γ¯abhab2, we can get the PDF of γab as(20)fγabx=αab∑n=0mab−1ξnxne−Δabx,where Δab=βab−δab/γ¯ab and(21)ξn=−δabn1−mabnn!2Vab2γ¯abn+1.By utilizing equation 3.351.2 of [41], the CDF of γab is given by(22)Fγabx=1−αab∑n=0mab−1∑t=0nn!ξnt!Δabn−t+1xte−Δabx.From [39, 44], the PDF and CDF of γbe can be expressed as, respectively,(23)fγbex=∑i=1ρΛbe∑j=1δiΛbeΞi,jΛbeλi−jj−1!xj−1e−x/λi,(24)Fγbex=1−∑i=1ρΛbe∑j=1δiΛbe∑t=0j−1Ξi,jΛbet!xλite−x/λi,where λii=1Ne is the average SNR of aerial-terrestrial links, Λbe=diagλ1,λ2,…,λNe, ρΛbe denotes the amount of different diagonal elements of Λbe, λρΛbe<⋯<λ2<λ1 are the different diagonal elements in ascending sequence, δiΛbe is the multiplicity of λi, and Ξi,jΛbe represents the i,jth characteristic coefficient of Λbe.


## 3.2. OP

OP can well evaluate the performance of the system, and in this paper, we define the OP as the probability of the instantaneous capacity for any nodes lower than its excepted capacity.


### 3.2.1. OP of PN

From the definition of OP, the OP of PN can be expressed as(25)Poutp=1−Pr12log21+γab1R≥R1,12log21+γab2R≥R2Pr12log21+γbc1R≥R1,12log21+γbc1⟶2R≥R1×Pr12log21+γbc2R≥R2.Then, by lettingγ1=22R1−1 and γ2=22R2−1, (25) can be rewritten as(26)Poutp=1−Prγab1R≥γ1,γab2R≥γ2Prγbc1R≥γ1,γbc1⟶2R≥γ1,γbc2R≥γ2.By substituting (11)–(15) into (26), we can obtain(27)Poutp=1−1−Fγabτmax1−Fγbc1φ11−Fγbc2φmax,where τmax=maxτ1,τ2, τ1=γ1/α−γ11−α, τ2=γ2/1−α, φmax=maxφ1,φ2, φ1=γ1/αβ−μ1γ1, and φ2=γ2/1−αβ−μ2γ2.At last, by taking (22) and (24) into (27), the final expression of OP for PN is obtained as(28)Poutp=1−αab∑n=0mab−1∑t=0nn!ξnt!Δabn−t+1τmaxte−Δabτmax∑i1=1ρΛbc1∑j1=1δi1Λbc1∑t1=0j1−1Ξi1,j1Λbc1t1!φ1λi1t1e−φ1/λi1×∑i2=1ρΛbc2∑j2=1δi2Λbc1∑t2=0j2−1Ξi2,j2Λbc1t2!φmaxλi2t2e−φmax/λi2.


### 3.2.2. OP of SN

Similar to the derivation of OP for PN, the OP for SN is given by(29)Pouts=1−Pr12log21+γab1R≥R1,12log21+γab2R≥R2Pr12log21+γbdR≥Rd=1−1−Fγabτmax1−Fγbdφd,where φd=γd/1−β−βγd and γd=22Rd−1. By utilizing (22) and (24) into (29), we can obtain(30)Pouts=1−αab∑n=0mab−1∑t=0nn!ξnt!Δabn−t+1τmaxte−Δabτmax×∑i=1ρΛbd∑j=1δiΛbd∑t1=0j−1Ξi,jΛbdt1!φdλit1e−φd/λi.


## 3.2.1. OP of PN

From the definition of OP, the OP of PN can be expressed as(25)Poutp=1−Pr12log21+γab1R≥R1,12log21+γab2R≥R2Pr12log21+γbc1R≥R1,12log21+γbc1⟶2R≥R1×Pr12log21+γbc2R≥R2.Then, by lettingγ1=22R1−1 and γ2=22R2−1, (25) can be rewritten as(26)Poutp=1−Prγab1R≥γ1,γab2R≥γ2Prγbc1R≥γ1,γbc1⟶2R≥γ1,γbc2R≥γ2.By substituting (11)–(15) into (26), we can obtain(27)Poutp=1−1−Fγabτmax1−Fγbc1φ11−Fγbc2φmax,where τmax=maxτ1,τ2, τ1=γ1/α−γ11−α, τ2=γ2/1−α, φmax=maxφ1,φ2, φ1=γ1/αβ−μ1γ1, and φ2=γ2/1−αβ−μ2γ2.At last, by taking (22) and (24) into (27), the final expression of OP for PN is obtained as(28)Poutp=1−αab∑n=0mab−1∑t=0nn!ξnt!Δabn−t+1τmaxte−Δabτmax∑i1=1ρΛbc1∑j1=1δi1Λbc1∑t1=0j1−1Ξi1,j1Λbc1t1!φ1λi1t1e−φ1/λi1×∑i2=1ρΛbc2∑j2=1δi2Λbc1∑t2=0j2−1Ξi2,j2Λbc1t2!φmaxλi2t2e−φmax/λi2.


## 3.2.2. OP of SN

Similar to the derivation of OP for PN, the OP for SN is given by(29)Pouts=1−Pr12log21+γab1R≥R1,12log21+γab2R≥R2Pr12log21+γbdR≥Rd=1−1−Fγabτmax1−Fγbdφd,where φd=γd/1−β−βγd and γd=22Rd−1. By utilizing (22) and (24) into (29), we can obtain(30)Pouts=1−αab∑n=0mab−1∑t=0nn!ξnt!Δabn−t+1τmaxte−Δabτmax×∑i=1ρΛbd∑j=1δiΛbd∑t1=0j−1Ξi,jΛbdt1!φdλit1e−φd/λi.


## 3.3. Asymptotic OP

To achieve deeper insights, we discuss the asymptotic OP in high SNR regime.


### 3.3.1. Asymptotic OP of PN

Firstly, in high SNR regime, the CDF ofγab and γbe are approximately represented as(31)Fγabx≜αabxγ¯a,(32)Fγbex≜1Ne!xγ¯bNe.By substituting (31) and (32) into (27), the asymptotic expression of OP for PN is derived as(33)Poutp⟶∞=αabτmaxγ¯a,Nc1>1,Nc2>1,αabτmaxγ¯a+1Nc1!φ1γ¯bNc1,Nc1=1,Nc2>1,αabτmaxγ¯a+1Nc2!φmaxγ¯bNc2,Nc1>1,Nc2=1,αabτmaxγ¯a+1Nc1!φ1γ¯bNc1+1Nc2!φmaxγ¯bNc2,Nc1=1,Nc2>1.From (33), the DO of PN can be clearly obtained as DOp=min1,Nc1,Nc2.


### 3.3.2. Asymptotic OP of SN

With the similar method to derive asymptotic OP of PN, we can get the asymptotic expression of OP for SN as(34)Pouts⟶∞=αabτmaxγ¯a,Nd>1,αabτmaxγ¯a+1Nc1!φ1γ¯bNc1,Nd=1.Besides, the DO of SN isDOs=min1,Nd.


## 3.3.1. Asymptotic OP of PN

Firstly, in high SNR regime, the CDF ofγab and γbe are approximately represented as(31)Fγabx≜αabxγ¯a,(32)Fγbex≜1Ne!xγ¯bNe.By substituting (31) and (32) into (27), the asymptotic expression of OP for PN is derived as(33)Poutp⟶∞=αabτmaxγ¯a,Nc1>1,Nc2>1,αabτmaxγ¯a+1Nc1!φ1γ¯bNc1,Nc1=1,Nc2>1,αabτmaxγ¯a+1Nc2!φmaxγ¯bNc2,Nc1>1,Nc2=1,αabτmaxγ¯a+1Nc1!φ1γ¯bNc1+1Nc2!φmaxγ¯bNc2,Nc1=1,Nc2>1.From (33), the DO of PN can be clearly obtained as DOp=min1,Nc1,Nc2.


## 3.3.2. Asymptotic OP of SN

With the similar method to derive asymptotic OP of PN, we can get the asymptotic expression of OP for SN as(34)Pouts⟶∞=αabτmaxγ¯a,Nd>1,αabτmaxγ¯a+1Nc1!φ1γ¯bNc1,Nd=1.Besides, the DO of SN isDOs=min1,Nd.


## 3.4. EC

EC is also a momentous index in transmission system, which is defined as the time average of the maximal transmission capacity from the transmitter to the receiver under all fading conditions.


### 3.4.1. EC of PN

The EC of PN is defined as the minimal EC of the satellite-aerial link and aerial-terrestrial links (equation 19 of [45]), which can be expressed as(35)EC=minECab,ECbc,where ECab and ECbc are the EC of satellite-aerial link and aerial-terrestrial links, respectively. To get the final expression of EC for PN, we should derive ECab and ECbc at first.Theorem 1.
The exact expression ofECab can be expressed as(36)ECab=12ln2αab∑n=0mab−1ξnΔabn+1G2,33,1Δab|0,11+n,1,1.Proof.
See AppendixA.Theorem 2.
The exact expression ofECbc can be expressed as(37)ECbc=12ln2∑i1=1ρΛbc1∑j1=1δi1Λbc1Ξi1,j1Λbc11j1−1!G2,33,11λi1|0,1j1,0,0−G2,33,11μ1λi1|0,1j1,0,0+∑i2=1ρΛbc2∑j2=1δi2Λbc2Ξi2,j2Λbc21j2−1!G2,33,11λi2|0,1j2,0,0−G2,33,11μ2λi2|0,1j2,0,0.Proof.
See AppendixB.Finally, by taking (36) and (37) into (35), we can obtain the final EC of PN.


### 3.4.2. EC of SN

Theorem 3.
The exact expression of EC for SN can be represented as(38)ECSN=12ln2∑id=1ρΛbd∑jd=1δidΛbdΞid,jdΛbd1jd−1!G2,33,11λid|0,1jd,0,0−G2,33,11βλid|0,1jd,0,0.Proof.
The proof is similar to AppendixB, and the detailed process is omitted here.


## 3.4.1. EC of PN

The EC of PN is defined as the minimal EC of the satellite-aerial link and aerial-terrestrial links (equation 19 of [45]), which can be expressed as(35)EC=minECab,ECbc,where ECab and ECbc are the EC of satellite-aerial link and aerial-terrestrial links, respectively. To get the final expression of EC for PN, we should derive ECab and ECbc at first.Theorem 1.
The exact expression ofECab can be expressed as(36)ECab=12ln2αab∑n=0mab−1ξnΔabn+1G2,33,1Δab|0,11+n,1,1.Proof.
See AppendixA.Theorem 2.
The exact expression ofECbc can be expressed as(37)ECbc=12ln2∑i1=1ρΛbc1∑j1=1δi1Λbc1Ξi1,j1Λbc11j1−1!G2,33,11λi1|0,1j1,0,0−G2,33,11μ1λi1|0,1j1,0,0+∑i2=1ρΛbc2∑j2=1δi2Λbc2Ξi2,j2Λbc21j2−1!G2,33,11λi2|0,1j2,0,0−G2,33,11μ2λi2|0,1j2,0,0.Proof.
See AppendixB.Finally, by taking (36) and (37) into (35), we can obtain the final EC of PN.


## 3.4.2. EC of SN

Theorem 3.
The exact expression of EC for SN can be represented as(38)ECSN=12ln2∑id=1ρΛbd∑jd=1δidΛbdΞid,jdΛbd1jd−1!G2,33,11λid|0,1jd,0,0−G2,33,11βλid|0,1jd,0,0.Proof.
The proof is similar to AppendixB, and the detailed process is omitted here.


## 4. Numerical Results

To testify the validity of our derivations, the simulation results are offered in this section. Particularly, we assume thatγ¯ab=γ¯bc1=γ¯bc2=γ¯bd=γ¯, σab2=σbc12=σbc22=σbd2=σ2, and Nc1=Nc2=Nd=N. Besides, the system and SR fading parameters mab,bab,Ωab are provided in Table 1, in detail [29].Table 1
Simulation parameters.
Parameter nameParameter valueSatelliteGEORain attenuationϑζ,σζ2(−3.125, 1.591)Carrier frequencyfab2 GHz3 dB angleθ3dB0.4°Maximal satellite gainεmax48 dBMaximal UAV gainℓmax4 dBCarrier bandwidthB15 MHzNoise temperatureT300°Variance of AWGNσ21Frequent heavy shadowing (FHS)(1, 0.063, 0.0007)Average shadowing (AS)(5, 0251, 0.279)Infrequent light shadowing (ILS)(10, 0.158, 1.29)Firstly, from the simulation results, we can clearly find that the Monte Carlo (MC) simulations results are in accordance with our theoretical results; thus, the effectiveness of the analysis in Section3 is demonstrated. Moreover, the exact and asymptotic OP coincides briefly in high SNR regime, which indicates that our asymptotic analysis is correct.Figure2 shows that OP of PN versus different numbers of antenna N with R1=R2=0.5b/s/Hz, α=0.67, and β=0.9. It can be easily seen that worse channel condition lead to the deterioration of outage performance. Besides, OP decreases with the number of antenna; this is because that more antennas will enhance the receiving capacity of the users. In addition, the increasing of average SNR will improve the outage performance.Figure 2
OP of PN versus different numbers of antenna,N.Figure3 depicts that OP of PN versus different power allocation coefficients α with setting γ¯=20dB, R1=R2=0.5b/s/Hz, N=3, and β=0.9. It is interesting that outage performance first enhances and then decreases with the growth of α. This is due to the fact that the OP can achieve minimum by adjusting power allocation coefficient.Figure 3
OP of PN versus different power allocation coefficients,α.Figure4 plots that OP of PN versus different target rates R1 and R2 with α=0.67, N=3, and β=0.9. It can be clearly observed that OP degrades with target rates. This is because that the decrease in system requirements will reduce the OP.Figure 4
OP of PN versus different target rates,R1 and R2.Figure5 illustrates OP of SN versus different number of antenna N with setting Rd=0.5b/s/Hz and β=0.9. We can find that the outage performance enhance in pace with N, which is similar to the results of PN.Figure 5
OP of SN versus different numbers of antenna,N.Figure6 shows that EC of PN versus different numbers of antenna N with α=0.67 and β=0.9. Obviously, better channel condition can improve the EC of system, which is coincident with outage performance. Furthermore, EC increases with γ¯, but the upward trend slows down and curves of different channel conditions coincide in high SNR regime. The reason is that the EC of second hop lower than that of first hop when average SNR is high, and ECbc is independent of SR fading parameters. In addition, the growth of N will enhance the system performance in high SNR regime, while the curves of different numbers of antenna overlap under low SNRs. It is because the changes of N have no impact on ECab, which is higher than ECbc in low SNR regime.Figure 6
EC of PN versus different numbers of antennaN.Figure7 depicts that EC of PN versus different power allocation coefficients α with setting γ¯=20dB and β=0.9. It can be clearly found that EC increases in pace with α under AS and ILS and is a fixed value under FHS. This is because the final ECs under AS and ILS are taken as ECbc in γ¯=20dB, while that under FHS is taken as ECab.Figure 7
EC of PN versus different power allocation coefficientsα.Figure8 plots that EC of PN versus different power spilt coefficients β with γ¯=20dB and α=0.67. We can observe that system performance enhances with the growth of β, which represents more power of B is allocated to transmit primary signal.Figure 8
EC of PN versus different power spilt coefficientsβ.Figure9 illustrates EC of SN versus different numbers of antenna N. As expected, EC increases with the number of antenna. Contrary to PN, EC of SN degrades with the improvement of β.Figure 9
EC of SN versus different numbers of antenna,N.


## 5. Conclusions

In this paper, a CISUAVTN with NOMA scheme and multiple primary users was established, in which a secondary UAV forwarded the signal of satellite to terrestrial users in the overlay mode. Considering the actual transmission loss, the system performance was discussed. Particularly, the closed-form expressions of OP for both PN and SN were provided. Besides, the asymptotic OP and DOs were derived to gain additional views. Moreover, the exact EC of the two networks were derived. According to numerical results, the better channel condition and larger number of antenna can enhance the system performance. In addition, the power allocation coefficient and power spilt coefficient can be optimized to get superior performance of PN and balance the performance of the two networks, respectively.



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