On performance analysis of NOMA-aided hybrid satellite terrestrial relay with application in small-cell network

Received September 25, 2020, accepted October 12, 2020, date of publication October 19, 2020, date of current version October 27, 2020. Digital Object Identifier 10.1109/ACCESS.2020.3032139 On Performance Analysis of NOMA-Aided Hybrid Satellite Terrestrial Relay With Application in Small-Cell Network NGOC-LONG NGUYEN 1, HONG-NHU NGUYEN1, ANH-TU LE 2, DINH-THUAN DO 3, (Senior Member, IEEE), AND MIROSLAV VOZNAK 1, (Senior Member, IEEE) 1Department of Telecommunications, VSB Technical University of Ostrava, 70833 Ostrava, Czech Republic 2Faculty of Electronics Technology, Industrial University of Ho Chi Minh City (IUH), Ho Chi Minh City 700000, Vietnam 3Department of Computer Science and Information Engineering, College of Information and Electrical Engineering, Asia University, Taichung 41354, Taiwan Corresponding author: Dinh-Thuan Do ([email protected]) This work was supported by the Czech Ministry of Education, Youth and Sports conducted at the VSB - Technical University of Ostrava under Grant SP2020/65. ABSTRACT Satellite communication systems need to be integrated with emerging small-cell network to provide seamless connectivity and high-speed broadband access for mobile users in future wireless networks. In this paper, we study a hybrid satellite-terrestrial relay system (HSTRS) employing small cell transmission under interference constraint with macro-cell users. To characterize such HSTRS-assisted small-cell network, Shadowed-Rician fading for satellite links and Nakagami-mfading for terrestrial links are adopted. We further deploy non-orthogonal multiple access (NOMA) to improve spectrum efficiency. To provide performance analysis, we derive exact formulas for outage probability and throughput of the considered HSTRS, and further examine its achievable diversity order. More importantly, we conduct the performance analysis by indicating performance gaps among two users, and such a gap depends on power allocation factors. We evaluate key performance metrics through the derived analytical expressions to provide useful framework of HSTRN and to characterize the impact of interference in different cells, and integer values of the per-hop fading severity parameters. The useful guidelines are introduced in the design of futuristic HSTRS for small-cell communications. INDEX TERMS Hybrid satellite-terrestrial systems, small-cell, outage probability, Shadowed-Rician fading. I. INTRODUCTION In past decades, satellite communication systems are widely deployed in various applications of broadcasting and navigation due to its broad coverage to terrestrial users [1]. Such systems have received considerable attentions from the research community [2], [3]. The transmission of the line of sight (LoS) link between source and a terrestrial destination in such systems is limited by obstacles related to the masking effect. When the satellite elevation’s angles are low or the terrestrial user is located indoor, it is reported that worse case caused by effects from obstacles. By exploiting relaying techniques to improve coverage and reliability, the particular work [1] proposed the hybrid satellite-terrestrial relay The associate editor coordinating the review of this manuscript and approving it for publication was Peng-Yong Kong . system (HSTRS) to reduce the masking effect. Presently, the HSTRS benefits to develop integrated technique by combining HSTRS and existing systems. For example, the authors in [4]–[6] presented amplify-and-forward (AF) relaying to improve the performance of HSTRS. While HSTRS has been studied with application of the decode-and-forward (DF) relaying mode [7] and [8]. The authors explored the impact of hardware imperfections on HSTRS, where a geosynchronous earth orbit (GEO) satellite sends its data to the terrestrial destination with the assistance of DF-aided terrestrial relays [9]. They derived expressions of the outage performance. The authors in [10] evaluated the delay-limited throughput of a HSTRS in hybrid automatic repeat request (HARQ) mode. In their system model, a satellite communicates with a user under the scenario of an AF terrestrial relay. Particularly, they provided the mathematical analysis for two cases, i.e. 188526 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 8, 2020 N.-L. Nguyen et al.: On Performance Analysis of NOMA-Aided Hybrid Satellite Terrestrial Relay the fixed gain AF relaying and the channel state information (CSI)-assisted protocols [10]. Sharma et al. [11] investigated a HSTRS where multiple DF three-dimensional (3-D) mobile unmanned aerial vehicle (UAV) relays assist a satellite to send information to a ground user equipment (UE). In other work, the secure performance at physical layer in a hybrid satellite and free-space optical (FSO) cooperative system is studied [12]. They derived exact analytical formula together with the asymptotic analysis for the average secrecy capacity and secrecy outage probability (SOP) for both cases of AF and DF relaying. However, the studies in [6]- [12] only considered hybrid terrestrial-satellite applied in traditional cellular networks. It is noted that the performance of such systems is inherently low due to the inefficient use for massive connections and higher coverage area. To overcome above difficulties, the non-orthogonal multiple access (NOMA) techniques have recently been proposed and applied to HSTRS [13]–[19]. In principle, NOMA systems studied in [13]–[15] allow multiple users to share the same resource such as the frequency, time, space, or code domain. The other benefits of NOMA include massive connectivity, high spectral efficiency and low delay. For example, considering as attractive attribute of NOMA, the requirements of fairness and spectrum efficiency can be satisfied by cognitive radio transmission [15]. In [16], the security and the reliability of the ambient backscatter (AmBC) NOMA systems are studied, where the base station is able to send information to two NOMA users while an eavesdropper still overhears main signal. In [17], [18] the benefits of unmanned aerial vehicle (UAV) are found in UAV-NOMA. Specifically, in multi-way relaying NOMA networks, multiple terrestrial users aim to communicate their mutual signals by enabling AF-aided UAV relay [18]. Further, [18] considered real situation of the residual hardware impairments (RHIs) at the transceivers. There exists some works integrating NOMA with HSTRNs [19]–[23]. The authors in [19] applied a user with better channel condition as a relay node and forwards signal to other users, thus alleviating the masking effect of users with poor channel conditions in heavy shadowing. The authors in [21] and [22] introduced NOMA to cognitive radio-based HSTRNs, which permits spectrum sharing in the manner of the underlay mode. The authors in [21] studied NOMA based HSTRN using cooperative transmission. Reference [21] and [22] extended previous works to architecture of spectrum sharing. In particular, they only considered the priority of primary user while the fairness between the primary network and the secondary network did not evaluate. The authors in [23] investigated the performance of an underlay cognitive hybrid satellite-terrestrial network which includes a primary satellite transmitter with corresponding terrestrial receiver while the secondary transmitter (ST) communicates with its paired users on the ground. In other emerging networks, a promising network architecture is known as the heterogeneous (Hetnet) cellular network. In such Hetnet-based cellular network, a macro cell typically coexists with some kinds of small cells, e.g., pico cells, femto cells and micro cells [24]. In heterogeneous cellular networks, expensive macro base station (MBS) needs assistance of a number of surrounding economical small base stations (SBSs) to expand the network coverage and capacity at a reduced expense [25]. Small-cell approach is better than the conventional macro-centric networks in term of capacity and coverage improvements [26]. Such system becomes an easy and cost-efficient deployment solution. Some other advanced technologies, such as full duplex (FD), caching and massive multiple-input and multiple-out (MIMO), are introduced to facilitate dense deployment of small cell base stations (SBSs) [27]. A small-cell network was studied in the context of Hetnet-based cellular networks for both downlink and uplink by introducing three techniques including full-duplex transmission mode, energy harvesting, and power domain-based NOMA schemes [28]. They derive analytical formula to evaluate the system’s performance in terms of the outage probability and throughput. A. RELATED WORK AND MOTIVATIONS The authors in [29] investigated a cooperative small-cell system containing Msmall-cell transmitters and Nrelays to exhibit the outage performance of opportunistic relaying scheme. A renewable energy-based resource allocation method was proposed for full-duplex small-cell networks [30]. They presented method namely an outage-aware power allocation scheme which is considered as an optimal transmission strategy for a two-way transmission between a base station and user equipment in one single small-cell network. Reference [31] explored a sleeping scheme in the 5G small-cell networks by enabling energy harvesting function. In addition, the cooperative caching and the energy consumption minimization problem are considered. To our best knowledge, recent work has not yet analyzed the performance of a small-cell HSTRS with the enabler of NOMA. This motivates us to study small-cell HSTRS relying on NOMA. Note that such a configuration can boost the performance of HSTRS, especially with extended coverage under bottleneck link behavior of traditional communications. B. OUR CONTRIBUTION Particularly, our main contributions can be outlined as follows: •We propose a small-cell HSTRS relying on NOMA and main analysis is based on system performance of small-cell users. The DF protocol adopted in relay to forward signals to improve performance of cell-edge users in the coverage of small-cell. We deploy the Shadowed-Rician fading model for the pertinent satellite links and Nakagami-mfaded channels model for the terrestrial links of the considered small-cell network. •The normal operation of small-cell network can achieved by satisfying the criterion for minimal impacts on performance of the macro-cell network network, and eventually, interference management between VOLUME 8, 2020 188527 N.-L. Nguyen et al.: On Performance Analysis of NOMA-Aided Hybrid Satellite Terrestrial Relay FIGURE 1. System model of small-cell HSTRS relying on NOMA. macro-cell and small-cell networks are guaranteed. To provide performance analysis, we first characterize the end-to-end signal-to-noise ratios (SNRs), then the closed-form expressions of the outage probability (OP) are derived for the two small-cell users. Hereby, we explore main factors affecting to performance gap among two small-cell users such as power allocation strategy applied to two such users. •To look at the diversity performance of the considered network, we further derive the asymptotic behavior of the derived formula of OP. In addition, we explore system performance in terms of both heavy shadowing (HS) and average shadowing (AS) scenarios related to the satellite links. As a result, more insights are provided to highlight the system performance. The rest of this paper is summarized as follows. In Section II, we elaborate the structure of small-cell HSTRS relying on NOMA, then we compute the end-to-end SNRs over considered channels. We characterize the satellite and terrestrial channels and analyze the OP performance of such small-cell network in Section III. Section IV provides the numerical and simulation results, and finally the conclusion is conducted in Section V. II. SYSTEM MODEL In this paper, a small-cell base station (SCB), a small-cell relay (SCR) and two small-cell user SUi(i∈ {1,2}) are considered to implement the advantage of NOMA, i.e. higher spectrum efficiency.1Furthermore, the small-cell network can be operated together with a macro-cell satellite (MCS) serving macro-cell users (MUs). The transmit power at the SCB and the SCR in the context of small-cell is limited by many factors [32]. These 1We limit our analysis to two-user model as the literature [19]- [21]. Similar analysis can be performed for the case of higher number of users. TABLE 1. The main denotations in the system model. factors partly depend on channels. In particular, we denote ψ=1 |hQM |2, then we have the transmit power at the SCB and the SCR are given by PSCQ =min ¯ PSCQ,PMψ,Q∈{B,R}.(1) In the first phase, the received signal at the SCR is formulated by ySCR =hBRpPSCB p81x1+p82x2 +pPMCShMRxM+nSCR.(2) To evaluate system metric, it need be computed the signalto-interferenceplus-noise ratio (SINR) at the SCR to detect signal x1. In particular, SINR is given by 0SCR→x1=PSCB |hBR|281 PSCB |hBR|282+PMCS |hMR|2+N0 .(3) By employing SIC, the SINR to detect x2at the SCR is given by 0SCR→x2=PSCB |hBR|282 PMCS |hMR|2+N0 .(4) In the second phase, the relay SCR transmits signal to the cell-edge users SUi. The received signal at SUiis given by ySUi=hRipPSCR p81x1+p82x2 +pPMCShMixM+nSUi.(5) The SINR measured at the SU1to detect signal x1is given by 0SU1→x1=PSCR |hR1|281 PSCR |hR1|282+PMCS |hM1|2+N0 .(6) 188528 VOLUME 8, 2020 N.-L. Nguyen et al.: On Performance Analysis of NOMA-Aided Hybrid Satellite Terrestrial Relay Then, the SINR at SU2for detecting of signal x1is expressed by 0SU2→x1=PSCR |hR2|281 PSCR |hR2|282+PMCS |hM2|2+N0 .(7) The user SU2benefits by SIC, then SINR to detect signal x2at SU2is given by 0SU2→x2=PSCR |hR2|282 PMCS |hM2|2+N0 .(8) In next section, we focus on main metric, outage probability (OP) and then throughput in delay-limited transmission mode is also provided. These metrics play important role in design relevant equipment for the considered system. III. PERFORMANCE ANALYSIS A. CHANNEL MODELS We adopt Shadowed-Rician fading model for the satellite links. In particular, the probability density function of |hMj|2 with j∈(R,1,2) is formulated by [4] f|hMj|2(x)=αMje−βMjx1F1mMj;1;δMjx,x>0,(9) where αMj =2bMjmMj 2bMjmMj+Mj mMj /2bMj,βMj =0.5bMj and δMj =Mj/2bMj2bMjmMj +Mj, with Mj and 2bMj represents the respective average power of the LOS and multi-path components, mMj is the fading severity parameter and 1F1(.) is the confluent hypergeometric function of the first kind [37, Eq. 9.210.1]. In this paper, we consider arbitrary integer-valued fading severity parameter [33]. Then, we can simplify (9) as f|hMj|2(x)=αMj mMj−1 X nMj=0 ζMj nMjxnMj e−9Mjx,(10) where ζMi nMj=(−1)nMj 1−mMjnMj δnMj Mj /nMj!2, (.)a is the Pochhammer symbol [37, p.xliii] and 9Mi =βMi −δMi. Thus, the cumulative distribution function (CDF) of |hMj|2is expressed by F|hMj|2(x)=1−αMj mMj−1 X nMj=0 ζMj nMj × nMj X q=0 nMj! q!9MjnMj−q+1xqe−9Mix.(11) The probability density function (PDF) and CDF of |hk|2 for k∈ {BR,BM,RM,R1,R2}are given respectively as f|hk|2(x)=xmk−1 0(mk)ωmk k e−x ωk,(12) and F|hk|2(x)=γ(mk,x/ωk) 0(mk) =1−e−x ωk mk−1 X nk=0 xnk ωnk knk!.(13) where ωk=λk mk,mkand λkdenotes the fading severity and average power, respectively. B. OUTAGE PERFORMANCE 1) OUTAGE PERFORMANCE OF SU1 To evaluate how the two edge-users work in the context of small-cell, we continue to look at the OP performance. The user SU1need to detect its signal x1. Based on conditions related to such outage event, the OP of user SU1is formulated by Px1=1−Pr min 0SCR→x1, 0SU1→x1, 0SU2→x1> γ1 =1−Pr 0SCR→x1> γ1 | {z } A1 ×Pr 0SU1→x1> γ1 | {z } A2 Pr 0SU2→x1> γ1 | {z } A3 ,(14) where γi=22Ri−1 is the threshold SNR corresponding to target rates Rifor two users; Rias the target rate of user SUi. Proposition 1: As a part of such OP, term A1can be expressed as (15), shown at the bottom of the next page. Proof: See Appendix A In term of computing of A2, substituting (6) into (14), we have A2=Pr |hR1|2>θ1ρS|hM1|2+1 ¯ρR ,¯ρR<ρM |hRM |2! +Pr |hR1|2>θ1|hRM |2ρS|hM1|2+1 ρM ,¯ρR>ρM |hRM |2!. (16) Similarly, A2can be calculated by A2 = mM1−1 X nM1=0 mR1−1 X nR1=0 nR1 X b=0nR1 bζM1(nM1) (nM1+b)!αM1 nR1!0(mRM ) × (ωR1¯ρR)nMR−nR1+b+1γ(mRM , ρM/ωRM ¯ρR)e−θ1 ¯ρBωR1 ρ−b Sθ−nR1 1(θ1ρS+9M1¯ρRωR1)nMR+b+1 +ρb SθnR1 1ωnR1 RM 9−nM1−b−1 M1(ρMωR1)mRM 0(nM1+b+1) (θ1ωRM +ωR1ρM)mRM +nR1 ×G1,1,1,1,0 1,[1:1],0,[1:1] ×    θ1ρSωRM 9M1(θ1ωRM +ωR1ρM) ωR1ωRM ¯ρR θ1ωRM +ωR1ρM  1+mRM +nR1 −nM1−b;1 −− 0;0       .(17) VOLUME 8, 2020 188529 N.-L. Nguyen et al.: On Performance Analysis of NOMA-Aided Hybrid Satellite Terrestrial Relay Moreover, we can write A3as A3 = mM2−1 X nM2=0 mR2−1 X nR2=0 nR2 X c=0nR2 cζM2(nM2) (nM2+c)!αM2 nR2!0(mRM ) × (ωR2¯ρR)nMR−nR2+c+1γ(mRM , ρM/ωRM ¯ρR)e−θ1 ¯ρBωR2 ρ−C Sθ−nR2 1(θ1ρS+9M2¯ρRωR2)nMR+c+1 +ρb SθnR2 1ωnR2 RM 9−nM2−c−1 M2(ρMωR2)mRM 0(nM2+c+1) (θ1ωRM +ωR2ρM)mRM +nR2 ×G1,1,1,1,0 1,[1:1],0,[1:1] ×    θ1ρSωRM 9M2(θ1ωRM +ωR2ρM) ωR2ωRM ¯ρR θ1ωRM +ωR2ρM  1+mRM +nR1 −nM2−c;1 −− 0;0       . (18) Finally, the closed-form expression of OP for user SU1can be obtained as below Px1=(1−A1×A2×A3,if :γ1<81 82 1,otherwise. (19) 2) OUTAGE PERFORMANCE OF SU2 Different from performance of SU1, user SU2is able to detect its signal for the first hop and the second hop based on achieved SINR, i.e. 0SCR→x2,0SU2→x2. In particular, the OP of user SU2is formulated by Px2=1−Pr min 0SCR→x2, 0SU2→x2> γ2 =1−Pr 0SCR→x2> γ2 | {z } ¯ A1 Pr 0SU2→x2> γ2. | {z } ¯ A2 (20) Proposition 2: The first term in (20) can be expressed as ¯ A1 = mMR−1 X nMR=0 mBR−1 X nBR=0 nBR X a=0nBR aζMR (nMR) (nMR +a)!αMR nBR!0(mBM ) × (ωBR ¯ρB)nMR−nBR+a+1γ(mBM , ρM/ωBM ¯ρB)e−θ2 ¯ρBωBR ρ−a Sθ−nBR 2(θ2ρS+9MR ¯ρBωBR)nMR+a+1 +ρa SθnBR 2ωnBR BM 9−nMR−a−1 MR (ρMωBR)mBM 0(nMR +a+1) (θ2ωBM +ωBRρM)mBM +nBR ×G1,1,1,1,0 1,[1:1],0,[1:1] ×    θ2ρSωBM 9MR(θ2ωBM +ωBRρM) ωBRωBM ¯ρB θ2ωBM +ωBRρM  1+mBM +nBR −nMR −a;1 −− 0;0       .(21) Proof: With the help of (1) and (4), we can write ¯ A1as ¯ A1 =Pr PSCB |hBR|282 PMCS |hMR|2+N0 > γ2! =Pr |hBR|2>θ2ρS|hMR|2+1 ¯ρB ,¯ρB<ρM |hBM |2! +Pr |hBR|2>θ2|hBM |2ρS|hMR|2+1 ρM ,¯ρB>ρM |hBM |2!, (22) where θ2=γ2 82. Similarly appendix A, the closed-form expression of ¯ A1can be obtained. The proof is completed. Similarly, ¯ A2is given as ¯ A2 = mM2−1 X nM2=0 mR2−1 X nR2=0 nR2 X c=0nR2 cζM2(nM2) (nM2+c)!αM2 nR2!0(mRM ) × (ωR2¯ρR)nMR−nR2+c+1γ(mRM , ρM/ωRM ¯ρR)e−θ2 ¯ρBωR2 ρ−C Sθ−nR2 2(θ2ρS+9M2¯ρRωR2)nMR+c+1 +ρb SθnR2 2ωnR2 RM 9−nM2−c−1 M2(ρMωR2)mRM 0(nM2+c+1) (θ2ωRM +ωR2ρM)mRM +nR2 ×G1,1,1,1,0 1,[1:1],0,[1:1] ×    θ2ρSωRM 9M2(θ2ωRM +ωR2ρM) ωR2ωRM ¯ρR θ2ωRM +ωR2ρM  1+mRM +nR1 −nM2−c;1 −− 0;0       . (23) Thus, the closed-form expression of OP for user SU2is obtained by Px2=1−¯ A1ׯ A2.(24) Remark 1: In this section, we provide our analytical result on OP. Although, these expressions of OP are complicated, A1= mMR−1 X nMR=0 mBR−1 X nBR=0 nBR X a=0nBR aζMR (nMR) (nMR +a)!ρa SαMRθnBR 1 nBR!0(mBM ) (ωBR ¯ρB)nMR−nBR+a+1γ(mBM , ρM/ωBM ¯ρB)e−θ1 ¯ρBωBR (θ1ρS+9MR ¯ρBωBR)nMR+a+1 +ωnBR BM 9−nMR−a−1 MR (ρMωBR)mBM 0(nMR +a+1) (θ1ωBM +ωBRρM)mBM +nBR G1,1,1,1,0 1,[1:1],0,[1:1]     θ1ρSωBM 9MR (θ1ωBM +ωBRρM) ωBRωBM ¯ρB θ1ωBM +ωBRρM  1+mBM +nBR −nMR −a;1 −− 0;0       .(15) 188530 VOLUME 8, 2020 N.-L. Nguyen et al.: On Performance Analysis of NOMA-Aided Hybrid Satellite Terrestrial Relay TABLE 2. Channel parameters related to the satellite. TABLE 3. Table of main parameters in simulation. but main impacts rely on the transmit SNR at he small-cell base station and various fading scenarios. For the considered Shadowed-Rician fading for satellite links and Nakagami-m fading for terrestrial links, we further examine these related parameters in numerical simulations. It is predicted that power allocation factors lead to different performance of two small-cell users. To obtain more insight in term of the desired OP expressions, one can derive the expression for asymptotic OP for two users. We also obtain the achievable diversity order. Such findings are extra benefits to design of such network in practice. C. ASYMPTOTIC AND DIVERSITY OUTAGE BEHAVIOR ANALYSIS In this paper, we examine the peak interference constraint. In particular, PMis fixed value and only ¯ PSCQ becomes large in the high SNR region. The asymptotic behaviors of OP for user SU1in this case is presented as Proposition 3 below. Proposition 3: The asymptotic OP of SU1can be expressed as (25), shown at the bottom of the next bottom page. Proof: See Appendix B. Similar to the derivation reported in appendix B, the asymptotic of OP for user SU2can be obtained as (26), shown at the bottom of the next bottom page. Regarding the diversity order, we have such formula D= − lim ¯ρ→∞ log10 Pxi(¯ρ) log10 (¯ρ).,(27) It can be concluded that when SNR is larger, the diversity order is zero. We further check this result in numerical simulation section. It is useful insights in design of practical system. D. THROUGHPUT PERFORMANCE It is necessary to consider other metric of such system. In particular, the overall throughput can be achieved based on obtained OP derived for performance evaluation of two users. In delay-limited mode, at fixed target rates R1,R2the throughput can be obtained. According to obtained OPs, we can calculate the overall throughput as Ttotal =1−Px1R1+1−Px2R2.(28) IV. NUMERICAL RESULTS To provide mathematical analysis, it is necessary to simulate and illustrate for the proposed small-cell HSTRN relying on NOMA scheme. According main configuration, we set the shadowing scenarios of the satellite links hPj, including the heavy shadowing (HS) and average shadowing (AS) in Table 2 [35]. We further set ¯ρ= ¯ρB= ¯ρRand the parameters in Table 3. Moreover, we vary m=1 for the Nakagami-mfading related to terrestrial links. In these following figures, Monte-Carlo simulations are performed to validate the analytical results. Fig. 2 and Fig. 3 plot the OPs of two users in the considered HSTRS versus the transmit SNR at the MCB ¯ρand the transmit SNR at the SCB ρM, respectively. It is valuable result as analytical and Monte-Carlo curves are matched very tightly and it confirms the exactness of derived OP in this paper. It is clearly seen that the OP performance would be improved at high SNR region. The performance gap among two users is resulted by different power allocation factors. More specifically, the OP performance of SU2is better than that of SU1and two OPs of two users are still better than that of the OMA-based HSTRS. The reason is that the OMA-based HSTRS needs more time slots to transmit two consecutive signals x1,x2while only one time slot is served for NOMA-based HSTRS counterpart. Moreover, the asymptotic curves of OP is matched with the exact OP curves at high SNR regime. It is further confirmed that OP will be unchanged at high SNR. Such situation is consistent with diversity order found in previous section. In Fig. 3, similar trends of OP can be seen. In Fig. 4, we can see the impact of ρSon the OP performance of small-cell network. It can be explained that higher transmit power at MCB leads to limit the transmit power at SCB, then OP will reduce. The other trend of these OPs can be seen similarly with Fig. 2 and Fig. 3. In this experiment, ρS=5 exhibits the best performance of small-cell network in term of OP. Fig. 5 illustrates the OPs of the two users as varying average SNR at SCB from 0 to 50, where the satellite link undergoes HS case. Three cases of channel coefficients are m=1,2,3. The performance gap is still seen for these curves related OPs of two users. It is reported that the OPs of two users are best case as m=3. It is obvious to conclude that the improved channels result in better OP performance. Fig. 6 depicts the OPs of the two users against two crucial parameters, i.e., status of satellite links (HS or AF cases) and the transmit SNR at the SCB ¯ρ. From the figure, the OPs of two users in the case of HS are better that of AS. At the considered range of the transmit SNR at the SCB ¯ρ, performance gaps of two users in cases of HS and AS are similar. It is concluded that such OP depends on ¯ρand power allocation VOLUME 8, 2020 188531 N.-L. Nguyen et al.: On Performance Analysis of NOMA-Aided Hybrid Satellite Terrestrial Relay FIGURE 2. The outage probability versus ¯ ρ, where m=1, ρM=20dB, ρS=5dB and the satellite link is set HS case. factors rather than on the specific parameters of satellite links (HS or AS). Fig. 7 continues to confirm power allocation scheme affecting the OPs of two users. It is worth noting that the OP of user SU1depends mainly on 81. In particular, when we increase 81from 0.5 to 1, the OP performance of user SU1improve significantly. In the contrast, the OP performance of SU2is FIGURE 3. The outage probability versus ρM, with different values of ¯ ρ, where m=1, ρS=5dB and the satellite link is set HS case. definitely better than that of SU2at the point of 81=0.5, but such OP becomes worse afterward. The main reason is that 81plays important role in varying value of SINRs, then the corresponding OPs will be changed. Fig. 8 further provides the curves of the total throughput versus the transmit SNR at SCB ¯ρ, i.e. throughput for case R1=R2=0.5. It is clear from (28) that higher fixed target P∞ x1=1− 1− mMR−1 X nMR=0 mBR X nBR=0mBR nBR ζMR (nMR)ρnBR SαMR (nMR +nBR)! 0(mBR +1)0(mBM )9nMR+nBR+1 MR θ1 ωBR mBR ×  γmBM ,ρN ¯ρBωBM  ¯ρmBR B +0mSP +mR,ρM ¯ρBωBM ωBM ρMmBR    × 2 Y i=1 1− mMi−1 X nMi=0 mRi X nRi=0mRi nRi ζMi (nMi)ρnRi SαMi (nMi +nRi)! 0(mRi +1)0(mRM )9nMi+nRi+1 Mi θ1 ωRi mRi ×  γmRM ,ρM ¯ρRωRM  ¯ρmR R +0mRM +mRi,ρM ¯ρRωRM ωRM ρMmRi   .(25) P∞ x2=1− 1− mMR−1 X nMR=0 mBR X nBR=0mBR nBR ζMR (nMR)ρnBR SαMR (nMR +nBR)! 0(mBR +1)0(mBM )9nMR+nBR+1 MR θ2 ωBR mBR ×  γmBM ,ρN ¯ρBωBM  ¯ρmBR B +0mSP +mR,ρM ¯ρBωBM ωBM ρMmBR    × 1− mM2−1 X nM2=0 mR2 X nR2=0mR2 nR2ζM2(nM2)ρnR2 SαM2(nM2+nR2)! 0(mR2+1)0(mRM )9nM2+nR2+1 M2θ2 ωR2mR2 ×  γmRM ,ρM ¯ρRωRM  ¯ρmR R +0mRM +mR2,ρM ¯ρRωRM ωRM ρMmR2  .(26) 188532 VOLUME 8, 2020 N.-L. Nguyen et al.: On Performance Analysis of NOMA-Aided Hybrid Satellite Terrestrial Relay FIGURE 4. The outage probability versus ¯ ρ, with different values of ρS, where m=1, ρM=20dB and the satellite link is set HS case. FIGURE 5. The outage probability versus ¯ ρ, with different values of m, where ρM=20dB,ρS=5dB and the satellite link is set HS case. FIGURE 6. The outage probability versus ¯ ρ, with different channel parameter of satellite link, where ρS=20dB,ρS=5dB and m=2. rates lead to high throughput. When we increase ¯ρfrom 0 to 30, the throughput changes significantly. It is reported that the case of m=2 and HS indicates the best throughput FIGURE 7. The outage probability versus 81, with different values of ¯ ρ=ρM, where ρS=5dB,m=2, R1=R2=0.5 BPCU and the satellite link is set HS case. FIGURE 8. The throughput versus ¯ ρwith different channel parameter of satellite link and m, where R1=R2=0.5 BPCU, ρM=20dB and ρS=5dB. FIGURE 9. The throughput versus ¯ ρwith different channel parameter of satellite link and ρS, where R1=R2=0.5 BPCU, ρM=20dB and m=2. performance. The reason is that the throughput is computed based on the OPs. In similar viewpoint, Fig. 9 demonstrates VOLUME 8, 2020 188533 N.-L. Nguyen et al.: On Performance Analysis of NOMA-Aided Hybrid Satellite Terrestrial Relay how the transmit SNRs (ρS=10, and ρS=20 make the influence to throughput. V. CONCLUSION In this paper, we have studied the operation of small cell to provide reliability transmission for HSTRS. Such system includes a geostationary satellite, two terrestrial users following the principle of NOMA scheme and terrestrial relays. We considered system performance of small-cell to reduce the impact of operations related to macro-cell users. Regarding the outage performance of HSTRS, we derived closed-form and asymptotic expressions of outage probability of two small-cell users. It was shown that the outage probability of HSTRS can be improved by increasing transmit power at base station. Moreover, the outage performance of HSTRS can be enhanced by employing the NOMA scheme compared to that using OMA scheme. In future work, multiple antennas and multiple users can be deployed in such HSTRS. APPENDIX A With the help (1) and (3), the first term A1can be written as (29), shown at the bottom of the page, in which ρB=PSCB N0, ¯ρB=¯ PSCB N0,ρM=PM N0and ρS=PMCS N0. Then, B1is rewritten as B1 =Pr |hBR|2>θ1ρS|hMR|2+1 ¯ρB ,|hBM |2<ρM ¯ρB! =Pr |hBR|2>θ1ρS|hMR|2+1 ¯ρB! | {z } B1,1 Pr |hBM |2<ρM ¯ρB | {z } B1,2 . (30) where θ1=γ1 81−γ182. Moreover, B1,1can be calculated by B1,1=Pr |hBR|2>θ1ρS|hMR|2+1 ¯ρB! = ∞ Z0 ¯ F|hBR|2θ1(ρSz+1) ¯ρBf|hMR|2(z)dz,(31) where ¯ F|h|2(x)=1−F|h|2(x). With the help of (10) and (13), we have B1,1= mMR−1 X nMR=0 ζMR (nMR) mBR−1 X nBR=0 nBR X a=0nBR a ×αMRρa Se−θ1 ¯ρBωBR ωnBR BR nBR!θ1 ¯ρBnBR × ∞ Z0 znMR+ae−θ1ρS ¯ρBωBR +9MRzdz.(32) Based on [37, Eq. 3.351.3], the closed-form of B1,1is obtained as B1,1= mMR−1 X nMR=0 mBR−1 X nBR=0 nBR X a=0nBR aζMR (nMR)(nMR +a)! nBR! ×αMR (ωBR ¯ρB)nMR−nBR+a+1e−θ1 ¯ρBωBR ρ−a Sθ−nBR 1(θ1ρS+9MR ¯ρBωBR)nMR+a+1.(33) With the help of (13), B1,2is rewritten as B1,2=Pr |hBM |2<ρM ¯ρB =γ(mBM , ρM/ωBM ¯ρB) 0(mBM ).(34) Next, B2can be calculated by B2 =Pr |hBR|2>θ1|hBM |2ρS|hMR|2+1 ρM ,|hBM |2>ρM ¯ρB! = ∞ Z ρM ¯ρB f|hBM |2(x) ∞ Z0 f|hMR|2(y) ׯ F|hBR|2θ1x(ρSy+1) ρMdydx.(35) With the help (10), (11) and (12), we can rewrite (35) as B2= mMR−1 X nMR=0 mBR−1 X nBR=0 nBR X a=0nBR aζMR (nMR) 0(mBM ) A1=Pr PSCB |hBR|281 PSCB |hBR|282+PMCS |hMR|2+N0 > γ1! =Pr ¯ρB|hBR|281 ¯ρB|hBR|282+ρS|hMR|2+1> γ1,¯ρB<ρM |hBM |2! | {z } B1 +Pr ρM|hBR|281 ρM|hBR|282+|hBM |2ρS|hMR|2+1> γ1,¯ρB>ρM |hBM |2! | {z } B2 .(29) 188534 VOLUME 8, 2020