Enabling NOMA in Overlay Spectrum Sharing in Hybrid Satellite-Terrestrial Systems

In this paper, a hybrid satellite-terrestrial spectrum sharing system allows terrestrial secondary network to cooperate with a primary satellite network and to further provide higher spectrum efficiency. For massive connections design, we implement non-orthogonal multiple access (NOMA) technique to form cognitive radio based satellite-terrestrial (CR-NSHT) system relying on NOMA and further achieve more benefits compared with traditional schemes. The secondary network only remains its stable operation when the outage probability of such system is guaranteed, and thereby, to explore advantages of spectrum sharing opportunities. Considering Shadowed-Rician fading for satellite links, and Nakagami- $m$ as well as Rician fading for terrestrial links, we derive the closed-form expressions of the outage probability to evaluate the performance of secondary network. We consider further system performance metrics including ergodic capacity, energy efficiency and multi-user scenarios. We also demonstrate the impacts of power allocation factors, transmit signal-to-noise ratio (SNR) at the source, parameters of satellite links, target rates, and fading severity parameters on the system performance. Numerical and simulation results validate our analysis and highlight the performance gains of the proposed schemes for CR-NSHT with relay link serving secondary network and direct link serving the primary network.


I. INTRODUCTION
To resolve the challenge of line-of-sight satellite communication systems blocked by heavy shadowing or obstacles [1], the authors in [2]- [6] has been studied a hybrid satellite-terrestrial system. In particular, a terrestrial relay is implemented in satellite communication systems to overcome challenges of large coverage and high data rate services. To enhance the wireless spectrum utilization, the satellite communication systems enable the cognitive radio (CR). Considering the benefits of the underlay CR scheme, cognitive hybrid satellite-terrestrial systems are proposed in [7], [8]. In such systems, the secondary users' spectrum access The associate editor coordinating the review of this manuscript and approving it for publication was Qinghua Guo . opportunities are limited by the tolerable interference level which is allowed by the primary user. The performance analyses of the primary and secondary networks depend on interference coordination and such issue is considered as one of the key parameters to control the quality of service (QoS) of the primary network in the context of underlay transmission mode. In the overlay mode of CR network reported in [9], the secondary users help the primary transmission through cooperative relaying protocols related to spectrum access. In [10], the authors analyzed an overlay CR architecture in hybrid satellite-terrestrial networks to exhibit its performance. The authors in [11] investigated a novel cognitive hybrid satellite-terrestrial model including two cognitive relays which are enabled to forward their received signal to a mobile user successively. The secrecy outage probability of the hybrid satellite-terrestrial network was analyzed to indicate the secrecy performance by introducing the closed-form formula for the single-relay selection and baseline round-robin scheduling modes [12]. By using Vickrey auction to achieve an efficient secondary relay selection, a cooperative spectrum sharing scheme is examined in the scenario of a multi-potential secondary relay selection [13]. X. Zhang et al. studied the generalized shadowed-Rician fading for satellite links while Nakagami-m fading is adopted in terrestrial links. Further, the authors derived the closed-form outage probability expressions for both the primary and secondary users [14]. To get extra spectrum efficiency, non-orthogonal multiple access (NOMA) was introduced in [15]- [24]. In principle of NOMA, multiple users are permitted to share the same resource elements in signal processing domains including time, frequency, space, or code. These studies presented a lot of benefits such as massive connectivity and high spectral efficiency. The satellite systems have more beneficial by implementing NOMA to form NOMA-aided hybrid satellite-terrestrial systems (NHST) [25]. The authors in [25] developed the model to allow a user with better channel condition to operate as a relay node and forwards signal to other users. Therefore, the impacts of the masking effect of users with poor channel conditions can be avoided in circumstance of heavy shadowing. The authors in [26] introduced how NOMA benefits to hybrid satellite-terrestrial relay network. Such NSHT enhances ability of spectrum sharing in the manner of the underlay architecture. The work in [27] considered NSHT by applying both the decode-and-forward (DF) and amplifyand-forward (AF) protocols at the relay and the imperfection of channel state information (CSI) at all nodes. Furthermore, NOMA can be applied to edge computing and content caching in wireless networks to enable the emerging networks which provide high-quality services for users [28], [29].
The performance of NOMA based cooperative spectrum sharing in hybrid satellite-terrestrial networks is studied in many scenarios [30]- [32]. The authors in [31] considered the underlay CR-HSTN including a primary satellite source with its terrestrial receiver and the secondary transmitter (ST) with its pre-paired users on the ground. They derived a novel closed-form formula to exhibit the outage performance of secondary network in the existence of primary interference power constraint imposed by the adjacent primary satellite network. The recent work reported the asymptotic outage performance of CR-HSTN at high signalto-noise-ratio (SNR) to show performance of the primary and secondary networks, and thereby achieve the diversity orders [32]. Those studies show open problem which motive us to study in this article.
Inspired by the comparison presented in Table 1, a CR-NHST need be studied in this paper to enhance the spectrum utilization and tackle the fairness issue benefiting by exploiting NOMA with fixed power allocation approach. The contributions of this work are manifolds as follows • First of all, we propose a CR-NHST system, where the secondary terrestrial network operates under the help of the base station in role of relay. Besides, the NOMA is adopted in system to show differences in outage performance of two-user model.
• Secondly, different performance of two users under overlay paradigm is examined by deriving expressions in the closed-form for outage probability, ergodic capacity and energy efficiency. We also present related analysis in case of multiple users which need more signal processing stages in such system. Our results indicated that main parameters need be adjusted to achieve the improvement in term of system performance.
• Thirdly, more insights in term of performance analysis are provided. Particularly, the asymptotic expressions of outage probability and diversity order are derived.
• Finally, the impacts of key parameters in the CR-NHST system are analyzed, and the superiority of the CR-NHST relying on NOMA scheme is proved to compare to conventional OMA-based satellite system in terms of outage and throughput performance. The rest of this paper is organized as follows. Section II introduces the CR-NHST system model, reformulates signal to interference plus noise ratio (SINR), and gives channels model. In Section III, the exact expressions of outage probability are derived. Section IV present the extended case for multiple users in the considered system and Section V shows simulation results. Finally, conclusions are drawn in Section VI.

II. SYSTEM MODEL
Considering system model in Fig. 1, a CR-NHST includes the secondary network (SN) serving NOMA users. The SN comprises of a satellite transmitter (S), terrestrial base station (R), two user D 1 , D 2 and the primary network with corresponding  primary destination PD. We will consider the situation of multiple users in section IV. Let such satellite be a GEO satellite and the terrestrial nodes be fixed service terminals. The base station and mobile users are single antenna nodes. We do not concern the Doppler spread at the terrestrial node due to static their nature. Therefore, the secondary transmitter (base station) performs for spectrum sharing opportunities to send signals to its intended secondary receivers. The main symbols and parameters can be clarified in table 2. The transmit power at S and R is constrained by [33] In two-phase transmission from satellite to users, S sends the superposed signal √ a 1 P S x 1 + √ a 2 P S x 2 to R in the first phase. Following principle of NOMA, operation of such network is conditioned on a 1 < a 2 and a 1 +a 2 = 1. In the second phase, R forwards signals to two secondary destinations.
In the first phase, the received signal at R is given by The signal to interference plus noise ratio (SINR) decoding x 2 is given by After applying SIC, the SINR computed at R is used for decoding signal x 1 and such SINR is given by In the second phase, the relay transmits the signal to D i with i ∈ {1, 2}. The received signal at D i can be expressed as The SINR at D 2 used for decoding x 2 is calculated by Then, the SINR at D 1 for detecting x 2 is computed by Applying SIC, the SINR for decoding x 1 at D 1 is given by

III. PERFORMANCE ANALYSIS A. CHANNEL MODELS
Under Shadowed-Rician fading model for the satellite links, the probability density function (PDF) of |h Sk | 2 with k ∈ (R, P) is given by [3] f where α Sk = 2b Sk m Sk 2b Sk m Sk + Sk m Sk /2b Sk , β Sk = 0.5b Sk and δ Sk = Sk / (2b Sk ) (2b Sk m Sk + Sk ), with Sk and 2b Sk denote the respective average power of the LOS and multipath components, m Sk is the fading severity parameter and 1 F 1 (.) is the confluent hypergeometric function of the first kind [41, Eq. 9.210.1]. In this paper, we consider arbitrary integer-valued fading severity parameter [34]. Then, we can simplify (9) as where ζ Sk (n Sk ) = (−1) n Sk (1 − m Sk ) n Sk δ n Sk Sk / (n Sk !) 2 and (.) n Sk is the Pochhammer symbol [41, p.xliii]. Thus, we can obtain the CDF of |h Sk | 2 as The PDF and cumulative distribution function (CDF) of |h l | 2 for l ∈ {RP, 1, 2} are computed respectively as where γ (., .) is the lower incomplete gamma functions [41, 8.310.1], m k and λ k denote the fading severity and average power, respectively.
For target rates R i , the OP of the secondary satellite network with relay link enabled. We deal with two kinds of fading channels in the secondary network, especially considering Nakagami-m and Rician fading environments for terrestrial links. The OP at user D 2 is expressed by where ψ th i = 2 2R i − 1 is the threshold SNR corresponding to target rates R i for two users D i . Lemma 1: The term F D i ,x 2 ψ th 2 can be expressed as (15), shown at the bottom of the next page.
Proof: See Appendix A Lemma 2: We can calculate F R,x 2 ψ th 2 as (16), shown at the bottom of the next page.
Proof: See Appendix B. Finally, with the help of (15), (16) and after some manipulations, the closed-form expression of OP for D 2 is obtained as In this section, we conduct the OP analysis of the secondary network of CR-NHST under NOMA scheme in the absence of direct R-D 1 link.
Based on (1) and (4), we can write F R,x 1 ψ th 1 as Similarly, with the help from Appendix B, it can be rewritten as Regarding the computation at R, F D 1 ,x 1 ψ th 1 is given by Finally, putting (20) and (21) into (18) OP D 2 can be obtained as (22), shown at the bottom of the next page.
Remark 1: Although the exact OP expression of CR-NHST based on (22) is useful and provide several insights from numerical plots, it is too complex to predict main impacts on system performance of the secondary network. Fortunately, transmit SNR at the satellite plays an important role in outage performance. Therefore, a further metric is necessary to highlight performance improvement of such CR-NHST. For this, we consider throughput performance in the following section. This is ergodic capacity in delay-limited mode. 1

C. DIVERSITY ORDER ANALYSIS
In this paper, we consider the peak interference constraint scenario as [33], where P D is fixed and onlyP j becomes large in the high SNR regime. It is worth noting that the diversity order for D 1 , D 2 are defined by First, we can write OP D 2 as It is interestingly to find F ∞ ψ th 2 which can be expressed in Proposition 1 and 2 as follows.
Proposition 1: The asymptotic expression of F ∞ R,x 2 ψ th 2 can be formulated as Proof: See Appendix D. Next, the asymptotic expression of OP for user D 1 and it is given by It is noted that (27) can be achieved based on the following given as respectively and Remark 2: We can infer from (24) and (27) that the secondary network of such CR-NHST exhibits different performance of two users which depends on transmit SNRThe diversity order of OP D i is zero in transmit power at some nodes. It can be concluded that the diversity order of OP D i is zero in high SNR. This is predicted that outage performance is flat curves at high region of transmit SNR at the source.

D. THROUGHPUT PERFORMANCE
The overall throughput is an another performance metric for such systems, which can be evaluated with the help of outage probabilities. In delay-limited mode, at fixed target rates R 1 , R 2 , the throughput can be achieved. As a result, the overall throughput can be formulated as

E. ERGODIC CAPACITY ANALYSIS
By using definition, the ergodic rate of x 1 is given by where Z 1 = min R,x 1 , D 1 ,x 1 . Then, the CDF of Z 1 is expressed as Based on (20) and (21), we obtain the PDF of Z 1 . Unfortunately, it is difficult to obtain a closed-form expression from (31) as [35]. VOLUME 9, 2021 Next, the ergodic rate of x 2 is given by where Z 2 = min R,x 2 , D 2 ,x 2 , D 1 ,x 2 . Furthermore, the CDF of Z 2 is obtained as With the help (15) and (16), the PDF of Z 2 could be computed.
To the best of authors' knowledge, (33) does not have a closed-form solution [35].

F. ENERGY EFFICIENCY
To further evaluate the performance of the considered systems, energy efficiency (EE) could be examined as an important criteria, which is defined as the bits of information reliably transferred the receivers per unit consumed energy at the transmitters [36] η EE = Total data rate Total energy consumption .
Based on the throughput analysis in (30), the energy efficiency of the considered systems is given by where T denotes the transmission time for the entire communication process.

IV. EXTENSION TO SCENARIO OF MULTIPLE USERS
We continue to evaluate how multiple users make degraded performance of specific group of users in the context of NOMA. Ideally, two-user scenario is considered in the previous section which motivate us to further examine the groups containing N users, i.e. denoting them as (D 1 , D 2 , . . . , D N −1 , D N ). In such circumstance, the source S intends to proceed the superimposed signals N n=1 √ a n P S x n + n R to R. For signal processing for user D N , x n is targeted to it, and this user is allocated the percentage of total power, i.e. a n with the constraint a 1 > a 2 > . . . > a N and N n=1 a n = 1. In term of multiple users in groups of NOMA system, it is usually assumed the channel ordering could be In practical scenarios, a multi-user multi-relay architecture for NOMA aided CR-NHST has been explored. However, by grouping pair of users, such system can satisfy particular requirements of paired users. In the first phase, the received signal at R can be formulated by y RN = h SR N n=1 P S a n x n + n R .
Further, after receiving the mixture signals, R needs assistance of the SIC in the context of NOMA [39]. In particular, R detects the signal x 1 and considers other signal(q = 2, 3, . . . , N ) as noise. In the next stage, R decodes the signal x 2 and the noise in this case could be x q , (q = 3, 4, . . . , N ). As expectation in the last step, R decodes the signal x N . Therefore, the SINR of detecting x q at R is computed by Finally, the SINR at R detects the signal x N is given as During the second phase, R forwards the detected signal to D m (m ∈ (1, 2, . . . , N )). The signal at D m is given as Similar to R, D m executes the SIC to decode the signal x q (1 q m N ). The SINR can be written as The SNR of D N to detect the own signal is given as Finally, the achievable rate of the messages devoted to D q (1 q m N ) and D N are accordingly expressed by [40]

V. NUMERICAL RESULTS
In this section, to verify mathematical analysis, it is necessary to simulate and illustrate for proposed assisted CR-NOMA scheme. Here, the shadowing scenarios of the satellite links h Sk , including the average shadowing (AS) and the heavy shadowing (HS) being given in Table 3 [1], [37]. We set power allocation factors a 1 = 0.2, a 2 = 0.8, ρ =ρ S =ρ R , the target rates R 1 = R 2 = 0.5 bit per channel use (BPCU) except for specific cases, the channel gains λ SP = 0.01, λ 1 = 2, λ 2 = 1 and m RP = m 1 = m 2 . Moreover, case of m RP = m 1 = m 2 = 1 is equivalent with the Rayleigh fading channel model. In these following figures, Monte-Carlo simulations are performed to validate the analytical results.
In Fig. 2, we plot the OP curves for the secondary network of CR-NHST (with two sets of channel, i.e. HS and AS) under impact of SNR at the satellite. In particular, it can be seen good matching between the analytical and simulated OP curves. Such observation definitely confirm how exactly our expressions presented in in Sections III. We can see that the OP performance can be improved if we increase SNR at the satellite approach 15 dB. It is very important to point out that asymptotic lines are matched with exact curves at high SNR region. This result is definitely confirmed exactness of our derived expressions. But, if we continue to increase SNR, the OP curves still remain unchanged. As a result, the expression of diversity order in previous section is verified. For comparison, we have also plotted the OP curves for benchmark of OMA transmission. The case of AS in such CR-NHST shows the best performance among these cases. It shows that OMA is worst case. Similar trends of OP curves can be seen in Fig. 3. When we increase ρ D , which means the transmit power at the satellite increases, OP performance can be enhanced. Fig. 4 plots the OP curves for the secondary network of considered system under Nakagami-m faded terrestrial links. Herein, it can be concluded that m 1 = m 2 = m RP = 2 exhibit the best performance. We can see that the analytical OP curves for two users converge to floor value when the transmit SNR is higher than 30 dB. The performance gap exists among two users due to different power allocation factors and condition of SIC. In Fig. 5, we investigate the target rates which make influence on OP curves for two NOMA users. As definition of OP, the target rates limit performance  of OP in such network. For such, the lower required target rates contribute to better OP performance for two users.
We can study the impacts of power allocation factors a 1 , a 2 on the OP of two users in Fig. 6. When we increase a 1 , the SINR to detect user D 1 's signal increases and hence the value of OP for user D 1 becomes smaller. While the OP performance of user D 2 would be worse as increasing a 1 . The main reason is that SINR is computed based many parameters including a 1 , a 2 .
In Fig. 7, depending on the OP performance, the throughput of considered system increases significantly as the transmit SNR at the satellite increases from 0 dB to 40 dB. It is clearly that there is existence of ceiling value of such throughput at high region of SNR.
Interestingly, in Fig. 8, we can find optimal throughput in HS and AS configuration for proper target rates R 1 = R 2 . The superiority of this system with AS scheme still remain in this experiment.
Due to difference among expressions of SINR for two users, we show different ergodic capacity performance, VOLUME 9, 2021   as shown in Fig. 9. It can be seen intuitively that, the ergodic capacity of the first user is better than that of the second user. In meantime, we also examine EE for two configurations (HS   and AS) for our considered system, shown in Fig. 10. At high SNR, EE curves also meet their ceiling values. The main reason it that the corresponding throughput is limited at high SNR region. It is more challenging when we consider multiple users scenario, shown in Fig. 11. In particular, user D 3 has power allocation factor a 3 = 0.2 and its performance is worse than the others. This circumstance can be explained that more interference and less power are joint happened in all users in a specific group and such issue becomes crucial if the number of users is greater than 2.

VI. CONCLUSION
In this study, we have investigated the system performance of the CR-NHST system relying on NOMA in terms of outage probability, ergodic capacity, energy efficiency and throughput. In particular, we have derived the closed-form expressions of outage probability, defined expression of ergodic capacity to show how different performance of the two users in the secondary network over some sets of channels. These derived expressions were validated by numerical results, and the outage events of two users were compared with OMA case. The asymptotic computation of outage probability and diversity order are also provided to show more insights related to performance analysis. Moreover, the numerical results showed that the proper selection of power allocation factors and transmit SNR at the satellite can guarantee the performance fairness for both users.
As most of papers in literature, it is assumed the knowledge of perfect channel state information (CSI) in such CR-NHST to facilitate the user selection process. Although the CSI for user selection may be outdated due to various reasons such as feedback delay, mobility, etc. Further, with dense frequency reuse in wireless networks, the HSTRN is prone to co-channel interference (CCI). These challenges need be addressed in extra effort in our future work.

APPENDIX A
We recall expression of F D 1 ,x 2 ψ th 2 as below in whichρ R =P R σ 2 , σ 2 = σ 2 R = σ 2 1 = σ 2 2 and ρ D = P D σ 2 . Then, we can rewrite A 1 as First, A 1 is expressed by Then, A 1 is rewritten as Secondly, it can be obtained A 2 as Then, A 2 is rewritten as Finally, we can achieve A 1 as Similarly, we easy obtain F D 2 ,x 2 ψ th 2 . This completes the proof of lemma 1.

APPENDIX B
First, F R,x 2 ψ th 2 can be formulated by whereρ S =P S N 0 There are two components can be further computed in the closed-form expressions. We can express B 1 as below Then, it can be obtained B 1 as Similarly, we can obtain B 2 as below This completes the proof of lemma 2.

APPENDIX C
By using (1), the asymptotic of F ∞ ρ S |h R | 2 (x) for peak interference constraint can be obtained as Further, at high SNR, we can rewrite F ∞ ρ S |h SR | 2 (x) as Then, substituting (57) and (58) into (55), we have Finally, with the help (3) and performing necessary manipulations. This proof is completed.

APPENDIX D
By using (1), the asymptotic of F ∞ P S |h R | 2 (x) for peak interference constraint can be obtained as Similarly, we have similar expressions as below. Firstly, the asymptotic of F |h i | 2 can be written as Then,Q 1 andQ 2 are given respectively bȳ Next, we have He is currently working with the Department of Electronics and Communication Engineering, Indian Institute of Information and Technology Allahabad, Prayagraj, India, as an Assistant Professor, where he is serving as a Faculty-in-Charge of the Mobile and Wireless Networking Laboratory (MoWiNeT). He has numerous publications in peerreviewed journals and conferences. His current research interests include wireless relaying techniques, cooperative communications, cognitive relaying networks, device-to-device communications, reconfigurable intelligent surfaces, signal processing, physical layer security, and MIMO systems. He served as a TPC member, the session chair, the program co-chair, and a reviewer for various national and international conferences. He is also serving as a reviewer in a number of international journals, including the IEEE TRANSACTIONS ON