Performance Analysis of NOMA-Based Hybrid Satellite-Terrestrial Relay System Using mmWave Technology

This paper investigates the performance of NOMA-based hybrid Satellite-Terrestrial relays system (HSTR) using the millimeter wave (mmWave) technology. Furthermore, the relays are equipped with multiple antennas and utilize the amplify and forward (AF) protocol to forward the satellite’s superimposed information to multiple destinations. Then, the rain coefficient is considered as the fading factor of the mmWave band to choose the best relay. We considered the shadowed-Rician fading and Nakagami-m fading for satellite links and terrestrial links respectively, and in addition, we evaluated the shadowing effect for satellite links with two modes of: frequent heavy shadowing (FHS) and average shadowing (AS). With these suggestions, the closed-form outage probability (OP) and approximate ergodic capacity (EC) are derived to evaluate the efficiency of the proposed system. Next contribution of the research is an asymptotic analysis for the OP, which is derived in order to gain additional insight into important system parameters. Finally, the theoretical derivation is validated through simulation results and analyzed the impact of significant parameters. These results demonstrate NOMA’s superiority to the traditional orthogonal multiple access (OMA) method in the proposed system.

in researching and proposing models of the integrated satellite terrestrial network (ISTN) [4], [5]. In SatCom, geostationary Earth orbit (GEO), middle Earth orbit (MEO), and low Earth orbit (LEO) satellites can operate efficiently in the high frequency bands of millimeter wave (mmWave) (e.g. Ka/Q/Vband) [6]. They effectively provide system throughput and extensive coverage of the terrestrial wireless network [7], [8]. However, using the traditional orthogonal multiple access (OMA) technique into SatCom would result in a waste of block resources, such as the time / frequency / code block due to the limitation in the number of simultaneously connected users, the ability to meet for the services requires low latency and high throughput [9], [10]. Contributing to solving the limitations of OMA, a promising technology has been proposed for 5G is non-orthogonal multiple access (NOMA) [11]. NOMA helps improve resource efficiency and increase the number of users served in the same resource block with higher data speed, higher reliability, and lower latency than the conventional OMA scheme [12]. With these advantages, the combination of SatCom with NOMA will greatly improve network performance; therefore, this is a promising job in the future.

A. RELATE WORK
Under the influence of rain, fog, and obstacles, the performance of ground users will be severely affected. Therefore, the hybrid satellite-terrestrial relay network (HSTRN) is proposed to solve the above problems. The authors in [13] presented the relay selection as well as round-robin scheduling schemes for the physical-layer security (PLS) in HSTRN, where secrecy performance has been analyzed with the decode and forward (DF) relaying protocol. To evaluate the security and reliability for a satellite-terrestrial network with multiple ground relays in the presence of an eavesdropper, the authors in [14] deployed a friendly jammer and an amplify-and-forward based relaying scheme to subtract the consequence of the eavesdropper on system performance. In [15], the authors investigated the ergodic capacity (EC) in HSTRN with adopted amplify-and-forward (AF) relaying protocol. Furthermore, the authors combined opportunistic scheduling for terrestrial destinations. To achieve optimal power performance, rate adaptation and truncated channel inversion with fixed rate in HSTRN have been proposed in [16]. In [17], the authors employed a cache-enabled for HSTRN, which is regarded as the common and most widely used content-based caching strategy. The average symbol error rate (ASER) has been examined in both cases of a degraded LoS link and without a degraded LoS link are presented in [18] and [19] respectively. The authors in [20] analyzed the OP performance of decodeand-forward HSTRN with the best relay selection technique while taking into account a multiple-relay scenario. Also, the performance of downlink HSTRN with relay selection was presented in [21]. Furthermore, hardware impairments (HIs) and interference are considered for the relay and terrestrial destination. The effect of co-channel interference (CCI) in HSTRN has been evaluated in terms of bit error rate at the relay and destination nodes in [22]. To increase the total throughput and reduce system complexity, full-duplex (FD) and relay selection techniques are applied at the relay proposed in [23].
The NOMA scheme is considered to improve spectrum efficiency and serve multiple users in a time/frequency/code block in conjunction with HSTRN. Recently, the investigations on the impact of NOMA on satellite-terrestrial network (STN) in order to use spectrum efficiently and serve multiple users at the block resources [24], [25], [26], [27]. The exact outage behaviors of NOMA-based STN and asymptotic analysis were studied by the authors in [24]. The identical OP analysis was achieved in [25], where the authors discussed the effectiveness of the NOMA-based uplink land mobile satellite (LMS) communications. The authors in [26] considered the outage probability (OP) and asymptotic OP obtained after evaluating the system performance of NOMA-based HSTRN with the AF protocol. To maximize the sum rate of the suggested NOMA-based HSTRN, the authors provided an iterative penalty function based beamforming (BF) method. This algorithm could quickly get the BF weight vector and power coefficient [27]. In order to collaborate with the primary satellite network for dynamic spectrum access, the secondary terrestrial network and overlay cognitive integrated satellite-terrestrial relay network (CISTRN) based on NOMA were examined in [28] and [29]. Moreover, the authors in [30] analyzed the performance of the secondary network when the near user employed the full-duplex mode and used the DF protocol to enhance the performance of far user in NOMA network. In [31], the authors investigated the OP and average transit time for an underlay cognitive NOMA-based HSTRN with a HD secondary receive. Table 1 summarized the related work on NOMA-based Satellite network, in which their features, Methodology and challenges are highlighted to previous works.

B. MOTIVATIONS AND CONTRIBUTIONS
To the best of our knowledge, the NOMA-based HSTRN with mmWave network has not yet been disclosed. And this paper is an expansion of [6], [28], and [37]. In particular, the following can be summarized as our significant contributions.
• First, we proposed a NOMA-based HSTRN with mmWave network, where a GEO satellite and AF protocol relaying are considered. Furthermore, we investigate the rain attenuation values to select the desired transition node. In addition, we consider the multi-device serving model in NOMA to improve the spectrum.
• Second, we analyze the performance of the system based on the channel fading distribution. The closed-form OP and EC are expressed. To obtain the insights, the asymptotic OP and diversity are derived for the system. To further confirm the accuracy of our findings, Monte Carlo (MC) simulations are presented.
• Finally, we consider the effects of key parameters on the proposed system. Additionally, the benchmarks for comparing the NOMA-based scheme to the OMA-based scheme are supplied, demonstrating the benefits of the NOMA scheme. The rest of this paper is organized as follows. Section II introduces the proposed system model, the type of satellite, and received SINR. In Section III, the channel model is introduced. Section IV, the closed-form OP, EC, and diversity order are derived. The simulation results are shown in Section IV. In Section V, conclusions are reached.

II. SYSTEM MODEL
In this paper, we consider an AF-multirelay satellite cooperative NOMA network as shown in Fig. 1, which VOLUME 11, 2023   consists of the source node S, the K terrestrial relay nodes R k (k = 1, 2, . . . , K ) equipped with N R receiving antennas and N T transmitting antennas, and M devices D m (m = 1, 2, . . . , M ). Furthermore, we assume that the direct communication links between S and D m are not available due to the heavy shadowing [38]. Therefore, satellite S communicates with the terrestrial devices with the help of the best terrestrial relay R k * based on opportunistic scheduling [6].
In the first phase, the satellite transmits the signal √ ϖ i x i to the relay node R k * , and the relay node performs the maximum ratio combining (MRC) to combine the received signals [39]. Hence, the received signal at the best relay node is given by where T is the N R × 1 channel coefficient vector between S and R k * , ϑ r,k * denote the expected rain attenuation between S and R k * , w SR k * = h SR k * ||h SR k * || F is the receive beamforming weight vector and n R k * is the vector of zero mean additive white Gaussian noise (AWGN) with variance N 0 . Then the desired relay node amplifies the received signal y SR k * by a gain factor , and performs maximum ratio transmission (MRT) to forward it to the desired destination node according to the feedback of pilot signal from each destination node during second phase [39]. Additionally, the free space pathloss coefficient L S can be expressed as [34], [40], and [31] where λ = c f c is the wavelength, c is the light speed, f c is the carrier frequency, d R is the distance between the satellite and R k * , N p = K B T B ω is noise power, K B denote the Boltzmann constant, T is the noise temperature of the terrestrial receiver and B ω represents the bandwidth. For the R k * location, φ represents the angle between R k * and beam center compared to the satellite. In addition, G R denotes the antenna gain at R k * , G S (φ) denotes the satellite beam gain, and the beam gain G S (φ) is given as [34] where G max S denotes the maximal beam gain and u can be expressed as where φ 3dB is the constant 3-dB angle for the beam. Next, the received signal at the desired destination node is given by and n D m is the zero mean additive white Gaussian noise (AWGN) with variance N 0 . In the mmWave network, the path loss L D m in the terrestrial link can be modeled as [41] where κ and ν denote the linear model parameters, θ is accounting for variances in shadowing fading and d m denotes the distance between R k * and D m . Following NOMA procedures [42], the received signal to interference and noise ratio (SINR) at m-th device to detect the information of q-th device (m > q) is given as follows (7), shown at the bottom of the next page. In which, Then the received SINR of m-th device to detect the information by treating M −p devices's signals as interference is given by After the information of M −1 devices can be detected, the received SINR for M -th device is given by

III. STATISTICAL ANALYSIS
The rain attenuation is the important attenuation factor in mmWave band channels. The expected value of rain attenuation from S to R k * link can be treated as a constant during a transmission phase. Hence, in order to reduce the computational complexity, satellite can select the desired relay node according to the feedback of expected rain attenuation rather than the channel gain vector, namely Therefore, the rain attenuation value of R k can be expressed as A * = min(ϑ r,1 , . . . , ϑ r,K ). We then assume that the rain attenuation values are independently and identically distributed (IID). The cumulative density function (CDF) of A * can be given by is the CDF of the lognormal rain attenuation distribution [43]. In order to investigate the effect of the different number of relays, we need to derive the expected value of A * , which can validate the means of our proposed relay selection scheme and shown in [6].
Next, we assume that the channel conditions of all hops are IID. Moreover, mmWave satellite-terrestrial communications are mainly impaired by the masking effect and weather conditions, especially rain attenuation [44]. Under the Shadowed-Rician fading model for the satellite links, the probability density function (PDF) of ρ S is given by [45] where Considering the characterization of Nakagami-m fading, the PDF and CDF of unordered estimated channel gainsρ D m VOLUME 11, 2023 are given respectively as [47] fρ Dm where RD m is the average power, m RD = m RD 1 = . . . = m RD M is the fading severity and λ RD m = m RD RDm . Using order statistics [48], the PDF and CDF of the ordered channel gains ρ D m are respectively given by where ε l = 1 l! , ω b c can be calculated as

IV. PERFORMANCE ANALYSIS
In this section, the outage performance of the satellite network cooperative with NOMA will be analyzed in terms of outage probability and system diversity order. To this end, both exact and asymptotic expressions for the outage probability will be studied.

A. OUTAGE PROBABILITY
The outage event will occur at D m if D m fails to decode its own signal or the signal of D q . The outage probability at D m is expressed as where E m,q denotes the event that D m can successfully detect the D q 's signal and can be given by where γ th q denotes the target rate of D q . Proposition 1: The closed-form outage probability of device D m can be expressed as (21), shown at the bottom of the next page.
Proof: Substituting (7) into (20) and putting the result into (19), we can write P m as (22), shown at the bottom of the next page.
Then, the diversity order of the terrestrial device can be given by [24] and [49] where P ∞ m (η) denotes the asymptotic outage probability. Proposition 2: The asymptotic outage probability of the device D m in the high SNR regime is given by Proof: See Appendix A Remark: Upon substituting (28) into (27), the achievable diversity order of m-th device is min (N R , m RD N T m)

C. ERGODIC CAPACITY (EC)
In this section, the ergodic rate of m-th device is discussed in detail, where the target rates of devices are determined by the channel conditions. Next, m-th device detects the qth device's information successfully, since it holds h R k D m ⩾ h R k D p . In this situation, the achievable rate of m-th is expressed asR m = 1 2 log 2 (1 + γ m ). Thus, the ergodic rates of m-th and M -th device are as follows andR M ,ave = E

Proposition 3:
The closed-form of ergodic rate for m-th and M -th device are given by (31) and (32), respectively, as shown at the bottom of the next page.
Proof: See Appendix B

V. NUMERICAL RESULTS
In this section, to verify the mathematical analysis, it is necessary to simulate and illustrate the proposed assisted NOMA scheme. Here, the shadowing scenarios of the satellite links, including frequent heavy shadowing (FHS) and average shadowing (AS) being given in Table 3. Furthermore, the parameters can be provided in Table 4. Monte Carlo simulations are performed to validate the analytical results shown in the following figures.
In Figure 2, we show the OP versus η in dB with different satellite links. First, the performance of the devices will be improved by increasing the transmit power. Next, the performance of device D 1 is the best due to the power allocation of D 1 is better than D 2 and D 3 . Moreover, the improvement of satellite link also greatly improves device performance, i.e. AS is the best case. Furthermore, the system uses the NOMA scheme that is better than OMA. The fundamental cause is that OMA-based systems require more time slots than NOMA-based systems to process the same number of devices. Over the whole SNR range, Monte Carlo simulation curves and analytical results accord very well. At high SNR, it can be seen that the asymptotic OP curves closely reflect the actual findings.  [50], [51], [52]. Figure 3 shows the OP versus η in dB under the influence of the relay antenna. We can easily see that increasing the number of antennas at the relay will significantly improve the system's performance. It proves the superiority of installing multiple antennas in the system. Compared to the case of the relay with N R = N T = 2, the large OP gap can be seen once the relay is designed with N R = N T = 3. The explanation is that a design with more diversity from many antennas could enhance the signal received for the devices on the ground. Figure 4 shows the simulation OP versus η in dB with different numbers of relays. When the number of relays is increased, the performance is improved more. It demonstrates the effectiveness of using a relay selection scheme. Fig. 5 shows The OP versus transmit η in dB varying the carrier frequency. It can be observed that the higher the carrier frequency the worse the OP. The rationale behind this phenomenon is that with higher frequency, the path-loss R m,ave ≈ π ϖ m 2 ln (2) I m SR −1   drops dramatically thus an appropriate antenna beamforming gain is necessary to compensate such losses. Regarding the selection of the 38GHz, we choose because it is in the range of GEO operation [41], [50]. Figure 6 indicates the EC versus η with different satellite links, as well as Figure 2. The EC rates at D 1 and D 2 are almost no change for the FHS and AS case. But the difference between the EC curves at D 3 in both modes is comparably quite large. Moreover, when increasing in high SNR, the gap of D 3 is different with D 2 and D 1 . Figure 7 and Figure 8 show the EC of D m versus η in dB varying the number of relay antennas and the number of relays, respectively. For EC of D 1 and D 2 , the gaps between cases change only in the low SNR region and will intersect at a point in the high region. Therefore, changing the number of antennas and the number of relays does not have much effect on EC. But for the EC of D 3 , the gaps between instances will be large. It shows the effect of the number of antennas and the number of relays to the EC.

VI. CONCLUSION
In this article, we investigated the performance of NOMA-based HSTRN with mmWave network where the devices are supported by multiple relays. Unlike previous studies, we consider multiple antennas receiving and transmitting at relay and NOMA in the context of serving multiple devices. In addition, we use the rain attenuation value to choose the best relay. The closed-form of OP, EC, and asymptotic expressions of OP were developed based on the model of the considered system. To support those performance studies and demonstrate how important factors like fading and rain attenuation affect system performance, simulations have been made available. Our results showed that the OP of the system under consideration can be greatly improved compared to the OMA scheme, highlighting the advantages of implementing the NOMA scheme to the system. These results provide a theoretical framework for further investigation.

APPENDIX A
First, when η S → ∞ and apply the Maclaurin series expansion of the exponential function in (11). So, the PDF of ρ S can be approximated as Next, the CDF ρ S has asymptotic behavior as Furthermore, when η R → ∞ and taking the first term (a = 0 of series representation, the asymptotic behavior of CDF ρ D m can be obtained as (35) Then, the asymptotic P ∞ m can be expressed as Using the inequality uv u+v ⩽ min(u, v). Thus, the asymptotic P ∞ m can be calculated as With help (34) and (35), we can obtain as 10704 VOLUME 11, 2023
Next, the ergodic rate of M -th device can be calculated as 1 + x dx (42) Similarly, the PDF of γ M can be expressed as . . .