Uplink and downlink of energy harvesting NOMA system: performance analysis

ABSTRACT In this paper, we consider an uplink non-orthogonal multiple access (NOMA) for energy harvesting at the base station or access point in the wireless system. By exploiting energy enough, a base station or access point can serve many users at the downlink. The fixed power allocation factors are adopted, and the power splitting energy harvesting protocol brings many benefits to both the uplink and downlink of a wireless system. The closed-form expressions of outage probability are investigated and examined in a group of two users. Moreover, the optimal outage probability for two users is shown numerically. Finally, Monte Carlo simulations are presented to further support the validity of our framework and findings.


Introduction
The NOMA technique performs the communication by superimposing the signals in a similar time, frequency, or code domain and varying power levels of each user signal (Dai et al., 2015).NOMA appears to be a better technique since the requirement for massive connectivity, efficient spectrum usage, and less latency has been growing.NOMA is divided into two groups namely Power Domain-NOMA (PD-NOMA) and Code Domain-NOMA (CD-NOMA).The important approach in the PD-NOMA is to allocate diverse power levels to different users and similar time/frequency resources, transmitting multiple user signals in a single block.To be specific, the transmitter in NOMA utilizes superposition coding (SC) to superimpose the signals, while the receiver performs successive interference cancellation (SIC) to distinct the multiple signals and extract the target user's signal (Islam et al., 2017;Lv et al., 2017).Non-orthogonal multiple access (NOMA) has been recently proposed for the next generation and is envisioned to be an essential component of 5G mobile networks.Multimedia broadcast/multicast service (MBMS) transmission, which distributes the media content to multiple users on the same radio resources using point-to-multipoint communications, is a highly spectrum-efficient mechanism for multimedia communications, where one near the user is employed as decodeand-forward relaying switching between full-duplex (FD) and half-duplex (HD) modes to help a far user (Ding et al., 2017;Yue et al., 2018b;Zhang et al., 2017).Refer to authors in Yang et al. (2017), Lv et al. (2019), Do, Van Nguyen, et al. (2021) and Do and Van Nguyen (2019), the performance of non-orthogonal multiple access (NOMA) is investigated and optimized in a downlink space division multiple access network with a multi-antenna base station and randomly deployed users under a general channel state information (CSI) limited feedback framework.Furthermore, the scheme to enhance of physical layer security of untrusted relay networks is also proposed in the NOMA system.Thus the research above proves that the NOMA technique has support massive connectivity, enhanced spectral efficiency, and enhanced user allocation fairness (Do, Le, et al., 2020;Liu et al., 2016;Timotheou & Krikidis, 2015;Xu & Cumanan, 2017).
Besides using NOMA technology in recent years, as we know the energy is limited because the Internet-of-things (IoT) devices have to work remotely or operate in mobile environments.Replacing or recharging IoT devices' batteries will be costly, unfavourable, and even infeasible in toxic territories or hazardous environments, etc.Therefore, using energy harvesting (EH) plays a very important role in communication systems and is a promising solution to overcome these issues.In 2008, Varshney (2008) introduced the concept of simultaneous wireless information and power transfer (SWIPT) to paint a system in which the radio frequency (RF) signals can carry both energy and information simultaneously.To continue the work in Varshney (2008), the authors in Grover and Sahai (2010) have investigated the information and power transfer on a coupled-inductor circuit.Different from Varshney (2008) and Grover and Sahai (2010), which only considered the one-way single-input-single-output (SISO) channel model, the authors in Nguyen, Tran, et al. (2019a) have investigated the one-way multi-input-singleoutput (MISO) system in which power splitting (PS) protocol is employed for EH.Unlike Nguyen, Tran, et al. (2019a), Nguyen, Tran, et al. (2019b) and Nguyen, Tran, Phuong, et al. (2019) have studied the EH for a one-way single-input-multi-output (MISO) network model in which only one destination is chosen to save the energy budget.In Nguyen et al. (2018) and Ha et al. (2020), the authors introduced a two-way HD relaying network model wherein the authors in Nguyen et al. (2018) explored the performance of the system by using PS protocol for EH and evaluated it in terms of outage probability (OP), throughput.Ha et al. (2020) have studied security and reliability for a two-way HD with the existence of an eavesdropper by utilizing the hybrid time-power switching (HTPS) protocol.Phuoc et al. (2017) proposed an EH cooperation scheme in which relays suffer in-phase and quadrature-phase imbalances (IQI) and harvest energy from a wirelessly transmit source.Moreover, they also evaluated the system performance in terms of exact closed-form throughputs over Rayleigh fading channels.Finally, regarding other aspects of EH, the authors in Tin et al. (2020) and Nhu et al. (2018) have presented the power-beacon (PB) to supply the energy for sources or base stations (BS) in the device-to-device (D2D) cooperation networks.
According to a few new research works, the authors in Do, Nguyen, et al. (2020) have examined the fixed power allocation method and forecasted the performance decrement in typical situations like in non-ideal power schemes and imperfect CSI are utilized.The papers discuss NOMA supporting multiple pairs of users achieving tolerable throughput in two models, i.e. delay-limited mode and delay-tolerant mode.The authors in R. Tang et al. (2019) have considered an NOMA system that is enabled with two-way cognitive communication that can compensate for communication efficiency and also assists weak channels while communicating its data using spectrum.To balance between efficient spectrum and saving energy, the power allocation issue is also aimed to enhance the energy efficacy of the system by continuing the bit rate requirements of NOMA users.Furthermore, in Do, Tu, et al. (2020), the authors have proposed the NOMA in cooperative underlay cognitive radio networks under imperfect SIC, in which they derived closed-form expressions of the OP for two users to judge the quality of their proposed system.X. Tang et al. (2019) have examined the capability of two-way relay NOMA networks with Hardware Impairments (HI).To enhance spectral efficiency, an opportunistic relay selection method is employed.Since the relay processing performance is increased, the decode-and-forward (DF) protocol was employed.The performance of the system was analysed by the analysis and simulation.In Li et al. (2020), the authors investigated the impact of residual transceiver HI on cooperative non-orthogonal multiple access (NOMA) networks, where a − m fading channel is adopted.They also studied the imperfect CSI, imperfect SIC and finally derived new closed-form and asymptotic expressions for the OP, ergodic capacity (EC), and energy efficiency (EE).On the other hand, combining NOMA and ambient backscatter communication has been envisioned as a promising technology for the IoT networks because of their high spectral efficiency and EE in Li et al. (2021) and Li et al. (2023).In there, the authors have evaluated the system quality in terms of OP.Other aspect of benefit by using the NOMA technique, Do, Tu, et al. (2021) have probed the comprehensive performance evaluation of unmanned aerial vehicle (UAV) relay networks employing NOMA technique by adopting both amplify-and-forward (AF) and DF relaying protocols.
Different from the above-mentioned works, in this paper, we examined an uplink and downlink NOMA system by using the PS scheme for EH in the two-way HD relaying network.In particular, we derive the closed-form OP expressions at two destinations.The main contributions and novelties are given as follows:

System model
A two-way DF relaying network enabled SWIPT to support two users (S 1 and S 2 ) via the help of relay R is shown in Figure 1, wherein S 1 , S 2 are denoted far user and near user, respectively.In this circumstance, S 1 is located far away from the relay than S 2 .The dedicated relay assists the two users in exchanging information.S 1 , S 2 , and the relay R are equipped with only one antenna for each other and operate in HD.We assume that the channels are assumed to be stable and reciprocal.
To illustrate the energy harvesting and information transmission, Figure 2 can be shown.In this figure, the total time for the signal processing block is called T and will be spitted equally into three-time slots.The first time slot will be divided into two sub-intervals in which the relay R will harvest the energy from a part of power S 1 by using the PS scheme with factor β (0 , b , 1) in the first sub-interval and in the second sub-interval, R will decode the received information from S 1 with the remaining power (1 − b)P S 1 by using SIC algorithm.In the second time slot, R will operate similarly as in the first time slot but for S 2 .Finally, in the third time slot, R will simultaneously forward previously decoded information to S 1 and S 2 .We presume that all wireless connections are affected by non-selective Rayleigh fading and

are model as an independent zero-mean circularly symmetric complex Gaussian random variable with variance {V
The harvested energy, E S i , i [ {1, 2} at the relay R is given by where η (0 , h ≤ 1) is the energy conversion efficiency, P S 1 and P S 2 are the normalized transmission powers at S 1 and S 2 , respectively.We assume P = P S 1 = P S 2 , as a result, from Figure 2, the total harvested energy at R can be thus obtained as (Jameel et al., 2018) by following: (2) By using the power splitting energy harvesting protocol, the percentage of transmit power β is used for energy harvesting.The average transmit power at relay R can be formulated by Wang et al. ( 2019) Next, the received signals at R during this time slot is given as follows (Van et al., 2017) where the noise at R has zero-mean and covariance N 0 and defined as n R CN (0, N 0 ).It is worth noting that the Relay wants to detect its signal, x 2 is considered noise in this phase, and as such the signal-to-interference-plus-noise ratio (SINR) is given by where r = P N 0 is defined as signal-to-noise ratio (SNR) at user S 1 as well as user S 2 .We assume transmit power of the two users is the same.
After decoding x 1 and then subtracting x 1 from the received signal, x 2 can be detected.Hence, SNR is given by After the relay gains enough energy, it employs NOMA to serve two users at the downlink.Considering fairness among two users S 1 and S 2 , the far user S 1 needs higher transmit power from the relay R. a 1 , a 2 are denoted as power allocation factors at the users S 1 and S 2 , respectively.It is noted the condition that a 1 + a 2 = 1.We assume that a 1 .a 2 (Yue et al., 2018a) and the received signal at S i , (i [ 1, 2) can be thus expressed by Here, n S i is the additive white Gaussian noise (AWGN) at two users with zero-mean and the same variance N 0 .Therefore, the received SINR at S 2 to detect message x 1 of S 1 is given by where u = hbr.
Similarly, the received SINR at S 1 to detect its own message x 1 is given by After apply SIC algorithm (we assuming perfect SIC at S 1 ), the SINR to detect x 2 at S 1 is computed as 3. Performance analysis for two users The detection procedure of signal x 2 occurs at two devices, i.e. relay and user S 2 .In particular, the OP of S 2 can be formulated by where g 2 = 2 2R 2 − 1 with R 2 stands for the target rate at the user S 2 .
Proposition 3.1 The closed-form expression of OP at the user S 2 is claimed as With a similar approach, the OP at the user S 1 can be thus given by where g 1 = 2 2R 1 − 1, R 1 stands for the target rate at the user S 1 .
Proposition 3.2 The OP of S 1 is expressed by following: In the next section, Monte Carlo simulations are provided to validate the theoretical expressions and the impacts of various parameters on the system performance.We expect a performance gap between two users which is determined by important system parameters.

Numerical results
In this section, we numerically simulate some theoretical results from some figures to show the outage performance.In particular, the main parameters can be seen in Table 2.In addition, the Gauss-Chebyshev parameter is selected as Q = 100 to yield a close approximation, and we perform in 10 6 independent trials.
In Figure 3, we can see that the outage performance of user S 2 is better than that of the user S 1 .The main parameter ρ increases from 0 to 40 dB, which leads to significant improvement of such outage performance.Further, target rates make crucial impacts on such outage probability.In this case, R 1 = 0.05, R 2 = 0.01 is the best case.
In Figure 5, we can find the optimal OP of two users by varying the percentage of power β from 0 to 1.It is intuitively that such OP depends on SNR.In this case, r = 15(dB) exhibits the lowest value of outage probability.The reason is as follows.The smaller power splitting β, the smaller average transmit power P R at the relay is assigned.So, the received SINR will be small and it can make the worst OP at two users.On the other hand, increasing β will create the higher P R , but it will reduce the information decoding in the broadcast phase by observing Figure 2. Hence, the worst OP can be occurred when β parameter goes to 1. From above reasons, choosing a reasonable β also plays an important role to enhance the quality of the system.
In Figure 5, two users experience different outage performance since the power factor is varied.Fortunately, we can find optimal outage probability in this case, the lowest outage probability at user S 1 for the case a 1 = 0.2, and the lowest outage probability at user S 2 for the case a 1 ≈ 1.It is explained by when a 1 is increased, a 2 will be decreased, so the received SINR at S 2 will be increased by observing Equation ( 8).Hence, the OP at S 2 source will always be decreased.But, the received SINR at S 1 will be increased (based on Equation 9) or decreased (based on Equation 10).Therefore, the OP expression in  Equation ( 13) must be a concave function and we can find the optimal power allocation factor a 1 for the OP of S 1 by observing this figure.
As can be seen from Figure 6, energy harvesting efficiency results in the amount of harvested energy at the relay, then the outage performance can be changed once we change η.This observation can be explained by considering (1a), harvested energy is  decided by η.It can be explained that the higher η, the more average transmit power at the relay is assigned.Therefore, in the broadcast phase, both S 1 and S 2 sources will easily receive the information from relay.It will make the better performance of OP.

Conclusion
This paper has studied the outage performance of an EH-NOMA system to highlight the performance gap.We derived a closed-form formula of the outage probability for the far user and the near user.The advance of energy harvesting allows the relay to serve two users at the downlink.We determine the main parameters affecting outage probability for two users, such as power allocation factor, transmit SNR, and target rates.We conduct Monte Carlo simulations to validate the accuracy of our formulas.Our future work will consider multiple users at the downlink of the EH-NOMA system.

Figure 1 .
Figure 1.System model of the EH-NOMA two-way DF relaying network.

Figure 5 .
Figure 5. OP of two users versus power factor a 1 .

Figure 6 .
Figure 6.The impact of energy harvesting to OP.