ON

— Along with the explosive growth of wireless communication network users who require large frequency bands and low latency, it is a challenge to create a new wireless communication network beyond 5G. This is because installing a massive 5G network requires a large investment by network providers. For this reason, the authors propose an alternative beyond 5G that has better quality than 5G and a relatively lower investment value than 5G networks. This study aims to analyze the downlink of the cooperative non-orthogonal multiple access (NOMA) network, which is usually used in 5G, combined with the use of a reconfigurable intelligence surface (RIS) antenna with decode and forward relay mechanisms. RIS is processed with a limited number of objects utilizing Rayleigh fading channels. The scenario is created by a user who relays without a direct link for users near the base station and with a direct link for users far from the base station. Under the Nakagami-m fading channel, the authors carefully evaluated the probability of loss for various users as a function of perfect channel statistical information (p-CSI) utilizing simply a single input-output (SISO) system with a finite number of RIS elements. As a key success metric, the efficiency of the proposed RIS-assisted NOMA transmission mechanism is evaluated through numerical data on the outage probability for each user. The modeling outcomes demonstrate that the RIS-aided NOMA network outperforms the traditional NOMA network.


I. INTRODUCTION
Reconfigurable intelligent surfaces (RIS) are viewed as cutting-edge technology for the beyond fifth generation (B5G) communication system due to their potential to produce considerable increases in communication coverage, throughput, and energy effectiveness [1]- [6].According to Liaskos et al. [7], due to the vast number of inexpensive reflecting devices that make up RIS, it is possible to cleverly rearrange the reflected signal propagation to meet specific communication objectives by changing the phase shifts of every reflecting unit [8], [9].RIS is a planar meta-surface combined with a number of passive parts that can dynamically vary their reflections for various applications, including enhancing signal strength and reducing interference [10], [11].In comparison to traditional techniques like active relaying and beam shaping.RIS reflects signals in a fullduplex and noise-free manner and significantly reduces energy consumption and hardware or deployment costs by utilizing only lightweight passive elements.[12], [13].By altering the phase shifts of its passive components, RIS can artificially boost combined channel strengths and enlarge channel strengths using reflected electromagnetic waves [14].
Future wireless communication systems may benefit from NOMA, also known as non-orthogonal multiple access, which can assist several users inside a single resource part [15]- [17].In conventional wireless networks without RIS, NOMA has concerned much attention and has shown to be an improvement over orthogonal multiple access (OMA) [18], [19].NOMA can boost spectrum effectiveness while complementary user fairness and boosting network connections.The user of the robust channel employs a successive interference cancellation (SIC) approach prior to understanding the message in the downlink NOMA.This method aims to cancel out co-channel impedance from users on feebler channels [20].
Additionally, NOMA still needs to lower the energy required for the "amplify and forward" (AF) process to serve as a 5G basis.To remedy NOMA's inadequacies, a technology other than 5G is therefore required.The authors were motivated by this to create NOMA, which serves as the foundation for the 5G system that implements RIS-aided NOMA and realizes the ideas of the 6G system.[21], [22].The feasible sum rate and outage probability for a downlink NOMA framework are covered in the reference [13].The capacity to serve several customers at the same time, frequency, and code with varying degrees of power is the main benefit of NOMA over traditional OMA [23]- [25].
Many different channel types make up a Nakagami-m fading channel, with the Gaussian and Rayleigh fading channels serving as special cases.[26], [27].Men, Ge, and Zhang [28] examined the performance of an AF relaying network based on NOMA.In terms of outage probability and ergodic sum rate, he discovered that NOMA outperformed OMA, while also providing greater spectral efficiency and user fairness than Nakagami-m fading channels.Cooperative NOMA delivers the same variety of direct and superior coding gains as cooperative OMA.It is also shown that assuming the relay has lower transmitted power than the base station, outage performance improved as the distance between the relay and the indirect link user decreased [11], [29], [30].Gradshteyn and Ryzhik [31] were used to analyze the downlink NOMA system's outage performance with fixed power allocation.NOMA can offer customers with higher channel gains across Nakagami-m fading channels higher single rates than OMA [32], [33].The majority of cooperative NOMA investigations up to this point have been conducted over Rayleigh fading channels in the p-CSI state.However, the channel estimate errors make them challenging to apply in practical wireless systems.Consequently, the authors proposed a study that is anticipated to contribute the following:  The downlink system in NOMA supported by RIS can offer a reduced probability of blackout than conventional NOMA, according to the study's model scenario. Closed-form outage probability estimates for the RISassisted NOMA system are created.Since they are defined in terms of a wide range of various system parameters, it is possible to mathematically analyze how each system parameter affects the probability of an outage.For occurrence, the effect of the number of meta-surfaces in a RIS on the likelihood of an outage can be analyzed to improve the system's performance in actual operation.This study demonstrates that the number of meta-surfaces in RIS significantly impacts the system's outage probability.

II. MATERIALS AND METHOD
As seen in Fig. 1, we propose a two-user NOMA downlink based on RIS.A set of user groups is divided using orthogonal access.We suppose that each group contains representative users, such as a near-user (U1) and a far-user (U2), who are categorized according to their geographic location.The BS generates two beamforming vectors using the zero-force beamforming technique to serve two NOMA users.RIS-NOMA is helpful for developing various services since it can accommodate a wide range of Quality of Service (QoS) needs by grouping paired users.Once the user relies on the direct link connected to the BS, it becomes difficult.
Fig. 1 The system models Users U1 and U2 receive signals that are described by equations ( 1) and ( 2), respectively.
Where, is interference term from U1 with (0, $ ) and $ is the constant.Additionally, nU1 and nU2 are AWGN noise terms, which are interference signals from outside sources that can be considered AWGN noise when combined with (0, &).The complex Gaussian channel vector terms for links RIS-U1 and BS-RIS, respectively, are denoted by the symbols and ℎ .User U2 and the BS follow Rayleigh fading, while hD2 is the corresponding fading channel between them.The matrix θl (l = N) contains diagonal elements '( − )* ) with θl standing for the reflection phase shift.
First, by performing SIC, the SINR of U1 to detect x2 is given as mentioned in Eq. ( 3), where, + = , - . .Then, the SINR at U1 to detect x1 is given as Eq. ( 4).U2 receives direct signal x2 from Base Station (BS).The SINR of U2 to detect x2 is given as Eq. ( 5). A. 9 ; < > ; ?@AC + + 1 (3) /0 1(2 ,E: ) = 5 ,FG = ℎ + + + 9 : > : As shown in Fig. 1, a link is defined as the BS transmitting a signal to U1 via RIS.Two channels are available on this link, one from BS to RIS and the other from RIS to U1.The U2 is one user who receives a signal from BS via one of the channels.The notation denotes the fading channel from RIS to U1 , while the channel's fading coefficient of BS to RIS is represented byℎ .Additionally, other links involve the BS communicating with U2 via hD2.
By using RIS, physically, the fading channel ℎ and are related by ℎ H I relation, where I is denoted as phase shift.Using RIS, the fading channels ℎ and are physically connected by the ℎ H I relation, where I stands for phase shift.The authors assume that the link is composed of several channels.Special instances of the Nakagami-m distribution's broad spectrum include the Gaussian channel and the Rayleigh channel.Therefore, it is assumed that each channel has a Nakagami-m distribution.
The general form of PDF for Nakagami-m distribution [34] for one channel function is mentioned by Eq. (6).
where, χ, η and m are path-loss coefficients, relative channel estimation error of channel and fading parameter, respectively.Because S(T) = (T − 1)!, then Eq. ( 6) could be rewritten as Eq. ( 7) Cumulative Distribution Function (CDF) could be obtained by integrating the PDF above and expressed by Eq. ( 8) Based on Eq. ( 7) and Eq. ( 8), we create the formula for calculating the connection outage probability for each user.Initially, let's assume that Z and Z stand in for the proper U1 and U2 target levels.The two SNR thresholds, + [ℎ and + [ℎ can be expressed as Equations.( 9) and (10), respectively.
Equations ( 3) and ( 4) can be used to obtain it as ^ and ^ , the first and second comparison parameters against the SNR threshold, resulting in the equations: To achieve closed-form outage performance, a parameterb c is defined as a gain in the channel coefficient of Eq. ( 13) is used to express mv as the gamma distribution shape factor for the link v large-scale fading channel.
where m1 and m2 are the gamma distribution shape factors for the large-scale fading channel on U1 and U2, respectively, and v is the link index in this instancet ∈ {1,2}.
The following might be written for PDF and CDF by integrating RIS in the NOMA network.
The additional events of the outage in this study take place at U1.When U1 correctly decodes both the signal x2 and its own signal x1, Eq. ( 16) could be used to express the outage probability of U1.
The outage probability at U1 could then be expressed in Eq. ( 21).
(Proof: See in Appendix A.) Similar reasoning might be used to determine the likelihood of an outage at U2.According to the system model, the received signals which are received by U2 consist of direct signals from BS and rely on a signal from U1.The relying signal from U1 is the link BS → U1 through RIS, which decodes signal x2 for U2, which has and could be mentioned as Eq. ( 16) above.We give the symbols dash-line the system model for this link, and there is no received signal by x2 from RIS.Furthermore, the direct signal from BS to U2 that has SNR as Eq. ( 5).
The first of two occurrences that make up the outage probability at U2 is the inability of U1 to decode the signal x2.In addition, in the second instance, U2 is unable to decode its own signal x2 from BS, while U1 can positively decode the signal x2.In light of these occurrences, the following equation can be used to express the U2 outage probability.
τ4 is fourth-comparison-parameter against to SNR threshold.The link's gamma distribution at U1, U2 has scale factors δ1, δ3.

III. RESULT AND DISCUSSION
In this part, the outage probability is simulated using mathematical derivations, and the simulation is validated using a Monte-Carlo simulation.Table 1 specifies the simulation parameters that will be used in the numerical simulation.Furthermore, the large-scale fading coefficient [dB] at near-user and far-user locations is modeled by βk..
where,˜∈ {/2 , /1, 12 , /2 , /1, 12 , 2 2 } and -OE is the shadow fading.Additionally, simulations are produced by changing settings in the MATLAB programming language.Monte Carlo simulations are used to validate the exact expressions of the outage probability.The previous investigations' findings were numerically supported by mapping the sites into the Cartesian coordinate system.

Description
The antenna gains at transmitter and receiver For user U1, Fig. 2 displays the simulation and analytical findings of the outage performance against SNR while using the RIS on the NOMA network for various RIS element counts.The outage performance versus SNR by NOMA Network is also compared.The graph clearly shows that as the number of RIS pieces rises, the probability of an outage falls.The NOMA network's RIS implementation performs better during outages after the installation of RIS components.Additionally, it performs better than the NOMA outage performance of the network system.This demonstrates that the suggested RIS-NOMA system performs effectively, as predicted by our study.For user U2, Fig. 3 displays the outage probability versus SNR simulation results and analytical findings without RIS.Additionally, the SNR of U2 is used to compare NOMA Network's outage performance to that of U2.We can see that the proposed system performs well without RIS-NOMA since U2 just receives the signal through the relaying link and receives the signals as direct links, enhancing signal dependability.According to our research, U2 performs better during outages when there are more RIS elements.Furthermore, it is evident from the aforementioned two figures that U2's outage probability outperforms that of U1.Fig. 4 compares the outage probability versus SNR for various numbers of RIS elements for near-user U1 and far-user U2 based on simulation and analytical results.In this comparison, it is clear that the near-user U1 performs significantly better than the far-user U2 as the number of RIS elements grows.It proves that even without amplification and forward (AF) mode, the RIS implementation on the NOMA network can outperform the NOMA network in terms of outage performance.The only mode utilized is decoded and forward (DF).

IV. CONCLUSION
In this study, we deduced how well a RISNOMA system performed during an outage.The closed-form equation was discovered for the probability of an outage for users U1 without a direct link and U2 with a direct link.We simplified the system performance study on the gap between two users by assuming Nakagami -m with p-CSI, and this paper only focuses on the major performance parameter, outage probability.To confirm the correctness of our formulas, Monte Carlo simulations are performed.Future development will take multiple users at the RIS-NOMA system into consideration.

APPENDIX B PROOF OF PROPOSITION
According to the equation of 5 ,FG , in the Eq.(B.1).

,FG =
We derive ^• base on the system model, which could be conducted as follows.If it is defined ¡ = ℎ V and} • = 9 : > : The outage probability at user U2 could be shown as follows.

Notation Definition Â(Ã)
A superimposed signal is sent to both the near (U1) and far (U2) users.
link v brought about by the implementation of RIS.If the RIS parts show random shifts, the definition b c = |ℎ H e c | is applicable.Furthermore, we determine f{b c } = f{|b c i + | }and variance Var(b c ) are calculated in appendix A.

TABLE I SIMULATION PARAMETERS
Distance of BS − U , BS − RIS, and RIS − U > : , > :; , > ; Distance of BS − U , BS − RIS, and RIS − U ℎ , ℎ , ℎ , , Coefficients of fading channel + Transmit signal-to-noise ratio (SNR) + →At U1, examine the incoming signal for interference and noise ratio in order to decode it (SINR).The first-comparison parameter, the secondcomparison parameter, and the thirdcomparison parameter are all variables.} , } Interference and noise due to the using of RIS-aided of U1 and U2 x , x Scale factor of the gamma-distribution of the channel of U1 and U2 ^ , ^ and ^•