Collaborative Relay Radio Network Using Reconfigurable Intelligent Surface

In this paper, we have studied a model of a relay radio network system using Reconfigurable Intelligent Surface (RIS). Specifically, we used a relay network that uses RIS when there is an extra direct link from the Source (S) to the Destination (D). Next, an approximate closed-form expressions of the Outage Probability (OP) and Ergodic Capacity (EC) are considered. Based on the simulation results of OP and EC, the results show that our proposed system is more optimal than the system using supported RIS without direct link and the system without using RIS. In addition, changing the number of the RIS reflecting elements and the RIS’s location near (S) or (D) has a significant impact on the performance of the system. The analytical expression match the simulation results through the Monte Carlo simulation method. Furthermore, the simulation results of energy efficiency (EE) also show that when the target spectral efficiency (SE), Rth, is high (more than 5.45 b/s/Hz), the system using supported RIS with direct link will help reduce the transmit power and optimize the most energy compared to the other two systems.


Introduction
5G network technology is the 5th network technology, the successor to the extremely popular 4G LTE connection before. As its successor, the 5G network enables the transmission of large amounts of data at outstandingly high speeds, improved bandwidth, reliability in connection, along with maintained signal latency. maintained to a minimum, … This will bring more challenging engineering problems, requiring new and more efficient communication models, especially at the physical layer.
To meet the diverse requirements of current 5G networks as well as for future B5G and 6G system design, Non-Orthogonal Multiple Access (NOMA) is identified as an important technology that can satisfy requirements mentioned above [1]. The most prominent feature of the NOMA technique is that it supports a larger number of USERs than the number of orthogonal resource slots through facilitating simultaneous power and wireless transmissions have been highlighted. in [28]. Bidirectional communication between users supported by RIS was investigated in [29], where compatible or incompatible channels were calculated.
Based on the combination of two protocols RIS-NOMA is also interested and selected in the systems. Recent studies such as a system to serve users with NOMA by designing passive beamforming weights at RISs have been proposed in [30]. The results of the analysis demonstrate that the base station (BS) and user associations have little effect on the diversity orders achieved when the number of RIS is high enough. Calculation results are provided to confirm that the high Signal-to-Noise-Ratio (SNR) gradient of the RISsupported network is one and that the proposed RISsupported NOMA network has superior network performance compared to its orthogonal counterpart. Another wireless communication IoT model is introduced that exploits the main benefits of NOMA and RIS technologies in Simultaneous Wireless Information and Power Transfer (SWIPT) network which has been proposed in [31] The results highlight the benefits of public exploitation. RIS technology in the SWIPT IoT network supports NOMA and future direction. Another system, Simultaneously Transmitting And Reflecting Reconfigurable Intelligent Surface Non-Orthogonal Multiple Access (STAR-RIS-NOMA) proposed in [32], demonstrates that: 1) STAR-RIS-NOMA outage probability is better than that of STAR-RISsupported Orthogonal Multiple Access (OMA) and conventional cooperative communication systems; 2) With the increase of K configurable factors and Rician factor κ, the STAR-RIS-NOMA network is capable of achieving performance enhancement; and 3) The ergodic rate of STAR-RIS-NOMA is higher than that of STAR-RIS-OMA.
The key contributions of this work are summarized as follows: • First, we introduce the method of moments for characterizing the end-to-end channel (e2e) of a wireless system. In the Nakagami-m fading environment, we show that the distribution of the e2e channel coefficient magnitude of the system can be approximately equal to the Gamma distribution. • Next, for system performance analysis, approximate closed-form expressions for the Outage Probability (OP) and Ergodic Capacity (EC) of the system are built. In addition, we provide specific analyzes on the accuracy of the proposed approximation distribution, i.e., accuracy in using the Gamma distribution to estimate the true distribution of the e2e channel coefficient. • Finally, in our simulation, we consider the actual simulation settings, as shown in Table 1. Notably, our simulation results are in good agreement with the analysis formulas. included in all articles. From the above results, they reveal that the system using RIS support has a better direct path than the two systems: the system using RIS supporting no direct path and the system using no RIS in terms of OP and EC. In addition, our system achieves the highest Energy Efficiency (EE)

EAI Endorsed Transactions on Mobile Communications and Applications
Online First Collaborative relay radio network using reconfigurable intelligent surface 3 within a specific range of the target Spectral Efficiency (SE). We also built a simulation result of the actual RIS installation location. This result only shows that the number of elements installed at the RIS and the location of the RIS has a significant impact on system performance. In summary, we show that our proposed system is the most optimal in all three important parameters OP, EC and EE compared with the remaining models, as well as the impact of RIS placement. actual and the number of passive reflectors on the RIS to the system performance.

System model
We consider a low complexity communication system. There, the system has a Source (S) and a User (Destination) (D), both of which are equipped with a single-antenna node. (S) communicates with (D) via direct link supported by a Reconfigurable Intelligent Surface (RIS), R, which passively reflects signals from (S) to (D). The system is described as follows (figure 1): Assuming that a RIS (N=1) has L discrete reflector elements, we set h0  C , h1r

Signal-to-noise ratio (SNR)
Definition: The signal-to-noise ratio, S/R, or SNR (Signal to Noise Ratio) is defined as the ratio between the output power of the transmitted signal and the power of the noise that damages that signal. This amplitude is measured, like almost everything related to sound and is expressed in decibel (dB) [38]. First, the signal that can be received at (D) is shown as follows: The end-to-end SNR (e2e) received at (D) is given by: Huu Q. Tran, Nguyen Trong Duy, and Huynh Phan Hieu Nghia Where m > 0 is the shape parameter and  > 0 is the spread parameter of distribution.
We have ( , ) X Nakagami m  . Note that the parameter  denotes the mean squared value of X, , which is equivalent to the mean channel gain (power). The magnitude distribution of each channel coefficient can be expressed as: Let Y be a RV that follows a Gamma Distribution, with parameters being , . The PDF and CDF are given by [40]: where,  > 0 is the shape parameter and  > 0 is the

Theorem 1:
To simplify the notations, in the analysis we set where D is the magnitude of the e2e channel coefficients. Since , which can be written as follows: Now, we turn our attention to the k -th moment of R . The exact PDF function of R given by ([39]-eq. (90)): In there, . The detailed derivation in (8) can be briefly presented as follows.
The purpose of this inference is not only to accurately represent the PDF function of R , but also to show that the magnitude of the synthesized channel of the individual dualhop channel with respect to a single reflecting element of a RIS in the system follows the Generalized- distribution [41,43]. Back, for a given r , R represents the passively reflectors as independent RVs and identically distributed, 12 , rr hhconversely as independent random variables but undistributed RVs. On the other hand, we know that , so the PDF of R can be rewritten to: Besides, we already have (3) the PDF of R is written as: The exact PDF of R is written to (8). Therefore, we can conclude that R follow the KG distribution with the shape parameters is 12 , hh mm. Based on the exact PDF of R , we get the can be rewritten as: Based on the k -th moment of R obtained in (11), we set according to the Gamma distribution. Note that, for a given r, R are independent and identical distributions RVs. We have [40]: Where:

EAI Endorsed Transactions on Mobile Communications and Applications
Online First Collaborative relay radio network using reconfigurable intelligent surface Therefore, the approximate distribution of AR is: Therefore, the approximate CDF and PDF of AR are given by: where (17)

Outage probability (OP)
Definition: The Outage Probability of the system is the probability that the e2e signal-to-noise ratio is less than a given threshold value [47]. We first construct the correct distribution of the main component of D, i.e., AR according to gamma distribution, which is shown in (15).
We then obtain the approximate closed-form expressions for PDF and CDF of D. Specifically, since 0 h and AR are independent RV and 0 , 0 R hA . We have the SNR e2e received at (D), (2) can be rewritten as: The statistical characteristics of the e2e channel coefficient magnitude are presented in the following theorem.
Theorem 2: The approximate closed-form expressions for CDF and PDF of D can be obtained as follows, respectively: (4) and (16).
Based on Theorem 2, a closed-form approximation for OP can be written as: (22) can be rewritten as: be written similarly to (20).

Total power consumption of the system Definition:
The total power consumed to operate the system including the transmit power at the Source (S), as well as the static power of the hardware components involved [34]. From there, the total power consumption of the system supported by RIS is presented as follows:

Energy Efficiency (EE)
Definition: Energy efficiency is defined as the ratio between the system achievable sum rate and the total power consumption of the system [23]. From the above definition, the energy efficiency (EE) of the system is expressed as follows:  To clarify how the system works, we design a diagram as shown in figure 2. It shows that the signal from the source is decoded at the same time for both cases: decoding the information to the user by direct link and decoding of information to the user by cooperative forwarding using RIS. If the user fails to decode its own signal from the direct link in the first place, its received signal from the direct link is retained and combined with the cooperative relay signal via the use of RIS in second place. The decoded signal at the user is a combination of the two signals above.

IV. Numerical results
In this section, we provide the results on the PDF and CDF of D that follow the Gamma distribution, as well as the OP, EC of the system. The simulation results verify the correctness of the analytical formulas developed above and also to provide detailed information about the system's performance. The results indicate that changing the number of reflective elements of the RIS (L) and the location of the RIS affects the PDF and CDF and more importantly, it also affects the OP and EC parameters of the system. This is very important for the practical application of this surface, as well as being the foundation for developing this completely new technique to work more effectively in the future.

EAI Endorsed Transactions on Mobile Communications and Applications
Online First       Figure 5. CDF of D in the following cases: L=50, L=75 and L=100.

Figures 4 and 5
describe approximate PDF and CDF that are well-suited to real PDF and CDF (theorem 2), which are numerically estimated based on data simulation. Besides, we also see that when we change the number of reflective elements (L), the variable range of x also changes, leading to changes in the variable values of PDF and CDF. Evidence, when increasing the number of RIS reflectors (L) from 50, 75 and 100, respectively, the x variability range also changes from 0.5 to 1.25, from 0.75 to 1.5 and from 1.25 to 2, respectively. And the x range changes, the value of the PDF and CDF also changes accordingly. Next, in figure 6, we have a simulation of the Outage Probability (OP) of the system with OP as a function of PS, presented in Eq. (23). As can be seen, the theoretical and simulated results are well corroborated, so our developed analytical formula is validated. In addition, we can see in figure 6, with fixed RIS coordinates, as the number of reflective elements (L) increases, the OP decreases sharply. The proof is that when we consider the case of the system using supported RIS with direct link, with L=50, when PS = 10 dBm, OP equals 10 -1 . With L=75, when PS= 10 dBm, OP drops to less than 10 -4 . With L=100, when the PS = 10 dBm, the OP drops much deeper to less than 10 -5 . In addition, the OP's simulation results also show that the system using supported RIS with direct link is the most optimal when compared with the other two systems: the system not using RIS and the system using supported RIS without direct link. Similarly, in figure 7, we have a schematic diagram of the Ergodic capacity (EC) simulation of the system with EC as a function of PS, presented in Eq. (24). As can be seen, the theoretical and simulated results are well corroborated, so our developed analytical formula is validated. In addition, with a fixed RIS position (xRIS = 50, yRIS = 5), changing the number of reflective elements also changes the EC. For example, we consider the case of a system using supported RIS with direct link, with L =50, when PS = 10 dBm, EC equals 1.5 [b/s/Hz]. With L = 75, when PS = 10 dBm, EC increases to 2 [b/s/Hz]. With the RIS coordinate of [85;5], when PS = 10 dBm, EC rises to almost 3 [b/s/Hz]. In addition, the simulation results of EC also show that the system using supported RIS with direct link is the most optimal when compared to the other two systems: the system not using RIS and the system using supported RIS without direct link.     Next, in figure 11, we have a simulation of the Outage Probability (OP) of the system with OP as a function of PS, presented in Eq. (23). As can be seen, the theoretical and simulated results are well corroborated, so our developed analytical formula is validated. In addition, we can see in figure 11, with fixed RIS coordinates, with the number of reflectors (L) kept the same in three cases of 50, when the closer the RIS position (S) or (D), the more sharply the OP decreases. For example, we consider the case of a system using supported RIS with direct link, with RIS coordinates of [50;5], when PS = 10 dBm, OP equals 10 -1 . With a RIS coordinate of [75;5], when PS = 10 dBm, OP drops to less than 10 -2 . With a RIS coordinate of [85;5], when PS = 10 dBm, OP drops to less than 10 -5 . In addition, the OP's simulation results also show that the system using supported RIS with direct link is the most optimal when compared with the other two systems: the system not using RIS and the system using supported RIS without direct link.  In addition, the simulation results of EC also show that the system using supported RIS with direct link is the most optimal when compared to the other two systems: the system not using RIS and the system using supported RIS without direct link.

Comparison of Energy Efficiency (EE)
between a system using supported RIS with direct link, a system using supported RIS without direct link and a system not using RIS Next, we will investigate the effect of the target SE (Rth) on the source transmit power (PS) and the Energy Efficiency of the system (EE). Furthermore, we also compare the above parameters for the cases where the system using supported RIS with direct link, the system using supported RIS without direct link and the system not using RIS.

EAI Endorsed Transactions on Mobile Communications and Applications
Online First Figure 13. Comparison of the transmit power at (S), PS [mW], between the system using supported RIS with direct link, the system using supported RIS without direct link and the system not using RIS, with PS is a function of the target SE, Rth [b/s/Hz]. Figure 13 shows the simulation results of the transmit power (PS) of the system, where PS is a function of Rth. When Rth > 5.45 [b/s/Hz], the non-RIS system requires the highest transmit power, the RIS-supported direct link system requires the lowest transmit power. From that, we conclude that using supported RIS with direct link systems can help reduce the transmit power, leading to improved EE for the system. To prove the above conclusion, we will analyze the simulation results of EE in Figure 14 below. In Figure 14, we have a schematic diagram of EE simulation of the system with the EE as a function of Rth, presented in the Eq. (27). Specifically, when Rth (0; 5.45] [b/s/Hz], the system non using RIS provides the highest EE compared to the other two systems. Meanwhile, when Rth > 5.45 [b/s/Hz], the system using supported RIS with direct link provides the highest EE compared to the other two systems. Therefore, we can conclude that a system that transmits information directly from (S) to (D) is more appropriate both in terms of minimizing transmit power (PS) and maximizing energy efficiency (EE), except when a high target SE (Rth) (greater than 5.45 b/s/Hz) is required, then we should use a supported RIS with direct link system to maximize system performance.

V. CONCLUSION
In this paper, we have studied a lowly complexity radio network model. Specifically, we used a relay network using a Reconfigurable Intelligent Surface (RIS) with a direct link. The Closed-form expressions of Outage Probability (OP) and Ergodic Capacity (EC) are considered. Based on the simulation of OP and EC, the results indicate that our proposed system is more optimal than the system using supported RIS without direct link and the system not using RIS. We have shown that given the total number of passive reflectors, the element allocation and location of the RIS have a significant effect on the performance of the system. Specifically, the more the number of reflectors and the closer the RIS is to the source or destination, the more it will help optimize the system. The analytical expressions match the simulation results through the Monte Carlo simulation method. Furthermore, the system using supported RIS with direct link achieves better EE than the other two systems when the value of the target SE reaches a specific value (more than 5.45 b/s/Hz). Therefore, the system using supported RIS with direct link will help reduce the transmit power and optimize the most energy compared to the other two systems.
APPENDIX C

APPENDIX D
First, we rely on the theorem of total probability [40] and the definition of conditional probability [40] to determine the probability of D. The CDF of D which can be given by: If we replace (16) in (29), it will lead to an integral analysis that is not expressed in closed-form. To solve this problem, (29) will be rewritten to: Using the M-staircase approximation (a method used to approximate the integral analysis of one or more layers, similar to the Riemann-Sum [42]), (30) can be rewritten to: