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# Performance Study of RIS Assisted NOMA
Based Wireless Network with Passive IoT
Communication

B. Aswini<fnref n="1" />(✉), Laxmikandan Thangavelu<fnref n="2" /> ID, and Manimekalai Thirunavukkarasu<fnref n="2" /> ID

aswinipkt@gmail.com

**Abstract.** Reconfigurable Intelligent Surface is a new promising solution for energy and spectrally efficient wireless communication. RIS consists of passive reflecting elements which are low-cost and small-sized elements. RIS reflects the phase-shifted form of incident electromagnetic waves. This work aims to study the passive IoT transmission through RIS in the NOMA network. At the base station, NOMA combines message signals for two different users at different power levels through a superposition coding process in a single resource block. Here passive transmission of IoT data connected to the RIS is enabled by changing the reflection pattern according to the information to be transmitted. While the phase shift introduced by the reflective elements is optimized to improve the rate at the far user, the system's ergodic rate is also marginally improved. The successive Interference Cancellation technique is utilized for decoding different message signals at the users. The performance of RIS-assisted NOMA with passive IoT communication is analyzed regarding its ergodic rate and outage probability.

**Keywords:** NOMA · RIS · IoT · Outage · Ergodic rate

## 1 Introduction

Recently many technologies have been developed to meet demand like high data rates, low response time, and denser connectivity. However, these technologies still have some degradation such as power consumption and hardware cost. The traditional reflecting elements can produce a controlled phase shift which is not adopted by the time-varying channel. RIS is being used as a solution for the above issue in the wireless network. A reconfigurable intelligent surface is a new two-dimensional hardware surface that consists of N number of passive reflective elements. Each reflective element can be reconfigured in a specific direction. The control is on the smart controller which is connected to RIS. Especially, RIS controls the phase angle of the incident signal to be a constructive addition to the receiver. This improves SNR at the receiver, which leads to an increase the energy and spectral efficiency. RIS is placed on a building, lamp post, etc., and easily fixed on a flat surface. Passive RIS does not need signal processing techniques such as amplification, analog-to-digital converter, and digital-to-analog converter.

<footnote n="1">¹ CEG, Chennai, India</footnote>

<footnote n="2">² CEG, Anna University, Chennai, India</footnote>
NOMA is being used for throughput enhancement in a 5G wireless network as it serves N number of (multiple) users in the single resource block (frequency, time, code), Where the users are distinguished in terms of their power levels. In a two-user downlink case, one of the users must be a far (weak) user which is far away from the base station with poor channel quality, and the other as a near (strong) user which is close to the base station with better channel quality. Superposition coding is done at the base station which combines encoded message signals. Successive interference cancellation is used for decoding message signals. Far users can directly decode their own information by treating others as interference. Near users first, decode far user message signal, and decoded information is subtracted from the received signal at the near user then finally decode their own message signal (near user message signal) with the help of SIC. Though NOMA has interference from other message signals, it improves data rate and connectivity even with a single resource block. OMA technique is interference-free transmission when compared with NOMA but with limited capacity. The strength of the desired signal should be high while decoding the received message signal. RIS-assisted NOMA network can provide improvement in rate due to simultaneous suppression of interference and increased received signal strength.

IoT device consumes more energy for sensing, collecting, and transmission of data in the wireless sensor network. IoT device requires data transmission for a short distance at low rate. As the battery is the power source for IoT devices, frequent recharging of the battery becomes a big issue in these networks. Power efficiency is a major challenge in IoT networks which is solved by using RIS. We are interested to perform NOMA transmission as well as IoT transmission in the same network.

The concept of NOMA, its scope in 5G is discussed in [1-3] and explores the opportunities, future research, and challenges of NOMA. An optimal power allocation scheme for users involve in NOMA network [4] is proposed, to maximize sum capacity with a fixed target and user fairness index. The outage and sum rate for uplink NOMA were derived and analyzed for its performance. AmBC [5] consists of a primary RF source (base station), a secondary backscatter device, and a reader. A backscatter device conveys information over an RF signal. A reader only recovers information from the backscatter device and not from the primary RF source. CAmBC [6] involves a reader which recovers information from both the primary RF source and secondary backscatter device. Ambient backscatter communication is investigated under the performance metrics of capacity and outage probability in [7]. BD device performs two operations: A small part of the signal from the source (base station) is used for energy harvesting and the remaining signal at the BD is used for cellular transmission. The low complexity algorithm was proposed for reducing computational complexity in [8]. Backscatter NOMA is obtained by combining downlink NOMA with backscatter devices. The base station serves two users along with a backscatter device. Backscatter NOMA turns into a symbiotic system when one of two users is absent. The outage probability and ergodic rate of both systems are derived and for their performance is analyzed.

The significance of RIS is listed in [9] for 6G generation and beyond the wireless network. In wireless systems, the strength of the received signal could be low due to channel conditions. This issue is resolved by using RIS whose elements introduce phase shifts so that received signals add constructively at the receiver. Large Intelligent Surface
simultaneously enhances primary transmission and also sends IoT data which is based on spatial modulation technique on LIS element. RIS-involved symbiotic radio system was proposed for the 6G network [10]. RIS-assisted NOMA proposed [10], where RIS produces phase shifted version of the incident signal to increase the SNR of the NOMA users. RIS-assisted NOMA obtains a high rate compared with conventional NOMA. From the literature survey, it is found that the incorporation of NOMA and RIS can achieve a higher rate and IoT devices connected to the RIS can also establish its own data communication by switching between the elements of meta-surfaces which could be referred as the spatial modulation scheme.

## 2 System Model

The system model consists of downlink NOMA, in which the base station is built with a single antenna and communicates with two single antenna users. The base station transmits superposition-coded signals to two users under NOMA protocols with the support of RIS. At the same time, IoT data is transmitted and modulated by switching on/off the elements present in the RIS which is based on the spatial modulation technique. RIS consists of 8 reflecting elements. The modulation of IoT information is given below (Table 1).

<table><caption>**Table 1.** IoT information and Index of active RIS elements</caption><thead><tr><td>IoT data symbol</td><td>Index of Active RIS elements</td></tr></thead><tbody><tr><td>0</td><td>1,2,3,4</td></tr><tr><td>1</td><td>5,6,7,8</td></tr></tbody></table>

The channel between BS-near user, BS-far user, BS-RIS, RIS-near user, and RIS-far user are assigned as $h_1$, $h_2$, f, $g_1$, and $g_2$ respectively. These channels follow Rayleigh fading distribution.

Superposition coded signal at the base station is given by

$$x(t) = \sqrt{\alpha}px_1(t) + \sqrt{(1-\alpha)}px_2(t) \quad (1)$$

where, p is the total transmit power, $\alpha$ is the power allocation factor for a near user, $(1-\alpha)$ is the power allocation factor for a far user, $x_1(t)$ and $x_2(t)$ are near and far user message signals respectively.

The transmitted signal reaches the near user, and the signal at the near user is expressed as

$$y_1(t) = h_1x(t) + g_1^T \Theta S f x(t) + n_1 \quad (2)$$

The signal at far user is expressed in mathematical form as

$$y_2(t) = h_2x(t) + g_2^T \Theta S f x(t) + n_2 \quad (3)$$
<figure><img src="image_3.png" /><figcaption>Fig. 1. RIS-assisted NOMA with IoT device</figcaption></figure>

The first term represents a direct link from the base station in both received signals. The second and third terms in the received signals denote link from RIS and AWGN noise. $\Theta$ is a diagonal phase shift matrix that is produced by RIS, and is represented as $\Theta = diag\{\theta\}$, where $\theta = [\theta_1, \theta_2, ..., \theta_N]^T$. Each element n in the RIS produces a controlled phase shift which is given by $\theta_n = \theta_{h1} - \theta_f - \theta_{g1}$. Let S be the diagonal state matrix which is expressed as $S = diag\{s\}$ and $s_n = [s_1, s_2, ..., s_N]$ contain IoT information. If we use BPSK scheme for IoT modulation, the active index of RIS elements is tabulated in Table 1. Suppose RIS has 4 reflecting elements, $\Theta S$ is given by

$$ \begin{bmatrix} e^{j\theta_1} & 0 & 0 & 0 \\ 0 & e^{j\theta_2} & 0 & 0 \\ 0 & 0 & e^{j\theta_3} & 0 \\ 0 & 0 & 0 & e^{j\theta_4} \end{bmatrix} \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{bmatrix} = \begin{bmatrix} e^{j\theta_1} & 0 & 0 & 0 \\ 0 & e^{j\theta_2} & 0 & 0 \\ 0 & 0 & e^{j\theta_3} & 0 \\ 0 & 0 & 0 & e^{j\theta_4} \end{bmatrix} $$

$s_n$ takes the value either 0/1 to denote on/off the reflecting elements. IoT data is modulated by making the reflecting elements on/off. The baseband equivalent channels are $h_j \in c^{1 \times 1}$, $g_j \in c^{N \times 1}$, $j = 1,2$ and $f \in c^{N \times 1}$ for BS-users, RIS-users, and BS-RIS links respectively. Here we assume that the perfect channel state information is known at the RIS.

The IoT device information is intended for the user 1. Therefore user 1 supposed to receive its own data as well as data from the IoT device. User1 first decodes far user message signal, then its own message signal, and finally ends with IoT data/information. User 1 decodes its own information with the help of successive interference cancellation. While decoding far user information, the SINR at user1 is,

$$ \gamma_{1,2} = \frac{p(1 - \alpha)|h_1|^2}{p\alpha|h_1|^2 + p|g_1 \Theta S f|^2 + \sigma_1^2} \quad (4) $$
When decoding near-user information at near user, the SINR is given by

$$ \gamma_{1,1} = \frac{p\alpha|h_1|^2}{p|g_1\Theta_Sf|^2 + \sigma_1^2} \qquad (5) $$

SNR for IoT information decoding at near user is given

$$ \gamma_{1iot} = \frac{p|g_1 \Theta_S f|^2}{\sigma_1^2} \qquad (6) $$

Far user message signal is directly decoded by treating others information as interference. While decoding far user information at far user, the SINR is

$$ \gamma_{2,2} = \frac{p(1 - \alpha)|h_2|^2}{p\alpha|h_2|^2 + p|g_2\Theta_Sf|^2 + \sigma_2^2} \qquad (7) $$

## 2.1 Outage Probability

At any receiver, if the SNR of a received signal is equal to or greater than the threshold (fixed) value of the target SNR, the received signal will be decodable. If the SNR of the received signal is less than the threshold (fixed) value of the target SNR, The received signal will not be decodable. If it is not decodable, it will lead to an outage. Decoding of the IoT data at the near user is possible after the successful decoding of far user and near user data, Hence the condition for the outage probability of IoT user is written by $P_{outiot} = P \{ \gamma_{12} < \gamma_2^* \gamma_{11} < \gamma_1^* \gamma_{1iot} < \gamma_{*iot} \}$.

Where $\gamma_{12}$ and $\gamma_{11}$ are the SNR of user 2, and the SNR of user1 respectively, $\gamma_{1iot}$ is a SNR of the IoT user at near user case. Where $\gamma_2^*$, $\gamma_1^*$ are target SNRs for far user and near user respectively, $\gamma_{*iot}$ is a target SNR for IoT. Near-user first decodes the far-user message signal, then the far-user message signal is subtracted from the received signal at the near user, decodes the near-user message signal, and then decodes IoT data/information. Outage probability for the near user is analyzed under three conditions. Different target SNRs will be fixed for each user. Target SNR which is based on rate i.e. $\gamma^* = 2^{R_1}$.

As the far user can decode directly its own information by considering others in the received signal as interference, the outage probability is given as $P_{out2} = \{ \gamma_{22} < \gamma_2^* \}$.

Near-user information can be decoded after the successful decoding of the far-user message signal. $P_{out1} = \{ \gamma_{12} < \gamma_2^*, \gamma_{11} < \gamma_1^* \}$.

## 2.2 Ergodic Rate

Ergodic rate is a measure of maximum data supported by the channel when the SNR is varying. The unit of ergodic rate is b/s/Hz. Ergodic rate for near user, far user, and IoT device are given as,

$$ R_1 = \log_2(1 + \gamma_{11}) \qquad (8) $$
$$R_2 = \log_2(1 + \gamma_{22}) \qquad (9)$$

$$R_{iot} = \log_2(1 + \gamma_{1iot}) \qquad (10)$$

## 3 Results and Discussion

The simulation environment contains a base station, two NOMA users, and RIS connected with an IoT device. The distance between each channel link that is BS-near user, BS-far user, BS-RIS, RIS-near user, and RIS-far user. These links are assumed to be 500 m, 750 m, 450 m, 50, and 600 m. The power allocation coefficient for the near and far users is fixed to be 0.25 and 0.75. The noise power considered is -90 dBm. Monte Carlo simulation is carried out for 10000 runs. The performance of the proposed system in terms of Ergodic rate and outage are plotted and compared with the system consisting of RIS-assisted NOMA without an IoT device.

<table><caption>**Table 2.** Target Rate for each receiver</caption><thead><tr><td>Receiver</td><td>Rate (b/s)</td></tr></thead><tbody><tr><td>Near user</td><td>1.9</td></tr><tr><td>Far user</td><td>1.9</td></tr><tr><td>IoT device</td><td>0.01</td></tr></tbody></table>

Fig. 2 shows outage probability for RIS-assisted NOMA. Outage probability for both users are plotted here. The outage is obtained based on its threshold value (target SNR). If the achievable SNR/SINR is greater than the threshold value, the received signal will be decodable. Otherwise, the received signal will not be decodable. A near user has better outage probability than a far user because a far user gets interference from the near-user message signal while decoding the message signal. An achievable SINR is low due to its interference. The near-user message signal can be decoded after decoding far user message signal. BS should allocate more power to the far user due to its high path loss (typical reason is due to few km meter between base station and far user).

Figure 3 depicts outage probability for the proposed system model. It is observed that the probability of outage decreases while increasing transmit power gradually. The outage performance of IoT is poor when compared with user1 and 2. This decline in outage is evident from the fact that decoding of IoT is possible only after decoding of other user's data. Near user has better performance in terms of an outage. If the power at the BS is increased, the outage performance for IoT will be better.

The ergodic rate of RIS-assisted NOMA is obtained as shown in Fig. 4. The rate for near and far users is plotted and also its sum rate. The rate for far users gets saturated because of interference from near user message signals. The rate for near user increases while varying transmit power. This graph clearly shows that if interference exists, the
<figure><img src="image_4.png" /><figcaption>Fig. 2. Outage probability of RIS assisted NOMA with two users</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Outage probability of RIS-assisted NOMA with IoT device</figcaption></figure>

rate is a constant whatever transmit power may be. The sum rate of this system has improved.

Ergodic capacity for the proposed system is plotted in Fig. 5. The rate performance for each user is different. As we see here the rate for IoT device is improving beyond the transmit power of 20dB. With the help of passive RIS, we can do passive IoT communication in the NOMA network.
<figure><img src="image_6.png" /><figcaption>Fig. 4. Ergodic rate for RIS-assisted NOMA</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 5. Ergodic rate RIS-assisted NOMA with IoT device</figcaption></figure>

**4 Conclusion**

The proposed system of RIS assisted NOMA with passive IoT communication, BS that serves two NOMA users, along with IoT devices. IoT data/information is modulated and transmitted by switching on/off the reflecting elements (based on spatial modulation technique). Thus the proposed system serves IoT devices additionally compared with the existing system. The performance metrics of outage probability and ergodic rate of the proposed system were obtained. The proposed system will serve passive IoT
communication through the RIS-assisted NOMA network. Further RIS is not suitable for communicating opposite side of the transmitter. This issue could be addressed by Intelligent Omni Surface (IOS) which is able to do two mechanisms of incident signal. IOS reflect the incident signal towards transmitter side and refract the incident signal to the opposite side of the transmitter. Therefore, IOS extend the coverage area compared with existing RIS technology.

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