In this paper, we consider a downlink non-orthogonal multiple access (NOMA) network assisted by two reconfigurable intelligent surfaces (RISs) over Rician fading channels, in which each user communicates with the base station by the virtue of a RIS to enhance the reliability of the received signal. To evaluate the system performance of our proposed RIS-NOMA network, we first derive the exact and asymptotic expressions for the outage probability and ergodic rate of two users. Then, we derive the exact and asymptotic upper bound expressions for the ergodic rate of the nearby user. Based on asymptotic analytical results, the diversity orders for the outage probability and the high signal-to-noise ratio (SNR) slopes for the ergodic rate of the two users are obtained in the high SNR regime. Moreover, we derive the system throughputs of the proposed RIS-NOMA network in delay-limited and delay-tolerant transmission modes. Numerical results confirm our analysis and demonstrate that: 1) The outage probability and ergodic rate of RIS-NOMA networks are superior to that of RIS-assisted orthogonal multiple access (OMA) networks; 2) The RIS-NOMA networks have ability to achieve a larger system throughput compared to RIS-OMA networks; and 3) The system performance of RIS-NOMA networks can be significantly improved as the number of reflecting elements and Rician factor increases.

As a promising multiple access technology in the next generation wireless communication network, non-orthogonal multiple access (NOMA) has the ability to tremendously enhance the spectral and energy efficiency [

Recently, reconfigurable intelligent surface (RIS) has been regarded as a promising technology for the next generation wireless communication, which can improve the spectral and energy efficiency of future wireless communication networks in a cost-effective way [

Since both RIS and NOMA can greatly improve the spectrum and energy efficiency, it is critical to study their combined advantages to further enhance the spectrum and energy efficiency of future wireless communication networks. In [

As mentioned in the above works, compared with the conventional relaying technology, the RIS is capable of reflecting the incident signal transmitted from the transmitter to the receiver in FD mode without self-interference and energy consumption, which not only enhances the spectrum and energy efficiency, but also has a very low cost. Therefore, the integration of RIS and NOMA can further improve the spectrum and energy efficiency of the next generation wireless communication networks. Furthermore, the current literature on RIS-NOMA mainly concentrates on the optimization problem, but the research on performance analysis is not enough. Compared with conventional NOMA systems, the performance analysis of RIS-NOMA systems is more complex and challenging owing to the influence of the RIS. These motivate us to study the performance of RIS assisted NOMA systems, which provides an important theoretical basis for deployment of RIS in the future.

In this paper, we consider a RIS assisted NOMA network, in which a pair of NOMA users in a cell cannot directly receive signals from the BS due to the obstruction of obstacles, and each user needs the help of a RIS. Moreover, we comprehensively analyze the performance of RIS-NOMA networks in terms of the outage probability, ergodic rate, and system throughput. The primary contributions of this paper are summarized as follows:

We derive the closed-form and asymptotic expressions for the outage probability of a pair of NOMA users over Rician fading channels for the proposed RIS-assisted NOMA network. To gain further insight, we obtain the diversity orders of the pair of NOMA users for RIS-NOMA network according to the asymptotic analyses at high signal-to-noise ratio (SNR). We observe that the diversity orders of the pair of NOMA users depend on the number of reflecting elements and Rician factor.

We compare the outage performance of the pair of users for RIS-NOMA and RIS-OMA networks. We demonstrate that the outage performance of RIS-NOMA outperforms that of RIS-OMA. We prove that the RIS-NOMA network is capable of improving outage performance with increasing the number of reflecting elements and Rician factor.

We derive the exact and asymptotic expressions for the ergodic rate of the pair of NOMA users over Rician fading channels for our proposed RIS-NOMA network. To approximate the exact ergodic rate, we also derive the exact and asymptotic upper bound expressions for the ergodic rate of the nearby user. Based on theoretical analyses, we obtain the high SNR slopes for the ergodic rate of the pair of NOMA users. We observe that the throughput ceiling appears in the ergodic rate of the distant user at high SNR. We demonstrate that the superiority of RIS-NOMA over RIS-OMA in terms of the ergodic rate. We evidence that the ergodic rate of RIS-NOMA becomes larger with the increase of the number of reflecting elements.

We analyze the system throughput of our proposed RIS-NOMA network in two transmission modes. In delay-limited transmission mode, we observe that the system throughput of RIS-NOMA converges to a constant at high SNR. Furthermore, we prove that the proposed RIS-NOMA is capable of enhancing the system throughput compared to RIS-OMA. In delay-tolerant transmission mode, we evidence that the proposed RIS-NOMA can achieve a larger system throughput than RIS-OMA at high SNR. Moreover, we confirm that as the number of reflecting elements increases, the system throughput of RIS-NOMA can be significantly improved in the two transmission modes.

The main notations used in this paper are explained as follows.

Consider a two-RIS assisted NOMA network with one single-antenna BS and two single-antenna users as shown in

It is assumed that the channel state information of all channels is completely known at the BS. The complex channel coefficients from the BS to

Defining

Based on the superposition coding scheme, the BS broadcasts superposed signal

The signal of

For comparison, we regard the RIS-OMA scheme as the benchmark, in which the BS sends information to two OMA users through two RISs in two time slots. In each time slot, signal

The received SINR at

In order to achieve optimal performance, we use the coherent phase shift design. For the wireless communication links of RIS-NOMA networks, our goal is to optimize the channel by adjusting the amplitude and phase of the RIS to achieve the optimal channel gain for each user. For the BS-RIS-

The channel coefficients

In communication systems, the outage probability can be defined as the probability that the outage occurs for a user when the information rate of the user is lower than its target rate. The outage probability is a widely used system performance metric in fixed-rate transmission systems. In this section, the outage performance of downlink RIS-NOMA networks is investigated.

By using the SIC scheme at nearby user

On account of the NOMA principle, the signal of

The outage probability of

For RIS-OMA networks,

In communication systems, the diversity order can be defined as the slope of the outage probability at high SNR. The diversity order describes the speed at which the outage probability decreases with the transmit SNR, which is usually used to evaluate the outage performance of wireless communication networks. The diversity order can be expressed as

In order to obtain further insights, the approximate results of the outage probability are analyzed at high SNR, which can be used to determine the diversity order. The asymptotic outage probabilities of

Substituting

Substituting

The system throughput is an important performance metric in wireless communication systems. The research on system throughput is of great significance for practical implementation. In the delay-limited transmission mode, the information is transmitted from the BS to users at a constant rate, which leads to outage due to the influence of the wireless fading channels. Therefore, the system throughput depends on the outage probability in the delay-limited transmission mode. The delay-limited system throughput of RIS-NOMA is expressed as

The ergodic rate is a commonly used system performance metric in adaptive-rate transmission systems. In this section, the ergodic rates of two users for RIS-NOMA networks are analyzed.

Based on SIC principle, if

The ergodic rate of

Assuming that

The ergodic rate of

For RIS-OMA networks, since

Similar to the derivation process of

Similar to the diversity order, the high SNR slope can be defined as the slope of the ergodic rate at high SNR, which describes how fast the ergodic rate increases with the transmit SNR. The high SNR slope can be expressed as

To gain deep insights into the system performance, the approximate ergodic rate at high SNR is studied, which can be used to calculate the high SNR slope. However, the approximate ergodic rate of

On the basis of

According to

Hence

The asymptotic upper bound for the ergodic rate of

Substituting

The asymptotic ergodic rate of

In view of

Hence

Substituting

Similar to the derivation process of

The asymptotic upper bound for the ergodic rate of

In the delay-tolerant transmission mode, the information is transmitted from the BS to users at any constant rate, which is subject to the channel conditions of the users. Hence the delay-tolerant system throughput of RIS-NOMA is expressed as

In this section, numerical results are presented to evaluate the performance of RIS-NOMA networks over Rician fading channels. The effects of the Rician factor, the number of reflecting elements of the RIS, and the pass loss exponent on the performance of RIS-NOMA networks are discussed. The accuracy of the derived theoretical results can be verified by Monte Carlo simulations. In order to compare the performance with the RIS-NOMA networks, the conventional RIS-OMA networks are also provided. Without loss of generality, the power allocation factors of two users are set to

Monte Carlo simulations repeated | |
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The power allocation factors | |

The targeted data rates | |

The normalized distances | |

The path loss exponent |

In order to explain the influence of the Rician factor on the outage performance of RIS-NOMA networks,

To further illustrate the impact of the path loss exponent on the outage performance of RIS-NOMA networks,

Considering the influence of the number of reflecting elements on the ergodic performance of RIS-NOMA networks,

As a further advance,

In this paper, the system performance of RIS-assisted downlink NOMA communication networks has been investigated in terms of the outage probability, ergodic rate, and system throughput over Rician fading channels. The exact and asymptotic expressions for the outage probability and ergodic rate of two users for RIS-NOMA networks have been derived. Based on the theoretical analyses, the diversity orders and high SNR slopes of the two users have been obtained at high SNR. In addition, the system throughputs of RIS-NOMA networks have been derived in delay-limited and delay-tolerant transmission modes. Simulation results have indicated that the outage probability and ergodic rate of RIS-NOMA outperform that of RIS-OMA. It has been shown that the system throughput of RIS-NOMA is superior to that of RIS-OMA. Moreover, it has been demonstrated that the system performance of RIS-NOMA networks becomes better with increasing the number of reflecting elements and Rician factor. Based on this work, we will consider extending the research to multiple users in the future. In addition, optimized power allocation and multiple antennas of device nodes are also promising research directions.

Substituting

Applying the series of Laguerre polynomials [

Substituting

Using

Applying the lower incomplete Gamma function [

Substituting

Similarly, the PDF of

Substituting

By referring to the lower incomplete Gamma function, the outage probability of

Substituting

The CDF of

Based on

Substituting

Hence

Substituting

The CDF of

Substituting

Using

Applying Chebyshev-Gauss quadrature [