[Paper Review] Reconfigurable Intelligent Surfaces Aided Multi-Cell NOMA Networks: A Stochastic Geometry Model

Chao Zhang, Wenqiang Yi+1 more|arXiv (Cornell University)|Aug 17, 2020

Advanced Wireless Communication Technologies41 references19 citations

TL;DR

This paper proposes a stochastic geometry model for multi-cell non-orthogonal multiple access (NOMA) networks enhanced by reconfigurable intelligent surfaces (RIS), leveraging a Poisson cluster process to analyze user coverage and ergodic rates. It derives closed-form expressions for coverage probability and ergodic rate, showing that RISs improve spectral efficiency by enabling new line-of-sight links and flexible successive interference cancellation ordering, with performance saturating as RIS size increases.

ABSTRACT

By activating blocked users and altering successive interference cancellation (SIC) sequences, reconfigurable intelligent surfaces (RISs) become promising for enhancing non-orthogonal multiple access (NOMA) systems. The downlink RIS-aided NOMA networks are investigated via stochastic geometry. We first introduce the unique path loss model for RIS reflecting channels. Then, we evaluate the angle distributions based on a Poisson cluster process (PCP) model, which theoretically demonstrates that the angles of incidence and reflection are uniformly distributed. Additionally, we derive closed-form analytical and asymptotic expressions for coverage probabilities of the paired NOMA users. Lastly, we derive the analytical expressions of the ergodic rate for both of the paired NOMA users and calculate the asymptotic expressions for the typical user. The analytical results indicate that 1) the achievable rates reach an upper limit when the length of RIS increases; 2) exploiting RISs can enhance the path loss intercept to improve the performance without influencing the bandwidth. Our results show that 1) RIS-aided NOMA networks have superior performance than the conventional NOMA networks, and 2) the SIC order in NOMA systems can be altered since RISs are able to change the channel quality of NOMA users.

Motivation & Objective

• To model RIS-aided multi-cell NOMA networks using stochastic geometry to analyze system performance under realistic propagation conditions.
• To develop a novel path loss model for RIS reflecting channels that accounts for incidence and reflection distances in both short- and long-distance scenarios.
• To theoretically demonstrate that angles of incidence and reflection are uniformly distributed under a Poisson cluster process (PCP) model.
• To derive closed-form expressions for coverage probability and ergodic rate of NOMA users in RIS-aided networks.
• To investigate how RIS deployment alters channel quality and enables flexible successive interference cancellation (SIC) ordering.

Proposed method

• Models the RIS-aided NOMA network using a Poisson cluster process (PCP) to capture spatial clustering of base stations and users.
• Proposes a unique path loss model for RIS channels based on the product of incidence and reflection distances, suitable for long-range outdoor communications.
• Uses the probability generating functional (PGFL) of a Poisson point process (PPP) to derive the Laplace transform of interference from other base stations.
• Applies binomial expansion approximations to model the distribution of Rician fading channels, enabling tractable analysis of signal-to-interference-plus-noise ratio (SINR).
• Employs Campbell’s theorem and generalized hypergeometric functions to compute the expected interference and coverage probability.
• Derives asymptotic expressions for ergodic rates under high-SNR and large-RIS conditions using moment-generating function approximations.

Experimental results

Research questions

• RQ1 How does the RIS path loss model differ based on the sum or product of incidence and reflection distances, and which is more suitable for outdoor multi-cell scenarios?
• RQ2 What is the distribution of angles of incidence and reflection in RIS-aided NOMA networks under a Poisson cluster process model?
• RQ3 How does RIS deployment affect the coverage probability of NOMA users in a multi-cell environment?
• RQ4 What are the analytical expressions for the ergodic rate of paired NOMA users in RIS-aided networks, and how do they scale with RIS size?
• RQ5 Can RISs alter the SIC decoding order in NOMA systems by changing user channel quality, and what is the performance impact?

Key findings

• The achievable ergodic rate of NOMA users reaches a saturation point as the RIS length increases, indicating diminishing returns beyond a certain size.
• RIS deployment improves the path loss intercept without requiring additional bandwidth, thereby enhancing spectral efficiency and user coverage.
• Coverage probability and ergodic rate expressions are derived in closed-form and asymptotic form, enabling performance evaluation under various network conditions.
• The SIC order in NOMA can be dynamically altered via RIS beamforming, as RISs can improve the channel quality of weak users, enabling better user pairing and rate fairness.
• The Poisson cluster process model confirms that angles of incidence and reflection are uniformly distributed, validating the tractability of the stochastic geometry framework.
• Numerical results show that RIS-aided NOMA outperforms conventional NOMA in terms of coverage and rate, especially for cell-edge users.