[Paper Review] A Comprehensive Study of Reconfigurable Intelligent Surfaces in Generalized Fading

Imène Trigui, Wessam Ajib+1 more|arXiv (Cornell University)|Apr 6, 2020

Advanced Wireless Communication Technologies29 references41 citations

TL;DR

The paper develops a unified Fox’s H-based framework to analyze RIS-assisted communications over generalized fading (Fox’s H), deriving exact outage probability and ergodic capacity expressions for single and multiple RISs, and providing high-SNR scaling laws for large-scale RIS deployments.

ABSTRACT

Leveraging on the reconfigurable intelligent surface (RIS) paradigm for enabling the next Internet of Things (IoT) and 6G era, this paper develops a comprehensive theoretical framework characterizing the performance of RIS-assisted communications in a plethora of propagation environments. We derive unified mathematical models for the outage probability and ergodic capacity of single and multiple-element RIS over Fox's H fading channel, which includes as special cases nearly all linear and non linear multi-path and shadowing fading models adopted in the open literature. For gleaning further insights, we capitalize on the algebraic asymptotic expansions of the H-transform to further analyze the outage probability and capacity at high signal-to-noise ratio (SNR) in a unified fashion. Asymptotic analysis shows two scaling rates of the outage probability at large average SNR. Moreover, by harnessing its tractability, the developed statistical machinery is employed to characterize the performance of multiple randomly distributed RIS-assisted communications over Fox's H fading channels. We show that there is a great potential to improve the outage performance and thereby the capacity when fewer RISs are deployed each with more reflecting elements.

Motivation & Objective

• Motivate RIS as a tool to control wireless environments for 6G and IoT applications under generalized fading.
• Provide a unified mathematical framework to model RIS channels using Fox’s H distributions.
• Derive exact outage probability and ergodic capacity expressions for RIS-assisted links with single and multiple RISs.
• Analyze performance in large-scale RIS deployments and derive scaling laws with respect to RIS element counts and path loss.
• Offer insights applicable across a wide range of fading models including RF and FSO environments.

Proposed method

• Model the BS–RIS–user channel with an N-element RIS and phase-shift matrix Phi.
• Assume Fox’s H-distributed fading for |h_i| and |g_i| to capture generalized multipath and shadowing effects.
• Derive outage probability Pi(rho,N) via multivariate Fox’s H transforms and associated Laplace/Mellin-Barnes techniques.
• Obtain high-SNR asymptotics using residue calculus to extract diversity and coding gains.
• Derive ergodic capacity E(rho_L,N) in closed-form using multivariate Fox’s H functions and exponential integral relations.
• Provide special-case simplifications for Nakagami-m, generalized K, and i.i.d. Fox’s H fading, including scaling laws.

Experimental results

Research questions

• RQ1 How can RIS-assisted communications be analyzed under generalized fading beyond Rayleigh or simple models?
• RQ2 What are the exact outage probability and ergodic capacity expressions for RIS with single and multiple RISs under Fox’s H fading?
• RQ3 How do large-scale deployments of RISs scale in terms of outage, capacity, and diversity gains?
• RQ4 What are the high-SNR performance insights (diversity, coding gains, scaling with N and M) under generalized fading?
• RQ5 How do different fading families (Nakagami-m, generalized K, F, etc.) affect RIS performance and scaling laws?

Key findings

• Outage probability and capacity for RIS under Fox’s H fading are obtained in closed form via multivariate Fox’s H functions.
• The SNR scales as M^{α/2} N^2 for M RISs each with N elements under generalized fading with path-loss exponent α.
• High-SNR analysis yields diversity gains determined by the residue-based expansion, highlighting a quadratic-like gain in SNR with RIS element count.
• For Nakagami-m and generalized K fading, the asymptotic outage shows explicit power-law decays with rho_L and N, illustrating the impact of multipath and shadowing on diversity.
• The framework accommodates i.ni.d fading and provides bounds and corollaries for i.i.d. Fox’s H fading, showing scalability and performance limits.
• Corollaries link RIS performance to common fading families, enabling direct mapping to RF and FSO turbulence models.