Ergodic Capacity Analysis of Multi-User RSMA in Rank-Deficient Confined-Space Channels: A Keyhole Nakagami-m Fading Framework
Year: 2026
Type: conference-paper
Abstract: This paper presents an analytical framework for the ergodic capacity (EC) of a downlink multi-user Rate-Splitting Multiple Access (RSMA) system over keyhole Nakagami-$m$fading channels, motivated by wireless connectivity in subway tunnels and indoor corridors. In such environments, structural constrictions force all multi-path energy through a single dominant waveguide mode. This collapses the effective channel rank to unity and reduces the channel to the product of two independent Nakagami-$m$random variables. For a multi-user network with$N$single-antenna users, closedform expressions are derived for the EC of both common and private RSMA streams under perfect successive interference cancellation (pSIC) using Meijer-$G$functions. For the imperfect SIC (ipSIC) case, a Gauss-Laguerre quadrature approximate expression is developed. Additionally, tight Jensen upper bounds are derived to provide compact design guidelines at moderateto-high signal-to-noise ratio (SNR). Under pSIC, asymptotic high- SNR analysis reveals that the EC for common and private streams is saturated at deterministic ceilings that depend on the power allocation coefficients. The ipSIC ceiling lies strictly below the pSIC ceiling and retains a residual dependence on the interference statistics. Monte Carlo simulations confirm all analytical results. As a comparison with Non-Orthogonal Multiple Access (NOMA), the findings show that RSMA achieves a consistent EC gain across low-to-medium SNR regimes, with more enhancement under ipSIC.
Language: English
Subfield: Electrical and Electronic Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7204164642