Exact Outage Probability and Ergodic Capacity Analysis of NOMA in Rayleigh Fading Channels

2026-04-13

AI Summary

This work addresses a critical limitation in conventional performance analyses of non-orthogonal multiple access (NOMA) systems, which typically neglect the statistical dependence between successive interference cancellation (SIC) residual noise and channel fading, leading to inaccurate outage probability and ergodic capacity evaluations. Focusing on a two-user downlink NOMA scenario, the study derives for the first time the joint probability density function of SIC-induced noise and Rayleigh fading channels. By leveraging random variable transformation and closed-form integration techniques, it obtains an exact closed-form expression for the near user’s outage probability and a single-integral representation for its ergodic capacity. The proposed parameter-free model exposes the fundamental inadequacy of treating the residual interference factor as statistically independent. Simulations confirm that conventional models—assuming Gaussian or fixed residual interference—exhibit significant deviations from actual system performance, particularly at medium to low signal-to-noise ratios.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Search and Optimization: Evaluation and Analysis
• Machine Learning: Evaluation and Analysis

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements

Abstract

This work derives the exact outage probability (OP) and ergodic capacity (EC) for the near user (NU) in the widely adopted two-user downlink non-orthogonal multiple access (NOMA) over fading channels. By noting that the noise and fading become dependent after successive interference cancellation (SIC), the exact analysis is derived by considering the joint probability density functions (PDFs) of the post-SIC noise and fading, which are typically considered to be independent and modeled using the same PDFs before the SIC. The derived exact PDFs are used to evaluate the impact of residual interference accurately. The derived interference and noise PDFs are used to derive an exact closed-form formula for NU outage and a single-integral expression for EC. Moreover, a closed-form, accurate expression is derived for the EC. Unlike existing work, the derived formulae are parameter-free, leading to more accurate performance evaluation of such systems. Monte Carlo simulation results validate the derived analysis and demonstrate that legacy Gaussian/residual-factor models can significantly misestimate outage and EC at low-to-moderate signal-to-noise ratios (SNRs) and under unbalanced power allocation. Moreover, the obtained results show that the widely considered residual interference factor, which is bounded by [0, 1], is not sufficient to capture the actual impact of residual interference due to a SIC failure, and it cannot be treated as an independent variable because it depends on the power allocation, SNR, and outage threshold. In addition to the fading-noise dependence, for two-dimensional modulations, the real and imaginary components of the noise become dependent as well.

Problem

• NOMA
• outage probability
• ergodic capacity
• successive interference cancellation
• Rayleigh fading

Innovation

• NOMA
• successive interference cancellation (SIC)
• joint PDF
• residual interference
• ergodic capacity