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

TL;DR

This paper derives exact outage probability and ergodic capacity formulas for NOMA systems over Rayleigh fading channels, considering residual interference and noise dependencies for improved performance evaluation.

Contribution

It provides parameter-free, exact closed-form expressions for outage and capacity, accounting for residual interference and noise dependence, surpassing previous models.

Findings

Derived exact outage probability and ergodic capacity formulas.

Validated analysis with Monte Carlo simulations.

Showed residual interference factor is insufficient alone to model interference.

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.