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.

翻译：本文推导了在广泛采用的两用户下行非正交多址接入（NOMA）系统中，近用户（NU）在衰落信道下的精确中断概率（OP）与遍历容量（EC）。通过注意到连续干扰消除（SIC）后噪声与衰落产生依赖性，本文利用SIC后噪声与衰落的联合概率密度函数（PDF）推导了精确分析结果——而现有研究通常认为两者独立，并沿用SIC前的相同PDF模型。所推导的精确PDF用于准确评估残余干扰的影响，并进一步推导了NU中断的精确闭式表达式以及EC的单积分表达式。此外，还推导了EC的精确闭式近似表达式。与现有工作不同，本文导出的公式不含参变量，从而能更准确地评估此类系统性能。蒙特卡洛仿真结果验证了所推导的分析模型，并表明传统高斯/残余因子模型在中低信噪比（SNR）及非均衡功率分配条件下会显著低估中断与EC性能。此外，结果还表明：广泛采用且取值区间为[0,1]的残余干扰因子不足以捕捉SIC失效导致的实际残余干扰影响，且由于该因子依赖于功率分配、信噪比及中断阈值，不能将其视为独立变量。除衰落-噪声依赖性外，对于二维调制，噪声的实部与虚部同样会产生依赖性。