Outage Fairness Optimization for Channel‐Sorted NOMA in Multi‐Antenna Satellite Downlinks

ABSTRACT This paper investigates a multiuser non‐orthogonal multiple access (NOMA) downlink satellite network, where a ‐antenna satellite serves single antenna ground terminals over Shadowed‐Rician fading channels. By ordering effective spatial channel gains, exact closed‐form outage probability expressions are derived for both perfect successive interference cancellation (pSIC) and practical imperfect SIC (ipSIC) utilizing order statistics and the moment generating function (MGF) method. High‐SNR asymptotic analyses demonstrate that pSIC achieves a full multiplicative diversity order of for the ‐th ordered user, whereas ipSIC experiences an irreducible error floor leading to zero diversity order. To resolve user unfairness caused by channel disparities, a min–max outage fairness power allocation problem is formulated. Leveraging high‐SNR asymptotic bounds, the nonconvex problem is rigorously transformed into a disciplined convex programming (DCP) model solved via efficient interior‐point methods. Simulations confirm the mathematical precision of our derivations and highlight the superior fairness performance of the proposed scheme over conventional orthogonal multiple access (OMA) baselines.