Robust Outage Characterization of STAR-RIS-NOMA Under Nakagami-m Fading: Curve Fitting, Central Limit and Convolution Approaches
摘要
Simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs) make it possible to provide full 360° wireless coverage, overcoming the half-space limitation of conventional RIS. In this work, we investigate a downlink STAR-RIS-NOMA system where users are randomly located and experience Nakagami-m fading. By adjusting energy allocation and the number of active elements, STAR-RIS can adapt the SIC decoding order, improving user separation and spectral efficiency. To capture the behavior of STAR-RIS channels under different operating conditions, we introduce three analytical models: a central limit theorem (CLT) model for large-surface approximations, a curve fitting (CF) model for flexible deployment scenarios, and an M-fold convolution (MF) model for exact diversity analysis. We derive closed-form outage probability expressions for the CLT and CF models under the energy splitting (ES) protocol, while the MF model is used to determine the diversity order for ES, mode switching (MS), and time switching (TS). Our results show that the CLT model provides an accurate upper bound on performance with a gap of no more than 0.3 dB from simulations, while the CF model gives a close lower bound within 0.5 dB. At high SNR, the MF model confirms that the diversity order grows as mM, reaching about 200 for M = 40 and m = 5. At an SNR of 115 dB, the ES protocol delivers an outage probability about three times lower than that of MS. Moreover, to reach a target outage of 10−6, ES needs roughly 0.5 dB less SNR than TS. These results underline ES as the most reliable and resource-efficient option, while our analytical models provide precise and practical predictions of system performance.