Simultaneous transmitting and reflecting intelligent omini-surfaces (STAR-IOSs) are able to achieve full coverage smart radio environments. By splitting the energy or altering the active number of STAR-IOS elements, STAR-IOSs provide high flexibility of successive interference cancellation (SIC) orders for non-orthogonal multiple access (NOMA) systems. Based on the aforementioned advantages, this paper investigates a STAR-IOS-aided downlink NOMA network with randomly deployed users. We first propose three tractable channel models for different application scenarios, namely the central limit model, the curve fitting model, and the M-fold convolution model. More specifically, the central limit model fits the scenarios with large-size STAR-IOSs while the curve fitting model is extended to evaluate multi-cell networks. However, these two models cannot obtain accurate diversity orders. Hence, we figure out the M-fold convolution model to derive accurate diversity orders. We consider three protocols for STAR-IOSs, namely, the energy splitting (ES) protocol, the time switching (TS) protocol, and the mode switching (MS) protocol. Based on the ES protocol, we derive analytical outage probability expressions for the paired NOMA users by the central limit model and the curve fitting model. Based on three STAR-IOS protocols, we derive the diversity gains of NOMA users by the M-fold convolution model. The analytical results reveal that the diversity gain of NOMA users is equal to the active number of STAR-IOS elements. Numerical results indicate that 1) in high signal-to-noise ratio regions, the central limit model performs as an upper bound, while a lower bound is obtained by the curve fitting model; 2) the TS protocol has the best performance but requesting more time blocks than other protocols; 3) the ES protocol outperforms the MS protocol as the ES protocol has higher diversity gains.
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