# Guaranteeing QoS for NOMA-Enabled URLLC Based on \(\kappa\)-\(\mu\) Shadowed Fading Model
## 1 Introduction
### Related Works  
Our paper builds on results derived from several research areas. On the physical layer, we consider the uplink CF mMIMO system with imperfect channel state information (CSI) under the \(\kappa\)-\(\mu\) shadowed fading model as well as FBL information theory. On top of a service description in the physical-layer fading channel model, we then investigate service processes. We determine that the effect of different types of small-scale fading on the performance in the design, modeling and analysis of several wireless communication systems cannot be neglected. The CF mMIMO system has been gradually considered in the URLLC scenario. [PERSON] et al. [38] first investigated a CF mMIMO system for downlink URLLC in the FBL regime and designed a special class of conjugate beamforming to achieve a lower computational complexity and improved URLLC rate performance. [PERSON] et al. [19] introduced power control schemes in a CF mMIMO system that supported URLLC applications for both traditional ground users and unmanned aerial vehicles, and they evaluated the superior rate performance of this CF mMIMO system. Due to the spatial domain, the CF mMIMO method can be a key to boosting the reliability of URLLC applications. The study in [39] compared different transmission modes in a factory automation scenario and demonstrated that the user-centric transmission mode and power control brought substantial performance improvements in terms of reliability and latency. [PERSON] et al. [40] integratedthe CF mMIMO approach with simultaneous wireless information and power transfer for statistical delay and error-rate bounded QoS to support URLLC and boost the data rate and energy efficiency. Hence, a CF mMIMO network can be viewed as a promising system to support URLLC with a high resource efficiency and low latency. The \(\kappa-\mu\) shadowed fading model [27; 28] was proposed as a more general yet equally tractable model to capture a wide range of propagation conditions with clear physical interpretation and good analytical properties. Furthermore, [PERSON] et al. [31] derived the probability density function (PDF) and cumulative distribution function (CDF) of the \(\kappa-\mu\) shadowed fading model with integer fading parameters. [PERSON] et al. [25] provided a statistical characterization of the \(\kappa-\mu\) shadowed fading model and asserted that these results could be used to derive some performance metrics of wireless communication systems over fading channels. With respect to the characterization of the \(\kappa-\mu\) shadowed fading model, its applications have been studied in several works. [PERSON] et al. [41] carried out a performance (i.e., ergodic capacity, outage probability and average bit error rate) analysis of downlink NOMA systems subject to the \(\kappa-\mu\) shadowed fading model. [PERSON] et al. [42] proposed an analytic framework to evaluate the average of an arbitrary signal-to-noise-plus-interference ratio (SINR) function over the \(\kappa-\mu\) shadowed fading model and evaluate the spectral efficiency, moments of the SINR and outage probability of heterogeneous cellular systems. The authors in [43] characterized the impacts of realistic propagation conditions on the achievable secrecy performance of MIMO systems over the \(\kappa-\mu\) shadowed fading model. Fully absorbing the attractive nature of the \(\kappa-\mu\) shadowed fading model is seen as one of the potential keys to characterizing the propagation media in emerging practical scenarios. Several works have also examined SNC-based network performance analysis and theoretical boundary calculation for URLLC. [PERSON] et al. used SNC to investigate the delay performance of a multiuser MIMO system with zero-forcing beamforming [44] and NOMA with joint decoding [45] under imperfect CSI and FBL. [PERSON] et al. [46] derived a closed-form of the upper bound of the queuing delay violation probability (UB-QDVP) in a downlink NOMA system and designed an optimal power allocation scheme for guaranteeing the delay violation probability.