# Guaranteeing QoS for NOMA-Enabled URLLC Based on \(\kappa\)-\(\mu\) Shadowed Fading Model
## 1 Introduction  
### Background and Motivation  
Due to the highly time-varying nature of wireless channels, it is difficult to design communication systems that support ultrareliable and low latency communications (URLLC) with reductions in energy consumption. For example, the explosively increasing volumes of delay-sensitive and bandwidth-intensive applications under stringent quality-of-service (QoS) requirements have required strict delay (<0.1 ms), ultrareliability (>99.99999%), and extra-high energy efficiency (EE) demands [1]. Notably, achieving higher data rates and lowering power consumption seem to be contradictory objectives. In particular, whenthe delay boundary approaches the channel coherence time, the transmit power required to obtain the QoS requirements becomes unbounded [2]. Although both academia and industry have paid attention to the EE of cellular networks in the past few years [3], the related works are still unable to address the increasing complexity of devices, antennas and many frequency bands in the future [4]. Orthogonal multiple access (OMA) systems (e.g., multiple-input multiple-output orthogonal frequency division multiple access (MIMO-OFDMA)) apply the orthogonal resource allocation method, in which different uplink users occupy different channel uses (CUs). This type of system distinguishes different users through different orthogonal time-frequency resource blocks. However, all users share time-frequency resources in the non-OMA (NOMA) system. As a promising technology, NOMA makes full use of the nonorthogonal nature over limited orthogonal resources so as to provide a higher transmission accuracy with lower computational complexity [5], and to meet the massive connectivity requirements in an Internet of things scenario [6;7] and even satellite-based communications [8]. For instance, power-domain NOMA (PD-NOMA), considered as the representative of single carrier NOMA technology [9], distinguishes different groups of users through the spatial domain, and different users in the same group share spatial domain resources. Under PD-NOMA systems, power control is required to meet the QoS requirements of URLLC for energy efficiency, latency and reliability [10]. However, fairness among the users in terms of their throughput is an important goal of NOMA power allocation [11]. For the upcoming sixth generation (6G) mobile networks, a beneficial embodiment of a distributed massive MIMO system is the cell-free massive MIMO (CF mMIMO) system proposed in [12]. As a type of NOMA system, the CF mMIMO system is a better solution between PD-NOMA and MIMO-OFDMA. All users share all CUs, and different users are distinguished by the spatial domain without considering the fairness experienced by uplink users. The CF mMIMO system contains a large number of randomly distributed access points (APs) to coherently serve massive mobile devices; its implementation is more feasible for practical issues than network MIMO with low overhead that exploits channel hardening phenomena and favorable propagation properties [4;13].Relative to traditional cellular mMIMO networks, the notable characteristics of CF mMIMO system are its superior macro diversity and interference suppression capabilities. Macro diversity offers orders of magnitude of coverage probability [12;14], reliability and delay optimization through suitable signal processing. Intercell interference is effectively mitigated by the user-centric approach and coordination [15;16], thereby improving the accuracy of multiuser detection. To the best of our knowledge, a CF mMIMO system that efficiently integrates the unified fading model to provide substantial performance improvements with respect to different types of small-scale fading has still not been well studied. On the other hand, most current papers concerning the performance analysis in CF mMIMO systems [4;17;18;19] perform analyses in the context of small-scale fading models such as the Rayleigh and Nakagami-\(m\) models, which ignore the random nature of wireless fading channels.