# Guaranteeing QoS for NOMA-Enabled URLLC Based on \(\kappa\)-\(\mu\) Shadowed Fading Model
## 1 Introduction
### Background and Motivation
Such classic fading models usually do not cover all types of fading scenarios encountered in practical cases. More importantly, the analyses performed for practical channel estimations depend on the channel's statistical properties, which are affected by the selected channel models [20]. Consequently, many results are not reasonably universal enough due to simplified assumptions, such as in many studies of CF mMIMO systems performance based on the Rayleigh model [12;14;21] or Rician model [22]. The design of reliable wireless communication systems is highly dependent on the accurate characterization of the wireless fading channel. However, for the complex communication scenarios in future 6G URLLC scenarios [23;24], the classic fading model is no longer applicable [25;26]. With the research on fading models in recent years, a new fading model that can losslessly portray a variety of fading types has the potential to become a unified fading model [27; 28; 29; 30], which can be used to accurately characterize fading channels in complex future 6G URLLC scenarios. This is a critical issue regarding the theoretical analysis and performance optimization of URLLC, given that the reliability of modeling is of capital importance. Specifically, the \(\kappa\)-\(\mu\) shadowed fading model, which unifies the \(\kappa\)-\(\mu\) fading distribution and the \(\eta\)-\(\mu\) fading distribution, was introduced in [27]. First, by adjusting the parameters \(\kappa\), \(\mu\) and \(m\), almost all classical fading models can be unified by the \(\kappa\)-\(\mu\) shadowed fading model [28] with similar mathematical flexibility levels. Second, this shadowed model provides much better tractability and flexibility [31]. These two features allow the \(\kappa\)-\(\mu\) shadowed fading model to accommodate different propagation conditions, such as in practical communication environments that experience the effects of nonhomogeneous fading conditions. However, although the \(\kappa\)-\(\mu\) shadowed fading model can characterize a variety of fading channels, adapting the \(\kappa\)-\(\mu\) shadowed fading model to the CF mMIMO system and specifically analyzing the system performance while supporting URLLC becomes a challenging research issue. With respect to mathematical tools, towards the exponentially growing demands of time-sensitive services, the traditional Shannon information theory based on the infinite blocklength assumption and a random coding scheme provides a poor benchmark in this scenario [32]. Finite-blocklength (FBL) information theory was proposed in [33] as a short-packet data communication technique for guaranteeing the stringent QoS requirements of URLLC [34]. Well-known results regarding the maximum achievable data rate of FBL packets were derived in [33] as a function of the blocklength and error probability. Moreover, as suggested by [PERSON] et al. [35] and [PERSON] et al. [36], the design of URLLC should capture the tail behavior of reliability (i.e., queuing delay violation probability) and delay instead of average metrics. Because the delay and overall reliability consist of multiple components, the corresponding performance indicators should be constrained by a delay boundary and a delay violation probability boundary for URLLC [36]. In this sense, the stochastic network calculus (SNC) approach proposed in [37] provides a nonasymptotic boundary on the delay violation probability as an effective analysis tool for connecting the delay and overall reliability. Therefore, the CF mMIMO system under the \(\kappa\)-\(\mu\) shadowed fading model is sufficient for analyzing performance in practical communication environments to meet the strict QoS requirement of URLLC. However, a major problem with this kind of performance analysis is appropriately characterizing stochastic queuing behaviors when they are integrated with the CF mMIMO system under the \(\kappa\)-\(\mu\) shadowed fading model with SNC and FBL information theory.