# Guaranteeing QoS for NOMA-Enabled URLLC Based on \(\kappa\)-\(\mu\) Shadowed Fading Model
## 4 Simulation Results and Analyses  
We present numerical results to validate and evaluate the stochastic queuing behaviors and the effects of fading characteristics on performance in the proposed CF mMIMO system under the \(\kappa-\mu\) shadowed fading model. Different from most studies [4; 12; 13; 17; 18], which explore the effects of the number of APs, the coverage radio, the number of potential users and other traditional system parameter configurations on performance in communication scenarios, we focus on fading characteristics. Throughout our simulations, we set such parameters constant. For large-scale fading \(\beta_{lk}=u_{p}\big{(}\frac{d_{k}}{d_{0}}\big{)}^{-\alpha_{p}}\), \(u_{\text{p}},\alpha_{\text{p}},d_{0}\) and \(d_{lk}\) are the constant path loss across the minimum distance, the path loss exponent, the minimum distance and the distance between the \(k\)th user and the \(l\)th AP, respectively. The key simulation parameters are listed in Table 1. The overall reliability for the \(k\)th user can be represented by the overall error probability \(\varepsilon_{k}\)[55], which is \(\varepsilon_{k}\approx\varepsilon_{k}^{d}+\varepsilon_{k}^{v}\). Because \(\varepsilon_{k}^{d}\to 0\), \(\varepsilon_{k}\) can be expressed by \(\varepsilon_{k}^{v,\text{UB}}\). First, we compared the maximum achievable data rates obtained under the same decoding error probability but different fading models in Figure 2, when the transmit power is 5 dBm and the distance from the user to the center of the coverage area is 200 m. It is obvious that the maximum achievable data rates corresponding to the same decoding error probability are inconsistent under different fading environments. This indicates that the effect of different fading environments cannot be ignored with respect to system performance. In particular, when designing a wireless communication system (e.g., the CF mMIMO system) for strict decoding error probability, it is crucial to design customized coding design and power control schemes by combining the fading characteristics of the wireless communication environment to adjust the service rate to meet the reliability requirements of NOMA-enabled URLLC QoS. Therefore, the \(\kappa\)-\(\mu\) shadowed fading model accommodating different propagation conditions that are applied to design or analyze the performance of a wireless communication system is necessarv and significant. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Farthest coverage radius (m) & 1000 \\ Number of potential users & 2000 \\ Activation rate of potential users & 5\% \\ Number of APs & 200 \\ Noise power spectral density (dBm/Hz) & \(-106\) \\ Path loss exponent, \(\alpha_{\text{p}}\) & 3 \\ Minimum distance, \(d_{0}\) (m) & 10 \\ Constant path loss, \(u_{\text{p}}\) (dB) & \(-10\) \\ Bandwidth, \(B\) (MHz) & 20 \\ Carrier frequency (GHz) & 3.5 \\ Arrival bit per slot, \(\lambda\) (bit/slot) & 50 \\ Length of time slot, \(t_{f}\) (ms) & 0.01 \\ Length of pilots, \(n\) & Max(\(K,0.2N\)) 1  \\ Target delay (target number of time slots), \(t_{\text{T}}\) & [1,10] \\ Decoding error probability, \(e_{k}^{l}\) & [\(10^{-9},10^{-8}\)] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters Values for Numerical Results. Figure 2: Relationship between the decoding error probability and the maximum achievable data rate. Figure 3 shows the fitting ability of our derived theoretical tool (Theorem 1) for the PDFs of the sum of i.n.i.d. RVs. We used the Monte Carlo method to randomly generate six independent RVs with different distributions and sum some of them. We verify that the cylindrical diagram (obtained by a simulation using the Monte Carlo method for \(10^{7}\) iterations) and the curve with an asterisk (obtained by numerical calculation (Equation (8)) have almost the same slope. This indicates that our proposed theoretical tools based on Theorem 1 can accurately characterize the statistical characteristics of the sum of multiple i.n.i.d. RVs.