# Non-Orthogonal eMBB-URLLC Radio Access for Cloud Radio Access Networks with Analog Fronthauling
## 6 Numerical Results  
Numerical results based on the previous theoretical discussion are shown in this section with the aim of providing some useful intuitions about the performance of C-RAN systems based on analog RoC in the presence of both URLLC and eMBB services. Unless otherwise stated, we consider the following settings: \(M=6\) ENs, \(n_{F}=60\) subcarriers (This choice is motivated by the fact that, while still resembling the properties of URLLC short-packet transmissions, \(n_{F}=60\) is a sufficiently long packet size to ensure tight lower and upper bounds for the limited-blocklength channel capacity [5]), \(P_{B}=7\,\text{dB}\), \(P_{U}=10\,\text{dB}\), URLLC channel gain \(\beta^{2}=1\), \(P_{\text{C}}=7\,\text{dB}\), \(l_{S}=4\), and, conventionally, \(\epsilon_{U}=10^{-3}\). In the case of OMA, the worst-case access latency for URLLC users is set to \(L_{U}=2\) minislots. Figure 10 shows URLLC and eMBB per-UE rates for both OMA and NOMA by varying the fronthaul crosstalk interference power \(\gamma^{2}\). We consider two values for the normalized bandwidth \(\mu\) of each copper cable, namely \(\mu=1/l_{S}=1/4\) and \(\mu=1\). Please note that the first value corresponds to the minimal bandwidth, while the latter enables each twisted-pair to carry the whole signal bandwidth. For reference, the eMBB rates obtained in the case of ideal fronthaul are shown for both OMA and NOMA. The inter-cell interference power is set to \(\alpha^{2}=0.2\), and the URLLC arrival probability to \(q=10^{-3}\). For NOMA, we consider here only puncturing. Figure 10: URLLC and eMBB per-UE rates as a function of fronthaul crosstalk interference power \(\gamma^{2}\) for OMA and NOMA with puncturing. The URLLC rates do not depend on cable crosstalk interference \(\gamma^{2}\), since URLLC packets are decoded at the EN and thus never forwarded to the BBU over the fronthaul. Furthermore, with NOMA, the access latency of URLLC is minimum, i.e., \(L_{U}=1\), while for OMA it equals \(L_{U}=2\). However, Figure 10 shows that the price to pay for this reduced latency is in terms of transmission rate, which is lower than in the OMA case. On the contrary, in the case of eMBB, NOMA allows for a communication at higher rates than those achieved by OMA, thanks to the larger available bandwidth when \(q\) is small enough. On the subject of eMBB rates, it is interesting to discuss the interplay between the normalized cable bandwidth \(\mu\) and crosstalk power \(\gamma^{2}\). For \(\mu=1\), the same signal is transmitted over all the \(l_{S}=4\) fronthaul twisted-pairs, and hence the four spatial paths sum coherently over the cable, thus turning crosstalk into a benefit. Hence, the eMBB rates under both OMA and NOMA increase with \(\gamma^{2}\) and ultimately converge to those achieved over the ideal fronthaul (In this work, we consider the same interference gain \(\gamma\) for all fronthaul links. In practice, the performance boost shown in Figure 10 for increasing \(\gamma\) and for \(\mu=1\) would still be present, albeit to a different extent dependent on the channel realization, even if considering complex channel gain. However, this would require the use of more complex precoding techniques, such as Tomlinson-Harashima [37], which require an estimate of the fronthaul channel. Since for wired fronthauling the channel is nearly static and time-invariant, channel state information can be easily obtained [42]). For \(\mu=1/4\) instead, disjoint portions of the radio signal are transmitted over different interfering twisted-pairs, and the performance progressively decrease with \(\gamma^{2}\). The leftmost portion of Figure 10 suggests that for mild cable interference, even when the cable bandwidth is small (i.e., \(\mu=1/4\)), it is still possible to provide communication with acceptable performance degradation, i.e., with a \(\approx 1\) bps/Hz loss from the ideal fronthaul case for NOMA, and an even smaller loss for OMA.