## 4 Numerical Analysis  
In this section, we show the numerical results to corroborate the analytical derivations. Furthermore, we evaluate the system performance in terms of reliability, e.g., 1-\(e_{th}\) for the considered schemes. In the analysis, we set \(\alpha=3.5\), based on practical radio propagation measurement in an industrial setup which corresponds to a dense setup [48]; whereas \(\delta=\frac{d_{0}}{d}\) while \(d_{0}<d\) thus \(0<\delta\leq 1\), we arbitrarily chose \(\delta=0.5\), unless stated otherwise. The topology comprises \(N=10\) RRHs located away from the UE of interest. We used a Monte Carlo simulation of \(10^{7}\) runs (Note that a larger number of samples reduces the variance at the tail of the distribution at the cost of longer simulation time. The latter could be avoided by resorting to more sophisticated Monte Carlo methods, which is out of the scope of this work). Notice that when there is no cooperation, \(k=0\) all the schemes revert to the case of full interference. Figure 2 illustrates the CDF of SIR distribution as a function of threshold \(\theta\) (dB) for the considered transmission schemes with \(k=6\) cooperating RRHs. As shown, for \(k=6\) the left tail distribution of the MRT scheme is already exceeding the outage probability value of \(10^{-5}\) as compared to the silencing scheme and TAS with silencing schemes. While with the \(k=6\), RRHs silenced the left tail of the silencing scheme exceeds \(10^{-2}\) in comparison  
with full interference. Similarly, the results seem to be better with the TAS with silencing scheme, where the left tail goes beyond \(10^{-5}\) for a higher threshold of \(\theta\) compared to the silencing and the full interference scenario. The MRT and TAS with silencing curves seemed to attain higher values of \(\theta\) than the silencing and the full interference schemes, which shows significant performance gain and a higher diversity gain at the UE. However, MRT curves bend to a higher SIR threshold in comparison with the TAS scheme because joint transmission with cooperating RRHs in MRT enhances the SIR gain at the UE. Finally, we validate the analytical results via Monte Carlo simulations. Figure 3 illustrates the expected value of SIR as function of number of cooperating RRHs \(k\) for considered transmission schemes. For all schemes, the expected SIR increases as \(k\) increases. While, with the same value of \(k\), the expected value of SIR of MRT schemes is higher than the silencing and TAS with silencing schemes. The reason is that RRHs are jointly transmitting to the intended UE to enhance diversity gain, which increases SIR, which in turn improves the system performance. MRT helps to cope with link failure and blockages enabling multi-connectivity to serve intended UE through several cooperating links. This increment of \(\mathbb{E}[\text{SIR}]\) with an increase in \(k\) improves outage performance at the tail of CDF as shown in Figure 2. Meanwhile, TAS with silencing and silencing shows very similar performance because both schemes have a single RRH transmitting to the UE, which has little diversity gain compared to MRT. Figure 4 shows the reliability analysis as a function of \(\theta\) for the different number of cooperating RRHs with silencing, TAS with silencing, and MRT schemes. The shaded region in the figure represents the ultra-reliable region of operation. In the case of \(k=4\) RRHs in cooperation, MRT and TAS with silencing schemes achieve the ultra-reliable region. However, MRT can ensure it at higher values of \(\theta\) compared to TAS with silencing. Thus, the diversity gained from MRT is superior to that of TAS with silencing schemes. This is because cooperating RRHs jointly transmit to the UE while diversifying the path loss by exploiting diverse resources. However, in silencing and TAS with silencing, this is not possible, since a typical RRH serves the UE, which has little diversity gain compared to MRT.