## 4 Numerical Analysis
If we consider only silencing schemes, there is a slight improvement in the reliability, with an increasing number of cooperating RRHs. However, the performance seems better with the same number of cooperating RRHs using TAS with a silencing scheme. This means silencing the same number of RRHs while using the best channel to transmit to the UE through the cooperation of RRHs can improve the reliability. For instance, when \(k=0\), all the schemes represent full interference and have the same level of performance gain. Figure 2: Overview of SIR distribution for full interference, silencing, TAS with silencing and MRT schemes as a function of \(\theta\). We set \(k=6\) RRH in coordination. Figure 5 shows the performance analysis of silencing, TAS with silencing, and MRT schemes as a function of \(N\) and \(\theta\), with the fixed number of cooperating RRH \(k=3\). As shown, the performance of MRT improves with an increase in \(N\) as compared to silencing and TAS with silencing because jointly transmitting from cooperating RRH or the involvement of more RRHs, provides more diversity and array gain, thus resulting in lower outage probability improving reliability. TAS with silencing outperforms silencing, but a reliability level of five nines is attainable only at a lower \(\theta\) value than MRT and for smaller \(N\). However, the silencing scheme attains a reliability level of one nine because of the selection of the best RRH link, which provides some additional diversity gain compared to silencing, and thus improves performance. Figure 4: Overview of reliability analysis as a function of \(\theta\) for silencing, TAS with silencing and MRT schemes with different level of \(k\). Figure 3: Expected value of SIR for silencing, TAS with silencing and MRT schemes as a function of number of cooperating RRHs \(k\). The distances from the UE to the RRHs have a significant role in this topology. We generalize the presented topology by comparing all the schemes in Figure 6 in terms of SIR threshold \(\theta\) (dB) and the ratio of distances \(\delta\). The higher value of \(\delta\) means the interfering and serving nodes are close to each other. For \(\delta=0.5\), the MRT schemes achieve five nines' reliability. In contrast, TAS with silencing scheme has a reliability of double nines for a SIR threshold of 5 dB, which is not workable for silencing and full interference schemes. For example, silencing schemes attain reliability targets at lower thresholds, while MRT and TAS with silencing schemes have some higher thresholds for the same target reliability. In addition, the slope of MRT and TAS with silencing curves are verticals with higher values of \(\delta\) while silencing and full interference are not. We observe that all the scheme's performance is sensitive to distance-based interference. The improvement in reliability seems better with the MRT and TAS with silencing for the same number of cooperating RRHs compared to the silencing schemes. At the same time, the MRT has significant performance gains from joint transmission from cooperating RRHs, which shows improvement in terms of the reliability. Figure 5: Illustration of reliability analysis for silencing, TAS with silencing and MRT schemes with respect to threshold \(\theta\) as a function of \(N\) with fixed \(k=3\) cooperating RRHs. Figure 6: Illustration of reliability analysis for full interference, silencing, TAS with silencing and MRT schemes with respect to ratio of distances \(\delta\) and threshold \(\theta\) with \(N=10\) and \(k=8\) cooperating RRHs. Figure 7 illustrates the target transmission rate as a function of the target reliability constraints \(\epsilon_{th}\) for silencing, TAS with silencing, and MRT schemes for different levels of cooperating RRHs \(k\). The target rate to attain target reliability for the silencing scheme is calculated from (11), while TAS with silencing and MRT schemes through numerical analysis from (12) and (13), respectively.