## 4 Numerical Analysis
We find that, as the number of cooperating RRHs (\(k\)) increases, there is a significant improvement over the rate in all schemes for given target reliability. However, MRT offers a higher rate for the given target reliability constraints. In comparison, TAS with silencing schemes also offer a higher rate compared to silencing schemes for the same target reliability. We see that limiting the interference with RRHs cooperation using silencing, TAS with silencing, or MRT schemes, shows a significant performance gain for target reliability constraints. As mentioned, for \(k=0\), all the schemes operate with the same target rate. The slope of MRT curves increases with increasing cooperating RRHs \(k\) compared to TAS and silencing schemes because the MRT offers higher diversity gain. Even with fewer RRHs, higher data rates are achieved. Figure 8 presents the CRAN EE as a function of the number of cooperating RRHs for each scheme. The parameters in the power consumption model in (17) are taken from [47] where \(\eta=2.8\), maximum transmit power for RRH \(\mathrm{P_{T}}=20\) Watts, active mode power for RRH \(\mathrm{P_{i,active}^{RRH}}=84\) Watts, sleep mode power for RRH \(\mathrm{P_{i,sleep}^{RRH}}=56\) Watts. The finding shows the improvement over the EE with the increase in cooperation for each scheme. However, from (17), power consumption increases with an increase in cooperation. As shown, the MRT scheme has EE relatively higher than TAS and silencing schemes. This is because the number of cooperating RRHs jointly transmitting to the UE increases the data rate, consequently enhancing the energy efficiency. Meanwhile, in the silencing scheme, we transmit through a single RRH, where increments over the rate is a relatively small and relatively small improvement in EE as compared with MRT and TAS with silencing. However, in the case of TAS with silencing, an increase in cooperation and selection among the best links in transmission gives a significant improvement over the rate while power consumption is the same as that of silencing schemes. Meanwhile, further increase in \(k>2\) MRT has an improvement over EE than TAS because the data rate is higher than TAS. Note that the data rate for MRT should grow as \(k\log_{2}k\), however, in this case, it grows exponentially with \(k\), which is counter-intuitive. The underlying reason is that once cooperating RRHs are increased for multi-point transmission, the data rate can be realized for intended UE while guaranteeing target reliability. This is evident for small networks,  
Figure 7: Illustration of rate control analysis with reliability constraint (\(\epsilon_{th}\)) for silencing, TAS with silencing and MRT schemes with \(N=10\) and different number of cooperating RRHs \(k\). thus small \(k\), while for large \(k\), the rate would converge to conventional cases due to the law of the large numbers. This analysis shows MRT scheme has an improvement in energy efficiency as compared with TAS and silencing schemes. We notice that the cooperation of RRHs in interference-limited networks enhances the reliability. In this sequel, we analyze the minimum number of RRHs required to cooperate to attain target reliability by solving the argument based on CDF from (3), (6) and (9) as subjected to casse with constrained Reliability \(\geq 1-\epsilon_{th}\). Figure 9 shows the reliability levels achieved with the minimum number of cooperating RRHs in a CRAN service area. We used \(N=10\) RRHs and threshold \(\theta=0.3\) dB. The analysis shows that with the MRT scheme, all reliability levels can be achieved with a different number of RRHs in comparison with silencing and TAS with silencing schemes. In the case of the reliability of five nines, which is considered as the URC operational region, only \(k_{min}=8\) out of 10 are required using the MRT scheme. In contrast, such reliability is unachievable in the case of silencing and TAS with silencing schemes.