# On Deploying the Internet of Energy with 5G Open RAN Technology including Beamforming Mechanism
## 4 Implementation of Beamforming in Open RAN Networks
### System Model and Simulation Results
As we can see, regardless of the number of users, beamforming transmission without precoding achieves very low values of spectral efficiency, even when few mobile devices are connected. Really, the apparition of any kind of interference (even one more user in the cell) makes the transmission unfeasible, unless some kind of coding is used. The introduction of ZF-BF can obtain a performance adjacent to the single-user scenario, reducing the interference in the multi-user environment. In Figure 4a,b, we may observe that the increase in the number of users from 4 to 8 means causes a falling of the spectral efficiency of around \(2\)\(\mathrm{bps}/\mathrm{Hz}\), irrespectively if the system implements zero-forcing coding or not. The next figure aims to better understand the effect of the number of users in the system. Figure 5 shows the impact of the number of users that provoke interferences. Figure 5a shows the spectral efficiency when ZF-BF precoding is installed. We may see that, by increasing twice the number of mobile devices in the cell, the efficiency falls around \(2\)\(\mathrm{bps}/\mathrm{Hz}\). In other words, when the number of users is doubled, the system needs around \(5\) dB more SNR to achieve the same spectral efficiency (see, for example, the value of \(8\)\(\mathrm{bps}/\mathrm{Hz}\) that requires \(10\), \(15\) and \(20\) dB for \(4\), \(8\) and \(16\) users, respectively). For SNR equal to \(30\) dB, we may observe a slight difference, however we think that this is an effect of the  
Figure 4: Comparison of ZF-BF precoding transmission and transmission without ZF-BF precoding: Achievable spectral efficiency for varying SNR in the range \([-10;30]\) dB with several transmission antennas and number of users’ mobile devices: (**a**) 64 Transmission antennas and 4 mobile devices; (**b**) 16 Transmission antennas and 8 mobile devices. short duration of the simulations. Figure 5b shows a decrease in the efficiency between 4 and 8 users; however, after that, the increase in the number of users does not have a practical impact on the efficiency. The reason is that the spectral efficiency is then bounded by the white noise, and not by the interferences. In any case, we need to highlight that such values of spectral efficiency make the transmission unfeasible, or at least highly inefficient. Let us remark that in our simulations, the number of antennas has a null impact on the results, under the condition that this (the number of antennas) is enough for serving the number of mobile devices in the covered area. In radio transmission, the number of Tx antennas has an impact in the SNR of the transmission, so that more antennas may allow a higher bitrate. However, upon a certain signal power, the increase in antennas does not increase the bitrate. This point is known as the bandwidth limit area and means that the bandwidth is the limit of the bitrate, i.e., the efficiency is maximum. The way to increase bitrate in that case is to increase the number of Rx antennas, so that we have more complex MIMO system. In our simulations, this effect is not demonstrable since we do not have full MIMO transmission, but more a multi-path transmission (the antennas send signal to specific user). As a conclusion, the reduction of spectral efficiency is due to the increase in mobile devices covered by the antenna. In the case of a high number of mobile devices (high interference), we suggest applying minimum mean square error (MMSE). MMSE reduces the interference by reflecting the noise. The MMSE is more accurate than zero-forcing and serves a wide range of channel state conditions (different \(SNR\)). In the case of MMSE, Equation (7) may be re-written as in Equation (9). Let us remark that we do not assume orthogonality in Equation (9). \[W_{mmse}=\widetilde{H}^{*}\bigg{(}\widetilde{H}\widetilde{H}^{*}+\frac{N_{t}}{ SNR}I_{Nr}\bigg{)}^{-1} \tag{9}\]  
The MMSE matrix is simply the inverse of the channel matrix (\(H^{-1}\)). Figure 6 shows the differences of the spectral efficiency when we provide MMSE algorithm instead of ZF-BF.