## 3 Numerical Results
### System-Level Simulations
SNR\({}_{\text{target}}\) is the SNR value for \(\text{BLER}_{ref}\) = 0.1. In practical terms, each block received with SNR \(<\) SNR\({}_{\text{target}}\) would be retransmitted until it is correctly received. However, we do not consider this situation in the simulations. Figure 7 is based on the link-level simulation of Figure 4 presented in the previous subsection. In general, it is observed that the greater the number of subcarriers, the greater will be the throughput. As expected, the digital precoder is the one that presents the best performance in terms of throughput as the number of subcarriers and users increases. However, it is possible to approach its performance by considering the use of hybrid algorithms and their different architectures. The ADMM based on an SPS scheme is the one that presents the worst performance for a lower number of subcarriers, but when this parameter is increased it obtains a similar performance to the AM precoding algorithm. The LASSO precoding algorithm with DPS and \(F\) = 512 can obtain a slightly higher performance when compared to the ADMM DPS with \(F\) = 512. However, by increasing the number of subcarriers we observe that both algorithms obtain very similar performances. The blue curves represent the theoretical curves of average throughput value expected to be obtained based on the formula \(\text{Throughput}=R_{b_{\max}}(1-\text{BLER}_{ref})\), where \(\text{BLER}_{ref}\) = 0.1 and \(R_{b_{\max}}\) is the maximum binary transmission rate considered for the two cases \(F\) = 512 and \(F\) = 828. Contrary to what can be seen for \(F\) = 512, a loss of performance of the algorithms for \(F\) = 828 when compared to the curve of average throughput value expected for the case of \(F\) = 828, is observed. Moreover, we observe that with a fixed number of RF chains, the throughput  
of hybrid schemes tends to be closer to digital with \(F=512\) than with \(F=828\). When considering the digital precoding for \(F=828\) and 3C, a maximum SE of 1.9 bps/Hz/user can be obtained. Note that, this fact is also verified in the later graphs. Following the study on the required number of RF chains to accommodate an increasing number of subcarriers discussed in Figure 5, it is necessary to understand how the system behaves when considering different RAN cluster sizes. In Figure 8, we can conclude that increasing the number of RF chains for higher values of \(F\) allows us to reach greater levels of throughput. Furthermore, when the cluster size increases to three (3C), as the number of users increases, the difference becomes more notorious due to the lesser inner interference caused by the network partitioning. When we have \(N_{u}=180\), the achieved throughput increases from 105.7 Gbps to 133.3 Gbps if the cluster size triples. It must be noted that for smaller blocks, such as \(F=16\) up to 128, the system performance is independent of cluster size. When \(F\) presents higher values, we observed that the performance difference of 1C and 3C increases with the block size. Figure 7: Throughput (Gbps) vs. number of users for different methods with \(N_{tx}=100\), \(N_{rx}=4\), \(N_{RF}^{tx}=12\) and \(N_{s}=2\), by changing the number of subcarriers (only NLOS component). At this point, we already know that the throughput increases as the number of subcarriers increases and the ADMM precoding algorithm constitutes an interesting alternative since it can present a good performance and can cope with different architectures, facilitating their implementation. However, it is worth understanding how the system behaves when the AP antennas are combined with different architectures based on phase shifters, as can be seen in Figure 9. Independently of the adopted architecture, it is observed that the throughput increases as the number of subcarriers increases. However, the adoption of a DPS architecture can provide a higher throughput when compared to an architecture based on SPS. This difference is even more notorious when we increase the cluster size from 1 to 3.