# Multi-User Linear Equalizer and Precoder Scheme for Hybrid Sub-Connected Wideband Systems
## 5 Performance Results  
In this section, we evaluate the performance of the proposed multi-user linear equalizer and precoder scheme designed for hybrid sub-connected wideband mmW systems. The carrier frequency was set to 72 GHz and for each user, the clustered wideband channel model was considered, as discussed in Section 2, with five clusters \(N_{cl}=5\), all with the same average power, such that \(\mathbb{E}\Big{[}\big{\|}\mathbf{H}_{u,d}\big{\|}_{F}^{2}\Big{]}=N_{rx}N_{tx}\), and each one contributed with \(N_{ray}=3\) propagation path. The path delays were uniformly distributed in the CP interval. We considered a ULA with antenna element spacing set to half-wavelength, but it should be emphasized that the schemes proposed in this paper can be applied to any antenna arrays. The azimuth angles of departure and arrival had a Laplacian distribution as in [20] and were considered to have an angle spread of \(10^{\circ}\) for both the transmitter and receiver. It was assumed a QPSK modulation, perfect synchronization, and that the CSI is known at the receiver side. At the transmitter, only a quantized version of the average angle of departure of each cluster was known. We assumed \(N_{c}=64\) subcarriers, and the CP was set to be a quarter of the number of subcarriers, such that \(D=N_{c}/4=16\). We considered a Monte-Carlo simulation with a length of 100,000 SC-FDMA blocks. The average BER was considered the performance metric, presented as a function of \(E_{b}/N_{0}\), where \(E_{b}\) is the average bit energy and \(N_{0}\) is the one-sided noise power spectral density. We considered that the average \(E_{b}/N_{0}\) was identical for all the users \(u\) and is given by \(E_{b}/N_{0}=1/(2\sigma_{n}^{2})\). We considered that each transmitter had a single RF chain and was equipped with \(N_{tx}=8\) antennas. At the receiver side, it was assumed that a sub-connected architecture existed, where each RF chain was connected to a group of \(R=N_{rx}/N_{RF}\) antennas, with \(N_{rx}=16\) antennas. The results were compared with the fully connected counterpart that could be obtained from the proposed one by relaxing the optimization constraints, since each RF chain was connected to all antennas. The main simulation parameters are presented in Table 1.  
Figure 3 depicts the results for the proposed hybrid sub-connected multi-user equalizer with the analog precoder for two, four, and eight users. In this figure, it was assumed perfect knowledge of the average AoD of each cluster. It was also assumed eight RF chains existed, which meant that each one was connected to two antennas. As it can be seen in Figure 3, the performance of both sub- and fully connected improved as the number of users decreased, as expected, since the multi-user equalizer \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Values** \\ \hline Number of user (\(U\)) & 2, 4, and 8 \\ Number of Receive antennas (\(N_{rx}\)) & 16 \\ Number of Transmit antennas (\(N_{tx}\)) & 8 \\ Number of RF chains (\(R\)) & 2,8, and 16 \\ Number of subcarriers (\(N_{c}\)) & 64 \\ Cyclic prefix & 16 \\ Number of quantization bits (\(n\)) & 2, 4, and 6 \\ Carrier frequency & 72 GHz \\ Number of clusters (\(N_{cl}\)) & 5 \\ Number of rays per cluster (\(N_{nny}\)) & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main simulation parameters. had to deal with less interference and the available degrees of freedom could be used to provide more diversity. We could also observe a performance penalty of the sub-connected approach against the fully connected one of approximately 2 dB, independently of the number of users, at a target BER of \(10^{-3}\). This was because the number of connections of the fully-connected architecture was larger than the number of connections for the sub-connected architecture and, as expected, the result for the fully-connected one was better than for the sub-connected architecture.