# Iterative Analog-Digital Multi-User Equalizer for Wideband Millimeter Wave Massive MIMO Systems
## 5 Performance Results  
In this section, we show the BER performance of the proposed receiver structure for both analog precoders designed in Section 2, whose parameters are presented in Table 1. The results presented from Figures 3-10 do not consider either path loss or shadowing effects between the UTs and the base station. The path loss and shadowing effects are evaluated in Figures 11 and 12, for \(n_{p}=4.17\) and \(\sigma_{s}=9\) dB [32]. We consider the wideband mmWave channel model defined in (1), perfect synchronization, and CSI at the receiver side. To evaluate the proposed hybrid multi-user equalizers, we consider the analog precoders discussed in Section 2. The analog precoder is generated either randomly according to (8), referred to here as the Non-CSI precoder (NCSI precoder) or the one computed on the basis of the average AoD of each cluster according to (10), referred to as the Partial CSI precoder (PCSI precoder). The performance results are presented in terms of the average BER as a function of \(E_{b}/N_{0}\), where \(E_{b}\) denotes the average bit energy, and \(N_{0}\) denotes the one-sided noise power spectral density. It was assumed that \(\sigma_{1}^{2}=\ldots=\sigma_{U}^{2}=1\) and that the average \(E_{b}/N_{0}\) is identical for all users \(u\in\{1,\ldots,U\}\) and is given by \(E_{b}/N_{0}=\sigma_{u}^{2}/(2\sigma_{n}^{2})=\sigma_{n}^{-2}/2\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Carrier frequency & 72 GHz \\ Antenna element spacing & Half-wavelength \\ Array configuration & ULA or UPA \\ \(N_{cl}\) & 4 \\ \(N_{ray}\) & 5 \\ \(\sigma_{\phi_{x}^{\prime\prime}},\sigma_{\phi_{x}^{\prime\prime}}^{\phi_{x}^{ \prime\prime}}\) & 10 degrees \\ \(N_{c}\) & 512 \\ \(D\) & 128 \\ \(S\) & 128 \\ \(U\) & 8 \\ \(N_{tx}\) & 16 \\ \(N_{rx}\) & 32 \\ \(N_{rx}^{RF}\) & 8 \\ Modulation & QPSK or 16-QAM \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 4: Performance of the proposed hybrid iterative multi-user equalizer (Algorithm 1) for the PCSI precoder with ULA configuration and QPSK modulation. Figure 5: Performance comparison between the Algorithm 1, the two-step, and GS/MMSE approaches for the NCSI precoder with ULA configuration and QPSK modulation. Figure 3: Performance of the proposed hybrid iterative multi-user equalizer (Algorithm 1) for the NCSI precoder with ULA configuration and QPSK modulation. Figure 8: Performance comparison between the Algorithm 1, the two-step and GS/MMSE approaches for the PCSI precoder with ULA configuration and 16 QAM modulation. Figure 6: Performance comparison between the Algorithm 1, the two-step, and GS/MMSE approaches for the PCSI precoder with ULA configuration and QPSK modulation. Figure 7: Performance of the proposed hybrid iterative multi-user equalizer (Algorithm 1) for the PCSI precoder with ULA configuration and 16 QAM modulation. Figure 11: Performance comparison between the Algorithm 1 and the two-step approach for the NCSI precoder with ULA configuration, path loss, and shadowing and QPSK modulation. Figure 10: Performance of the proposed hybrid iterative multi-user equalizer (Algorithm 1) for the PCSI precoder with UPA configuration and QPSK modulation. Figure 9: Performance of the proposed hybrid iterative multi-user equalizer (Algorithm 1) for the NCSI precoder with UPA configuration and QPSK modulation. First, let us analyze the results of the proposed fully iterative analog-digital equalizer (Algorithm 1 in the legends) for the referred two precoders, with no path loss or shadowing effects between the UTs and the base station. The curve for fully digital equalizer discussed in [29] is added because it can be considered as a lower bound for the hybrid architectures. The results are also compared with the semi-analytical BER approximation (15). We only added the theoretical curves for the first and fourth iterations for clarity.