## 4 Simulation Results  
In this section, we present the simulation results to evaluate the performance of the proposed architecture. For comparison, we consider the MMSE precoding scheme for fully digital MIMO precoding, conjugate precoding scheme for VPS-based HBF [17], and scheme for CPS-based HBF [19]. For the CPS-based HBF scheme, we assume that each CPS is connected only to a single antenna for even distribution of signal power across transmit antennas. For a BS, we consider a ULA antenna array [17] with antenna spacing \(d=\lambda\) / 2. The number of scattering paths is set to \(N_{p}=10\). The signal-to-noise ratio (SNR) in all simulation results is defined as \(\text{SNR}=P\) / \(U\sigma^{2}\). First, we analyze the optimality of the proposed greedy algorithm. In massive MIMO systems, which comprise a large number of antennas, the total number of candidates to be examined in exhaustive search is massive, which makes it almost impossible to test its performance. Therefore, we compare the performances of the exhaustive search and the proposed greedy algorithm by applying them to a relatively small system. Figure 2 shows the sum-rate performances of various schemes, including the proposed architecture with exhaustive search for \(N_{t}=12\), \(U=2\), and \(M=6\). Moreover, we assume two VPSs and four CPSs for each subarray in the proposed architecture. The simulation results in Figure 2 show that when the exhaustive search algorithm is employed for VPS/CPS allocation, the performance of the proposed architecture is close to that of the VPS-based PC-HBF scheme over the entire SNR range. Moreover, Figure 2 shows that the performance of the proposed greedy algorithm is only marginally lower than that of the exhaustive search algorithm. Furthermore, at SNR = 20 dB, the sum rate achieved by the proposed architecture is 22% higher than that of the CPS-based PC-HBF scheme. Figure 3 shows the simulation results obtained for a system with 64 antennas, which serves four users. We assume the number of VPSs as 2, 4, and 8, and the number of CPSs as 15, 12, and 8 in each subarray of the proposed architecture. In Figure 3, the performance of the proposed PC-HBF architecture with the greedy algorithm is close to that of the VPS-based PC-HBF system over the entire SNR range. For example, the performance loss of the proposed architecture is only 4.1% and 1.1% at SNR = 20 dB, respectively, when \(N_{V}\) is 2 and 8. In this environment, the proposed PC-HBF architecture with the exhaustive algorithm is not tested, but the sum-rate of greedy algorithm is close to that of the VPS-based PC-HBF architecture, which implies that the greedy algorithm provides a near-optimal solution to the VPS/CPS allocation problem in the proposed PC-HBF architecture. Similar to Figure 2, the FC-HBF scheme outperforms the PC-HBF scheme. However, the former scheme requires a significantly greater number of phase shifters, which can result in higher energy consumption and lower energy efficiency compared to those of the PC-HBF scheme, as evidenced by the following simulation results. Figure 2: Average sum rate versus SNR. \(N_{t}=12\) and \(U=2\). Moreover, we evaluate the energy efficiency (EE) of the proposed architecture, which is defined as  
\[\text{EE}=\frac{\text{Spectral efficiency}}{\text{Total power consumption}}[\text{bps}/ \text{Hz}/\text{W}]. \tag{5}\]  
In other words, EE indicates the number of bits that can be reliably transmitted per unit of energy [14]. Figure 4 shows compares the energy efficiency for various numbers of antennas and users. For this comparison, we employ the energy consumption model conventional given in [8]. In Figure 4, the proposed architecture outperforms the conventional schemes in terms of energy efficiency. In particular, the energy efficiency of the proposed HBF scheme is \(19.0\%,21.6\%,\) and \(27.3\%\) higher than those of the CPS-based PC-HBF, VPS-based PC-HBF, and CPS-based FC-HBF schemes, respectively, when \(N_{t}=128\) and \(U=8\) are assumed.