## 5 Simulation Results and Discussions  
This section includes a comprehensive collection of simulation results that investigate the performance of our proposed matching scheme in terms of total power consumption and EE in the uplink cell-free mm-Wave massive MIMO. In order to emphasize the importance of our results through matching between several fixed values of activated antennas based on the channel quality and RF chains at each AP, our proposed scheme is compared with the methods from conventional mm-Wave multi-users MIMO in [22] expanded to cell-free mm-Wave massive MIMO systems, which are decremental search-based antenna selection (DSAS), channel magnitude-based with dynamically selected antennas (CMDAS), and channel magnitude-based with fixed selected antennas (CMFAS). The proposed scheme can enhance the total EE in the cell-free uplink network and achieve the tradeoff between system performance in terms of SE, EE, and the complexity of the proposed matching scheme. Similar to what has been done in the literature on cell-free massive MIMO, and to improve the modelling of network performance by removing boundary effects, \(M\) APs are randomly distributed in a \(D\times D\) square service area, where \(D=1000\) m [6,18], and boundaries are wrapped around. In addition, due to the limited scattering in mm-Wave channels, the effective channel paths between \(k_{th}\) UE and \(m_{th}\) AP is assumed as \(P_{k,m}=20\ \forall k,m\)[11,18,24]. Based on (2), the large scale fading coefficients can be determined by setting \(\varepsilon=4.1\) and \(\varsigma=7.6\)[18,26]. Table 1 contains the parameters used in all simulations in this section. Figures 3 and 4 show the impact of the number of \(N_{r}\) on both EE and total power consumption when \(M=80\), \(K=8\), \(N_{Q}=8\), and the transmit power \(\rho=23\) dBm. Figure 3 shows the EE for an increasing number of \(N_{r}\). It is observed that the EE for all schemes decrease when \(N_{r}\) increases, which is obvious because the additional \(N_{r}\) come with a resultant increase in power consumption. The proposed matching scheme for antenna selection in uplink cell-free mm-Wave massive MIMO systems is advantageous when the APs have fewer antennas or more antennas. In the case of the APs having fewer antennas, the channel quality worsens, leading to degradation in system performance in terms of the SE. However, the proposed scheme can mitigate this issue by offering each half of the RF chains be assigned to more than 50% of the \(N_{r}\) at each AP, while each of the remaining RF chains is matched to 50% or less of \(N_{r}\). Therefore, half of the RF chains assigned to more than 50% of the selected antennas at each AP can guarantee improvement of the sum rate, and the remaining RF chains set to 50% or less can maximize EE. For example, when  
\(N_{r}=16\) antennas are equipped for each AP, the proposed antenna matching selection strategy can achieve 12.5171%, 18.33%, 21.384%, 21.6%, and 40.387% compared to the CMFAS scheme with both 50% and 75% of the selected antennas fixed, and CMDAS, DSAS, and FCPSs in [15], respectively. On the other side, Figure 4 shows total power consumption increases when \(N_{r}\) increases. It is obvious that CMFAS with 50% of the selected antennas fixed has the lowest total power consumption. Then, the proposed matching scheme comes in second place and then CMDAS, DSAS, and FCPSs, in which DSAS and FCPSs attain similar total power consumption. Therefore, it can be seen that the proposed matching based on the Hungarian algorithm can outperform CMDAS, DSAS, and FCPSs. For example, when \(N_{r}=48\), the proposed matching scheme uses 1108.48 W, while CMFAS with 50% of the selected antennas fixed uses 1023.63 W. In addition, CMDAS, DSAS, and FCPSs use 1487.67 W, 1627.09 W, and 1639.39 W, respectively.