## 4 Results and Discussion
### Impact of the Number of Users and the Pilot Reuse Factor on Energy Efficiency  
Figure 9 shows the comparison of the proposed estimator with the existing estimator using the parameter average UL EE with the number of antennae per UE. The simulation result implies that as the number of antennae per UE increases, EE increases for a large value of the number of APs, whereas for a small value of M, EE initially rises and then diminishes as N increases. The MMSE estimator reached the maximum average UL EE = 214.2 Mbit/joule at N = 6 and M = 80, whereas the proposed estimator obtained the average UL EE = 234.5 Mbit/joule; i.e., the proposed estimator outperformed the other estimator by 9.77% at this point. The maximum EE achieved by the proposed estimator for M = 10 is at N = 3, which is 122.8 Mbit/joule, whereas for the existing estimator, it is 114.3 Mbit/joule. The pilot length is 60 since w = 1, N = 6, and K = 10. Figure 10 shows the effect of users on energy efficiency with a varied number of APs and at different numbers of antennae per UE. The proposed estimator achieved energy efficiency EE = 175.249 Mbit/joule at N = 4 and M = 80, whereas for the existing estimator, EE = 165.704 Mbit/joule at N = 4 and M = 80; i.e., the proposed estimator outperformed the existing estimator by 5.76% at this point. At N = 3 and M = 40, the energy efficiency achieved by the existing and proposed estimators became 138.755 Mbit/joule and 144.847 Mbit/joule, respectively. At N = 2 and M = 20, the energy efficiency achieved by the existing and proposed estimators became 98.932 Mbit/joule and 98.932 Mbit/joule,  
Figure 8: Spectral efficiency versus the number of antennas per UE for fully centralized processing with the MMSE combiner at K = 20, L = 4, \(\tau_{\rm c}\) = 200, and w = 2. Figure 7: Spectral efficiency versus the number of antennas per UE for fully centralized processing with the MMSE combiner at K = 10, L = 4, \(\tau_{\rm c}\) = 200, and w = 2.  
respectively. This indicates that as the number of users increased, the energy efficiency decreased. The pilot length is 60 since K = 15, N = 4, and w = 1. The pilot length depends on the number of users, the number of antennae per UE, and the pilot reuse factor; i.e., as the number of users increased, the pilot length also increased. Figure 11 shows that the effect of the pilot reuse factor on the energy efficiency varied across the number of antennae per UE at different numbers of APs when the pilot reuse factor was raised to two. The proposed estimator achieved energy efficiency EE = 176.7 bit/joule at N = 6 and M = 80, whereas for the existing estimator, EE = 162.2 Mbit/joule at N = 6 and M = 80. The proposed estimator improves the performance by 8.94% at this point. At N = 6 and M = 20, the energy efficiency achieved by the existing and proposed estimators became 97.04 Mbit/joule and 108.2 Mbit/joule, respectively. The maximum energy efficiency reached by the proposed estimator occurred at N = 4, i.e., 184.2 Mbit/joule, whereas for the existing estimator, an energy efficiency of 178.2 Mbit/joule was achieved at N = 3. As the pilot reuse factor increased from w = 1 to w = 2, the energy efficiency initially increased and then decreased as the number of antenna per UE increased. The pilot length became 30 since K = 10, N = 6, and w = 2, which means that the pilot length decreased as the pilot reuse factor increased. Figure 10: Energy efficiency versus the number of access points for fully centralized processing with the MMSE combiner at K = 15, L = 4, \(\tau_{c}\) = 200, and w = 1. Figure 9: Energy efficiency versus the number of antennas per UE for fully centralized processing with the MMSE combiner at K = 10, L = 4, \(\tau_{c}\) = 200, and w = 1. Figure 12 describes the effect of the pilot reuse factor on the energy efficiency varied across the number of antennae per AP at different numbers of UE when the pilot reuse factor was raised to two.