## 4 Results and Discussion
### Impact of the Number of Users and the Pilot Reuse Factor per Access Point on Spectral Efficiency  
Figure 5 demonstrates the comparison of the proposed estimator with the existing estimator when the number of UE increases. For instance, for N = 3 and M = 40, the average UL SE for the existing estimator decreased from 34.03 bit/s/Hz to 31.72 bit/s/Hz as K increased. Similarly, the average UL SE for the proposed estimator decreased from 35.55 bit/s/Hz to 33.09 bit/s/Hz as K increased. For M = 10, the average UL SE raised to N = 3 and then diminished as N increased. This is due to the number of user antennas being low compared to the number of AP antennas, which increasing the chance of interference occurring between the user antenna and the access point antenna. But the proposed estimator still has better performance than the existing estimator. The proposed estimator obtained the average UL SE = 49.1 bit/s/Hz at N = 5 and M = 80, whereas the MMSE estimator reached the average UL SE = 42.72 bit/s/Hz; i.e., the proposed estimator outperformed the other estimator by 14.93%. The pilot length becomes \(\tau_{p}\) = 60; i.e., the pilot length increases as the number of users increases. \begin{table}
\begin{tabular}{c c c} \hline
**No.** & **Simulation Parameter** & **Type and Value** \\ \hline
1 & Pilot reuse factor (w) & 1, 2 \\
2 & Uplink transmitter power (p) & 200 mW \\
3 & Number of access points (M) & 10, 20, 40, 80 \\
4 & Number of antennae per UE (N) & 1, 2, 3, 4, 5, 6 \\
5 & Number of antennae per APs (L) & 4 \\
6 & Number of user equipment (K) & 8, 10, 15, 20 \\
7 & Coherence block & 200 to 800 \\
8 & Bandwidth (B) & 1 MHz \\
9 & Coverage area & 1 km by 1 km \\ \hline \end{tabular}
\end{table} 
Table 1: Simulation parameter. Figure 5: Spectral 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 6 shows the comparison of the average UL SE for completely centralized processing as a function of the number of APs (M), with the MMSE combining over varied numbers of antennae per user equipment (N). When the number of users increases to K = 20, the maximum average UL SE achieved by the proposed method is 30.14 bit/s/Hz. For the single-antenna user, the performance is diminished highly from 10.26 bit/s/Hz to 4.408 bit/s/Hz for the existing estimator and from 15.07 bit/s/Hz to 30.14 bit/s/Hz for the proposed estimator. This shows that the proposed estimator is not effective for the single-antenna user equipment for a large number of users. The proposed estimator obtained the average UL SE = 30.14 bit/s/Hz at N = 4 and M = 80, whereas the MMSE estimator reached the average UL SE = 28.55 bit/s/Hz; i.e., the proposed estimator outperformed the other estimator by 5.57%. The pilot length is 80 since K = 20 and N = 4. Figure 7 emphasizes the impact of the pilot reuse factor on the SE for different numbers of APs across the number of antennae per UE. The proposed estimator obtained the average UL SE = 17.268 bit/s/Hz at N = 6 and M = 80, whereas the MMSE estimator reached the average UL SE = 15.894 bit/s/Hz; i.e., the proposed estimator outperformed the other estimator by 8.53%. The increment of the pilot reuse factor results in a decrease in average UL SE. The proposed estimator has better performance as compared to the existing estimator when the number of antennae per UE for different numbers of APs is different. The pilot length is 30 since w = 2, K = 1, and N = 6. The pilot length decreases due to the pilot reuse factor; i.e., as the pilot reuse factor increases, the pilot length decreases. The maximum average UL SE achieved for the proposed method is 18.228 bit/s/Hz at N = 4 and M = 80, whereas for the existing one, it is 17.69 bit/s/Hz. Figure 8 describes the impact of the pilot reuse factor on the SE for a different number of UE antennas across a number of APs as the pilot reuse factor increases to two.