## 4 Massive MIMO Performance Evaluation
Furthermore, 10,000 sets of \(K\)-concurrent users randomly distributed inside the circular sector were adopted. It is worth observing that a smart user's selection inside the sector can improve the massive MIMO performance and the energy efficiency of the wireless communication [55]. However, this aspect was neglected, since the main goal of the paper is to highlight the performance differences between square and triangular lattices. The achievable SE as a function of the \(\delta\) value, which is the ratio between the transmitted power (\(P_{t}\)) and the noise power (\(\sigma_{0}\)), is reported in Figure 16 for both square and triangular lattices in the event of eight simultaneous users inside the investigated circular sector. Figure 16: SE comparison for a planar array composed of 8 \(\times\) 8 elements, in cases of square and triangular lattices, as a function of the \(\delta\) ratio in dB in the event of 8 concurrent users. It can be seen that the triangular lattice deployment of the array antenna elements allows for the achievement of a considerable improvement in the SE. The SE starts to grow almost linearly with the increase in the \(\delta\) value, after which it reaches a superior limit due to the SIR, and the system becomes interference limited. Therefore, once the upper SE boundary is reached, further increasing the transmitted power does not represent an efficient way of improving the SE. The improved SE in the triangular lattice array is apparent from looking at the statistical behavior of the CDF of the SIR (Figure 17), and both the average SIR (\(\eta_{SIR}\)) and 90% of the SIR occurrence (\(SIR_{90\%}\)), as highlighted in Table 3.  
Since to improve the SE it is better to serve more users inside the predefined sector cell rather than increasing the transmitted power, the SE is plotted as a function of the number of users (\(K\)) for both triangular and square lattices in the event of a \(\delta=20\) dB (Figure 18). Figure 17: SIR CDF comparison for a planar array composed of 8x8 elements, in cases of square and triangular lattices, in the event of 8 concurrent users. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**24.25 GHz**} & \multicolumn{2}{c}{**26.875 GHz**} & \multicolumn{2}{c}{**29.5 GHz**} \\ \hline  & Tri & Squ & Tri & Squ & Tri & Squ \\ \(\eta_{SIR}\) & 11.1 & 10 & 12 & 11.25 & 13.3 & 12.2 \\ \(SIR_{90\%}\) & 0.4 & 0 & 0.9 & 0.5 & 1.4 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulated average SIR (\(\eta_{SIR}\)) in dB and \(SIR_{90\%}\) across triangular and square lattice planar arrays composed of 64 elements (\(8\times 8\)), in the event of 8 served users inside the circular sector. Figure 18: (**a**) SE comparison as a function of the number of users (\(K\)) between square and triangular lattice planar arrays composed of 64 elements; and (**b**) percentage SE improvement in the event of \(\delta=20\) dB. The remarkable advantage of using a triangular lattice arrangement of the array elements instead of a square one is confirmed by observing the SE in Figure 17(a). To emphasize the SE comparison, the percentage SE improvement is calculated and reported in Figure 17(b). As can be seen, the achievable SE between the two lattices turns out to be comparable for few users, even if the triangular lattice's SE is somewhat higher due to a superior array gain value (Figure 8). Conversely, with the increase in the number of concurrent users, the SE improvement guaranteed by the triangular lattice array grows continuously, and reaches a value between 8.5% and 12 % in the event of 20 simultaneous users inside the sector. In view of highlighting the advantageous impact of the triangular lattice on planar arrays in massive MIMO systems, the percentage SE improvement of the most suitable triangular lattice, compared to rectangular or square lattices, is reported in Table 4 for a case of 20 concurrent users deployed inside the different sector cells.