## 7 Performance Evaluation
### Mesh Antenna Array  
The second experiment involves a UMA of 36, 64, 100, and 256 elements designed for maximum mainlobe toward \(\phi=90^{\circ}\) as well as the sidelobe suppression in region \((0^{\circ},360^{\circ}]\) and prescribed nulls at \([30^{\circ},50^{\circ},100^{\circ},180^{\circ},220^{\circ}]\). Figure 8 shows that broad nulls as deep as \(-38\) dB, \(-60\) dB, and \(-65\) dB are achieved. Table 4 summarizes the optimal values obtained using CPSO where the performance is somehow superior than those of convex optimization and conventional linear array. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{2}{c}{**36 Sensors**} & \multicolumn{2}{c}{**64 Sensors**} & \multicolumn{2}{c}{**100 Sensors**} & \multicolumn{2}{c}{**256 Sensors**} \\ \cline{2-9}  & **min** & **max** & **min** & **max** & **min** & **max** & **min** & **max** \\ \hline CPSO & \(-30\) dB & \(13\) dB & \(-62\) dB & \(18\) dB & \(-55\) dB & \(15\) dB & \(-50\) dB & \(18\) dB \\ Convex & \(-8\) dB & \(11\) dB & \(-22\) dB & \(15\) dB & \(-22\) dB & \(15\) dB & \(-40\) dB & \(18\) dB \\ Conventional & \(-47\) dB & \(13\) dB & \(-20\) dB & \(18\) dB & \(-22\) dB & \(18\) dB & \(-15\) dB & \(20\) dB \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Geometry of the mesh antenna array consisting of 36, 64, 100, and 256 elements using three different algorithms. Figure 8: Mesh. (**a**) Mesh Sensors 36, (**b**) Mesh Sensors 64, (**c**) Mesh Sensors 100, (**d**) Mesh Sensors 256. Results from the CPSO given in Figure 8a-d depict almost similar beamforming patterns compared to the conventional beamforming patterns. Each sample of beamforming in UMA indicates at first a deterministic and then closely approximates the mainlobe of conventional beamforming pattern achieving the objective function better than convex optimization and below the conventional beamforming pattern. However, this implies that beamforming pattern of each sample does not spread away from the average of conventional beamforming pattern. This is because the proposed selection algorithm based on CPSO acquires a new diversity of solution from outside the area of interest but inside its population solutions by sampling the solution from the \(\int_{\kappa=1}^{h(\overline{\
u})}\) instead of generating a new one from individual or several solutions. Furthermore, the updating velocity in Equation (27) is adjusted based on sampling of solution to guide the future search toward the global solution and then to produce improved samples closer to the optimal solution. We have noticed that the differences in the mainlobe and sidelobe performance among the three algorithms are obvious within increasing the collaborative sensors in antenna array. On the other hand, the gap of the mainlobe as seen in Figures 8a,b becomes smaller in the three algorithms as illustrates in Figures 8c,d. CPSO shows a clear advantage of selecting collaborative sensors in the reduction of the sidelobe below 0 dB which is essential in reducing interference and saving the lifetime of each sensor. From the results, it is noted that the CPSO overcomes the undesired increment of the sidelobe in conventional beamforming pattern and convex optimization. This arises some questions: Is the increased connectivity among the collaborative sensors that is achieved or not due to these sensors have more neighbors (i.e., have more degree of connectivity \(\wp\))? Is the increased connectivity path probability obtained from the directional antenna at the higher sensor degree connectivity and causes a higher inference and overhearing among the collaborative sensors? To address these questions, we concluded that with increasing number of sensors, \(\wp\) increases linearly with increasing \(\kappa\). In other words, when the beamforming pattern is narrow, the probability of connectivity increases and achieves the optimal results.