## 7 Performance Evaluation
### Random Antenna Array  
The third experiment investigates RAA configurations of 36, 64, 100, and 256 elements designed for mainlobe towards \(\phi=90^{\circ}\) as well as the sidelobe suppression in the region \((0^{\circ},360^{\circ}]\) and prescribed nulls at \([60^{\circ},120^{\circ},180^{\circ},220^{\circ}]\). Broad nulls as deep as \(-5\) dB, \(-8\) dB,\(-18\) dB, and \(-22\) dB are observed using the CPSO as seen in Figure 9a-d. Table 5 summarizes the optimal values obtained using CPSO where the performance is somehow superior than those obtain form 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 & \(-22\) dB & \(18\) dB & \(-15\) dB & \(18\) dB & \(-11\) dB &  
This experiment applies to military applications whereas collaborative sensors are distributed randomly without supporting facilities (such as energy sources or wired) to specified position close to enemy territories. Consequently, their positions may be or not close to the area of interest and the transmission requires high directivity at the desired direction. Multiple sensors are deployed form multihop topology which leads to difficulty in regulating these sensors as a specific topology because of the environmental constraints such as the sensors' position and connectivity with their neighbors. Hence, the RAA population is formulated next along with its corresponding conventional beamforming pattern and compared with convex optimization as shown in Figure 9a-d, respectively. The probability distribution function for the connectivity factor is then formed amid RAA collaborative sensors located with an area of interest. Given \(\int_{x=1}^{h(\vec{x})}\) of the collaborative sensors in random arrangement, the properties of RRA are determined to include the expected beampattern, peak and null locations of the mainlobe and sidelobes. As illustrated in Figure 9a, the proposed CPSO algorithm achieves the most significant suppression of the sidelobes prominent in the regions of 55\({}^{\circ}\), 152\({}^{\circ}\), and 190\({}^{\circ}\), whereas  
Figure 9: Random. (**a**) Random Sensors 36, (**b**) Random Sensors 64, (**c**) Random Sensors 100, (**d**) Random Sensors 256.  
the approximate solution decreases the corresponding level to \(-5.12\) dB, \(-6\) dB, and \(-23\) dB compared to conventional RAA. A higher gain is obtained in mainlobe whereas optimizing the maximum mainlobe is distinguished in the region of \(30^{\circ},50^{\circ},100^{\circ},180^{\circ},220^{\circ}\), whereas the approximate solution provides an increase of 18 dB compared to conventional RAA. Figure 9(b) considers 64 sensors in which the conventional RRA exhibits relatively minimum sidelobe as compared to convex optimization. It can be observed from Figure 9(b) that the lowest sidelobes are \(-20\) dB, and \(-88\) dB at \(55^{\circ}\), and \(220^{\circ}\) for convex optimization and conventional RRA, respectively. However, CPSO significantly minimizes the sidelobe to \(-60\) dB, and \(-63\) dB at \(30^{\circ}\) and \(190^{\circ}\), respectively. Different effects are revealed by increasing the number of sensors as shown in Figure 9(c,d). The radiation pattern of 100 sensors are given for the conventional RRA showing minimum sidelobe of 3 dB compared to sidelobe of convex optimization of 0 dB at \(50^{\circ}\), and \(150^{\circ}\). Meanwhile, the radiation pattern of 256 sensors is shown using the conventional beamforming RRA which exhibits the minimum sidelobe at \(65^{\circ}\), and \(150^{\circ}\) compared to convex optimization.