## 3 Full-Wave Simulation Results
Finally, Table 11 shows a performance evaluation by comparing the 2-D phased array architectures with respect to previous work, considering different methods for bi-dimensional arrays. As shown in this table, this comparison assessment analyzes the phase shifter reduction, beam-steering in azimuth and elevation, and side lobe level. It is very interesting to observe that the proposed 2-D antenna systems obtained a phase shifter reduction of 57% and 81%. These proposed configurations provide excellent design features for the reduction of phase shifters obtained in the system. These design characteristics are a side lobe level of \(-19\) dB generated by the CST electromagnetic solver (taking the mutual coupling into account) for a limited beam-scanning range, as set in Table 11. It is interesting to highlight that the proposed case 2 in this paper generates the highest reduction of phase shifters with respect to other works previously published concerning 2-D phased array systems. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Number of Elements** & **Number of Phase Shifters** & **Elevation** & **Azimuth** & **Phase Shifters** & **Simulated Peak** \\  & **Elements** & **Shifters** & **Scanning Range** & **Scanning Range** & **Reduction** & **Side Lobe Level** \\ \hline Conventional & & & & & & & \\ phased array (raised cosine taper) & 81 & 81 & \(\pm 45^{\circ}\) & \(\pm 45\) & 0\% & \(-20\) dB (AF) \\ \hline This work (configuration 1) & 81 & 35 & \(\pm 18^{\circ}\) & \(\pm 40^{\circ}\) & 57\% & \(-18.9\) dB \\ \hline This work (configuration 2) & 81 & 15 & \(\pm 18^{\circ}\) & \(\pm 30^{\circ}\) & 81\% & \(-18.9\) dB \\ \hline  & 49 & 27 & \(\pm 25^{\circ}\) & \(\pm 40^{\circ}\) & 45\% & \(-19\) dB \\ \hline [PERSON] et al. [25] & 42 & 15 & \(\pm 25^{\circ}\) & \(\pm 25^{\circ}\) & 64\% & \(-19\) dB \\ \cline{2-6}  & 49 & 15 & \(\pm 25^{\circ}\) & \(\pm 25^{\circ}\) & 69\% & \(-18\) dB \\ \hline [PERSON] et al. [13] & 256 & 60 & \(\pm 15^{\circ}\) & \(\pm 40^{\circ}\) & 57\% & \(-12\) dB (AF) \\ \hline [PERSON] et al. [18] & 28 & 14 & \(\pm 24^{\circ}\) & Not specified & 50\% & \(-15\) dB \\ \cline{2-6}  & 28 & 7 & \(\pm 11^{\circ}\) & Not specified & 75\% & \(-15\) dB \\ \hline \end{tabular}
\end{table} 
Table 11: Performance evaluation by comparing the proposed systems with respect to previous work considering other methods. Figure 21: Behavior of the mutual coupling between different antenna elements (1, 11, 21, 31, 40, 41) that include different spacing between them. More configurations can be studied and analyzed in order to generate better design solutions for 2-D phased array systems. The iterative solution of CORPSs provides more freedom degrees to split and sum the signals using less control ports. For example, our approach is based on the use of linear CORPSs blocks: the 4 \(\times\) 9 CORPSs block. However, planar CORPSs blocks can be designed and generated to feed in a more efficient way the architectures of 2-D phased array systems. This requires more research and analysis in the blocks of the feeding network. Furthermore, other design techniques can be integrated with CORPSs, such as random feeding sub-arrays and interleaving systems. This can generate a complete methodology to reduce even more the phase shifters in the 2-D phased array system. In addition, the application of CORPSs and sub-arrays is particularly focused on phased antenna arrays with uniform spacing. The advantages of the antenna systems based on CORPSs can exploit the benefits of the non-uniformity of the antenna array systems. This opens more antenna design possibilities to create phased array systems with less complexity and efficient radiation characteristics. Future works will deal with these topics.