## 3 Results
Design A prioritizes optimization at the initial operating frequency \(f_{l}\), making it well-suited for applications that demand high precision and stability within a defined baseband. This design approach may partially compromise wideband performance in favor of enhanced behavior at the operational frequency. Conversely, Design B aims to achieve a balanced radiation response across the operational bandwidth, making it more appropriate for applications requiring frequency agility and consistent performance over a wider range. For higher fractal stages (\(p\geq 3\)), thinned array configurations are generated by applying the self-replication and upscaling properties to the optimized stage 2 structure. This hierarchical approach has shown improved results compared to direct optimization at higher stages. Findings indicate that the self-replication method enhances performance at the operational design frequency, while the upscaling method maintains a more uniform response across the array bandwidth. Table 3 provides a comparative analysis of performance metrics for the proposed Designs A and B, the complete Eisenstein fractal array configurations with 64 and 256 elements, and conventional uniform square planar arrays with equivalent element counts. The comparison highlights the advantages of employing the Eisenstein fractal geometry for wideband applications. The proposed designs demonstrate improved performance in terms of SLL reduction and directivity, despite using fewer active elements. These results validate the effectiveness of the proposed optimization methodology and underscore its potential for developing efficient, wideband antenna arrays. The analysis focuses on stages 3 and 4 of the proposed designs, where the number of active elements remains within a practical range that is feasible for fabrication and appropriate for experimental prototyping. Figure 7 presents the wideband SLL performance comparison between Design A, Design B, and the original 64-element Eisenstein configuration. The results demonstrate notable improvements in SLL suppression, even with a reduced number of active elements. Design A achieves a significant reduction of approximately \(-10\,\mathrm{dB}\) in SLL at the initial operating frequency \(f_{l}\), with a trade-off of about \(2\,\mathrm{dB}\) degradation across the broader \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Array Structure** & **Elements** & **Bandwidth** & **SLL at \(f_{l}\) (dB)** & **SLL over Bandwidth (dB)** \\ \hline Planar & 64 & 1:1 & \(-12.76\) & – \\  & 256 & 1:1 & \(-13.14\) & – \\ \hline Original Eisenstein & 64 & 4:1 & \(-25.59\) & \(-25.59\) \\  & 256 & 4.2:1 & \(-26.29\) & \(-26.28\) \\ \hline Design A & 40 & 4:1 & \(-38.72\) & \(-19.25\) \\  & 160 & 4.2:1 & \(-38.74\) & \(-34.55\) \\ \hline Design B & 40 & 4:1 & \(-27.17\) & \(-27.17\) \\  & 160 & 4.2:1 & \(-29.86\) & \(-29.83\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance comparison of the proposed optimized designs (Design A and B) against the original Eisenstein fractal array and a conventional uniform planar array. bandwidth. In contrast, Design B maintains a more consistent performance, achieving an SLL reduction of approximately \(-3\) dB across the entire operational frequency range. The array factor (AF) performance of both proposed designs at the frequency boundaries \(f_{l}\) and \(f_{u}\) is illustrated in Figure 8. Design A exhibits excellent performance at \(f_{l}\), with significantly reduced SLL, while still maintaining acceptable behavior at \(f_{u}\), despite the reduced element count. Design B delivers improved performance at both frequency boundaries, achieving a narrower main beamwidth and enhanced directivity, all while maintaining a lower number of active elements. These results highlight the effectiveness of the proposed optimization strategy in balancing bandwidth, directivity, and element count. Figure 9 shows the wideband SLL performance for each stage of both designs.