## 4 Discussion  
The multi-objective implementation presents designs that exhibit efficient SLL suppression and stable wideband performance, even with a reduced number of active elements. These findings underscore the advantages of integrating Eisenstein fractal symmetry with evolutionary optimization techniques, facilitating the development of compact, efficient, and high-performance antenna array designs.  
The proposed Design A, based on the thinned Eisenstein fractal structure, exhibits superior SLL reduction across all evaluated frequency bands when compared to various recent studies on wideband antenna array optimization. Table 6 presents a detailed performance comparison, emphasizing the advantages of Design A over other wideband-optimized array designs that employ different geometries and optimization methodologies. Notably, Design A achieves its strongest performance at the foundational operating frequency (0.5\(\lambda\)), where it not only surpasses most existing designs in terms of SLL reduction but also does so using fewer active elements, underscoring its efficiency and effectiveness.  
Evaluated normalized performance metrics such as SLL and HPBW were the focus as they are directly affected by the array synthesis method. The normalized gain is inherently linked to these metrics, which serves as an indicator of directional performance in an idealized context. In contrast, realized gain accounts for practical considerations such as element efficiency, mutual coupling, impedance matching, and feed network losses, which are not addressed in the present analysis.  
The proposed Eisenstein fractal-based array designs exhibit unidirectional radiation characteristics with narrow main beams, making them particularly suitable for applications requiring spatial interference suppression and precise angular targeting, such as radar systems, directional IoT links, or satellite [35; 36]. As the fractal stage increases, the SLL improves, while the beam becomes narrower, which may impact performance in certain  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Ref.**} & \multirow{2}{*}{**Array Geometry**} & \multirow{2}{*}{**Elements**} & \multicolumn{4}{c}{**SLL (dB)**} \\ \cline{3-6}  & & & \(\mathbf{0.5\lambda}\) & \(\mathbf{1.0\lambda}\) & \(\mathbf{1.5\lambda}\) \\ \hline
[13] & Perturbed Peano–Gosper curve & \(\begin{array}{c}50\\ 344\end{array  
wide-coverage scenarios. Potential solutions to address this trade-off may include adjusting the mask function to desired beam width, incorporating adaptive beamforming techniques, or using multiple array configurations to achieve desired coverage.  
The optimization framework can be generalized to other aperiodic array geometries and allows for straightforward adaptation to alternative algorithms, depending on the problem complexity or convergence requirements. This flexibility makes the methodology broadly applicable to diverse array synthesis scenarios. The computational demands remain manageable for even large-scale arrays, due to the decoupled optimization stages and the use of lightweight evaluation metrics. Improvements in runtime can be achieved by incorporating Machine Learning and GPU acceleration techniques, strengthening the suitability for real-time applications or large-dimensional antenna design tasks.