# Low-Frequency Square Kilometer Array Pattern Optimization via Convex Programming
## 5 Conclusions and Future Perspectives  
This work presents a convex optimization-based methodology aimed at enhancing the electromagnetic performance of Square Kilometer Array (SKA) Low-Frequency stations employing fixed Vogel-pattern array configurations. The proposed framework was designed to suppress sidelobes while maintaining key main beam characteristics, using a constrained optimization approach that ensures globally optimal solutions with manageable computational complexity, an important advantage for large-scale aperture arrays. This ensures the effectiveness of the antenna synthesis algorithm in overcoming critical performance challenges inherent to low-frequency radio telescopes such as those in the SKA. Numerical evaluations, conducted using realistic embedded element patterns at 350 MHz, demonstrated a 3.6 dB reduction in the peak sidelobe level when compared to the uniform excitations case. Crucially, this improvement was achieved without altering the array geometry or degrading the main beam shape. In particular, both the Half Power Beamwidth and the null-to-null beamwidth remained unchanged. Although the directivity experienced a reduction (from 32.2 dB to 30.1 dB), this trade-off reflects the intentional redistribution of energy from the sidelobes into broader angular regions as part of the sidelobe suppression strategy. To provide a more comprehensive and objective assessment of performance, the Integrated Sidelobe Ratio (ISR) was employed as an additional evaluation metric. The ISR, which quantifies the ratio of total radiated power in the sidelobe region to that within the main lobe, improved from \(-11.45\) dB before the optimization to \(-13.57\) dB after the optimization. This 2.12 dB improvement in the ISR confirms that the proposed synthesis technique reduces the total sidelobes' energy across the full radiation sphere, providing improved signal-to-noise ratio performance in noise-affected environments such as radio astronomy. A key strength of this approach lies in its generalizability. In fact, it can be adapted to different frequencies and array configurations, supporting flexible and scalable beamforming strategies. Additionally, this foundation enables future advancements, including multi-frequency and wideband optimization, as well as adaptive weighting techniques tailored for dynamic observation conditions. The methodology presented in this work can serve as a foundational tool to support future experimental developments related to SKA-Low. In fact, by enabling the computational identification of potential performance limitations or synthesis errors, it can guide the re-weighting or re-design of antennas prior to field validation. This form of pre-assessment is particularly valuable given the scale and complexity of SKA-Low systems. Future research, to be pursued within the framework of the upcoming SKA international project, will focus on integrating the proposed synthesis methods with experimental validation campaigns. These efforts aim to develop practical calibration strategies and exploring reconfigurable weighting schemes, ultimately enhancing the system-level performance and reliability through a combined numerical-experimental approach. In summary, this work marks a significant advancement toward intelligent and scalable design methodologies for next-generation radio telescope arrays. G.M.B. : conceptualization, methodology, validation, formal analysis, investigation, writing--original draft preparation, writing--review and editing. G.C. : conceptualization, methodology, validation, formal analysis, investigation, writing--original draft preparation, writing--review and editing. P.B. : conceptualization, methodology, investigation, writing--originaldraft preparation, writing--review and editing. M.G.L. : conceptualization, methodology, investigation, writing--original draft preparation. R.P. : conceptualization, methodology, validation, writing--original draft preparation. A.F.M.