# Low-Frequency Square Kilometer Array Pattern Optimization via Convex Programming  
[PERSON]  
1 Dipartimento DIIES, Universita degli Studi Mediterranea di Reggio Calabria, IT-89123 Reggio Calabria, Italy; [EMAIL_ADDRESS] (G.C. ); [EMAIL_ADDRESS] (R.P. ); [EMAIL_ADDRESS] (A.F.M.) 1 Dipartimento DIIES, Universita degli Studi Mediterranea di Reggio Calabria, IT-89123 Reggio Calabria, Italy; [EMAIL_ADDRESS] (G.C. ); [EMAIL_ADDRESS] (R.P. ); [EMAIL_ADDRESS] (A.F.M. array layout configuration, characterized by a dense central core and logarithmic spiral arms (see Figure 1), is optimized to balance sensitivity and spatial resolution, enabling the SKAO to explore the universe with an unprecedented level of detail [1; 3]. Given the very large number of antennas and stations in both SKA-Low and SKA-Mid, it is essential to employ design techniques that are extremely effective from a computational point of view, that is, in fact, the aim of the present research work. Coming to details, this study focuses on SKA-Low, with particular attention to the current antenna implementation, i.e., Square Kilometer Array Log-periodic Antenna (SKALA) 4.1 [6]. A primary challenge in its design lies in the optimization of key performance metrics such as sensitivity, angular resolution, and survey speed, while simultaneously mitigating interference and minimizing noise contributions. The development of the Aperture Array Verification Systems (AAVSs) plays a critical role in evaluating end-to-end performance across a range of deployment scenarios. Over time, AAVS prototypes have undergone multiple design refinements. Early versions (AAVS1 and AAVS2) employed pseudo-random layouts (see Figure 2a), which effectively suppressed mutual coupling and reduced far-field sidelobe levels. Nonetheless, residual inter-element coupling introduced spectral anomalies, particularly at 55 MHz and 77 MHz [7], primarily due to current imbalances in the bow-tie dipoles. To address these issues, exclusion zones around the antennas, enforcing a minimum inter-element spacing of 2.5 m along directions within 20\({}^{\circ}\) of the principal axes were recently proposed [8]. While this approach partially mitigated coupling-related artifacts, the resulting irregular and dense arrangement poses practical challenges for physical access and maintenance. To improve spatial uniformity and accessibility, AAVS3 adopted a more structured (sunflower-inspired) layout based on a Vogel pattern, as shown in Figure 2b. This configuration distributes antenna elements with a radial density proportional to the square of the distance from the array center [8], resulting in high spatial uniformity and a dense filling factor. However, this layout gives rise to elevated sidelobe levels [9], which degrade the array's sensitivity to faint astronomical signals by reducing noise immunity and increasing susceptibility to interference. Another issue with this layout is a strong resonance around 125 MHz, which perturbs the array station beam and, consequently, affects the spectral smoothness [10]. Figure 1: Layouts of SKA arrays (from [1]): Red dots indicate the locations of the stations, (**a**) SKA-Low, where blue lines delineate the site boundary; (**b**) SKA-Mid. Both arrays exhibit a dense central core with extending logarithmic spiral arms. These trade-offs highlight the need for an advanced and systematic approach to optimizing the elements' layout and weights to reconcile spatial uniformity with electromagnetic performance. As a result, a revised station configuration has been adopted [11]; however, a comprehensive beamforming analysis is still pending. The challenges outlined above necessitate a combined optimization of both the array elements' layout and weight coefficients. The goal of this work is to determine a set of weights that maximize the receiving pattern in a desired target direction while simultaneously minimizing sidelobe levels across the remainder of the angular domain.