SLL Minimization for Planar Uniformly Excited Sparse Arrays Using Gradient Descent

This paper applies the gradient descent method to the problem of peak sidelobe level (PSLL) minimization in a flat, uniform-amplitude phased array antenna. Since optimizing the radiation pattern sidelobes represents a highly non-convex problem, standard gradient descent is widely considered inefficient for such applications; therefore, we introduce a modified gradient descent framework. Furthermore, the gradient descent method strictly requires high evaluation precision of the PSLL cost function. The classical grid-based computational approach is unsuited for this implementation, as it demands an excessively dense discretization mesh to achieve sufficient target function accuracy. To overcome this limitation, we developed a spectrally grounded local Newton-Raphson method to locate the absolute maximum sidelobe peak. This approach guarantees the necessary analytical precision while strictly preventing any inflation of the algorithm's total computational complexity.The framework is benchmarked against state-of-the-art designs without enforcing any artificial rotational symmetry constraints. For an unconstrained 600-element layout ($\nu=60.0$), the method achieves a verified 2D peak SLL of $-21.80$dB. For a large-scale 2000-element configuration ($\nu=181.90$), the optimization converges to an absolute value of $-25.04$dB, providing a definitive $5.58$dB suppression improvement over the reference evolutionary algorithm. Physical minimum inter-element spacing constraints are strictly satisfied across all evaluated scenarios.