Pattern synthesis in reconfigurable intelligent surface (RIS)-assisted systems presents a formidable non-convex optimization challenge, particularly when implemented through phase-only control of the reflective elements. This paper proposes an advanced optimization framework leveraging the Adam algorithm to address this problem. We formulate a sophisticated multi-component loss function to simultaneously synthesize a flat-top main beam, deep multi-nulls, and stringent side-lobe level (SLL) control. Simulation results confirm that the Adam optimizer achieves superior convergence and stability compared with conventional gradient descent. Crucially, the solution preserves radiation pattern integrity even under practical discrete-phase quantization, demonstrating its viability for finite-resolution RIS hardware.

Reconfigurable intelligent surface (RIS), beam pattern synthesis, Adam optimizer, phase quantization