RIS-Aided Spatial Nulling: Algorithms, Analysis, and Nulling Limits

Reconfigurable Intelligent Surfaces (RIS) have recently gained attention as a means to dynamically shape the wireless propagation environment through programmable reflection control. Among the numerous applications, an important emerging use case is employing RIS as an auxiliary mechanism for spatial interference nulling, particularly in large ground-based reflector antennas where sidelobe interference can significantly degrade the system performance. With the growing density of satellites and terrestrial emitters, algorithms with faster convergence speed and better performance are needed. This work investigates RIS-equipped reflector antennas as a representative example of RIS-assisted spatial nulling and develop algorithms for sidelobe cancellation at specific directions and frequencies under various constraints. For the continuous-phase case, we adapt the gradient projection (GP) and alternating projection (AP) algorithms for scalability and propose a closed-form near-optimal solution that achieves satisfactory nulling performance with significantly reduced complexity. For the discrete-phase case, we reformulate the problem using a penalty method and solve it via majorization-minimization, outperforming the heuristic methods from our earlier work. Further, we analyze the electric field characteristics across multiple interference directions and frequencies to quantify the nulling capability of the RIS-aided reflectors, and identify a simple criterion for the existence of unimodular weights enabling perfect nulls. Simulation results demonstrate the effectiveness of the proposed methods and confirm the theoretical nulling limits.