Joint Wide Illumination and Null Insertion Design in RIS-assisted System

In this paper, we focus on reconfigurable intelligent surface (RIS)-aided joint wide illumination and null insertion design. This design can be applied in cellular networks, broadcasting, and radar systems, enabling multiple wide null and illumination at arbitrary directions. Our objective is to minimize the deviation between the target pattern and the practical power pattern by designing the passive beamforming at RIS, while the RIS unit modulus weights constraint is illustrated. To tackle the non-convex optimization problem, the low-complexity alternating direction method of multipliers (ADMM) algorithm is proposed. In particular, the augmented objective function is firstly formulated with introduced auxiliary variables, which is then rephrased as a Lagrangian function. By alternatively updating the variables, the objective function converges with the optimized RIS phase shifts. The convergence of simulation results proves the validity of our proposed algorithm, and the proposed algorithm performs quite well in matching the desired and actual power patterns with practical channel model under different number and size of illumination and null areas.