Optimum Beamforming and Grating-Lobe Mitigation for Intelligent Reflecting Surfaces

Ensuring adequate wireless coverage in upcoming communication technologies such as 6G is expected to be challenging. This is because user demands of higher data rate require an increase in carrier frequencies, which in turn reduce the diffraction effects (and hence coverage) in complex multipath environments. Intelligent reflecting surfaces (IRSs) have been proposed as a way of restoring coverage by adaptively reflecting incoming electromagnetic waves in desired directions. This is accomplished by judiciously adding extra phases at different points on the surface. In practice, these extra phases are only available in discrete quantities due to hardware constraints. Computing these extra phases is computationally challenging when they can only be picked from a discrete distribution, and existing approaches for solving this problem were either heuristic or based on evolutionary algorithms. We solve this problem by proposing fast algorithms with provably optimal solutions. Our algorithms have linear complexity, and are presented with rigorous proofs for their optimality. We show that the proposed algorithms exhibit better performance. We analyze situations when unwanted grating-lobes arise in the radiation pattern, and discuss mitigation strategies, such as the use of triangular lattices and prephasing techniques, to eliminate them. We also demonstrate how our algorithms can leverage these techniques to deliver optimum beamforming solutions.