Optimal Pattern Determination in Reconfigurable Intelligent Surface aided Communications

Reconfigurable Intelligent surface (RIS) has emerged as a candidate technology for enhancing coverage in millimeter wave wireless networks at a lower energy and cost footprint. RIS has several antenna elements that can each be configured to reflect impinging electromagnetic waves after imparting a chosen phase shift with possibly some amplitude attenuation (a.k.a. chosen reflection coefficient). Over the canonical RIS-enabled communications scenario, an optimal choice of reflection coefficients (or optimal RIS pattern) can be efficiently determined for an ideal unit-amplitude unconstrained phase alphabet. However, for most practical RIS that entail finite alphabets with amplitude imbalance and per-group-of-elements control, efficiently determining optimal patterns remain open problems. In this paper we resolve two such open problems by designing optimal and efficient pattern determination algorithms for binary and quaternary alphabets. We show that our algorithms can noticeably improve over the state-of-art conventional heuristic, especially in the presence of high amplitude imbalance and more restrictive per-group control. The designed algorithms also yield companion sets, which we show offer very significant advantages in RIS pattern selection under interference limit (leakage suppression) constraints.