Novel Hybrid RIS Architectures and Beamforming Optimization for Energy-Efficient Multi-User MISO

In this work, we introduce novel hybrid reflecting intelligent surface (RIS) architectures where at least one reflecting sub-surface (RS) resembles a sub-connected RIS. Next, assuming a multiple-input single-output broadcasting system where the base station (BS) is aided by a hybrid RIS adopting either one of the proposed structures or the fully-connected active/passive design, we jointly optimize the transmit precoding and reflect beamforming schemes to maximize the energy efficiency subject to the power consumption constraints of the BS and any active RS. We develop efficient, low-complexity iterative algorithms based on the Fractional Programming, Block Coordinate Descent, Lagrange multipliers, and Majorization-Minimization methods to tackle these challenging non-convex optimization problems and obtain closed-form expressions of the optimal solutions. We also derive the necessary conditions for feasible allocation of RIS elements. Numerical evaluations unveil the performance gains of the proposed designs over benchmarks and provide insights.