Spectral and Energy Efficiency Optimization of Hybrid Reconfigurable Intelligent Surfaces: A Sequential Convex Programming Approach

This paper presents the spectral and energy efficiency optimization of Hybrid Reconfigurable Intelligent Surfaces (RIS) in downlink multi-user multiple-input single-output (MU-MISO) wireless communication systems. A hybrid RIS architecture, comprising both active and passive reflecting elements, is considered to balance the trade off between system performance and energy consumption. We formulate a sum rate maximization problem under practical power constraints on the active RIS elements and propose an efficient alternating optimization algorithm. Specifically, the beamforming vectors at the base station are updated via Zero-Forcing (ZF) precoding, while the active RIS configuration is optimized using sequential convex programming (SCP) techniques. To ensure numerical stability and practical feasibility, robust regularization and power control mechanisms are integrated into the RIS optimization. Simulation results demonstrate that the proposed hybrid RIS-assisted system achieves significant improvements in both spectral efficiency (SE) and energy efficiency (EE) compared to conventional passive RIS, fully active RIS, and no-RIS baseline systems. These findings highlight the potential of hybrid RIS architectures as a promising solution for next generation green and high capacity wireless networks.