Hybrid Optimization Framework for Energy Efficiency Maximization in NOMA-Aided Internet of Vehicles with Beyond Diagonal RIS

The integration of beyond diagonal reconfigurable intelligent surfaces (BD-RIS) with non-orthogonal multiple access (NOMA) in the Internet of Vehicles (IoV) networks presents the transformative potential for 6G vehicular communications, promising unprecedented gains in energy and spectral efficiency. However, existing research fails to address the joint optimization of BD-RIS configuration, NOMA power allocation, and dynamic IoV association–a critical oversight given their inherent interdependence in practical deployment scenarios. Current literature predominantly examines these components in isolation, with conventional RIS architectures and orthogonal multiple access schemes, leading to suboptimal performance in high-mobility vehicular environments. This work bridges this gap by proposing a novel hybrid optimization framework for NOMA-aided BD-RIS assisted IoV networks. The proposed framework simultaneously optimizes the IoV association with the base station (BS), NOMA power allocation, and BD-RIS phase shift design to maximize the energy efficiency of the system while ensuring the minimum signal-to-interference plus noise ratios (SINRs) of IoVs. The proposed framework is formulated as non-linear optimization due to joint decision variables and rate expressions of IoVs, resulting in an NP-hard problem where achieving a joint optimal solution is computationally complex. To handle this complexity, the original joint formulation is decomposed into three subproblems: IoV association with BS, BS power allocation, and BD-RIS phase shift design. An efficient iterative solution is then developed through the synergistic combination of deep reinforcement learning, first-order Taylor expansion, and manifold optimization methods. For comprehensive evaluation, we introduce a NOMA-aided conventional RIS assisted IoV framework as a benchmark. Extensive numerical results based on Monte Carlo simulations demonstrate that the proposed NOMA-aided BD-RIS assisted IoV network achieves significant improvements of 32% in energy efficiency and 28% in spectral efficiency compared to conventional RIS-assisted architectures, validating its potential for next-generation vehicular networks.