Optimization Algorithms for Joint OFDM Waveform Design and RIS Configuration in 6G Networks: From Convex Relaxation to Foundation Models
Joint OFDM-RIS optimization for 6G is a mixed-integer nonlinear programming (MINLP) problem covering sum-rate maximization, energy efficiency, max-min fairness, and peak-to-average power ratio (PAPR)-constrained objectives. Seventy-eight joint OFDM-RIS optimization works published between 2021 and 2026 are surveyed. No standardized benchmark exists, and cross-paper comparisons remain infeasible. This survey classifies these works into four paradigms: (I) model-based convex relaxation, (II) heuristic and metaheuristic search, (III) deep reinforcement and unsupervised learning, and (IV) emerging methods including foundation models (FM), diffusion-based generative AI, and quantum optimization. A literature synthesis of self-reported benchmarks shows that ML-based methods (Paradigm~III) report 95-99\% of model-based spectral efficiency at 10^2-10^4 x faster per-inference runtime (method-pair dependent; literature values are self-reported and exclude ML pre-training cost). A companion tutorial benchmark at N=16, N=64, and N=128 reveals a critical scaling property: GPU-based neural network inference (DDQN, PPO, graph neural network (GNN), unsupervised DL) is N-invariant, with identical runtime at N=16 and N=128, while iterative solvers (AO+SCA, PSO) scale polynomially. Energy efficiency (P2) and PAPR-constrained (P4) benchmarks are deferred to future work with standardized power models and waveform generators. Six open challenges emerge from the synthesis: the cross-paradigm benchmark deficit, real-world hardware-constrained deployment, joint waveform-RIS optimization for doubly-dispersive channels, multi-objective PAPR trade-offs, LLM safety in live network control, and diminishing returns of standalone heuristics. We specify requirements for a standardized benchmark. This study serves as a roadmap for researchers and practitioners working on joint OFDM-RIS optimization in 6G networks.