# Optimization Algorithms for Joint OFDM Waveform Design and RIS Configuration in 6G Networks: From Convex Relaxation to Foundation Models

arXiv: https://arxiv.org/abs/2606.31334 · HTML: https://mlsanity.com/paper/2606.31334/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 50 of its 103 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Builds on (most cited first, 30 of 50)

- [Large Language Model Enhanced Multi-Agent Systems for 6G Communications](https://mlsanity.com/paper/2312.07850/) (2023)
- [Intelligent Reflecting Surface Enhanced Wireless Network via Joint Active and Passive Beamforming](https://mlsanity.com/paper/1810.03961/) (2018)
- [When Large Language Model Agents Meet 6G Networks: Perception, Grounding, and Alignment](https://mlsanity.com/paper/2401.07764/) (2024)
- [Wireless Communications Through Reconfigurable Intelligent Surfaces](https://mlsanity.com/paper/1906.09490/) (2019)
- [Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces: How it Works, State of Research, and Road Ahead](https://mlsanity.com/paper/2004.09352/) (2020)
- [Intelligent Reflecting Surface Aided Wireless Communications: A Tutorial](https://mlsanity.com/paper/2007.02759/) (2020)
- [A Survey on Channel Estimation and Practical Passive Beamforming Design for Intelligent Reflecting Surface Aided Wireless Communications](https://mlsanity.com/paper/2110.01292/) (2021)
- [A Survey on Model-based, Heuristic, and Machine Learning Optimization Approaches in RIS-aided Wireless Networks](https://mlsanity.com/paper/2303.14320/) (2023)
- [Intelligent Reflecting Surface: Practical Phase Shift Model and Beamforming Optimization](https://mlsanity.com/paper/1907.06002/) (2019)
- [Generative Diffusion Models for Wireless Networks: Fundamental, Architecture, and State-of-the-Art](https://mlsanity.com/paper/2507.16733/) (2025)
- [An Overview of Signal Processing Techniques for RIS/IRS-aided Wireless Systems](https://mlsanity.com/paper/2112.05989/) (2021)
- [ComAgent: Multi-LLM based Agentic AI Empowered Intelligent Wireless Networks](https://mlsanity.com/paper/2601.19607/) (2026)
- [Heuristic Algorithms for RIS-assisted Wireless Networks: Exploring Heuristic-aided Machine Learning](https://mlsanity.com/paper/2307.01205/) (2023)
- [Low-Complexity Joint Beamforming for RIS-Assisted MU-MISO Systems Based on Model-Driven Deep Learning](https://mlsanity.com/paper/2311.15313/) (2023)
- [Quantum Computing in Wireless Communications and Networking: A Tutorial-cum-Survey](https://mlsanity.com/paper/2406.02240/) (2024)
- [Decision Transformers for RIS-Assisted Systems with Diffusion Model-Based Channel Acquisition](https://mlsanity.com/paper/2501.08007/) (2025)
- [Towards Native Intelligence: 6G-LLM Trained with Reinforcement Learning from NDT Feedback](https://mlsanity.com/paper/2601.09992/) (2026)
- [Queue-Aware STAR-RIS Assisted NOMA Communication Systems](https://mlsanity.com/paper/2202.12333/) (2022)
- [Beyond Diagonal Reconfigurable Intelligent Surfaces in Wideband OFDM Communications: Circuit-Based Modeling and Optimization](https://mlsanity.com/paper/2405.07297/) (2024)
- [Beamforming Design and Association Scheme for Multi-RIS Multi-User mmWave Systems Through Graph Neural Networks](https://mlsanity.com/paper/2504.14464/) (2025)
- [Channel Estimation for RIS-Assisted mmWave Systems via Diffusion Models](https://mlsanity.com/paper/2506.07770/) (2025)
- [Foundation Model-Aided Deep Reinforcement Learning for RIS-Assisted Wireless Communication](https://mlsanity.com/paper/2506.09855/) (2025)
- [Large Wireless Foundation Models: Stronger over Bigger](https://mlsanity.com/paper/2601.10963/) (2026)
- [A Graph Foundation Model for Wireless Resource Allocation](https://mlsanity.com/paper/2604.07390/) (2026)
- [Input-Output Relation and Performance of RIS-Aided OTFS with Fractional Delay-Doppler](https://mlsanity.com/paper/2210.13989/) (2022)
- [Algorithm Unrolling-Based Distributed Optimization for RIS-Assisted Cell-Free Networks](https://mlsanity.com/paper/2301.02360/) (2023)
- [Variational Bayesian Multiuser Tracking for Reconfigurable Intelligent Surface Aided MIMO-OFDM Systems](https://mlsanity.com/paper/2304.11884/) (2023)
- [Active RIS-Assisted MIMO-OFDM System: Analyses and Prototype Measurements](https://mlsanity.com/paper/2307.15280/) (2023)
- [Parametric Channel Estimation with Short Pilots in RIS-Assisted Near- and Far-Field Communications](https://mlsanity.com/paper/2308.10668/) (2023)
- [Deep Contextual Bandit and Reinforcement Learning for IRS-Assisted MU-MIMO Systems](https://mlsanity.com/paper/2401.16901/) (2024)

## Abstract (arXiv)

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 102-104 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.