# Energy-Efficient RIS-Enabled SISO-OFDMA Communication via Lower Bound Optimization
## 1 Introduction
### Related Works  
The design of reflection coefficients (or passive beamforming) for narrowband transmission over frequency-flat channels was the main focus of earlier studies on RIS-enhanced wireless communication [3, 5]. However, more recent studies in [6, 7, 8, 9, 10, 11, 12, 13, 14] have looked at the more general broadband transmission over frequency-selective channels for the case of a single-user setup. In [6], the authors proposed a majorization-minimization (MM)-based iterative approach for optimizing RIS passive beamforming in an OFDM system, achieving near-optimal performance with lower computational complexity compared to the existing sine cosine algorithm (SCA). The work in [7] introduces a scalable framework for channel estimation and reflection optimization in RIS-enhanced OFDM systems, achieving improved rate performance with reduced training overhead and computational complexity. The authors in [8] proposed a practical transmission protocol for RIS-enhanced OFDM systems under frequency-selective channels, optimizing the achievable rate through a joint optimization of transmit power allocation and RIS passive array reflection coefficients while reducing training overhead. The work in [9] addresses the ergodic achievable rate optimization in RIS-assisted mmWave MIMO-OFDM systems with statistical CSI, utilizing majorization theory and alternating optimization for the joint design of the transmit covariance matrix and RIS reflection coefficients. The work in [10] proposed a framework for integrating RIS technology into wireless networks by leveraging localization information for robust user multiplexing, minimizing the overhead of channel estimation and phase shift optimization in OFDM systems. The authors in [11] suggested an intelligent resource allocation scheme utilizing reinforcement learning (RL) for maximizing the sum-rate in RIS-enhanced OFDM systems, considering both primary and secondary user scenarios, and demonstrated significant transmission rate improvements compared to benchmark schemes. The work in [12] investigates spectral efficiency improvement in an OFDM system with a 1-bit resolution RIS, utilizing a deep RL algorithm for optimizing reflection phase shifts, leading to significant performance gains and reduced calculation delay. The work in [13] addresses the optimization of RIS-enhanced two-way D2D OFDM systems, maximizing the bidirectional sum-rate via sub-band, power, and discrete phase shift optimization. In [14], the authors presented joint optimization of the UAV trajectory, RIS scheduling, and resource allocation in OFDMA systems to maximize the sum-rate while considering heterogeneous QoS requirements, showing promising performance gains with RIS deployment in UAV-based communication. To the best of our knowledge, very few articles have examined a passive beamforming design and resource allocation for multi-user broadband communication. The multi-user system design is more complex than the single-user case because the RIS reflection coefficients must be concurrently optimized with the multi-user transmission scheduling and resource allocation. The use of RIS in orthogonal frequency-division multiple access (OFDMA) systems, a multi-user variant of the well-known orthogonal frequency-division multiplexing (OFDM) digital modulation method, has been the subject of an expanding body of study. The fundamental benefit of OFDMA is that it enables variable resource allocation, which is essential for enhancing wireless networks' energy efficiency. Designing efficient resource allocation algorithms that can effectively use the available resources is one of the major issues in putting RIS-assisted OFDMA systems into practice. To tackle this problem, many scholars have suggested numerous optimization strategies, including machine learning, convex optimization, and game theory. These techniques have the potential to increase the system's energy efficiency by allocating resources as efficiently as possible.