Optimization of Energy Efficiency for Federated Learning over IRS-assisted Cell-free Massive MIMO Networks

In recent years, federated learning (FL), a promising machine learning technique, has drawn increasing attention. Unlike conventional methods that centralize data for model training, FL ensures the safety and confidentiality of data by enabling the model training process on intelligent devices. However, the unpredictable and continuously changing channel characteristics pose a significant challenge to the implementation of FL in wireless communication. Consequently, optimizing energy efficiency becomes crucial, particularly for devices with constrained power resources. In this study, we tackle the problem of minimizing the total energy consumption during the training phase of FL over a cell-free massive multiple-input multiple-output (CFMM) system assisted by intelligent reflecting surfaces (IRSs) composed of hardware-efficient passive elements. Based on the operation mode of user equipments (UEs) during the uplink phase, the proposed CFMM-IRS system is categorized into System I employing time division multiple access mode, and System II allowing simultaneous user operation. Distinct problems are formulated for these systems, aiming to minimize all UEs’ overall energy consumption. To deal with these non-convex complex problems, we propose an alternating optimization approach by transforming the original problems into three sub-optimal ones and designing iterative algorithms utilizing the inner approximation method. Extensive experiments show the effectiveness of the proposed alternating optimization approach when resolving the given complex problems, highlighting their superior performance compared to other benchmark algorithms. Finally, simulation results indicate that System II, with UEs operating in simultaneous mode and associated with the proposed alternating algorithm, achieves the best result in terms of energy efficiency.