Low-Latency and Energy-Efficient Federated Learning Over Cell-Free Networks: A Trade-Off Analysis

Federated learning (FL) enables distributed model training by exchanging models rather than raw data, preserving privacy and reducing communication overhead. However, as the number of FL users grows, traditional wireless networks with orthogonal access face increasing latency due to limited scalability. Cell-free massive multiple-input multiple-output (CFmMIMO) networks offer a promising solution by allowing many users to share the same time-frequency resources. While CFmMIMO enhances energy efficiency through spatial multiplexing and collaborative beamforming, it remains crucial to adapt its physical layer operation to meticulously allocate uplink transmission powers to the FL users. To this aim, we study the problem of uplink power allocation to maximize the number of global FL iterations while jointly optimizing uplink energy and latency. The key challenge lies in balancing the opposing effects of transmission power: increasing power reduces latency but increases energy consumption, and vice versa. Therefore, we propose two power allocation schemes: one minimizes a weighted sum of uplink energy and latency to manage the trade-off, while the other maximizes the achievable number of FL iterations within given energy and latency constraints. We solve these problems using a combination of Brent’s method, coordinate gradient descent, the bisection method, and Sequential Quadratic Programming (SQP) with BFGS updates. Numerical results demonstrate that our proposed approaches outperform state-of-the-art power allocation schemes, increasing the number of achievable FL iterations by up to 62%, 93%, and 142% compared to Dinkelbach, max-sum rate, and joint communication and computation optimization methods, respectively.