Federated learning facilitates collaborative model training across multiple clients while preserving data privacy. However, its performance is often constrained by limited communication resources, particularly in systems supporting a large number of clients. To address this challenge, integrating over-the-air computations into the training process has emerged as a promising solution to alleviate communication bottlenecks. The system significantly increases the number of clients it can support in each communication round by transmitting intermediate parameters via analog signals rather than digital ones. This improvement, however, comes at the cost of channel-induced distortions, such as fading and noise, which affect the aggregated global parameters. To elucidate these effects, this paper develops a theoretical framework to analyze the performance of over-the-air federated learning in large-scale client scenarios. Our analysis reveals three key advantages of scaling up the number of participating clients: (1) Enhanced Privacy: The mutual information between a client’s local gradient and the server’s aggregated gradient diminishes, effectively reducing privacy leakage. (2) Mitigation of Channel Fading: The channel hardening effect eliminates the impact of small-scale fading in the noisy global gradient. (3) Improved Convergence: Reduced thermal noise and gradient estimation errors benefit the convergence rate. These findings solidify over-the-air model training as a viable approach for federated learning in networks with a large number of clients. The theoretical insights are further substantiated through extensive experimental evaluations.

Federated learning enables multiple clients to collaboratively train a common model while concurrently preserving data privacy. However, its performance is often constrained by limited communication resources, especially when the system encounters a large number of clients. Under those circumstances, integrating over-the-air computations into the model training procedure is considered an effective approach to coping with the communication bottleneck. Specifically, by uploading each client's intermediate parameters via analog transmissions instead of digital ones, the system can dramatically extend the number of clients it simultaneously supports in each communication round. However, that is achieved at the expense of introducing channel distortions, particularly fading and noise, in the aggregated global parameter. To demystify these effects, the present paper develops a theoretical framework to analyze the performance of the over-the-air federated model training process. Our analysis unveils a three-fold benefit from system scaling up, i.e., as the number of participating clients increases: (i) the privacy leakage, quantified by the mutual information between each client's locally possessed gradient and the edge's globally aggregated one, substantially decreases, (ii) the impairment of small-scale fading disappears due to the channel hardening effect, and (iii) the convergence rate is enhanced as thermal noise and gradient estimation error can be reduced. To that end, it establishes over-the-air model training as a viable approach for implementing federated learning in scenarios with a large number of clients. We corroborate the theoretical findings with extensive experiments.

We leverage the Multiplicative Weight Update (MWU) method to develop a decentralized algorithm that significantly improves the performance of dynamic time division duplexing (D-TDD) in small cell networks. The proposed algorithm adaptively adjusts the time portion allocated to uplink (UL) and downlink (DL) transmissions at every node during each scheduled time slot, aligning the packet transmissions toward the most appropriate link directions according to the feedback of signal-to-interference ratio information. Our simulation results reveal that compared to the (conventional) fixed configuration of UL/DL transmission probabilities in D-TDD, incorporating MWU into D-TDD brings about a two-fold improvement of mean packet throughput in the DL and a three-fold improvement of the same performance metric in the UL, resulting in the D-TDD even outperforming Static-TDD in the UL. It also shows that the proposed scheme maintains a consistent performance gain in the presence of an ascending traffic load, validating its effectiveness in boosting the network performance. This work also demonstrates an approach that accounts for algorithmic considerations at the forefront when solving stochastic problems.