FedSME: Spatial Mode Entropy Aware Aggregation for Federated Learning

Sixth generation (6G) and Industrial IoT (IIoT) networks often operate in overload regimes. In these settings, the number of devices (Ktot) far exceeds the number of base station antennas (N), that is, Ktot ≫ N. Federated learning (FL) enables distributed training across devices for AI-native radio access (AI-RAN) networks in 6G. It supports learningbased optimization of RAN functions such as beamforming, link adaptation, and dynamic resource management. However, in dense deployments, treating every device as an FL client magnifies wireless channel heterogeneity. It also intensifies the impact of non-IID data. These challenges slow convergence. They also waste communication and energy resources. To address this, client selection becomes essential for FL training. Client selection must exploit channel structure and update informativeness. Higher spatial mode entropy (SME) reflects richer spatial diversity in the uplink channel, leading to more stable and informative updates during aggregation. This motivates FedSME, an SME-aware FL aggregation framework. FedSME leverages the uplink channel eigenspace through an entropyguided scoring rule that jointly captures SME, Fisher information, and data quality, while supporting differential privacy (DP) for secure aggregation. Experiments across ten non-IID client profiles demonstrate the effectiveness of FedSME. The framework achieves 97.94% classification accuracy. It reduces communication rounds from 33 to 11 compared to FedAvg. FedSME maintains high fairness, with a Jain's index of 0.924. It also improves normalized energy efficiency by 8.15%. The framework preserves approximately linear server-side scaling with fixed antenna configurations. To the best of our knowledge, this is the first federated learning framework to exploit entropydriven channel eigenspace structure and client informativeness for scalable client selection.