Collision-Aware Optimization Framework for Wireless Federated Learning Over Grant-Free NOMA

This paper proposes a collision-aware successive convex optimization (CA-SCO) framework for wireless federated learning (WFL) over grant-free non-orthogonal multiple access (GF-NOMA). GF-NOMA enables scalable and asynchronous uplink transmission and introduces stochastic collisions, residual interference due to imperfect successive interference cancellation (SIC), and retransmissions, thereby degrading latency and energy efficiency. To address these challenges, we develop a tractable optimization framework based on surrogate modeling that captures collision dynamics, residual SIC, and retransmission effects under imperfect channel state information (CSI). A joint latency–energy minimization problem is formulated over transmit power and access probability, subject to reliability and signal-to-interference-plus-noise ratio (SINR) constraints, serving as a communication-level proxy for federated learning performance. To solve the resulting non-convex problem, a successive convex approximation (SCA) algorithm is developed that incorporates smooth surrogates, trust-region adaptation, and SIC-aware decoding-order updates. The proposed method exhibits stable convergence behavior under the considered settings. The framework relies on approximations of outage probability, SIC behavior, and collision interactions, and evaluates their impact empirically. Simulation results under representative channel models show that CA-SCO achieves up to a 35% reduction in latency and improved energy efficiency compared to benchmark schemes, with corresponding improvements in learning convergence observed empirically. These results demonstrate that CA-SCO provides a communication-efficient framework for wireless federated learning in beyond-5G edge networks.