This paper explores the application of federated learning (FL) in 5G and 6G wireless networks, focusing on achieving a global model from user-local datasets. To enhance efficiency, we investigate minimizing training time within the collocated massive multiple-input multiple-output (CL-mMIMO) network framework. We propose an online successive convex approximation (SCA) approach to decompose the stochastic nonconvex problem of time minimization in FL into two convex optimizations for short-term and long-term coherent timescales. The online SCA method effectively separates the nonconvex problem into two convex subproblems: optimizing local updating frequency, data rates, and beamforming vectors in the short-term, and focusing on learning accuracy in the long-term. Additionally, considering the energy constraints of edge nodes in 5G and beyond networks, we employ the simultaneous wireless information and power transfer (SWIPT) technique to support device energy needs. The power-splitting SWIPT (PS-SWIPT) method impacts the optimization problem primary constraints based on energy and power limits. Numerical results demonstrate that our proposed scheme reduces FL training time by up to 70.01% and 21.29%, while maintaining accuracy compared to cell-free time division multiple access massive MIMO (CF-TDMA mMIMO) and sensing-assisted sustainable federated learning (S2FL) schemes, respectively.
