With the rapid proliferation of smart mobile devices, federated learning (FL) has been widely considered for application in wireless networks for distributed model training. However, data heterogeneity, e.g., non-independently identically distributions and different sizes of training data among clients, poses major challenges to wireless FL. Limited communication resources complicate the implementation of fair scheduling which is required for training on heterogeneous data, and further deteriorate the overall performance. To address this issue, this paper focuses on performance analysis and optimization for wireless FL, considering data heterogeneity, combined with wireless resource allocation. Specifically, we first develop a closed-form expression for an upper bound on the FL loss function, with a particular emphasis on data heterogeneity described by a dataset size vector and a data divergence vector. Then we formulate the loss function minimization problem, under constraints on long-term energy consumption and latency, and jointly optimize client scheduling, resource allocation, and the number of local training epochs (CRE). Next, via the Lyapunov drift technique, we transform the CRE optimization problem into a series of tractable problems. Extensive experiments on real-world datasets demonstrate that the proposed algorithm outperforms other benchmarks in terms of the learning accuracy and energy consumption.

本文针对数据异构性与无线资源分配相结合的无线联邦学习问题，提出了性能分析与优化的方法，在考虑数据异构性的同时，优化客户端调度、资源分配和本地训练轮数，通过实验验证了该算法在学习准确性和能量消耗方面的优势。

无线联邦学习中数据异构的分析与优化