In this paper, we investigate the communication designs of over-the-air computation (AirComp) empowered federated learning (FL) systems considering uplink model aggregation and downlink model dissemination jointly. We first derive an upper bound on the expected difference between the training loss and the optimal loss, which reveals that optimizing the FL performance is equivalent to minimizing the distortion in the received global gradient vector at each edge node. As such, we jointly optimize each edge node transmit and receive equalization coefficients along with the edge server forwarding matrix to minimize the maximum gradient distortion across all edge nodes. We further utilize the MNIST dataset to evaluate the performance of the considered FL system in the context of the handwritten digit recognition task. Experiment results show that deploying multiple antennas at the edge server significantly reduces the distortion in the received global gradient vector, leading to a notable improvement in recognition accuracy compared to the single antenna case.

翻译：本文研究了空中计算（AirComp）赋能的联邦学习（FL）系统中的通信设计，综合考虑了上行模型聚合与下行模型分发。我们首先推导了训练损失与最优损失之间期望差值的上界，该上界表明优化FL性能等价于最小化每个边缘节点接收到的全局梯度向量中的失真。基于此，我们联合优化每个边缘节点的发送和接收均衡系数以及边缘服务器转发矩阵，以最小化所有边缘节点间的最大梯度失真。进一步地，我们利用MNIST数据集在手写数字识别任务中评估了所考虑FL系统的性能。实验结果表明，与单天线情况相比，在边缘服务器部署多天线可显著降低接收到的全局梯度向量中的失真，从而显著提升识别准确率。