In this paper, the performance optimization of federated learning (FL), when deployed over a realistic wireless multiple-input multiple-output (MIMO) communication system with digital modulation and over-the-air computation (AirComp) is studied. In particular, a MIMO system is considered in which edge devices transmit their local FL models (trained using their locally collected data) to a parameter server (PS) using beamforming to maximize the number of devices scheduled for transmission. The PS, acting as a central controller, generates a global FL model using the received local FL models and broadcasts it back to all devices. Due to the limited bandwidth in a wireless network, AirComp is adopted to enable efficient wireless data aggregation. However, fading of wireless channels can produce aggregate distortions in an AirComp-based FL scheme. To tackle this challenge, we propose a modified federated averaging (FedAvg) algorithm that combines digital modulation with AirComp to mitigate wireless fading while ensuring the communication efficiency. This is achieved by a joint transmit and receive beamforming design, which is formulated as an optimization problem to dynamically adjust the beamforming matrices based on current FL model parameters so as to minimize the transmitting error and ensure the FL performance. To achieve this goal, we first analytically characterize how the beamforming matrices affect the performance of the FedAvg in different iterations. Based on this relationship, an artificial neural network (ANN) is used to estimate the local FL models of all devices and adjust the beamforming matrices at the PS for future model transmission. The algorithmic advantages and improved performance of the proposed methodologies are demonstrated through extensive numerical experiments.

翻译：本文研究了在采用数字调制与空中计算（AirComp）的实际无线多输入多输出（MIMO）通信系统中部署联邦学习（FL）的性能优化问题。具体而言，考虑一个MIMO系统，其中边缘设备通过波束成形将其本地FL模型（基于本地收集数据训练）传输至参数服务器（PS），以最大化调度传输的设备数量。作为中央控制器的PS利用接收到的本地FL模型生成全局FL模型，并将其广播回所有设备。由于无线网络带宽有限，本文采用空中计算实现高效的无线数据聚合。然而，无线信道的衰落可能导致基于空中计算的FL方案产生聚合失真。为应对这一挑战，我们提出一种改进的联邦平均（FedAvg）算法，该算法将数字调制与空中计算相结合，在保证通信效率的同时缓解无线衰落影响。通过联合设计发射与接收波束成形实现这一目标，该问题被建模为一个优化问题，根据当前FL模型参数动态调整波束成形矩阵，以最小化传输误差并确保FL性能。为此，我们首先从理论上刻画波束成形矩阵对FedAvg各迭代性能的影响机制。基于该关系，使用人工神经网络（ANN）估计所有设备的本地FL模型，并在PS处调整后续模型传输的波束成形矩阵。通过大量数值实验验证了所提方法的算法优势与性能提升。