We study joint downlink-uplink beamforming design for wireless federated learning (FL) with a multi-antenna base station. Considering analog transmission over noisy channels and uplink over-the-air aggregation, we derive the global model update expression over communication rounds. We then obtain an upper bound on the expected global loss function, capturing the downlink and uplink beamforming and receiver noise effect. We propose a low-complexity joint beamforming algorithm to minimize this upper bound, which employs alternating optimization to breakdown the problem into three subproblems, each solved via closed-form gradient updates. Simulation under practical wireless system setup shows that our proposed joint beamforming design solution substantially outperforms the conventional separate-link design approach and nearly attains the performance of ideal FL with error-free communication links.

翻译：本文研究多天线基站场景下无线联邦学习的联合下行-上行链路波束赋形设计。考虑噪声信道上的模拟传输和上行空中聚合，推导了跨通信轮次的全局模型更新表达式，进而获得预期全局损失函数的上界，该上界捕获了下行与上行波束赋形及接收机噪声的影响。提出一种低复杂度联合波束赋形算法对该上界进行最小化，该算法采用交替优化将问题分解为三个子问题，每个子问题均通过闭式梯度更新求解。实际无线系统设置下的仿真表明，所提出的联合波束赋形设计方案显著优于传统分离链路设计方法，且近乎达到理想无差错通信链路下联邦学习的性能。