Over-the-air (OTA) computation has recently emerged as a communication-efficient Federated Learning (FL) paradigm to train machine learning models over wireless networks. However, its performance is limited by the device with the worst SNR, resulting in fast yet noisy updates. On the other hand, allocating orthogonal resource blocks (RB) to individual devices via digital channels mitigates the noise problem, at the cost of increased communication latency. In this paper, we address this discrepancy and present ADFL, a novel Analog-Digital FL scheme: in each round, the parameter server (PS) schedules each device to either upload its gradient via the analog OTA scheme or transmit its quantized gradient over an orthogonal RB using the ``digital" scheme. Focusing on a single FL round, we cast the optimal scheduling problem as the minimization of the mean squared error (MSE) on the estimated global gradient at the PS, subject to a delay constraint, yielding the optimal device scheduling configuration and quantization bits for the digital devices. Our simulation results show that ADFL, by scheduling most of the devices in the OTA scheme while also occasionally employing the digital scheme for a few devices, consistently outperforms OTA-only and digital-only schemes, in both i.i.d. and non-i.i.d. settings.

翻译：空中计算（Over-the-air, OTA）近期作为一种通信高效的联邦学习（FL）范式出现，用于在无线网络上训练机器学习模型。然而，其性能受限于信噪比最差的设备，导致更新速度快但噪声较大。另一方面，通过数字信道为单个设备分配正交资源块（RB）可以缓解噪声问题，但代价是增加了通信延迟。在本文中，我们解决了这一矛盾，并提出了一种新颖的模数联邦学习（ADFL）方案：在每一轮中，参数服务器（PS）将每个设备调度为要么通过模拟OTA方案上传其梯度，要么使用“数字”方案在正交RB上传输量化梯度。聚焦于单个FL轮次，我们将最优调度问题建模为在满足延迟约束条件下最小化PS处估计全局梯度的均方误差（MSE），从而得出数字设备的最优调度配置和量化比特数。我们的仿真结果表明，ADFL通过将大多数设备调度至OTA方案，同时偶尔对少数设备采用数字方案，在独立同分布和非独立同分布设置下均持续优于纯OTA和纯数字方案。