In this work, we investigate federated edge learning over a fading multiple access channel. To alleviate the communication burden between the edge devices and the access point, we introduce a pioneering digital over-the-air computation strategy employing q-ary quadrature amplitude modulation, culminating in a low latency communication scheme. Indeed, we propose a new federated edge learning framework in which edge devices use digital modulation for over-the-air uplink transmission to the edge server while they have no access to the channel state information. Furthermore, we incorporate multiple antennas at the edge server to overcome the fading inherent in wireless communication. We analyze the number of antennas required to mitigate the fading impact effectively. We prove a non-asymptotic upper bound for the mean squared error for the proposed federated learning with digital over-the-air uplink transmissions under both noisy and fading conditions. Leveraging the derived upper bound, we characterize the convergence rate of the learning process of a non-convex loss function in terms of the mean square error of gradients due to the fading channel. Furthermore, we substantiate the theoretical assurances through numerical experiments concerning mean square error and the convergence efficacy of the digital federated edge learning framework. Notably, the results demonstrate that augmenting the number of antennas at the edge server and adopting higher-order modulations improve the model accuracy up to 60\%.

在这项研究中，我们针对多路径fading信道进行了联合边缘学习的研究，通过引入一种创新的数字过空中计算策略，采用q进制正交幅度调制，提出了一种低时延通信方案。我们分析了消除无线通信中的fading所需的天线数量，并通过数值实验证实了理论的保证，证明了边缘服务器增加天线数量和采用高阶调制可以提高模型准确性达到60％。

通过无线信道进行的q-QAM盲联合学习