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 nonasymptotic 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%.Index Terms-blind federated learning, digital modulation, federated edge learning, over-the-air computation[15]-[17], they studied FEEL problem over wireless fading multiple access channel (MAC).In parallel, the FEEL domain has observed substantial advancements in digital aggregation methods for wireless communication in federated learning applications. The onebit broadband digital aggregation (OBDA) method, outlined in [18], aims at reducing data communication, thereby conserving bandwidth and energy. Another significant development is adopting majority vote frequency-shift keying (FSK) techniques [17], which aims at harnessing modulation techniques for efficient and reliable data aggregation in wireless networks. Moreover, a phase asynchronous orthogonal frequency division multiplexing (OFDM)-based variant of OBDA has been introduced [19], characterized by the integration of joint channel decoding and aggregation decoders, specifically designed for digital OAC applications, enhancing privacy and efficiency by eliminating the necessity for raw data sharing.Nevertheless, these OBDA-centric methods exhibit certain limitations, predominantly confined to specific functions such as sign detection and particular machine learning training procedures, such as the signSGD problem [20]. To widen the class of functions for digital OAC, authors in [21] use balanced number systems for computing summation functions. Despite its potential, this approach requires the allocation of unique frequencies for each quantized level, thus rais...
