This paper presents the first orthogonal frequency-division multiplexing(OFDM)-based digital over-the-air computation (AirComp) system for wireless federated edge learning, where multiple edge devices transmit model data simultaneously using non-orthogonal OFDM subcarriers, and the edge server aggregates data directly from the superimposed signal. Existing analog AirComp systems often assume perfect phase alignment via channel precoding and utilize uncoded analog transmission for model aggregation. In contrast, our digital AirComp system leverages digital modulation and channel codes to overcome phase asynchrony, thereby achieving accurate model aggregation for phase-asynchronous multi-user OFDM systems. To realize a digital AirComp system, we develop a medium access control (MAC) protocol that allows simultaneous transmissions from different users using non-orthogonal OFDM subcarriers, and put forth joint channel decoding and aggregation decoders tailored for convolutional and LDPC codes. To verify the proposed system design, we build a digital AirComp prototype on the USRP software-defined radio platform, and demonstrate a real-time LDPC-coded AirComp system with up to four users. Trace-driven simulation results on test accuracy versus SNR show that: 1) analog AirComp is sensitive to phase asynchrony in practical multi-user OFDM systems, and the test accuracy performance fails to improve even at high SNRs; 2) our digital AirComp system outperforms two analog AirComp systems at all SNRs, and approaches the optimal performance when SNR $\geq$ 6 dB for two-user LDPC-coded AirComp, demonstrating the advantage of digital AirComp in phase-asynchronous multi-user OFDM systems.

翻译：本文提出了首个基于正交频分复用（OFDM）的数字空中计算（AirComp）系统，用于无线联邦边缘学习。在该系统中，多个边缘设备使用非正交OFDM子载波同时传输模型数据，边缘服务器直接从叠加信号中聚合数据。现有的模拟AirComp系统通常通过信道预编码实现理想的相位对齐，并采用未编码的模拟传输进行模型聚合。相比之下，我们的数字AirComp系统利用数字调制和信道编码来克服相位异步问题，从而在相位异步的多用户OFDM系统中实现精确的模型聚合。为实现数字AirComp系统，我们开发了一种介质访问控制（MAC）协议，允许不同用户使用非正交OFDM子载波同时传输，并提出了针对卷积码和LDPC码定制的联合信道解码与聚合解码器。为验证所提出的系统设计，我们在USRP软件无线电平台上构建了数字AirComp原型，并演示了支持最多四个用户的实时LDPC编码AirComp系统。基于轨迹驱动的测试精度与信噪比仿真结果表明：1）在实际多用户OFDM系统中，模拟AirComp对相位异步敏感，即使在高信噪比下精度性能也无法提升；2）我们的数字AirComp系统在所有信噪比下均优于两种模拟AirComp系统，并在两用户LDPC编码AirComp信噪比≥6 dB时接近最优性能，这证明了数字AirComp在相位异步多用户OFDM系统中的优势。