In this study, a digital over-the-air computation (OAC) scheme for achieving
continuous-valued gradient aggregation is proposed. It is shown that the
average of a set of real-valued parameters can be calculated approximately by
using the average of the corresponding numerals, where the numerals are
obtained based on a balanced number system. By using this property, the
proposed scheme encodes the local gradients into a set of numerals. It then
determines the positions of the activated orthogonal frequency division
multiplexing (OFDM) subcarriers by using the values of the numerals. To
eliminate the need for a precise sample-level time synchronization, channel
estimation overhead, and power instabilities due to the channel inversion, the
proposed scheme also uses a non-coherent receiver at the edge server (ES) and
does not utilize a pre-equalization at the edge devices (EDs). Finally, the
theoretical mean squared error (MSE) performance of the proposed scheme is
derived and its performance for federated edge learning (FEEL) is demonstrated.

本文提出了一种数字化无线计算方案，使用均衡数系统中相应数字的平均值来近似计算一组实数参数的平均值，并使用该方案将本地梯度编码为一组数字，以确定活动的正交频分复用子载波的位置，同时不需要精确的采样级时间同步、信道估计开销和功率不稳定性，并演示其在联邦边缘学习（FEEL）中的性能。