发表机构
Chungnam National University; Institute of New Media and Communications; Seoul National University（忠南大学; 新媒体与通信研究所; 首尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对空中联邦学习中PAPR高和传输未压缩的问题，提出AirGC-CD方案，用部分高斯循环预编码实现精确无偏削波并压缩传输，在低SNR下优于基线。
AI 中文摘要
空中联邦学习使边缘设备能够同时传输其本地更新，从而减少通信开销。然而，由此产生的波形具有随模型维度增长的峰均功率比（PAPR），而将放大器保持在线性范围内有两种补救措施：削波或回退发射功率。这两种措施都有代价：i) 削波失真在接收端表现为无法去除的偏差；ii) 回退保持信号完整但降低了平均信噪比（SNR）。独立于这种权衡，传输仍然未压缩，每个模型参数占用一个信道使用，这使得大规模模型训练难以实现。为解决这些挑战，我们提出了AirGC-CD，一种空中方案，在削波之前用部分高斯循环矩阵对每个本地更新进行预编码。在AirGC-CD中，无论更新的稀疏性如何，预编码器的输出都精确服从高斯分布，因此削波函数是为已知分布设计的，而不是从数据中继承。这使得削波可以通过一个闭式形式的标量Bussgang增益在平均意义上被反转，我们证明了由此产生的聚合是精确无偏的，削波仅增加方差。削波比于是成为唯一剩下的自由参数，在削波的方差与回退带来的SNR损失之间进行权衡，我们推导出其近最优值的闭式解。由于预编码器是线性的，它同时也充当压缩器，通过两次快速傅里叶变换将传输从模型维度d减少到草图维度m，成本仅为O(dlog d)，而高斯草图成本为O(md)。在五个图像数据集上的实验表明，在大多数设置下，特别是在低SNR下，AirGC-CD优于基线空中联邦学习方案，同时每轮使用更少的信道使用次数。
英文摘要
Over-the-air federated learning lets edge devices transmit their local updates simultaneously, reducing the communication overhead. The resulting waveform, however, has a peak-to-average power ratio (PAPR) that grows with the model dimension, and keeping the amplifier in its linear range leaves two remedies: clipping the peaks or backing off the transmit power. Neither remedy is without cost: i) the clipping distortion appears at the receiver as a bias that cannot be removed, and ii) back-off keeps the signal intact but degrades the average signal-to-noise ratio (SNR). Independent of this trade-off, the transmission remains uncompressed, spending one channel use per model parameter, which keeps large-model training out of reach. To address these challenges, we propose AirGC-CD, an over-the-air scheme that precodes each local update with a partial Gaussian circulant matrix before clipping. In AirGC-CD, the precoder's output is exactly Gaussian regardless of the update's sparsity, so the clipping function is designed for a known distribution instead of inheriting it from the data. This enables the clipping to be inverted on average by a single scalar Bussgang gain in closed form, and we prove that the resulting aggregate is exactly unbiased, with clipping adding only variance. The clipping ratio is then the only free parameter left, trading the variance of the clipping against the SNR loss from back-off, and we derive its near-optimum in closed form. Since the precoder is linear, it also acts as a compressor, reducing the transmission from the model dimension d to the sketch dimension m at a cost of only O(dlog d) via two fast Fourier transforms, whereas a Gaussian sketch costs O(md). Experiments on five image datasets show that AirGC-CD outperforms baseline over-the-air FL schemes in most settings, particularly at low SNR, while using fewer channel uses per round.
