Wait or Rotate: Statistical Repair of the Backward Pass in Over-the-Air Split Learning Under Channel Aging
Abstract
Over-the-air split learning returns the receiver's loss gradient through the reciprocal channel, so terminal motion between the forward and backward transmissions corrupts the backward pass. We repair the aged return at a fixed receive array using only second-order statistics. Two numbers taken from the forward-backward cross-covariance, the alignment reachable by the best common phase and by the best unitary correction, bound the main term of every repair. In the 3GPP tapped-delay-line channels TDL-A/B/C, where every antenna ages by the same scalar, the two numbers coincide, and at a correlation zero all tested fixed corrections stay between 58% and 62% accuracy, whereas a return delayed to the next correlation lobe reaches 98.4%. In 3GPP clustered-delay-line channels a statistical unitary correction stays within 0.02 in mean cross-entropy of ideal channel knowledge in all six tested profile and speed combinations, while common-phase correction falls to 69% for CDL-A at 3 km/h and the tested delay loses up to 10 points. In a two-cluster model spatial correction is decisive only where the common-phase alignment nearly vanishes (64% to 95%). With a ResNet-18 on CIFAR-10, only the delayed return trains at a separable correlation zero (86% against at most 16%), and at 30 km/h in a clustered-delay-line channel the unitary correction reaches 80% where the common phase reaches 60%. Given geometry, displacement and angular statistics, a port permutation chosen by linear assignment reaches 99.5-99.7% accuracy for hexagonal and square arrays in oblique motion without pilots or digital feedback during training, where nearest-position matching drops to 89%.
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BibTeX
@misc{li2026wait,
title = {{Wait or Rotate: Statistical Repair of the Backward Pass in Over-the-Air Split Learning Under Channel Aging}},
author = {Xianzhong Li and Yuzhi Yang and Tianhao Guo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23137},
eprint = {2610.23137},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23137},
}
RIS
TY - UNPB
TI - Wait or Rotate: Statistical Repair of the Backward Pass in Over-the-Air Split Learning Under Channel Aging
AU - Xianzhong Li
AU - Yuzhi Yang
AU - Tianhao Guo
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.23137
UR - https://arxiv.org/abs/2610.23137
AB - Over-the-air split learning returns the receiver's loss gradient through the reciprocal channel, so terminal motion between the forward and backward transmissions corrupts the backward pass. We repair the aged return at a fixed receive array using only second-order statistics. Two numbers taken from the forward-backward cross-covariance, the alignment reachable by the best common phase and by the best unitary correction, bound the main term of every repair. In the 3GPP tapped-delay-line channels TDL-A/B/C, where every antenna ages by the same scalar, the two numbers coincide, and at a correlation zero all tested fixed corrections stay between 58% and 62% accuracy, whereas a return delayed to the next correlation lobe reaches 98.4%. In 3GPP clustered-delay-line channels a statistical unitary correction stays within 0.02 in mean cross-entropy of ideal channel knowledge in all six tested profile and speed combinations, while common-phase correction falls to 69% for CDL-A at 3 km/h and the tested delay loses up to 10 points. In a two-cluster model spatial correction is decisive only where the common-phase alignment nearly vanishes (64% to 95%). With a ResNet-18 on CIFAR-10, only the delayed return trains at a separable correlation zero (86% against at most 16%), and at 30 km/h in a clustered-delay-line channel the unitary correction reaches 80% where the common phase reaches 60%. Given geometry, displacement and angular statistics, a port permutation chosen by linear assignment reaches 99.5-99.7% accuracy for hexagonal and square arrays in oblique motion without pilots or digital feedback during training, where nearest-position matching drops to 89%.
ER -