Keep Pace to Learn: Movable Antennas Restore the Backpropagated Gradient Under User Mobility
Abstract
When a mobile terminal takes part in over-the-air training, its own motion rotates the gradient that travels back through it; a movable antenna that keeps pace with the terminal rotates it back---without any channel estimate. We give a speed law: under a scalar conditional-mean model of the physical return, landing the residual displacement inside the first positive lobe of the spatial correlation keeps the conditional mean gradient a descent direction, which, given sufficient travel, fixes a critical actuator-to-terminal speed ratio. We further prove a bias--jitter law: under the same scalar conditional-mean model and with zero effective bias, independent zero-mean Gaussian jitter of any finite amplitude scales the conditional mean gradient without reversing its direction, whereas a sub-wavelength systematic bias can reverse it. This result motivates prioritizing bias calibration to preserve gradient direction. Simulations on 3GPP CDL-A channels show that an antenna keeping pace with the terminal achieves near-CSI accuracy without digital channel correction, reaching 98.58 % compared with 98.59% for the ideal-CSI reference. The simulations also show that partial compensation can support learning when the residual displacement falls within a later positive correlation lobe, so a faster actuator does not necessarily yield higher accuracy. Separate positioning simulations show a sharp accuracy loss under systematic bias but little degradation under zero-mean Gaussian jitter of comparable spatial scale.
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BibTeX
@misc{li2026keep,
title = {{Keep Pace to Learn: Movable Antennas Restore the Backpropagated Gradient Under User Mobility}},
author = {Xianzhong Li and Yuzhi Yang and Tianhao Guo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23118},
eprint = {2610.23118},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23118},
}
RIS
TY - UNPB
TI - Keep Pace to Learn: Movable Antennas Restore the Backpropagated Gradient Under User Mobility
AU - Xianzhong Li
AU - Yuzhi Yang
AU - Tianhao Guo
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23118
UR - https://arxiv.org/abs/2610.23118
AB - When a mobile terminal takes part in over-the-air training, its own motion rotates the gradient that travels back through it; a movable antenna that keeps pace with the terminal rotates it back---without any channel estimate. We give a speed law: under a scalar conditional-mean model of the physical return, landing the residual displacement inside the first positive lobe of the spatial correlation keeps the conditional mean gradient a descent direction, which, given sufficient travel, fixes a critical actuator-to-terminal speed ratio. We further prove a bias--jitter law: under the same scalar conditional-mean model and with zero effective bias, independent zero-mean Gaussian jitter of any finite amplitude scales the conditional mean gradient without reversing its direction, whereas a sub-wavelength systematic bias can reverse it. This result motivates prioritizing bias calibration to preserve gradient direction. Simulations on 3GPP CDL-A channels show that an antenna keeping pace with the terminal achieves near-CSI accuracy without digital channel correction, reaching 98.58 % compared with 98.59% for the ideal-CSI reference. The simulations also show that partial compensation can support learning when the residual displacement falls within a later positive correlation lobe, so a faster actuator does not necessarily yield higher accuracy. Separate positioning simulations show a sharp accuracy loss under systematic bias but little degradation under zero-mean Gaussian jitter of comparable spatial scale.
ER -