{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23118",
  "author_total": 3,
  "authors": [
    {
      "name": "Xianzhong Li"
    },
    {
      "name": "Yuzhi Yang"
    },
    {
      "name": "Tianhao Guo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3rk8kz6g3wn4x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23118",
  "fulltext_url": null,
  "id": "3rk8kz6g3wn4x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23118",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "eess.SP"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "2208|Advanced Wireless Communication Techniques"
    ]
  ],
  "openalex": "W7222943537",
  "pdf_url": "https://arxiv.org/pdf/2610.23118",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3rk8kz6g3wn4x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23118",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23118"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Keep Pace to Learn: Movable Antennas Restore the Backpropagated Gradient Under User Mobility",
  "title_text": "Keep Pace to Learn: Movable Antennas Restore the Backpropagated Gradient Under User Mobility",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/3rk8kz6g3wn4x",
  "venue": "arXiv",
  "versions": []
}