{
  "abstract": "In physical backpropagation, users return loss derivatives over the time-division duplex uplink, giving the base station the downlink gradient without channel reconstruction. Reciprocity calibration conventionally prioritizes base-station chains, as column-normalized zero-forcing reduces a per-user factor to a stream rotation. This priority can reverse. With ideal base-station chains and no noise, per-user amplitude errors make the returned field a weighted sum-rate gradient. With zero-forcing full service at both optima, the loss is independent of array size. Otherwise the selection penalty, serving the wrong users, carries 86 to 94 percent of the amplitude-induced loss in five of six configurations. Per-user phase errors mainly slow the iteration. Base-station chain errors scale the returned field per antenna, and at 3 dB and 25 degrees they cost one user 1.3 dB of signal-to-noise ratio (SNR) that no array size removes. With 80 users, such errors on both sides, and mismatched pilots, oracle per-user and base-station calibration leave 6.2 and 12.3 percent loss at 256 antennas on clustered channels. This ordering holds at 30 dB SNR and reverses for 1 dB, 10 degree user errors. A capped one-echo estimator comes within 2.4 percentage points of oracle per-user calibration but underperforms no calibration at 10 dB SNR.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02390",
  "author_total": 3,
  "authors": [
    {
      "name": "Xianzhong Li"
    },
    {
      "name": "Yuzhi Yang"
    },
    {
      "name": "Tianhao Guo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a52en40dwakvq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02390",
  "fulltext_url": null,
  "id": "a52en40dwakvq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02390",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "eess.SP"
    ],
    [
      "arxiv",
      "math.IT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02390",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a52en40dwakvq.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02390",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02390"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Which Chains to Calibrate for Physical Backpropagation: Per-User Factors Versus Base-Station Chains",
  "title_text": "Which Chains to Calibrate for Physical Backpropagation: Per-User Factors Versus Base-Station Chains",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/a52en40dwakvq",
  "venue": "arXiv",
  "versions": []
}