{
  "abstract": "Closed-form fractional programming (FP), weighted MMSE (WMMSE), and the 2026 surrogate-enhanced methods SEFP and XMMSE all maximize the weighted sum rate by iteratively maximizing a surrogate linear in the interference power. We show that this family admits a unique best member: the interference-conjugate transform (ICT), which replaces each rate term $\\log(1+a/b)$ by $\\max_{κ\\ge0}[Ω(κa)-κb]$, where $Ω$ is the closed-form partial convex conjugate of the rate in the interference variable and the optimal multiplier is the interference price $a/(b(a+b))$. We prove that, for any fixed price, $Ω(κ\\,\\cdot)$ is the pointwise largest own-signal function compatible with a valid interference-linear lower bound, and that tightness at an anchor forces the price. Hence all four benchmark surrogates, which share this price and differ only in their own-signal term, are dominated pointwise by ICT. At SINR $γ$, the benchmarks' own-signal curvature exceeds the true curvature by factors behaving as $γ/2$ (FP/WMMSE) and $(\\logγ)/2$ (SEFP/XMMSE), against $1+1/(γ(γ+2))$ for ICT, and this ordering carries over to the certified ascent per iteration and the asymptotic linear convergence rate. ICT yields closed-form updates at the benchmarks' per-iteration cost for single-antenna power control, uplink joint scheduling and power control, and multi-cell MISO beamforming, and the first solver-free algorithm for sum-least-$q$th-percentile rate maximization, via a $K$-dimensional convex dual with closed-form gradient and Hessian and a certified duality gap. In uplink scheduling, ICT improves proportional-fairness utility over FP by +7.03 and over SEFP by +3.35 (60/60 drops) using 18.7 iterations per slot vs. 49.7 and 38.0; in MISO beamforming with $M=8$, it reaches 99.9% of its final value in a median of 9 iterations vs. 16 (XMMSE) and 1160 (FP/WMMSE).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37794",
  "author_total": 1,
  "authors": [
    {
      "name": "Ahmad Khan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dj35zrgwz1mzg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37794",
  "fulltext_url": null,
  "id": "dj35zrgwz1mzg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37794",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.37794",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dj35zrgwz1mzg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.37794",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37794"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "The Interference-Conjugate Transform: The Tightest Interference-Linear Surrogate for Power Control, Scheduling and Beamforming in Wireless Networks",
  "title_text": "The Interference-Conjugate Transform: The Tightest Interference-Linear Surrogate for Power Control, Scheduling and Beamforming in Wireless Networks",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/dj35zrgwz1mzg",
  "venue": "arXiv",
  "versions": []
}