{
  "abstract": "Decisions about dense populations depend on how much will cross a boundary by a deadline and when the first member arrives. Conventional radar forms a range-Doppler map, whose cells add noise and whose detections merge unresolved members. We introduce over-the-scene computation, where illumination makes the scene compute such functionals without resolving members. With random echo phases, a correlator's mean output energy sums member reflectivities weighted by a kernel set by the waveform and template. The waveform's ambiguity function is this computation's transfer function, determining computable functionals and their noise cost. One readout aggregates members over a small delay-Doppler area but along a line segment growing with duration, longest for the chirp of matching slope among constant-envelope waveforms. Members predicted to share a range lie on such a line, so a chirp's mean beat spectrum is the predicted range profile at a look-ahead horizon set by its rate. For unbiased estimation, a Cramer-Rao bound over all equal-energy waveforms favors resolving members above unit signal-to-noise ratio (SNR) and grouping weaker ones into unit-SNR sets. At 0.65 members per cell, -10 dB member SNR, and one sweep, the chirp's bin sum inside the boundary comes within 16% of this bound in root-mean-square error and, with 77 times fewer samples per horizon, outperforms every unbiased estimator from a coherent processing interval of equal dwell, bandwidth, and energy. No finite set of waveform-template probes determines an unconstrained Rayleigh-fluctuating population's first arrival, but bisection localizes it if first arrivals outweigh later arrivals' sidelobes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07732",
  "author_total": 2,
  "authors": [
    {
      "name": "Seyed Mohammad Azimi-Abarghouyi"
    },
    {
      "name": "Christopher G. Brinton"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/24x53bg2e2r71.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07732",
  "fulltext_url": null,
  "id": "24x53bg2e2r71",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07732",
  "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.ET"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07732",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/24x53bg2e2r71.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07732",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07732"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Over-the-Scene Computation: Illumination-Programmed Functional Sensing of Unresolvable Populations",
  "title_text": "Over-the-Scene Computation: Illumination-Programmed Functional Sensing of Unresolvable Populations",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/24x53bg2e2r71",
  "venue": "arXiv",
  "versions": []
}