{
  "abstract": "Sparse near-field arrays phase-cohere $M$ widely separated sub-arrays of $N$ elements and underpin distributed MIMO, satellite formations, and integrated sensing and communication. We show that their interference suppression over a protected region is set by coherence within a single sub-array rather than by the span of the formation: the effective rank of the region covariance can collapse from $MN$ to $M$. Two independent arguments establish this. For canonical line and disk regions each diagonal covariance block is exactly a classical concentration operator, which supplies sharp per-block rank thresholds and makes fewer than one spatial degree of freedom per sub-array a conservative design rule; an orthogonal decomposition with eigenvalue interlacing gives a nonasymptotic sufficient condition that assumes nothing about the coupling between platforms. The consequences are covariance-side and beamformer-independent: the unloaded Capon functional upper-bounds worst-case signal-to-interference ratio, while its regularized counterpart scales very differently for angularly separated and for in-cone targets. An eight-satellite LEO study validates the theory, including realized worst-case SIR.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15184",
  "author_total": 3,
  "authors": [
    {
      "name": "Changhao He"
    },
    {
      "name": "Xiaojuan Zhang"
    },
    {
      "name": "Francois Chin Po Shin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aq27prw6pvrkx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15184",
  "fulltext_url": null,
  "id": "aq27prw6pvrkx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15184",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.15184",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aq27prw6pvrkx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15184",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15184"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Effective DoF Collapse in Sparse Near-Field Beamforming: A Block-Rank-1 Mechanism",
  "title_text": "Effective DoF Collapse in Sparse Near-Field Beamforming: A Block-Rank-1 Mechanism",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/aq27prw6pvrkx",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1109/lwc.2026.3742528",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}