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fix(isac): correct bibliographic reference, clarify CRB model assumptions - #33

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copilot/fix-crb-model-parameterization
Mar 8, 2026
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fix(isac): correct bibliographic reference, clarify CRB model assumptions#33
j143 merged 2 commits into
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copilot/fix-crb-model-parameterization

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Copilot AI commented Mar 8, 2026

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The DFRC module cited the wrong Liu et al. paper (JSAC vs TSP) and claimed the scalar Kay SISO formula was directly equivalent to Liu's MIMO CRB — it is not. Several physical assumptions (flat spectrum, one-way range convention, orthogonal subcarrier capacity model) were also silent.

Bibliographic fix

  • Paper: "Cramér–Rao Bound Optimization for Joint Radar-Communication Beamforming", IEEE Trans. Signal Process. 2018, DOI 10.1109/TSP.2018.2864261
  • Renamed baselines/liu_jsac2018_crb.csvbaselines/liu_tsp2018_crb.csv
  • Propagated throughout run.rs, config.json, README.md, docs/, ROADMAP.md

CRB model clarification (dfrc.rs, liu_tsp2018_crb.csv)

The formula c² / (8π²B²γ_s) is a simplified SISO approximation (Kay eq. 3.31), not Liu et al.'s MIMO CRB (which depends on antenna count, transmit covariance, snapshot count). Constants are tuned to be numerically comparable to Table II — not derived from Liu's model.

// Before (overclaims equivalence):
/// `CRB = c² / (8π²B²γ_s)` where `γ_s = α · γ_total`.

// After:
/// Uses the simplified SISO time-delay CRB (Kay, SPSS Vol. I, eq. 3.31)
/// assuming a flat (rectangular) power spectrum and one-way range convention
/// (`R = c·τ`). This is an approximate scalar model; see module-level
/// documentation for assumptions and differences from Liu et al. (TSP 2018).

Unstated assumptions now documented

  • Flat spectrum: B is used as RMS bandwidth — valid only for rectangular spectrum; OFDM shaping changes the constant
  • Range convention: one-way (R = c·τ); round-trip radar would add a factor of ¼
  • Capacity model: Shannon C = B·log₂(1+γ_c) with orthogonal subcarrier assignment, no sensing-waveform reuse as data symbols
  • Monotonicity: holds by construction for the scalar α-split model only; shared-precoder DFRC designs can break strict ordering

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…nd unstated assumptions

Co-authored-by: j143 <53068787+j143@users.noreply.github.com>
Copilot AI changed the title [WIP] Fix CRB model parameterization and references fix(isac): correct bibliographic reference, clarify CRB model assumptions Mar 8, 2026
Copilot finished work on behalf of j143 March 8, 2026 19:17
@j143
j143 marked this pull request as ready for review March 8, 2026 19:39
@j143
j143 merged commit 99df88c into main Mar 8, 2026
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