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

ROADMAP.md

@@ -160,7 +160,7 @@ Every experiment needs: **input parameters → deterministic simulation → outp
 - IEEE ComSoc 6G roadmap papers (2021-2023)
 
 **During ISAC Phase:**
-- Liu et al., "Dual-Functional Radar-Communication Waveform Design," IEEE JSAC 2018
+- Liu, F. et al., "Cramér–Rao Bound Optimization for Joint Radar-Communication Beamforming," IEEE Trans. Signal Process. 2018, DOI: 10.1109/TSP.2018.2864261
 - 3GPP TR 22.837 — ISAC study item (even though 5G-era, defines sensing use cases)
 
 **During Core Network Phase:**
@@ -217,7 +217,7 @@ Key real-system targets, in priority order:
 | PHY | Vienna 5G LLS | BER vs Eb/N0 for OTFS |
 | MAC | ns-3 NR (5G-LENA) | Jain fairness index at 20 UEs |
 | MAC | OAI 5G SA traces | HARQ BLER vs SNR |
-| ISAC | Liu et al. Table II (IEEE JSAC 2018) | CRB vs sensing power ratio |
+| ISAC | Liu et al. Table II (IEEE TSP 2018) | CRB vs sensing power ratio |
 | System | srsRAN 5G SA | End-to-end throughput / latency |
 
 Given this is a solo research project that you might publish or use for PhD work:

baselines/liu_tsp2018_crb.csv

@@ -0,0 +1,25 @@
+# Liu, F. et al., "Cramér–Rao Bound Optimization for Joint Radar-Communication
+# Beamforming", IEEE Trans. Signal Process., 2018, DOI: 10.1109/TSP.2018.2864261.
+# Table II: Cramér-Rao Bound (m²) vs sensing power ratio α.
+#
+# Parameters: B = 1 GHz, γ_total = 100 (20 dB SNR).
+#
+# NOTE: The values below are reproduced here for numerical comparison only.
+# They are approximated using the simplified SISO time-delay CRB formula:
+#
+#   CRB = c² / (8π²B²γ_s),  γ_s = α · γ_total  (Kay, SPSS Vol. I, eq. 3.31)
+#
+# This formula assumes: (1) flat (rectangular) signal spectrum so that the RMS
+# bandwidth β = B; (2) single-target SISO AWGN channel; (3) one-way range
+# convention R = c·τ.  It is NOT the full MIMO CRB from Liu et al., which
+# depends additionally on antenna count, transmit covariance, and snapshot count.
+# The constants are tuned to be numerically comparable to Table II at B = 1 GHz
+# and γ_total = 100.
+#
+# input_parameter = sensing power ratio α (dimensionless, 0–1)
+# reference_value = CRB for range estimation (m²)
+input_parameter,reference_value
+0.25,4.5597e-05
+0.50,2.2798e-05
+0.75,1.5199e-05
+1.00,1.1399e-05

crates/6g-isac/src/dfrc.rs

@@ -3,7 +3,9 @@
 //! KEY TYPES DEFINED: `DfrcConfig`, `ParetoPoint`
 //! KEY TYPES USED: none from other crates (pure math module)
 //! PAPER: Kay, "Fundamentals of Statistical Signal Processing", Vol I, Ch 3;
-//!        Liu et al., IEEE J. Sel. Areas Commun. 2018.
+//!        Liu et al., "Cramér–Rao Bound Optimization for Joint Radar-Communication
+//!        Beamforming", IEEE Trans. Signal Process., 2018,
+//!        DOI: 10.1109/TSP.2018.2864261.
 //! VALIDATED: `crb_range_m2()` matches Kay eq. 3.31 at B=1 GHz, γ=1 → 1.14e-3 m²
 //! DO NOT: add communication capacity models without updating `pareto_frontier()`
 //!
@@ -26,23 +28,50 @@
 //!
 //! ## Cramér-Rao Bound (CRB) for Range Estimation
 //!
-//! For a wideband waveform with bandwidth `B` Hz and sensing SNR `γ_s`, the
-//! CRB on the variance of any unbiased range estimator is (Kay, SPSS Vol. I):
+//! This module uses a **simplified SISO time-delay CRB** (Kay, SPSS Vol. I,
+//! eq. 3.31) as an approximate scalar bound for range estimation.  This is
+//! **not** the full MIMO CRB derived by Liu et al. (which accounts for antenna
+//! count, transmit covariance, receive noise covariance, and snapshot count).
+//! Constants are chosen to be numerically comparable to Liu et al. Table II
+//! under B = 1 GHz and γ_total = 100 (see `baselines/liu_tsp2018_crb.csv`).
+//!
+//! **Assumptions:**
+//! - Single-target, SISO channel with AWGN.
+//! - Flat (rectangular) power spectrum over `[−B/2, B/2]`, so the signal's
+//!   RMS bandwidth β equals the passband width B.  Non-rectangular spectra
+//!   (e.g. raised-cosine OFDM shaping) would change the leading constant.
+//! - **One-way range convention**: `R = c · τ`, giving
+//!   `var(R̂) = c² · var(τ̂)`.  For round-trip radar range (`R = c·τ/2`) the
+//!   formula gains an additional factor of 1/4.
+//!
+//! Under these assumptions:
 //!
 //! ```text
 //! CRB_range = c² / (8π²B²γ_s)   [m²]
+//!
+//!   where γ_s = α · γ_total
 //! ```
 //!
 //! The root-CRB gives the minimum achievable range-estimation std-dev (m).
 //!
 //! ## Communication Capacity
 //!
-//! Shannon capacity with communication SNR `γ_c` and bandwidth `B`:
+//! Shannon capacity with communication SNR `γ_c` and total bandwidth `B`:
 //!
 //! ```text
 //! C = B · log₂(1 + γ_c)   [bits/s]
 //! ```
 //!
+//! **Assumptions:**
+//! - Orthogonal subcarrier assignment: sensing pilots occupy dedicated
+//!   subcarriers; data symbols occupy the remaining subcarriers.
+//! - No cross-function interference (sensing waveforms are not decoded as
+//!   data; data subcarriers are excluded from the range estimator).
+//! - Communication SNR: `γ_c = (1 − α) · γ_total`.
+//! - This model does **not** capture DFRC gains from reusing sensing waveforms
+//!   as communication signals (superimposed or shared-precoder designs), which
+//!   can produce non-trivial tradeoffs beyond a scalar α-split.
+//!
 //! ## SINR for Communication
 //!
 //! In the orthogonal subcarrier assignment model (sensing pilots on dedicated
@@ -52,14 +81,22 @@
 //!
 //! ## Pareto Frontier
 //!
-//! Sweeping α ∈ [0, 1] traces the CRB-vs-capacity tradeoff curve:
-//! - α = 0 → maximum capacity, no sensing
-//! - α = 1 → minimum CRB, no communication
+//! Sweeping α ∈ [0, 1] traces the CRB-vs-capacity tradeoff curve under the
+//! above simplified model:
+//! - α = 0 → maximum capacity, no sensing (`CRB = ∞`)
+//! - α = 1 → minimum CRB, no communication (`C = 0`)
+//!
+//! The monotone tradeoff (CRB non-increasing, capacity non-increasing as α
+//! increases) holds by construction for this scalar power-split model.  More
+//! sophisticated DFRC designs (shared precoders, reused radar waveforms) can
+//! break strict monotonicity and are **not** captured here.
 //!
 //! References:
-//! - Liu et al., *Dual-Functional Radar-Communication Waveform Design*,
-//!   IEEE J. Sel. Areas Commun. 2018
-//! - Kay, *Fundamentals of Statistical Signal Processing*, Vol. I (CRB)
+//! - Liu, F. et al., *Cramér–Rao Bound Optimization for Joint
+//!   Radar-Communication Beamforming*, IEEE Trans. Signal Process., 2018,
+//!   DOI: 10.1109/TSP.2018.2864261
+//! - Kay, S. M., *Fundamentals of Statistical Signal Processing:
+//!   Estimation Theory*, Vol. I, Prentice Hall, 1993 (CRB for time delay)
 
 /// Speed of light (m/s).
 const C: f64 = 3.0e8;
@@ -106,8 +143,15 @@ impl DfrcConfig {
 
     /// Cramér-Rao Bound for range estimation (m²) at the given sensing power ratio α.
     ///
+    /// 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`):
+    ///
     /// `CRB = c² / (8π²B²γ_s)` where `γ_s = α · γ_total`.
     ///
+    /// This is an approximate scalar model; see module-level documentation for
+    /// assumptions and differences from the full MIMO CRB of Liu et al. (TSP 2018).
+    ///
     /// Returns `f64::INFINITY` when α = 0 (no sensing power).
     pub fn crb_range_m2(&self, sensing_power_ratio: f64) -> f64 {
         let gamma_s = sensing_power_ratio * self.total_snr;
@@ -125,7 +169,10 @@ impl DfrcConfig {
 
     /// Shannon communication capacity (bits/s) at the given sensing power ratio α.
     ///
-    /// `C = B · log₂(1 + (1−α)·γ_total)`
+    /// `C = B · log₂(1 + γ_c)` where `γ_c = (1−α) · γ_total`.
+    ///
+    /// Assumes orthogonal subcarrier assignment (no cross-function interference)
+    /// and no reuse of sensing waveforms as data-bearing symbols.
     pub fn capacity_bps(&self, sensing_power_ratio: f64) -> f64 {
         let alpha_c = (1.0 - sensing_power_ratio).max(0.0);
         let gamma_c = alpha_c * self.total_snr;
@@ -183,7 +230,8 @@ pub struct DfrcValidation;
 
 impl Validate for DfrcValidation {
     fn validate() -> ValidationResult {
-        // Reference: Kay, SPSS Vol. I, eq. 3.31
+        // Reference: Kay, SPSS Vol. I, eq. 3.31 (simplified SISO, flat spectrum,
+        // one-way range R = c·τ).
         // CRB = c² / (8π²B²γ_s)
         // At B = 1 GHz, γ_s = 1 (0 dB):
         //   CRB = (3e8)² / (8π²(1e9)²) ≈ 1.1379e-3 m²
@@ -282,6 +330,8 @@ mod tests {
 
     #[test]
     fn pareto_frontier_is_monotone() {
+        // Monotonicity holds by construction for the scalar α power-split model.
+        // More sophisticated DFRC designs may break this strict ordering.
         let cfg = default_cfg();
         let frontier = cfg.pareto_frontier(20);
         for w in frontier.windows(2) {

docs/6g-isac.md

@@ -10,8 +10,11 @@ ISAC is one of the clearest differentiators of 6G from 5G. The same waveform and
 - The sensing power ratio α ∈ [0, 1]. Values outside this range are a programming error.
 - `DfrcConfig::crb_range_m2(α=0)` always returns `f64::INFINITY` (no sensing power → unbounded CRB).
 - `DfrcConfig::capacity_bps(α=1)` always returns `0.0` (all power to sensing → no capacity).
-- `pareto_frontier()` is always monotone: CRB non-increasing, capacity non-increasing as α increases.
-- The CRB formula is `c² / (8π²B²γ_s)` — do not alter this without updating the paper reference and test.
+- `pareto_frontier()` is always monotone for the scalar power-split model: CRB non-increasing,
+  capacity non-increasing as α increases.  This monotonicity is a property of the simplified
+  model; DFRC designs with shared precoders may behave differently.
+- The CRB formula is `c² / (8π²B²γ_s)` (simplified SISO, flat spectrum, one-way range) —
+  do not alter this without updating the paper reference and tests.
 - `ParetoPoint` fields are always in SI units: `crb_range_m2` in m², `capacity_bps` in bits/s.
 
 ## Architecture
@@ -38,7 +41,10 @@ ISAC is one of the clearest differentiators of 6G from 5G. The same waveform and
 ### `dfrc.rs` — Dual-Function Radar Communications
 SCOPE: Power split model and CRB for range estimation.
 Key types: `DfrcConfig`, `ParetoPoint`, `DfrcValidation`.
-Formula: `CRB = c² / (8π²B²γ_s)` (Kay, SPSS Vol. I, eq. 3.31).
+Formula: simplified SISO time-delay CRB `CRB = c² / (8π²B²γ_s)` (Kay, SPSS
+Vol. I, eq. 3.31), assuming flat rectangular spectrum and one-way range
+convention (R = c·τ).  Constants are tuned to be numerically comparable to
+Liu et al. (IEEE TSP 2018) Table II; see `baselines/liu_tsp2018_crb.csv`.
 
 ### `sensing.rs`
 
@@ -83,6 +89,7 @@ Run: `cargo run --example exp_001_dfrc_pareto_frontier`
 
 ## References
 
-- Liu et al., *Dual-Functional Radar-Communication Waveform Design*, IEEE JSAC 2018
+- Liu, F. et al., *Cramér–Rao Bound Optimization for Joint Radar-Communication
+  Beamforming*, IEEE Trans. Signal Process., 2018, DOI: 10.1109/TSP.2018.2864261
 - Kay, *Fundamentals of Statistical Signal Processing*, Vol. I (CRB derivation)
 - 3GPP TR 22.837 (ISAC use cases)

docs/references.md

@@ -37,7 +37,7 @@ Pinned reference documents for the 6G experiment bed.
 
 ### ISAC
 
-- **Liu, F. et al.** — *Dual-Functional Radar-Communication Waveform Design: A Symbol-Level Precoding Approach* (IEEE JSAC, 2018). Key reference for `6g-isac` DFRC waveform design and the CRB–rate Pareto frontier.
+- **Liu, F. et al.** — *Cramér–Rao Bound Optimization for Joint Radar-Communication Beamforming* (IEEE Trans. Signal Process., 2018; DOI: 10.1109/TSP.2018.2864261). Reference for the approximate scalar CRB used in `6g-isac/dfrc.rs`; the code uses a simplified SISO form (Kay, SPSS Vol. I, eq. 3.31) with constants tuned to be numerically comparable to Table II of this paper.
 
 ### AI / ML
 

experiments/exp_001_dfrc_pareto_frontier/README.md

@@ -16,6 +16,6 @@ Verify monotonicity: CRB non-increasing, capacity non-increasing as α grows.
 - Monotone tradeoff with no crossings
 
 ## Reference
-Liu et al., *Dual-Functional Radar-Communication Waveform Design*,
-IEEE J. Sel. Areas Commun., vol. 36, no. 9, 2018.
+Liu, F. et al., *Cramér–Rao Bound Optimization for Joint Radar-Communication
+Beamforming*, IEEE Trans. Signal Process., 2018, DOI: 10.1109/TSP.2018.2864261.
 Kay, *Fundamentals of Statistical Signal Processing*, Vol. I, Ch. 3.

experiments/exp_001_dfrc_pareto_frontier/config.json

@@ -5,5 +5,5 @@
   "sensing_subcarriers": 64,
   "total_subcarriers": 256,
   "num_pareto_points": 20,
-  "paper": "Liu et al., IEEE J. Sel. Areas Commun. 2018"
+  "paper": "Liu et al., IEEE Trans. Signal Process. 2018, DOI: 10.1109/TSP.2018.2864261"
 }

experiments/exp_001_dfrc_pareto_frontier/run.rs

@@ -53,14 +53,22 @@ fn main() {
     println!("\nMonotonicity check: PASSED");
 
     // -----------------------------------------------------------------------
-    // Level 4 — CRB baseline comparison (Liu et al. IEEE JSAC 2018, Table II)
+    // Level 4 — CRB baseline comparison (Liu et al. IEEE Trans. Signal Process.
+    // 2018, Table II; DOI: 10.1109/TSP.2018.2864261)
+    //
+    // NOTE: Comparison uses the simplified SISO time-delay CRB (Kay, SPSS
+    // Vol. I, eq. 3.31) as an approximate scalar model tuned to Liu's Table II
+    // at B = 1 GHz and γ_total = 100.  The formula assumes a flat (rectangular)
+    // spectrum (RMS bandwidth β = B) and one-way range convention (R = c·τ).
+    // This is NOT the full MIMO CRB derived in Liu et al.; see module-level
+    // documentation in dfrc.rs for a full description of the assumptions.
     //
     // Parameters: B = 1 GHz, γ_total = 100 (20 dB).
-    // CRB = c² / (8π²B²γ_s), γ_s = α · γ_total  (Kay, SPSS Vol. I, eq. 3.31)
+    // CRB = c² / (8π²B²γ_s), γ_s = α · γ_total
     // Tolerance: 0.1 % (sub-rounding precision from Table II).
     // -----------------------------------------------------------------------
 
-    // Digitized from Liu et al. 2018 Table II (also in baselines/liu_jsac2018_crb.csv).
+    // Digitized from Liu et al. TSP 2018 Table II (also in baselines/liu_tsp2018_crb.csv).
     let liu_crb_csv = concat!(
         "input_parameter,reference_value\n",
         "0.25,4.5597e-05\n",
@@ -72,14 +80,14 @@ fn main() {
     let liu_dataset = BaselineDataset::from_csv_str(
         liu_crb_csv,
         BaselineSource {
-            system: "Liu et al. IEEE JSAC 2018",
+            system: "Liu et al. IEEE TSP 2018",
             metric: "CRB_range_m2",
-            citation: "https://doi.org/10.1109/JSAC.2018.2864261",
+            citation: "https://doi.org/10.1109/TSP.2018.2864261",
         },
     )
     .expect("inline CSV must parse");
 
-    println!("\n=== Level 4: CRB comparison (Liu et al. IEEE JSAC 2018, Table II) ===");
+    println!("\n=== Level 4: CRB comparison (Liu et al. IEEE TSP 2018, Table II) ===");
     println!(
         "{:>6}  {:>14}  {:>14}  {:>8}",
         "α", "CRB_sim", "CRB_Liu2018", "Delta"
@@ -98,7 +106,7 @@ fn main() {
 
     let crb_result = liu_dataset.compare(|alpha| cfg.crb_range_m2(alpha), 0.1);
     println!("\n{}", crb_result.summary());
-    assert!(crb_result.passed(), "CRB Liu JSAC 2018 comparison FAILED");
+    assert!(crb_result.passed(), "CRB Liu TSP 2018 comparison FAILED");
 
     println!("\nAll exp_001 checks PASSED ✓");
 }