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Parametric Empirical Wireless Model (Legacy)

The Parametric Empirical Wireless Model revives the fast, closed-form empirical channel formulation originally ported from pyv2xsimulator in commit 6885a2f3.

It is designed for rapid execution, large-scale macro simulations, analytical comparisons, and ablation studies.

1. Physical Layer: Empirical Distance Loss

Rather than computing path loss in dB and calculating cumulative interference, the empirical model evaluates delivery probability using a 10th-degree polynomial fitted to measured 802.11p vehicular packet delivery curves.

Implemented in LegacyPolynomialPathLoss:

\[P_{loss, dist}(d) = \sum_{k=0}^{10} C_k d^k\]

Polynomial Coefficients

const C10: f64 = 1.111_823_869_040_061e-25;
const C9:  f64 = 3.597_485_384_820_973_5e-23;
const C8:  f64 = -8.038_884_092_343_818e-21;
const C7:  f64 = -9.158_429_982_705_657e-18;
const C6:  f64 = -2.132_059_001_989_335e-15;
const C5:  f64 = 8.192_060_372_243_259e-13;
const C4:  f64 = 4.764_017_738_147_641e-10;
const C3:  f64 = -1.596_566_671_433_574_4e-7;
const C2:  f64 = 1.867_541_672_239_932e-5;
const C1:  f64 = -0.000_498_485_400_857_115_6;
const C0:  f64 = 0.0;

350-Meter Cutoff & Boundary Clamping

In commit 6885a2f3:

  • If distance \(d > 350.0\,\text{m}\), packet loss is strictly 100%: \(P_{loss, dist} = 1.0\).
  • For \(d \le 350.0\,\text{m}\), the raw polynomial is clamped to \([0.0, 1.0]\) to prevent negative probabilities at close range (\(d < 20\,\text{m}\)).

2. Spatio-Temporal Logistic Congestion Loss

Medium congestion is evaluated using a logistic function over the volume of bytes transmitted within a local spatio-temporal neighborhood:

  1. Neighborhood Window:
  2. Packets active in the medium within the last 1.0 second.
  3. Within a 200-meter radius of the transmitting vehicle.
  4. Bytes on Air:

$\(x = N_{packets} \times \bar{L}_{bytes}\)$

  1. Logistic Loss Probability:

$\(P_{loss, cong}(x) = \frac{1}{1 + \exp\Big(-k \cdot (x - b_0)\Big)}\)$

  • Parameter \(k = 0.0005\) (steepness of the congestion curve).
  • Parameter \(b_0 = 20\,000.0\) (midpoint threshold where congestion loss reaches 50%).

3. Line-of-Sight (LoS) Check

Building occlusion is evaluated via 2D ray intersection against building polygons:

  • Binary occlusion: If any building edge intersects the line of sight between transmitter and receiver, the packet is dropped unconditionally:

$\(\text{If } \neg\text{LoS} \implies P_{deliver} = 0.0\)$

4. Total Delivery Decision

A packet is delivered if and only if it survives distance loss, line-of-sight obstruction, and congestion loss:

\[P_{deliver} = (1 - P_{loss, dist}(d)) \times (1 - P_{loss, cong}(x)) \quad \text{if LoS, else } 0.0\]

A uniform random variable \(u \sim \mathcal{U}(0, 1)\) determines whether the transmission is successful (\(u < P_{deliver}\)).

5. Gaussian Propagation Delay

If the packet is successfully delivered, its delivery timestamp is drawn from a Gaussian distribution:

\[\text{Delay} \sim \mathcal{N}(\mu, \sigma^2) \quad \text{clamped to } \ge 2\,\text{ms}\]
  • Mean delay: \(\mu = 0.02\,\text{s} = 20\,\text{ms}\).
  • Standard deviation: \(\sigma = 0.01\,\text{s} = 10\,\text{ms}\).

6. How to Enable the Parametric Model

Run with the CLI flag:

cargo run --release --example cam_simulation -- --technology parametric

Or configure in your TOML scenario:

[phy]
model = "legacy_poly"