cn0-interference-sampling

Simulates the carrier-to-noise-density ratio (C/N0) reported by a GNSS receiver for four reception classes — line-of-sight, ground multipath, building multipath and non-line-of-sight — using an image-source plane-wave model with Fresnel reflection coefficients, and evaluates how much of the inter-antenna or inter-frequency C/N0 difference survives receiver estimation noise and quantization.

Typical questions it answers:

• Which antenna-pair geometries have an exact C/N0-difference null for a given reflector (e.g. a horizontal pair over flat ground)?
• At what vertical spacing does the ground-reflection response first peak, as a function of elevation?
• How much four-class separability remains once the receiver rounds C/N0 to 0.25 dB and adds 0.5 dB of noise?
• For a specified two-ray alternative, what is the minimum error of any detector operating on the quantized difference (numerical Bayes error)?
• How do differential channel biases, correlated noise and a change of scene affect a classifier trained on the nominal model?

Installation

git clone https://github.com/hamamh66/cn0-interference-sampling.git
cd cn0-interference-sampling
python -m venv .venv && source .venv/bin/activate
pip install -e ".[test]"

Python ≥ 3.10; dependencies are NumPy, SciPy, scikit-learn and Matplotlib. requirements.txt pins the exact versions used to produce the archived results.

Quick start

pytest -q                          # physical self-checks + reproduction of results/results.json (~30 s)
cn0-run-experiments --out results  # experiments E1–E7, ~20 s on a laptop CPU
cn0-make-diagrams                  # framework and operation schematics

Or open notebooks/cn0_difference_detectability.ipynb (Jupyter, or Google Colab — the first cell clones this repository into the Colab local disk).

Python API:

from cn0sampling import simulation as sim
s  = sim.make_scene(4000, seed=0)                      # balanced LOS / MPG / MPB / NLOS scenes
d  = sim.signal(s, baseline=(0, 0, 0.10)) - sim.signal(s)   # inter-antenna C/N0 difference, vertical 10 cm
y  = sim.measure(sim.signal(s)[:, None], seed=1, sigma=0.5, q=0.25)   # receiver noise + quantization
pe = sim.bayes_error(alpha=0.05, dphi=3.14159, sigma=0.5, q=0.25)      # quantized binary Bayes error

Repository layout

Path	Content
cn0sampling/simulation.py	Propagation, antenna-channel and receiver models; analytic phase step and weak-signal RMS; quantized binary Bayes error; self_checks()
cn0sampling/run_experiments.py	Experiments E1–E7, paired seeds, LaTeX table generation (cn0-run-experiments)
cn0sampling/make_diagrams.py	Schematics (cn0-make-diagrams)
notebooks/cn0_difference_detectability.ipynb	Executed notebook: self-checks, full run, figures, tables and interpretation
results/results.json	Archived results with per-seed metrics, validation checks, software versions and source hashes
results/figures/, results/tables/	Archived figures (PDF/PNG/SVG) and LaTeX tables
tests/	Physical self-checks and a reproduction test against the archived results

Model

• Signals: GPS L1 (1575.42 MHz) and L5 (1176.45 MHz); direct ray, single specular ground reflection, single vertical-wall reflection; image-source plane waves with positive path excess; Fresnel coefficients for circular polarization with a scalar cross-polar leakage term; RHCP hemispherical antenna pattern with below-horizon suppression.
• Classes (balanced): LOS (direct), MPG (direct + ground), MPB (direct + ground + wall), NLOS (wall only).
• Receiver: Y = round((mu + s + eta)/q)·q — Gaussian estimation noise eta (per-channel σ, optional inter-channel correlation ρ) followed by uniform quantization with step q.
• Experiments: E1 relative phase step versus elevation; E2 median |ΔC/N0| versus baseline length; E3 four-class decision-tree classification under six (σ, q) settings, five seeds, paired across nine feature configurations (single channel, horizontal / vertical / oblique pairs, H+V and H+H triplets, L1–L5); E4 phase-marginalized quantized binary Bayes error; E5 frozen-model stress tests (differential bias, open-sky calibration, correlated noise, scene shift); E6 exact bin likelihood versus the additive-quantization-noise approximation across reporting step, noise and quantizer origin; E7 Bayes error with unknown reflection amplitude and differential channel offset marginalized under explicit priors.

Results are deterministic for fixed seeds. Other library versions may change values at the last reported decimal.

Scope and limitations

Everything here is simulated. The model is planar, specular and narrowband: it omits diffraction, diffuse scattering, finite reflector extent, multiple bounces, antenna coupling, vector polarization patterns, tracking loss and correlator response. Bayes errors apply to the specified binary observable, not to the four-class classifier. No measured receiver data are included, and no positioning solution is computed.

Archive

Tagged releases are deposited in the Federated Research Data Repository (FRDR), which assigns a persistent DOI; the DOI for each release is recorded in CITATION.cff and in the release notes.

Citing

See CITATION.cff (GitHub's "Cite this repository" button).

License

MIT — see LICENSE.