Simulator/intel/radar/Physics_Symmetry_Milestone_R4.md

🏆 Milestone: Pure Physical 1/R⁴ & Zero-Tilt Symmetry

Date: 2026-04-08
Iteration Range: 20 — 26
Status: LOCKED-IN BASELINE

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🏗️ 1. The Physics Breakthrough: 1/R⁴ Power Law

Prior to this milestone, the C-Shenron engine used various "normalization" workarounds (like Iteration 16's DENSITY_REF = 1000) to prevent distant buildings from overwhelming the scene. However, these were artificial and lacked dynamic fidelity.

The Problem:

• Distant buildings (massive surface area) were integrated with the same weight as near cars.
• Because distance-based attenuation was "neutralized" in the code, the building's magnitude (1600) was higher than a near car (1400).
• This made ADAS algorithm testing impossible as the SNR profiles were physically incorrect.

The Solution:

We have stripped all artificial normalizations and returned to Pure Free-Space Physics:

1. **Transmitter Power ($P_{inc} \propto 1/R^2$)**: Each LiDAR point's incident power now follows the inverse square law.
2. **Receiver Voltage ($V_{adc} \propto 1/R^2$)**: The final ADC signal is attenuated by the return path ($1/R^1 \text{ voltage} \implies 1/R^2 \text{ power}$).
3. Result: The total power follows the $1/R^4$ Radar Range Equation. A distant building is now physically $ \sim 50,000\times$ weaker in power than a near car, making the car the natural dominant peak.

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📐 2. The Geometric Breakthrough: Zero-Tilt Symmetry

The Range-Azimuth "Fan" plot in earlier iterations appeared slightly tilted (sheared) toward the left.

The Problem:

• Index Asymmetry: Standard FFT indexing np.arange(-N/2, N/2) results in an asymmetric range (e.g., $-32 \to +31$ for 64 points).
• Angular Mapping: This created a ~15° mismatch between the left and right boundaries of the Field of View.

The Solution:

• Symmetry-Lock: We updated radar_processor.py to use perfectly centered index linear spaces: np.linspace(-N/2 + 0.5, N/2 - 0.5, N).
• Result: The 120° FOV fan is now perfectly symmetric around the boresight. This is critical for ADAS verification where lateral accuracy is paramount.

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🖼️ 3. Visual Standard: "Radar Blue"

We have standardized the diagnostic visualization suite for all future automated MCAP sessions:

• Colormap: viridis (Professional high-contrast blue/green/yellow).
• Normalization: Global Frame Normalization. No per-range-bin stretching is allowed, as it obscures the physical $1/R^2$ amplitude decay.
• Dynamic Range: Diagnostic heatmaps now preserve the "Energy Difference" between targets, ensuring human and AI agents can accurately judge target priority.

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Generated by Antigravity | Fox CARLA ADAS Pipeline Calibration Milestone | 2026-04-08