A free-space radar twin ignores ground-bounce lobing: how wrong is it, and can a two-ray twin with a slightly wrong target height be worse?

What it found

Two-ray detection 16 sin⁴u, u=2πh_rh_t/(λr): lobe-mean gain exactly 6 and a detected phase fraction 1−(2/π)asin((c/16)^1/4), exactly 2/3 at the free-space range edge. The real system misses 20% of ranges inside the free-space range and detects 44% of those beyond it. A deterministic two-ray twin with height error δh disagrees ≈4h_rδh/(λr) (0.200 at 0.5 m, matching simulation) and is worse than free space at short range; a height-jitter ensemble scores Brier 0.119 against 0.197 deterministic and 0.533 free space. Stylised: perfect reflection, flat earth, hard threshold, no radar data.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.