A radar twin whose targets occupy a single range cell: how far around a strong target does the real matched filter ghost, and does tapering fix it?

research/sidelobe-twin

Single-cell radar twin vs a real matched filter: exact Rician ghost false alarms (0.020 at 20 dB, 1.0 at 30 dB for rect vs the twin's 1e-6), ghost zone radius growing √10 per 10 dB, taper gain exactly sidelobe difference + ENBW loss, and a 60 dB Hamming zone 6× Hann's despite the lower peak sidelobe. Stylised.

17 tests

What it found

A lone strong target through a matched filter alarms at neighbouring cells with an exact Rician probability where the point-response twin says P_fa0=10⁻⁶: at the rect peak sidelobe (−13.3 dB) it is 0.020 at 20 dB SNR and 1.0 at 30 dB, and the ghost zone radius grows √10 per 10 dB (3 to 331 cells for 20–60 dB). Tapers raise the ghost-free SNR by exactly the sidelobe-level difference plus the ENBW loss (20.0 dB Hann, 30.8 dB Hamming) at 1.5–1.6× mainlobe width, but ordering by peak sidelobe misleads at very strong targets: Hamming’s 1/x far sidelobes give a 42-cell zone against Hann’s 7 at 60 dB. A weak target beside a 40 dB one is ‘detected’ with P_d=1.0 where the empty cell alarms with probability 1.0. Stylised: white output noise, no CFAR or clutter, no radar data.

A figure from its own output

Figure produced by research/sidelobe-twin: ghost_free_range — sidelobe-twin/experiments/ghost_free_range.svg, written by the project's own experiment code.

Paper, code and results

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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.