Detection range per band — the loudest one finds you

Loudest band (sets Rdet) Quieter bands Rdet = max over bands

Sweep reduction into the loudest band — Rdet staircase

Rdet vs dB applied to loudest band where the next band inherits the limit
Signature reduction (dB)
Radar (σ)0 dB
IR (J)0 dB
Visual (C)0 dB
Acousticfixed 4 km
Loudest band
the limiter
R_det
you are found at
Radar / IR
km
Visual / Acou
km
Detection is a union: any band over its threshold finds you, so the range that matters is Rdet = maxb Rb. Radar range scales as σ1/4, IR and visual as √J and √C; acoustic is a fixed 4 km floor. Reduce the loudest band and the limiter simply jumps to the next — the staircase flattens the moment it does.
You are only as quiet as your loudest band.