Clutter and MTI

Code: radarsim/physics/clutter.py, radarsim/simulation/engine.py.

Surface reflectivity

Surface	Model	Domain
land (rural, urban, forest, …)	constant-γ: \(\sigma^0 = \gamma \sin\psi\), γ from a short table or a measured value	any grazing angle
bare soil (ground_surface.model: oh1992)	Oh, Sarabandi & Ulaby (1992) empirical model	1–10 GHz, 10–70° incidence, \(0.1 \le ks \le 6\)
sea	NRL five-parameter model (Gregers-Hansen & Mital 2012), HH and VV	0.5–35 GHz, sea state 0–6, 0.1–60° grazing

Outside the Oh-1992 incidence range (a ground radar looking at a distant target sees grazing angles of a fraction of a degree) the engine falls back to constant-γ instead of extrapolating. Polarisation tilt mixes the HH and VV values. Clutter sectors in a scenario change the surface class and add a calibration offset for regions of azimuth and range.

Clutter in the target's cell

The surface patch sharing the target's range cell has area

\[ A_c \approx \frac{\pi}{4}\, \min\!\left(\frac{c\tau_c}{2\cos\psi},\, \frac{2R\tan(\theta_{el}/2)}{\sin\psi}\right) \cdot 2R\tan\!\left(\frac{\theta_{az}}{2}\right) \]

with the compressed pulse length \(\tau_c\). The beam is pointed at the target, so the patch, at depression angle \(-\psi\), is seen through the elevation pattern \(g(\Delta) = \max\{e^{-4\ln 2\,\Delta^2/\theta_{el}^2},\,10^{SLL/10}\}\) at \(\Delta = \epsilon_t + \psi\), twice (transmit and receive):

\[ \sigma_c = \sigma^0 A_c\, g(\Delta)^2 . \]

A low flyer competes with the full main-beam clutter; an aircraft several beamwidths up sees it only through the sidelobes. The test suite checks that a target at 6 km altitude loses at least 10 dB less to clutter than one at 50 m at the same range.

MTI

A two-pulse canceller removes returns near zero Doppler. Its improvement factor against clutter with a Gaussian spectrum of width \(\sigma_c = 2\sigma_v/\lambda\) (Skolnik 2008, eqs. 2.41–2.42) is

\[ I_1 = 2\left(\frac{f_r}{2\pi\sigma_c}\right)^2, \qquad I = \left(\frac{1}{I_1} + \frac{1}{I_{s}}\right)^{-1}, \]

limited by the system stability \(I_s\) = 50 dB. The clutter velocity spread defaults to 0.25 m/s over land and 1 m/s over sea (Nathanson 1999) and can be set per scenario. Targets whose radial speed is below the MTI threshold are cancelled with the clutter.

Validity

• Clutter is treated as noise-like in the SINR (no Weibull/K-distribution tails in the detection decision); the distributions are available as samplers in ClutterModel for signal-level work.
• One clutter patch per target cell; range-ambiguous clutter from earlier pulses is not added.