Aircraft Scatter Link Budget

Bistatic radar eq.  ·  Earth curvature k=4/3 · Re=8500 km  ·  Fresnel-Kirchhoff knife-edge diffraction  ·  100 MHz – 10 GHz

Propagation geometry
Aircraft scatter propagation geometry Side-view diagram showing transmitter and receiver stations, terrain with mountain obstruction, blocked direct line-of-sight path, and aircraft scatter path with R1 and R2 leg distances. TX RX
Loading...
Fresnel info loading... ↓ Theory & formulas
Mathematical Model

Theory & Formulas

The calculator combines the Friis transmission equation (direct path), the bistatic radar equation (aircraft scatter), and Fresnel-Kirchhoff knife-edge diffraction with an effective Earth radius (k = 4/3, Re = 8 500 km) for standard atmospheric refraction.

Free-space path loss (direct link)

Friis FSPL(dB) = 20·log10(4π·d / λ)     λ = c / f

Direct-path received power: Prx(dBm) = Ptx + Gtx + Grx − FSPL.

Earth curvature (k = 4/3)

Earth bulge & horizon hbulge(d1) = d1·(D − d1) / (2·Re)     dhorizon = √(2·Re·h)

Knife-edge diffraction

Fresnel-Kirchhoff parameter ν = −hclearance · √( 2·(d1 + d2) / (λ·d1·d2) )

Diffraction loss L(ν) is computed from the standard piecewise approximation (Lee, 1985); additional loss is applied whenever a terrain obstacle or the Earth bulge intercepts the line of sight. First Fresnel-zone radius r1 = √(λ·d1·d2 / (d1+d2)).

Bistatic aircraft scatter

Bistatic radar equation Prx = Ptx · Gtx · Grx · λ2 · σ / ( (4π)3 · R12 · R22 )

R1 and R2 are the slant distances TX→aircraft and aircraft→RX, computed as R = √(x2 + hac2). Because the power is dominated by the product R12·R22, the strongest signal occurs when the aircraft is close to one of the two stations rather than at the geometric midpoint. Each scatter leg receives additional knife-edge diffraction loss if it passes below the radio horizon (Earth bulge) or if the terrain obstacle lies within that leg and rises above the station-to-aircraft sight line.

Equivalent flat-panel RCS

Monostatic peak (square panel, side a) σ = 4π · a4 / λ2    ⇒    a = (σ·λ2 / 4π)1/4