Radar Cross Section (RCS)

Formal definition:

σ = lim_R→∞ 4πR² · |E_s|² / |E_i|²

Here R is the distance to the target, E_s is the scattered electric field and E_i is the incident electric field. The limit R→∞ ensures that we measure in the far field (plane wavefront).

σ_dBsm = 10 · log₁₀(σ / 1 m²)

Example: σ = 0.01 m² → σ_dBsm = 10 · log₁₀(0.01) = -20 dBsm

Practical example (77 GHz radar, λ ≈ 3.9 mm):

A DJI Mavic Mini (wingspan ~25 cm) has a/λ ≈ 64 → optical region.
A raindrop (d ≈ 2 mm) has a/λ ≈ 0.5 → Mie region.
A dust particle (d ≈ 50 μm) has a/λ ≈ 0.013 → Rayleigh region.

Limitation: the „optical region“ is not „simple“ at 77 GHz

The classification by a/λ only says something about the overall size of the target. What also matters for scattering behavior is how smooth the surface is relative to the wavelength. At λ ≈ 3.9 mm, screws, edges, cables, sensor domes and material seams of a drone are already on the order of the wavelength itself.

Such a target therefore behaves less like a single smooth reflector and more like a collection of many scattering centers, whose contributions add constructively or destructively depending on viewing angle. The result is a strongly fluctuating, aspect-dependent RCS — even where pure size considerations would suggest a calm, frequency-independent backscatter. This is one of the reasons a single average RCS value only describes the detectability of small flying objects to a limited extent.

Why is the flat plate so important?

A 1×1 m metal plate at 77 GHz (λ = 3.9 mm) has an RCS of σ = 4π(1)² / (0.0039)² ≈ 826,000 m² (59 dBsm)! This value, however, only holds at the specular maximum: the main lobe of such a reflector is extremely narrow at about λ/D ≈ 0.22°, and outside it RCS drops by orders of magnitude. Smooth surfaces therefore produce very strong but tightly directed echoes — typical building clutter otherwise also arises from surface roughness, diffuse scattering and multiple reflections at edges.

Monostatic radar equation:

P_r = (P_t · G² · λ² · σ) / ((4π)³ · R⁴)

P_r = received power, P_t = transmit power, G = antenna gain,
λ = wavelength, σ = RCS, R = range to target

Maximum detection range:

R_max = ((P_t · G² · λ² · σ) / ((4π)³ · P_r,min))^1/4

Important: the R⁴ dependence means that doubling the range requires 16× the transmit power or 16× the RCS. This is one of the reasons small drones (σ ≈ 0.01 m²) are demanding targets. A concrete range does not follow from this alone, however: it only emerges from the full link budget with transmit power, antenna gain, noise figure, required P_d/P_fa and the integration gain of coherent processing, which the single-measurement form of the equation above does not include.