Page 158 - Fundamentals of Radar Signal Processing

baseband complex reflectivity or just reflectivity of the differential scatterer

and will be denoted as dρ. Making these substitutions and removing the carrier
term with coherent demodulation leaves only the baseband complex received
voltage dy for the single differential scatterer

(2.112)

Equation (2.112) gives the contribution to the received echo voltage of a
differential scatterer element at coordinates (R,θ,ϕ). The total received voltage
is obtained by integrating these differential contributions over all space:

(2.113)

Equation (2.113) is a coherent scattering model: the differential scatterers
are assumed to add as complex voltages. This is most appropriate for

reflectivity fields characterized by relatively static configurations of scatterers,
e.g., man-made vehicle and urban areas. The case where the scatterers are not
static is considered in Sec. 2.7.4.
2
Now write dρ(R, θ, ϕ) = ρ(R, θ, ϕ) · dV = ρ(R, θ, ϕ) R cosϕ dR dθ dϕ to
obtain

(2.114)

Define the effective reflectivity ρ′ to include the attenuation due to atmospheric

loss, the phase rotation due to two-way propagation range, and the cosϕ term of
the differential volume element:

(2.115)

Applying Eq. (2.115) to Eq. (2.114), the received signal is seen to be similar to