Page 100 - Fundamentals of Radar Signal Processing

FIGURE 2.3 Relative geometry of antenna footprint and pulse envelope: (a)
beam-limited case and (b) pulse-limited case.

(2.26)

In area scattering the differential RCS is proportional to the differential
area of the scattering surface and can be represented as

(2.27)

where σ (called “sigma nought”) is the area reflectivity in m /m and is
0
2
2
therefore dimensionless. The area reflectivity of many surface types is a
significant function of the grazing angle δ. The generalized range equation [Eq.
(2.17)] becomes

(2.28)

where ΔA is the illuminated area at range R .
0
If the illuminated area is beam limited, applying the geometry of Fig. 2.3a

to the differential scattering element at range R shows that the area contributing
0
2
to the backscatter at one instant is R ϕ θ /sinδ. Thus, a differential area
3 3
contributing to the received power is of the form

(2.29)

Applying this to Eq. (2.28) and again using the constant-gain approximation to
the antenna 3-dB beamwidth gives the beam-limited range equation for area
scatterers:

(2.30)