Page 101 - Fundamentals of Radar Signal Processing

If the illuminated area is pulse limited, the geometry of Fig. 2.3b shows

that the area contributing to the backscatter at one instant is Rθ ΔR/cosδ. The
3
differential contribution is thus

(2.31)

The first-order approximation of constant gain over the mainlobe can be used

again, though the integral over ϕ is now limited to the range that covers the
extent of the pulse on the ground. Equation (2.28) becomes

(2.32)

–2
Note that power varies as R in the beam-limited case because, as with the
volume scattering, the resolution cell size grows in both cross-range and down-

range extent with increasing range. In the pulse-limited case, power varies as R –
3 because the resolution cell extent increases in only the cross-range dimension
with increasing range.
If the range of interest varies by a large amount, there will be significant
variation in the grazing angle δ and therefore in both the antenna beam and pulse
footprint extents. For instance, for a radar at a constant altitude h and a slant

range R to the ground, sinδ = h/R. As R increases, the beam-limited antenna
3
2
footprint area will then increase as R instead of R so that the clutter power
–1
0
would be expected to fall only as R . However, σ may also vary significantly
with grazing angle (see Section 2.3.1). Additional complications occur when R
increases so much that a radar that was beam limited at a relatively short range
and steep grazing angle becomes pulse limited at a longer range and shallower
grazing angle, or the grazing angle falls below the “critical angle”.
Consequently, the received clutter power may fall off at various rates from R –1
–3
to R or even more rapidly at very shallow angles (Long, 2001; Currie, 2010).

2.2.3 Radar Cross Section

Section 2.2.1 introduced the radar cross section to heuristically account for the
amount of power reradiated by the target back toward the radar transmitter. To
restate the concept, assume that the incident power density at the target is Q and
t
the backscattered power density at the transmitter is Q . If that backscattered
b
power density resulted from isotropic radiation from the target, it would have to
satisfy