Page 96 - Fundamentals of Radar Signal Processing

(R ,θ ,ϕ ),
0
0
0

(2.19)

If the point scatterer is located on the antenna boresight θ = ϕ = 0, P(θ , ϕ ) =
0
0
0
0
G and Eq. (2.19) is identical to Eq. (2.11).
Next consider the volume scattering case where the RCS seen by the radar
is presumed to be due to a distribution of scatterers evenly distributed
throughout the volume, rather than associated with a single point. In this case, σ
is expressed in terms of RCS per cubic meter, or volume reflectivity, denoted
2
as η. The units of reflectivity are m /m = m . The RCS of a differential volume
–1
3
element dV is then

(2.20)

where dΩ is a differential solid angle element. The range equation becomes

(2.21)

If it is assumed that atmospheric loss is slowly varying over the extent of a
range resolution cell, then L (R) can be replaced by L (R ), where R is the
a
0
0
a
center of the range resolution cell, and removed from the integral. The integral
over range that remains is

(2.22)

provided the range resolution is small compared to the absolute range, which is
usually the case. Using Eq. (2.22) in Eq. (2.21) gives

(2.23)

Integration over the angular coordinates requires knowledge of the antenna
pattern. One common approximate model of the mainlobe of many antennas is a
Gaussian function (Sauvageot, 1992). It can be shown that a good approximation