Page 102 - Fundamentals of Radar Signal Processing

(2.33)

for some total backscattered power P . RCS is the fictional area over which the
b
transmitted power density Q must be intercepted to collect a total power P that
b
t
would account for the received power desnity. In other words, σ must satisfy

(2.34)

Combining Eqs. (2.33) and (2.34) gives

(2.35)

This definition is usually written in terms of electric field amplitude. Also, in
order to make the definition dependent only on the target characteristics, range
is eliminated by taking the limit as R tends to infinity. Thus, the formal definition
of radar cross section becomes (Knott et al., 1985)

(2.36)

b
t
where E and E are the backscattered and transmitted electric field complex
amplitudes, respectively.
The RCS just defined is a single real scalar number. Implicit in the
definition is the use of a single polarization of the transmitted wave and a single

receiver polarization, usually the same as the transmitted polarization.
However, the polarization state of a transverse electromagnetic plane wave is a
two-dimensional vector, and therefore two orthogonal polarization basis
vectors are required to fully describe the wave. The most common basis choices
are linear (horizontal and vertical polarizations) and circular (left and right
rotating polarizations). Furthermore, a general target will modify the

polarization of an incident wave, so that the energy backscattered from, say, the
vertical component of the incident wave may have both vertical and horizontal
components. To account fully for polarization effects, RCS must be generalized
to the polarization scattering matrix (PSM) S, which relates the complex
amplitudes of the incident and backscattered fields. For a radar using a linear
polarization basis this relation is (Knott et al., 1985; Mott, 1986; Holm, 1987)