High Resolution Tactical Synthetic Aperture Radar (TSAR) - MATLAB Simulations for Radar Systems Design - page 589

z

radar

c τ
2

θ

-----

h

ψ g

x

m g

c τ
2

----- sec ψ g

Figure 12.5. Definition of a range cell on the ground.

λ R
2 L

∆ A = ------- (12.10)

Furthermore, since the synthetic aperture length L is equal to vT ob , Eq.

(12.10) can be rewritten as

λ R
2 vT ob

∆ A = --------------

(12.11)

The azimuth resolution can be greatly improved by taking advantage of the
Doppler variation within a footprint (or a beam). As the radar travels along its
flight path the radial velocity to a ground scatterer (point target) within a foot-
print varies as a function of the radar radial velocity in the direction of that
scatterer. The variation of Doppler frequency for a certain scatterer is called the
ÐDoppler history.Ñ

Let R () denote the range to a scatterer at time , and t v r be the correspond-

ing radial velocity; thus the Doppler shift is

2 v r
λ

2 R ' ()
λ

--------------

f d = – = -------

(12.12)

where is the range rate to the scatterer. Let and be the times when
the scatterer enters and leaves the radar beam, respectively, and be the time
that corresponds to minimum range. Fig. 12.6 shows a sketch of the corre-
sponding . Since the radial velocity can be computed as the derivative of
with respect to time, one can clearly see that Doppler frequency is maxi-
mum at

R ' () t 1 t 2

t c

R ()

R ()

t 1 , zero at t c , and minimum at t 2 , as illustrated in Fig. 12.7.