Radar System Engineering

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646 MOVING- TARGET INDICATION [SEC.164
where ro and ROare the rms values of r and R, 0 is the beamwidth, n is
the number of pulses per beamwidth, and j(d) is the antenna pattern
(voltage two ways). For the case of a Gaussian antenna pattern, we
obtain the equation
To 1.66
(lo)
K=T”
It is convenient to analyze the fluctuation into an amplitude part and
a phase part. To do this we can resolve the vector r into two components,
one in the direction of R, the other at right angles to R. The rms value
of each of these components is rO/@. Thus the rms fluctuation in
amplitude is rO/@ and the rms fluctuation in phase is approximately
ro/ (Rov@). We can therefore write
Rms pulse-to-pulse amplitude fluctuation = = R,
n 42
Rms pulse-to-pulse phase fluctuation
1.66
= — radians.
n ~$
These equations apply to the case of uniformly distributed scattering
elements. It might appear that a sudden discontinuity in the density
of scattering elements would cause a larger fluctuation. To see that this
is not so we can consider the integral {f[j’(e)]z de} ~~,which is proportional
to therms pulse-to-pulse fluctuation TO. In the case of a uniform distribution
of scattering elements, the limits of integration are from – cc to + ~.
When there is a discontinuityy at an angle O,from the center of the beam,
the limits are O, to m, and the integral will be less than before since the
integrand is everywhere positive.
16.8. Receiver Characteristics. -Ideally, an MT1 system would
remove all clutter signals from the scope, maintaining the greatest possible
sensitivity for moving targets both in the clear and in the clutter.
Practically, this is not always possible, because of clutter fluctuations,
the finite perfection of cancellation, etc. Under these circumstances, it
appears desirable to adjust the residual clutter, after cancellation, so that
it resembles receiver noise in amplitude and texture when it is presented
on the scope.
Clutter fluctuations already have an amplitude distribution like that
of noise, whether they are due to scanning or to the action of the wind.
Thus the only problem left is to reduce the rms fluctuation to the same
value everywhere. There are two ways of doing this, the first depending
on the nature of the amplitude fluctuations of the clutter, the second on
the nature of the phase fluctuations.
As we have seen, the rms fluctuation in amplitude is proportional
to the rms clutter amplitude. Thus if z is the size of the clutter at the
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