Page 359 - Fundamentals of Radar Signal Processing

moment only a specific target Doppler shift, the improvement factor can be

written in the form

(5.48)

where G is the filter gain. Figure 5.9 makes clear that the effect of the MTI filter

on the target signal is a strong function of the target Doppler shift. Thus, G is a
function of target velocity, while clutter attenuation CA is not. The improvement
factor is the signal processing gain G in the radar range equation due to MTI
sp
filtering.
To reduce I to a single number instead of a function of target Doppler, the
definition calls for averaging uniformly over all target Doppler shifts “of
interest.” If a target is known to be at a specific velocity, the improvement factor

can be obtained by simply evaluating Eq. (5.48) at the known target Doppler. It
is more common to assume the target velocity is unknown a priori and use the
average target gain over all possible Doppler shifts, which is just

(5.49)

An alternative expression for the gain that is often easier to compute for simple
MTI filters follows from converting Eq. (5.49) back to normalized frequency
units and applying Parseval’s theorem:

(5.50)

For example, a two-pulse canceller has only two nonzero coefficients, +1 and –

1, giving immediately G = 2. Combining Eqs. (5.47) and (5.49) in gives the
expression for the improvement factor

(5.51)

Equivalent expressions for improvement factor can be developed in terms