Page 362 - Fundamentals of Radar Signal Processing

TABLE 5.1 Improvement Factor for Gaussian Clutter Power Spectrum

The third approach for computing the improvement factor uses the vector

analysis techniques employed in determining the matched filter for MTI. For
comparison with the autocorrelation analysis given previously, consider the
T
case where (clutter only) and h = [1 – 1] (two-pulse canceller).
Improvement factor is the ratio of the signal-to-interference ratio at the filter
output to the SIR at the filter input. While the optimum MTI filter was derived
by averaging over possible target Doppler frequencies, in evaluating the
improvement factor it is assumed that any specific target has a specific Doppler

frequency. The improvement factor is calculated for that specific target Doppler
frequency and then averaged over allowable Doppler frequencies. Since SIR at
the input does not depend on Doppler frequency, it is sufficient to do the
averaging on the output SIR.
Consider therefore the signal vector given by Eq. (5.23) and the clutter

covariance matrix given by Eq. (5.19) (with ). The input SIR is just .
Equation (5.7) gave an explicit expression for the output SIR. The numerator of
this expression is

(5.61)

This is the two-pulse canceller MTI filter output signal power for a target at
Doppler shift F Hz. Averaging over all target Doppler shifts gives for the
D
numerator

(5.62)

The denominator of Eq. (5.7) is