Page 378 - Fundamentals of Radar Signal Processing

signal model of Eq. (5.25) leads to the pulse canceller as a near-optimum MTI

filter for small order N. In contrast, DFT-based pulse Doppler processing
attempts to separate target signals based on their particular Doppler shift.
Assume that the signal is a pure complex sinusoid (ideal moving target) at a
Doppler shift of F Hz. Based on Eq. (5.21), the model of the signal vector is
D
then

(5.85)

where the complex scalar A absorbs all constants. If the interference consists
only of white noise (no correlated clutter), S reduces to I. It follows that for
I
T
an arbitrary data vector y the output h y of the matched filter becomes

(5.86)

This is the DTFT of y[m] to within the scale factor A. When F = k/KT =
D
kPRF/K for some integer k, Eq. (5.86) is simply the K-point DFT of the data
sequence y[m] to within the scale factor A. Consequently, the DFT is a matched
filter to ideal constant radial velocity moving target signals, provided that the
Doppler shift equals one of the DFT sample frequencies and the interference is
white. This result is very closely related to the two-pulse canceller for a
specific target Doppler and noise interference only considered in Sec. 5.2.3.

Since the K-point DFT computes K different outputs from each input
vector, it effectively implements a bank of K matched filters at once, each tuned
to a different Doppler frequency. The frequency response shape of each matched
filter is just the asinc function. To see this, denote the impulse response vector
in Eq. (5.86) when F = k/MT as h . To within a scale factor
D
k

(5.87)

The corresponding discrete time frequency response H (ω) is
k

(5.88)