Page 296 - Fundamentals of Radar Signal Processing

Equation (4.127) shows that the slow-time sequence at a fixed coarse range bin

l when using a linearly stepped frequency waveform is a discrete time sinusoid.
The frequency is proportional to the displacement of the scatterer from the
nominal range bin location of R = ct /2 meters. The amplitude of the sequence is
l
l
weighted by the triangular simple pulse matched filter response evaluated at the
incremental delay s (δt).
p
Following the earlier discussion of pulse-by-pulse processing for the

conventional pulse burst waveform, the slow-time matched filter impulse
response for a target located at the nominal delay t + δt is h[m] =
l
exp(–j2πmΔFδt). Thus, the matched filter impulse response is different for
every value of δt. Consider a DTFT of the slow-time data

(4.128)

The summation will yield an asinc function having its peak at ω = 2πΔFδt. Thus,
the peak of the DTFT of the slow-time data in a fixed range bin with a linearly
stepped frequency waveform provides a measure of the delay of the scatterer

relative to the nominal delay t . Specifically, if the peak of the DTFT is at ω =
l
ω , the scatterer is at an incremental delay
p

(4.129)

Note also that the DTFT evaluated at ω is the matched filter for the slow-time
p
sequence, so that the data samples are integrated in phase

(4.130)

The factor of M is the coherent integration gain from using M pulses. If δt = 0,
meaning the matched filter output was sampled at its peak, Y[l, ω) = ME = E,
p
the total waveform energy. If δt ≠ 0 the ambiguity function of the individual
pulses reduces the amplitude of the slow-time samples by |s (δt)|. This
p
represents a straddle loss.