Page 252 - Fundamentals of Radar Signal Processing

FIGURE 4.14 Slow-time sequence to be integrated for matched filtering of a
pulse burst waveform.

4.5.3 Range Ambiguity
Evaluating the pulse burst matched filter output at t = 0 gave the peak output for

a target at the time delay t under consideration. Normally t < T and if a peak is
0
0
observed it will be interpreted as implying the presence of a target at range R =
0
ct /2 m. However, suppose the data instead contain echoes from a target an
0
additional T seconds of delay further away. The received waveform will be
unchanged except for a delay of T seconds and a reduced amplitude according to
the range equation. The amplitude reduction is not pertinent to the discussion

and is ignored. By shift invariance, the matched filter output of Eq. (4.58) will
also be delayed by T seconds

(4.64)

Now when the matched filter output is evaluated at t = 0 the result is

(4.65)

In this expression (and continuing to assume T > 2τ) only the m = –1 term is
nonzero, so that

(4.66)

This equation shows that the output at the sample time is reduced from ME to
p
(M – 1)E . The situation is illustrated in Fig. 4.15 from both the whole-
p
waveform matched filter and pulse-by-pulse viewpoints. From the former
viewpoint, a local peak of the matched filter output is sampled, but the global
peak is missed because the filter is “tuned” for the wrong delay. The result,
while not zero, is a reduced-amplitude sample, reducing SNR. From the latter
viewpoint, the echo appears in only M – 1 of the M slow-time samples
integrated because it first returns after the sampling window following
transmission of the second pulse rather than the first.