Page 264 - Fundamentals of Radar Signal Processing

exceeds R the target echo will not be present in all of the slow-time samples
ua
and the Doppler resolution will degrade in Y [l, ω ) in the same manner it did in
D
Â(t, F ).
D
When the transmitted pulse burst waveform is extended by P pulses to
provide full integration gain of a factor of M for targets extending over P range
ambiguities, the matched filter output maintains its full maximum peak value of
ME over the P range ambiguities (delay interval 0 to (P – 1)T) of interest as
p
shown in Fig. 4.16a. The same result over only that delay interval could be
obtained by at least two equivalent calculations: correlation of an M-pulse
transmitted waveform with an infinitely extended reference, evaluated over [0,
(P – 1)T], or circular correlation of an M-pulse waveform with an M-pulse
reference. The periodic ambiguity function (PAF) is a modification of the
complex AF of Eq. (4.30) that, when applied to a pulse burst waveform,
produces the full-gain AF over this delay interval. A typical definition is

(Levanon, 2010; Levanon and Mozeson, 2004)

(4.81)

A significant property of the PAF is its relation to the AF of the single
constituent pulse in the pulse burst when T > 2τ: 4

(4.82)

That is, the PAF is the AF of the single pulse multiplied by the DTFT of a
discrete M-sample pulse. This is exactly the DTFT Y [l, ω ) that will result
D
from the pulse-by-pulse processing approach as described above.

4.6 Frequency-Modulated Pulse Compression

Waveforms

A simple pulse has only two parameters, its amplitude A and its duration τ. The
range resolution cτ/2 is directly proportional to τ; better resolution requires a
shorter pulse. Most modern radars operate with the transmitter in saturation.
That is, any time the pulse is on, its amplitude is kept at the maximum value of
A; amplitude modulation other than on/off switching is not used. The energy in
the pulse is then A τ. This mode of operation maximizes the pulse energy, which
2
is then also directly proportional to τ. As will be seen in Chaps. 6 and 7,
increasing pulse energy improves detection and estimation performance. Thus,
improving resolution requires a shorter pulse, while improving detection and