Page 188 - Fundamentals of Radar Signal Processing

according to Eq. (3.3) and broadened according to Eq. (3.6) by relative motion

between the terrain and platform, the shift in center frequency is not relevant to
selection of the PRF; only the bandwidth determines the Nyquist rate. Also, note
that antenna patterns are not strictly limited in angular extent, and therefore the
motion-induced Doppler spectrum is not strictly bandlimited to the value based
on the 3-dB bandwidth given in Eq. (3.6). Nonetheless, Eq. (3.6) provides a
good basis for estimating motion-induced bandwidth.

3.1.3 Doppler and Range Ambiguities
For any sampled time signal, the sampling frequency determines the aliasing
interval of the DTFT of that signal. The DTFT of the slow-time signal in a given
range bin is the Doppler spectrum. The PRF is the slow-time sampling rate and
therefore determines the aliasing interval of the Doppler spectrum. For reasons
to be seen in Chap. 5, this interval is called the blind Doppler shift, denoted
F . The equivalent radial velocity interval is called the blind velocity v . They
Db
b
are given by

(3.7)

Because the Doppler or radial velocity spectrum is usually plotted on the

interval [–F /2, + F /2) or [–v /2, + v /2), the quantities F /2 and v /2 are
Db
b
b
b
Db
Db
sometimes called the unambiguous Doppler or velocity, F Dua or v . Care must
ua
be taken to determine if a stated value refers to the full unambiguous interval F Db
or v , or to the frequency (velocity) cutoff point ± F Dua or ±v .
b
ua
Because the Doppler spectrum measured with a pulse burst waveform is
periodic in frequency, targets having a Doppler shift F (radial velocity v)
D
outside of the unambiguous Doppler or radial velocity interval will be aliased
into that interval. The apparent (aliased) Doppler shift F or radial velocity v a
Da
will satisfy

(3.8)

where the integer n is chosen such that F and v fall in the unambiguous
a
Da
interval.
As a numerical example, consider a 10-GHz radar viewing a target with a
radial velocity v of +100 m/s. The Doppler shift will be F = 6.67 kHz. If the
D
radar collects a CPI of data using a PRF of 3 kHz and obtains the Doppler