Page 195 - Fundamentals of Radar Signal Processing

in some particular direction. The radar emits a CPI of data consisting of 20
pulses at a 2-kHz PRF. The CPI is then 10 ms. Suppose the radar collects three
such CPIs while illuminating the same region, with 50 ms from the start of one
CPI to the start of the next. The total data collection time of 110 ms from the
beginning of the first CPI to the end of the third would be the dwell time for the
radar in that look direction.

The terms “dwell” and “CPI” are sometimes used synonymously, but the
preceding example illustrates that they are not the same. For a coherent radar
that organizes its data into CPIs, a dwell can correspond to one or more CPIs.
For rotating and similar mechanically scanned radars, a dwell is usually the
time it takes to scan across a point target.

3.2 Sampling the Doppler Spectrum
Selecting a value for the pulse repetition frequency determines the sampling rate

for the slow-time signal. The frequency spectrum of the slow-time signal is
traditionally called the Doppler spectrum, because the nonzero frequency
components are due to the spatial Doppler effect arising from the relative
motion between the radar and target scene. Doppler processing, which is the
analysis or modification of the information about the target scene contained in
the Doppler spectrum, will be the subject of Chap. 5. Doppler processing will
sometimes be performed directly in the slow-time domain, that is, directly on
the time signal represented by a row of y[l, m]; but frequently the spectrum of

each row will be explicitly calculated. In a digital processor, this must be done
with a discrete Fourier transform (DFT) or other discrete spectral analysis
technique. In this section, it is assumed that the spectrum is computed using
conventional DFT techniques; no nonlinear spectral estimation methods or other
alternatives are considered. The question then arises as to how closely

successive samples of the computed Doppler spectrum should be spaced, i.e.,
what should be the Doppler sampling interval?

3.2.1 The Nyquist Rate in Doppler
The Nyquist criterion concept can be applied to sampling in frequency as well
as the more usual application to sampling in time. The result will be a frequency
sampling rate that is dependent on a “bandwidth” in the time domain.
The Nyquist sampling rate in the frequency domain can be determined by
reviewing the relation between the sampled Doppler spectrum and the slow-

time signal. Let a single finite duration slow-time signal (one row of y[l, m]) be
denoted as y [m], 0 ≤ m ≤ M – 1. The DTFT of y [m] is (Oppenheim and
s
s
Schafer, 2010)