Page 185 - Fundamentals of Radar Signal Processing

pulses. The time between pulses is denoted as the pulse repetition interval

(PRI) or inter-pulse period (IPP) and denoted as T. Its inverse is the pulse
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repetition frequency (PRF). The PRF may range from a few hundred pulses
per second (also called, casually, hertz) to tens and sometimes a few hundreds
of kilohertz.
The vectors of L fast-time samples collected for each of the M pulses are

typically organized into a two-dimensional matrix y[l, m] as shown in Fig. 3.2b.
The pulse number dimension is called the slow time axis. The time required to
collect this data is simply MT seconds. If a coherent series of pulses was used
that time is called the coherent processing interval (CPI). The term CPI is used
to refer both to the matrix of data and the time required to collect it. While there
are exceptions, a CPI of data is usually collected using a constant PRI, constant
radar frequency (RF), and the same pulse waveform for all pulses in the CPI.

Although the data for a single CPI is collected by columns (pulses), once it
is stored in memory it may be accessed in any fashion. In Fig. 3.2b the fourth
range bin for each pulse is shaded gray. This row of samples in the data matrix
is the slow-time signal for that range bin. These samples represent the echo
received after the same delay from the time of transmission for successive
pulses. Assuming the antenna boresight is not moving significantly from pulse to

pulse, these samples represent the reflectivity from the same range and angle,
i.e., the same region in three-dimensional space, measured with a sampling
interval equal to the pulse repetition interval PRI. The slow-time sampling
frequency is therefore the PRF.
How should the PRF be chosen? The PRF affects, and is affected by, many
aspects of the radar and environment. As was seen in the discussion of spatial
Doppler in Chap. 2, the slow-time phase history reflects the Doppler

components in the received signal. One criterion for choosing the PRF is to
avoid aliasing of the spectrum replicas so as to preserve the information in the
Doppler spectrum for subsequent processing such as pulse Doppler target
detection or synthetic aperture imaging. Thus, the Nyquist requirement in slow
time is that the PRF be at least as large as the slow-time signal bandwidth.
A nonzero Doppler bandwidth results from two sources: intrinsic motion

of the scatterers in the area being measured, and motion of the radar platform. If
the area being measured is a target in the conventional sense of a man-made
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vehicle or object, its intrinsic motion is simply the motion of the vehicle. If it is
clutter, then intrinsic motion can be due to wind blowing the leaves of trees or
blades of grass, waves on the ocean, falling and swirling rain, air-conditioning
fans on tops of buildings, and so forth. For instance, the Doppler power

spectrum corner frequencies in Table 2.7 imply an intrinsic Doppler spread on
the order of 0.5 to 1.0 m/s for rain at X band. The intrinsic Doppler spread of
moving man-made objects can be much larger. Consider an urban clutter scene
where a stationary radar observes automobile traffic with a maximum speed of
55 mph both toward and away from the radar. The radar therefore sees targets