Page 126 - Fundamentals of Radar Signal Processing

This is not the only way a set of related measurements can arise. Many
modern systems are designed to transmit a rapid burst of M pulses at a constant
PRF, often with the antenna staring in a fixed or nearly fixed direction, forming

a coherent processing interval (CPI) of data. As will be seen in Chap. 4, the M-
pulse burst is a common waveform well suited to Doppler measurements and
interference suppression. The radar may then repeat the measurement, collecting
a series of N CPIs in the same look direction. Successive CPIs may share the
same radar parameters, or the radar may change the PRF, the waveform, or the

RF (frequency agility). The data from the same range bin within a single CPI are
usually combined coherently, for instance to form a Doppler spectrum for that
range bin. However, combining data across CPIs must generally be done
noncoherently. An example would be noncoherent integration of N
measurements of the same range-Doppler resolution cell in the N CPIs as shown
in Fig. 2.15b, prior to testing that cell for the presence of a target.
If the target, the radar, or both are moving during the time a set of N
measurements is collected, a natural question is whether the target RCS during

that time should be considered constant or varying. That is, assuming frequency
agility is not used, does the radar-target aspect angle vary so little that the RCS
should be modeled as the same random variable during the entire set of N pulses
or CPIs? Or is the aspect changing so rapidly that the RCS decorrelates from
one pulse or CPI to the next, and so should be modeled as independent random

variables from the appropriate PDF? The answer has a significant impact on
both the procedure and the results for computing detection probabilities, as will
be seen in Chap. 6.
These questions require consideration of the dynamics of the radar-aircraft
encounter in light of the decorrelation interval in angle given in Eq. (2.63). As
an example, consider the crossing encounter of Fig. 2.16a. Aircraft #1 views
aircraft #2 at broadside from a range of 5 km with an X band (10 GHz) radar.

Assume aircraft #2 is traveling at 100 m/s and has a length (width as viewed
from the radar) of 10 m. Assume that aircraft #1 transmits a burst of M = 10
pulses at a 1-kHz PRF. In the resulting 10 ms CPI, aircraft #2 will travel 1 m,
resulting in an angular change with respect to aircraft #1 of approximately
1/5000 = 0.2 mrad. From Eq. (2.63), the decorrelation interval in angle is
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expected to be (3 × 10 )/(2·10·10 × 10 ) = 1.5 mrad. Because the actual angle
change within a CPI is less than the angular decorrelation interval, one would
expect all the pulses within a CPI to experience essentially the same RCS. Now
suppose that the radar transmits a series of pulse bursts, each one starting 100
ms after the previous burst. The angular change between aircraft #1 and #2 from
one CPI to the next is then 2 mrad, which is greater than the 1.5 mrad
decorrelation interval. Consequently, it is expected that the aircraft RCS during
a given CPI will be uncorrelated with that during other CPIs.