Page 128 - Fundamentals of Radar Signal Processing

decorrelation” would be very descriptive. If frequency agility were used or
radar-target motion and collection time were such that each pulse exhibits a
different RCS value, the term “pulse-to-pulse decorrelation” would be apt.
The “scan-to-scan” and “pulse-to-pulse” terminology has a long legacy in
performance analysis of radars using noncoherent integration. It is used in much
of the classical literature, but in modern coherent radars it often does not relate

well to the actual data collection and processing methods used. In the CPI-based
data collection protocol of Fig. 2.15b and the related numerical example of Fig.
2.16, the data are correlated from one pulse to the next but are uncorrelated from
one CPI to the next. However, the intra-CPI data will likely be combined
coherently. The noncoherent combination will occur from one CPI to the next,
for instance by noncoherently integrating the same range-Doppler bin from each
CPI. Because the measurements that are actually integrated noncoherently will

be uncorrelated in this example, the appropriate detection analysis results from
the literature would be those for “pulse-to-pulse” decorrelation even though the
actual data are highly correlated from one pulse to the next!
Another example of this confusion can arise when a series of CPIs
represents a single short-term “look” at the target region, often called a dwell,
rather than the result of different passes over the same region from a regular

scan pattern. In the former case the elapsed time may still be short and the target
may not decorrelate between CPIs, while in the latter the timeline would likely
be longer and the target would be more likely to decorrelate. If noncoherent
integration across CPIs is performed, the data might be best modeled as “scan-
toscan” decorrelation in the former case because the data values from integrated
are expected to be similar, while in the second case they would be different and
the appropriate mathematical results would be those for noncoherently

integrating dissimilar values, namely the classical “pulse-to-pulse” case.
These terminology concerns can become an issue in detection performance
analysis. Many published results use the “scan-to-scan” and “pulse-to-pulse”
decorrelation terminology. In interpreting radar literature for modern radars, the
reader is cautioned to consider carefully the correlation properties of the
measurements that will be noncoherently combined for a single detection

decision. The critical point is whether those measurements are expected to be
highly correlated, i.e., all approximately the same random variable, or whether
they are expected to be highly decorrelated (different random variables). If the
measurements are highly correlated, published results on “scan-to-scan”
mathematical models are applicable. If they are uncorrelated, “pulse-to-pulse”
models are applicable. Newer literature is less likely to use the “scan-to-scan”
and “pulse-to-pulse” terminology, obviating this problem over time.

A target fluctuation model is a combination of a PDF describing the RCS
variation with angle, RF, or other important parameters and a decorrelation
model for measurements to be combined noncoherently. Any PDF that models
the RCS distribution for the targets and radar of interest could be used.