Page 474 - Fundamentals of Radar Signal Processing

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Consideration will be largely restricted to the square law detector in this
section.
When coherent integration is used, detection results are obtained by using
single-sample (N = 1) results with χ replaced by the integrated χ . The situation
N
1
for noncoherent integration is more complicated. As shown in Chap. 1, the
integrated signal z cannot be expressed as the sum of a target-only part and a
noise-only part, so that an integrated SNR cannot be defined directly. It will
prove necessary to determine the actual probability density function of the
integrated random variable z to compute detection results; this is done in the
next subsection.
Binary integration takes place after an initial detection decision has taken

place. That initial decision may be based on a single sample or on data that have
already been coherently or noncoherently integrated. Whatever the processing
before the threshold detection, after it the result is a choice between hypothesis
H , “target absent,” and H , “target present.” Because there are only two
1
0
possible outputs of the detector each time a threshold test is made, the output is
said to be binary. Multiple binary decisions can be combined in an “M out of N”

decision logic in an attempt to further improve the performance. This type of
integration is discussed in Sec. 6.4.

6.3.2 Nonfluctuating Targets
Now consider detection based on noncoherent integration of N samples of a
nonfluctuating target (sometimes called the “Swerling 0” or “Swerling 5” case)
in white Gaussian noise. The amplitude and absolute phase of the target
component are unknown. Thus, an individual data sample y is the sum of a
n
complex constant for some real amplitude and phase θ, and a
complex white Gaussian noise sample w of power in each of the I and Q
n
channels (total noise power )

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Under hypothesis H , the target is absent and y = w . The PDF of z = |y | is
0
n
n
n
n
Rayleigh