Page 441 - Fundamentals of Radar Signal Processing

6.1 Radar Detection as Hypothesis Testing

For any radar measurement that is to be tested for the presence of a target, one
of two hypotheses can be assumed to be true:

1. The measurement is the result of interference only.
2. The measurement is the combined result of interference and echoes from

a target.

The first hypothesis is denoted as the null hypothesis H and the second as the
0
non-null hypothesis H . The detection logic therefore must examine each radar
1
measurement to be tested and select one of the hypotheses as best accounting for
that measurement. If H best accounts for the data, the system declares that a
0
target was not present at the range, angle, or Doppler coordinates of that
measurement; if H best accounts for the data, the system declares that a target
1
was present. 1
Because the signals are described statistically, the decision between the
two hypotheses is an exercise in statistical decision theory. A general approach
to this problem is described in many texts (e.g., Kay, 1998). The analysis starts
with a probability density function (PDF) that describes the measurement to be
tested under each of the two hypotheses. If the sample to be tested is denoted as

y, the following two PDFs are required:

p (y|H ) = PDF of y given that a target was not present
0
y
p (y|H ) = PDF of y given that a target was present
1
y
Thus, part of the detection problem is to develop models for these two PDFs. In
fact, analysis of radar performance is dependent on estimating these PDFs for
the system and scenario at hand. Furthermore, a good deal of the radar system
design problem is aimed at manipulating these two PDFs in order to obtain the

most favorable detection performance.
More generally, detection will be based on N samples of data y forming a
n
column vector y

(6.1)

The N-dimensional joint PDFs p (y|H ) and p (y|H ) are then used.
0
y
1
y
Assuming the two PDFs are successfully modeled, the following
probabilities of interest can be defined:

Probability of The probability that a target is declared (i.e., H is
1
Detection, P : chosen) when a target is in fact present.
D