Receiver operating characteristic curves by false-alarm probability
[ returns the single-pulse
Pd, and required SNR
SNR, for the false-alarm probabilities
in the row or column vector
Pfa. By default,
for each false-alarm probability, the detection probabilities are
computed for 101 equally spaced SNR values between 0 and 20 dB. The
ROC curve is constructed assuming a single pulse in coherent receiver
with a nonfluctuating target.
returns detection probabilities and SNR values with additional options specified by
one or more name-value arguments.
rocpfa(...) plots the ROC curves.
Plot ROC Curves for Different PFAs
Plot ROC curves for false-alarm probabilities of
1e-3, assuming no pulse integration.
Pfa = [1e-8 1e-6 1e-3]; rocpfa(Pfa,SignalType="NonfluctuatingCoherent")
Pfa — False-alarm probabilities
False-alarm probabilities, specified as a row or column vector.
[1e-8 1e-6 1e-3]
Specify optional pairs of arguments as
the argument name and
Value is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name in quotes.
MaxSNR — Maximum SNR to include in the ROC calculation
20 (default) | positive scalar
Maximum SNR to include in the ROC calculation, specified as a positive scalar.
MinSNR — Minimum SNR to include in the ROC calculation
0 (default) | positive scalar
Minimum SNR to include in the ROC calculation, specified as a positive scalar.
NumPulses — Number of pulses to integrate
1 (default) | positive integer
Number of pulses to integrate when calculating the ROC curves,
specified as a positive integer. A value of
indicates no pulse integration.
SignalType — Type of received signal
"NonfluctuatingCoherent" (default) |
This property specifies the type of received signal or, equivalently,
the probability density functions (PDF) used to compute the ROC. Valid
Values are not case sensitive.
"NonfluctuatingCoherent" signal type assumes
that the noise in the received signal is a complex-valued, Gaussian
random variable. This variable has independent zero-mean real and
imaginary parts each with variance
σ2/2 under the null
hypothesis. In the case of a single pulse in a coherent receiver with
complex white Gaussian noise, the probability of detection,
PD, for a given
false-alarm probability, PFA is:
erfc-1 are the
complementary error function and that function’s inverse, and
χ is the SNR not expressed in decibels.
For details about the other supported signal types, see .
Pd — Detection probabilities
Detection probabilities corresponding to the false-alarm probabilities,
returned as a vector. For each false-alarm probability in
Pd contains one column of
SNR — Signal-to-noise ratios
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
Does not support variable-size inputs.
Supported only when output arguments are specified.
 Richards, M. A. Fundamentals of Radar Signal Processing. New York: McGraw-Hill, 2005, pp 298–336.
Introduced in R2011a