rocpfa
Receiver operating characteristic curves by false-alarm probability
Description
[
returns the single-pulse
detection probabilities, Pd
,SNR
]
= rocpfa(Pfa
)Pd
, and required SNR
values, 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.Pd
,SNR
]
= rocpfa(Pfa
,Name=Value
)
rocpfa(...)
plots the ROC curves.
Examples
Plot ROC Curves for Different PFAs
Plot ROC curves for false-alarm probabilities of 1e-8
, 1e-6
, and 1e-3
, assuming no pulse integration.
Pfa = [1e-8 1e-6 1e-3];
rocpfa(Pfa,SignalType="NonfluctuatingCoherent")
ROC Curve for Noncoherent Integration
Examine the effect of SNR on the probability of detection for a detector using noncoherent integration with a false-alarm probability of 1e-4. Assume the target has a nonfluctuating RCS and that you are integrating over 5 pulses.
[Pd,SNR] = rocpfa(1e-4,... 'SignalType','NonfluctuatingNoncoherent',... 'NumPulses',5); figure; plot(SNR,Pd); xlabel('SNR (dB)'); ylabel('Probability of Detection'); grid on; title('Nonfluctuating Noncoherent Detector (5 Pulses)');
Input Arguments
Pfa
— False-alarm probabilities
vector
False-alarm probabilities, specified as a row or column vector.
Example: [1e-8 1e-6 1e-3]
Data Types: double
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
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.
Example: MaxSNR=15,NumPoints=64,NumPulses=10
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: 'MaxSNR',15,'NumPoints',64,'NumPulses',10
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.
Data Types: double
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.
Data Types: double
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 1
indicates no pulse integration.
Data Types: double
SignalType
— Type of received signal
"NonfluctuatingCoherent"
(default) | "NonfluctuatingNoncoherent"
| "Real"
| "Swerling1"
| "Swerling2"
| "Swerling3"
| "Swerling4"
This property specifies the type of received signal or, equivalently,
the probability density functions (PDF) used to compute the ROC. Valid
values are: "Real"
,
"NonfluctuatingCoherent"
,
"NonfluctuatingNoncoherent"
,
"Swerling1"
, "Swerling2"
,
"Swerling3"
, and "Swerling4"
.
Values are not case sensitive.
The "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:
where erfc
and
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 [1] .
Data Types: char
| string
Output Arguments
Pd
— Detection probabilities
vector
Detection probabilities corresponding to the false-alarm probabilities,
returned as a vector. For each false-alarm probability in
Pfa
, Pd
contains one column of
detection probabilities.
SNR
— Signal-to-noise ratios
column vector
References
[1] Richards, M. A. Fundamentals of Radar Signal Processing. New York: McGraw-Hill, 2005, pp 298–336.
Extended Capabilities
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.
Version History
Introduced in R2011a
See Also
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