rocpfa

Receiver operating characteristic curves by false-alarm probability

Syntax

[Pd,SNR] = rocpfa(Pfa)

[Pd,SNR] = rocpfa(Pfa,Name=Value)

rocpfa(...)

Description

[Pd,SNR] = rocpfa(Pfa) returns the single-pulse detection probabilities, 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.

[Pd,SNR] = rocpfa(Pfa,Name=Value) returns detection probabilities and SNR values with additional options specified by one or more name-value arguments.

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

NumPoints — Number of SNR values to use when calculating the ROC curves

101 (default) | positive integer

Number of SNR values to use when calculating the ROC curves, specified as a positive integer. The actual values are equally spaced between MinSNR and MaxSNR.

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, P_D, for a given false-alarm probability, P_FA is:

$$P_D=\frac{1}{2}\text{erfc}({\text{erfc}}^{-1}(2P_{FA})-\sqrt{\chi })$$

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

Signal-to-noise ratios, returned as a column vector. By default, the SNR values are 101 equally spaced values between 0 and 20. To change the range of SNR values, use the optional MinSNR or MaxSNR input argument. To change the number of SNR values, use the optional NumPoints input argument.

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