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Receiver operating characteristic curves by SNR


[Pd,Pfa] = rocsnr(SNRdB)
[Pd,Pfa] = rocsnr(SNRdB,Name,Value)


[Pd,Pfa] = rocsnr(SNRdB) returns the single-pulse detection probabilities, Pd, and false-alarm probabilities, Pfa, for the SNRs in the vector SNRdB. By default, for each SNR, the detection probabilities are computed for 101 false-alarm probabilities between 1e–10 and 1. The false-alarm probabilities are logarithmically equally spaced. The ROC curve is constructed assuming a coherent receiver with a nonfluctuating target.

[Pd,Pfa] = rocsnr(SNRdB,Name,Value) returns detection probabilities and false-alarm probabilities with additional options specified by one or more Name,Value pair arguments.

rocsnr(...) plots the ROC curves.

Input Arguments


Signal-to-noise ratios in decibels, in a row or column vector.

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.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.


Maximum false-alarm probability to include in the ROC calculation.

Default: 1


Minimum false-alarm probability to include in the ROC calculation.

Default: 1e-10


Number of false-alarm probabilities to use when calculating the ROC curves. The actual probability values are logarithmically equally spaced between MinPfa and MaxPfa.

Default: 101


Number of pulses to integrate when calculating the ROC curves. A value of 1 indicates no pulse integration.

Default: 1


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].

Default: 'NonfluctuatingCoherent'

Output Arguments


Detection probabilities corresponding to the false-alarm probabilities. For each SNR in SNRdB, Pd contains one column of detection probabilities.


False-alarm probabilities in a column vector. By default, the false-alarm probabilities are 101 logarithmically equally spaced values between 1e–10 and 1. To change the range of probabilities, use the optional MinPfa or MaxPfa input argument. To change the number of probabilities, use the optional NumPoints input argument.


collapse all

Plot ROC curves for different SNR's for a single pulse.

SNRdB = [3 6 9 12];
[Pd,Pfa] = rocsnr(SNRdB,'SignalType','NonfluctuatingCoherent');
grid on
legend('SNR 3 dB','SNR 6 dB','SNR 9 dB','SNR 12 dB',  'location','northwest')
title('Receiver Operating Characteristic (ROC) Curves')

Figure contains an axes object. The axes object with title Receiver Operating Characteristic (ROC) Curves contains 4 objects of type line. These objects represent SNR 3 dB, SNR 6 dB, SNR 9 dB, SNR 12 dB.


[1] Richards, M. A. Fundamentals of Radar Signal Processing. New York: McGraw-Hill, 2005, pp 298–336.

Extended Capabilities

Version History

Introduced in R2011a