Receiver Operating Characteristic (ROC) curves present graphical summaries of a detector's performance. You can generate ROC curves using the
If you are interested in examining the effect of varying the false-alarm probability on the probability of detection for a fixed SNR, you can use
rocsnr. For example, the threshold SNR for the Neyman-Pearson detector of a single sample in real-valued Gaussian noise is approximately 13.5 dB. Use
rocsnr to plot the probability of detection varies as a function of the false-alarm rate at that SNR.
T = npwgnthresh(1e-6,1,'real'); rocsnr(T,'SignalType','real')
The ROC curve lets you easily read off the probability of detection for a given false-alarm rate.
You can use
rocsnr to examine detector performance for different received signal types at a fixed SNR.
SNR = 13.54; [Pd_real,Pfa_real] = rocsnr(SNR,'SignalType','real',... 'MinPfa',1e-8); [Pd_coh,Pfa_coh] = rocsnr(SNR,... 'SignalType','NonfluctuatingCoherent',... 'MinPfa',1e-8); [Pd_noncoh,Pfa_noncoh] = rocsnr(SNR,'SignalType',... 'NonfluctuatingNoncoherent','MinPfa',1e-8); semilogx(Pfa_real,Pd_real) hold on grid on semilogx(Pfa_coh,Pd_coh,'r') semilogx(Pfa_noncoh,Pd_noncoh,'k') xlabel('False-Alarm Probability') ylabel('Probability of Detection') legend('Real','Coherent','Noncoherent','location','southeast') title('ROC Curve Comparison for Nonfluctuating RCS Target') hold off
The ROC curves clearly demonstrate the superior probability of detection performance for coherent and noncoherent detectors over the real-valued case.
rocsnr function accepts an SNR vector input letting you quickly examine a number of ROC curves.
SNRs = (6:2:12); rocsnr(SNRs,'SignalType','NonfluctuatingNoncoherent')
The graph shows that, as the SNR increases, the supports of the probability distributions under the null and alternative hypotheses become more disjoint. Therefore, for a given false-alarm probability, the probability of detection increases.
You can examine the probability of detection as a function of SNR for a fixed false-alarm probability with
rocpfa. To obtain ROC curves for a Swerling I target model at false-alarm probabilities of (1e-6,1e-4,1e-2,1e-1), use
Pfa = [1e-6 1e-4 1e-2 1e-1]; rocpfa(Pfa,'SignalType','Swerling1')
rocpfa to 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)');