Hello,

first, I strongly recommend to have a look at S. M. Kay's book "

Fundamentals of Statistical Signal Processing, Volume II: Detection Theory". It will give you tools to understand detection problems.

To answer your question, I'll try to sum up detection problem:

- You get observations from your sensor (antenna, camera, etc.). The problem is: is there something "interesting" in this observation (e.g. do I get an echo from a possible target, in radar application?) ? This defines the classical binary detection problem (there is something to observe, or there is nothing except noise).

These observations have a random nature, since it is "noisy something" (e.g. noisy echo) or noise only.

- You extract a measure from your observation (energy, correlation, etc.)

- Suppose that you know the nature of the noise (its probability density function PDF for instance) and the nature of the expected signal, then you deduce the PDF of the measures in both presence and absence of the expected signal.

- Deduce from PDF the probability of detection and false alarm as a function of a given threshold, if possible. For instance, if my measure is energy, then I will decide presence of my expected signal if the measure is larger than a threshold.

In matlab, just create to sets of observations: A) signal + noise, and B) noise only. From A), get the Pd, and from B) the Pfa. To do so, set a threshold value, if Measure(A)>threshold, decide good detection, and Measure(B)>threshold, decide false alarm. Draw ROC curves with different threshold values.

The difference you get between matlab and theory may be due to the model of noise and signal, which may lead to simplifications in theoretical derivations.

Note: this is a very brief answer to a very wide question, so I made shortcuts and missed some fundamentals of detection theory such as Neyman-Pearson lemma.

Best regards,

Vincent

Thanku Vincent

Generating a ROC curve is much easier with simulation. What you need to do is vary the detection threshold over a dense grid. For every value of that threshold, determine the number of true and false detections,then plot PD vs PF. So the detection threshold kind of disappears.