Calculate the true positive rate. Sum the number of true positives and false negatives. Divide the number of true positives by this sum. The result is the true positive rate.
Calculate the false positive rate. Sum the number of false positives and the number of true negatives. Divide the number of false positive by this sum. This is the false positive rate.
Plot the true positive rate against the false positive rate. Realize that you will have a series of true positive and false positive rates, because of the different criteria of the signal detection system. You should be running the system under multiple criteria to accumulate a large set of data. The true positive rate should be the y-axis, whereas the false positive rate should be the x-axis. The plot will look like a logistic function -- like an elbow with the curve at the upper-left.
Calculate the concordance index logistic. This value will be the integral of the curve plotted. This means you have two choices for the calculation method. First, if your statistical software gives you an equation with the plot, you can use calculus directly to compute the integral of that equation over x (the false positive rate) from 0 to 1. Alternatively, you can use the statistical software to calculate the area under the plotted curve. This result will be approximately equal to the mathematical calculation performed earlier.
Interpret the final result (the concordance index logistic) by comparing it to the numbers 0.5 and 1. If it is close to 0.5, it means that your signal detection system is no better than a random system, flipping a coin and making a call based on that random outcome. If it is close to 1, it means your system is particularly sensitive, and can detect the signal with high accuracy. Needless to say, most researchers hope for a concordance index logistic close to 1.