Читать книгу Dynamic Spectrum Access Decisions - George F. Elmasry - Страница 60

This appendix describes the ROC model in simple terms to give the reader who is not familiar with the different statistical decision concepts related to ROC models a basic understanding of the model characteristics. The ROC plots are well studied in multiple fields where two basic evaluation measures are needed. These evaluation measures are referred to as sensitivity and specificity in some fields. With DSA, sensitivity is known as the probability of detection of the sensed signal while specificity is known as the probability of false alarm indication of the sensed signal. Any DSA design has to consider a tradeoff between these two evaluation measures. Signal measurements in some cases can lend higher probability of detection at lower probability of false alarm, but the tradeoff always exist.

Figure 3A.1 Ideal labeling of a dataset.

Let us consider a dataset where the values in the dataset can be classified as positive (P) or negative (N). As shown in Figure 3A.1, all the values in the dataset ideally can be classified as P or N.

An observer classifying the dataset into P or N may create four outcomes, as shown in Figure 3A.2. The four outcomes are true positive (TP), true negative (TN), false positive (FP), and false negative (FN). Notice that the observer hypothesizes the positive and negative value creating the FP and FN events.

Figure 3A.2 A classifier outcome of the dataset.

The idea behind the ROC model is to create plots such that one axis specifies the false positive rate while the other axis specifies the false negative rate,²⁶ as shown in Figure 3A.3.

Figure 3A.3 Specifying FP and FN rates.

Let us assume that our ROC model plots the false positive (specificity) rate as the x axis and false negative (sensitivity) rate as the y axis. We refer to this ROC model as the ROC space and it is a two‐dimensional space that allows us to create the tradeoff needed in DSA design. A DSA decision‐making process is a classifier in the ROC space.