Читать книгу Dynamic Spectrum Access Decisions - George F. Elmasry - Страница 51

Equations (3.5) and (3.6) express the probability of detection and the probability of false alarm, respectively, for a single threshold ROC model. A third probability calculation could be the probability of misdetection. If we are to evaluate the accuracy of this hypotheses‐based decision making, we could create the following three metrics:

(3.10)

(3.11)

(3.12)

where P_D is the probability of hypothesizing the presence of the sensed signal given that the sensed signal is present, P_F is the probability of hypothesizing the presence of the sensed signal given that the sensed signal was not present, and P_m is the probability of hypothesizing the absence of the sensed signal given that the sensed signal was present.

Notice that there is a fourth possibility that is irrelevant to performance evaluation. Table 3.1 shows the four cases of signal presence and absence versus hypotheses with the “N, N” case (the signal is not present and the sensor did not detect it) being irrelevant.⁹

Table 3.1 Signal presence versus hypotheses.

Signal presence	Hypotheses	Evaluation metric
Y	Y	P D
Y	N	P F
N	Y	P m
N	N	N/A

The P_D, P_F, and P_m metrics can be used to measure the efficiency of the decision‐making process given some design requirements. Notice that:

(3.13)¹⁰

Although¹⁰ Equations (3.10)–(3.13) can apply to different systems, the system under design should influence how a machine‐learning algorithm would estimate λ_E. Let us consider the following two cases:

 Case 1: A commercial communication system of a secondary user attempting to opportunistically use the primary user spectrum. In this case, a higher probability of false alarm can be acceptable as the higher probability of misdetection can cause the secondary user to interfere with the primary user.11 With this case, the design of the machine learning algorithm would accept a higher probability of false alarm to minimize the probability of misdetection.

 Case 2: A military MANET system that can operate in an antijamming mode and the formed MANET can switch to a different waveform type only if the interference level is too high. With this case, a higher probability of misdetection may be acceptable since the antijamming waveform can operate in the presence of some level of interference. With this case, the design of the machine learning algorithm may target a higher probability of misdetection to minimize the probability of false alarm.