of a false alarm for a variety of different thresholds. Based on given requirements and machine learning techniques that count for the dynamics of the sensed environments, a close‐to‐optimal threshold can be reached. Figure 3.2 exemplifies different ROC curves for different SNIR values using the equations above. SNIR is defined as the ratio of the sensed signal power to noise power Figure 3.2 Different ROC curves for different SNIR (not to scale).
One can see from Figure 3.2 that as SNIR increases,6 we can achieve higher PD at lower PF. While one can see the same tendency in demodulation and decoding of a signal where higher SNIR results in less symbol error probability, it is critical to understand that this energy detection process relies on estimating the noise variance. Noise power estimation error can cause significant performance loss (significant shift in λE in Figure 3.1). Noise level can be estimated dynamically and more accurately if the spectrum sensor is able to separate the noise subspace from the signal subspace. Some sensors estimate noise variance as the smallest eigenvalue of the sensed signal's autocorrelation. This estimated noise variance can then be used to find the decision threshold λE that satisfies the requirements for a given false alarm rate. This noise estimation algorithm is applied iteratively, where N can be a moving average window that continuously normalizes the noise power.
In addition to noise power estimation, a machine learning technique7 that uses the ROC model can leverage the following techniques to tune the decision threshold:
1 Measure the success of its own decisions.8
2 Take into consideration external variables such as emitter power, emitter distance to the sensor, terrain, rain, and fog that can affect SNIR.
3 Increase accuracy by increasing the number of decision samples. Cooperative distributed DSA and centralized DSA techniques can be looking at more comprehensive information than a single node to make the ROC estimation more accurate.
The purpose of using the above three techniques is to make the DSA system able to adapt the decision threshold to adhere to the same PD at the same given requirement of PF even with the increase of uncertainty.
Example: Evaluation Metrics and ROC Design for Different Applications
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 PD is the probability of hypothesizing the presence of the sensed signal given that the sensed signal is present, PF is the probability of hypothesizing the presence of the sensed signal given that the sensed signal was not present, and Pm 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 PD, PF, and Pm 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 λE. 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.
3.2 Adapting the ROC Model for Same‐channel in‐band Sensing
Same‐channel in‐band sensing use of the ROC model has some factors that can make the hypothesizing process more accurate but also has its own challenges. As mentioned in Chapter 2, with same‐channel in‐band sensing, the receiver can have a clear dwell time in the presence of the communications signal and a clear dwell time in the absence of the communication signal. For example, if we have
