Dynamic Spectrum Access Decisions. George F. Elmasry

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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 P_D at lower P_F. 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 λ_E 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 λ_E 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:

      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 P_D at the same given requirement of P_F 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 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.

      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:

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 СКАЧАТЬ