probability of detection and the probability of false alarm of this decision fusion process corresponding to Equations (3.17) and (3.18) can be expressed as:
3.21
3.22
where MVn is a vector normalization of the different vectors M from Equation (3.2) for the different RF neighbors when the transmitting signal is not detected.
Notice in Equations (3.19,3.20,3.21,3.22) that the term λEvn is used to indicate both vector normalization of the different RF neighbors decision thresholds but also indicates the adaptation of the decision threshold to the dynamics of the MANET where factors such as transmission power, geolocation of RF neighbors, terrain, rain, and fog are used by the machine learning process to adapt the decision threshold.
In a hybrid distributed cooperative MANET system that uses local fusion and distributed decisions, the MANET nodes would share information that includes the result of hypothesizing the presence of interference and the direction of the detected interference such that an accurate spectrum map can be made available to every node in the network. With hybrid heterogeneous network systems that use centralized spectrum managers, the centralized spectrum manager can create the most accurate spectrum map of the area of operation based on the fusions and decisions done at all the networks and also based on its own further decision fusion that can further fine‐tune the direction and boundaries of interference based on how each network perceives interference directions.
3.3.1.2 Local Decision Fusion with Directional Energy Detection
While Section 3.3.1.1 showed how the same‐channel in‐band ROC model can grow from the two‐threshold model to adding the RF neighbor dimension, this section shows that for the simple energy detection case illustrated in Figure 3.1 one can add the directionality dimension if the spectrum sensor is able to use a multisector antenna. Note that the single‐threshold simple energy detection model, which can be utilized by an augmented sensor, has no consideration of an RF neighbor as the same‐channel in‐band case does. Directional energy detection can be done by a secondary user that has a directional antenna and can transmit directionally and thus would sense the primary user signal directionality as well as the primary user signal energy level.
Let us illustrate this case with the 12‐sector antenna layout shown in Figure 3.8 where each sector is a 30° angle. Each sector senses energy independently from other sectors. The spectrum sensor would apply a single threshold ROC model per each sector and hypothesize the presence of a primary user per each sector independently.
Figure 3.8 Directional sensing with multisector antenna.
First, the antenna sectors can be expressed as a matrix
(3.23)
If the ROC model of two neighboring sectors hypothesizes the presence of the primary user at a given time, there will be some spectrum sensing overlapping and we can express that state as a union of the two sectors. For example, when sectors 0 and 1 hypothesize the presence of the primary user simultaneously, we have a union that can be expressed as ∪ {S0, S1}. Similarly, when sectors 0, 1, and 2 hypothesize the presence of the primary user simultaneously, we create ∪ {S0, S1,S2}. The omni‐state O when all the sectors hypothesize the presence of the primary user simultaneously can be expressed as:
(3.24)
At any given time, the secondary user would want to decide not to emit spectrum at given sectors as it will interfere with the primary user. In order for the secondary user to reach this decision, it has to fuse the hypotheses of the different sectors. The outcome of the decision fusion process is a filter matrix that can eliminate the use of certain antenna sectors. This elimination matrix can be expressed as:
(3.25)
where 1 means the sector can emits spectrum to the destination secondary user and Φ means the sector cannot emit spectrum to the destination secondary user.
Note that this decision fusion to reach Equation (3.25) is not straightforward and it requires the consideration of other factors such as the side lobes of the secondary user emitted spectrum. Figure 3.9 shows an example of the spectrum emitted by a single sector of the 12‐sector antenna depicted in Figure 3.8 and how it is not purely directional. The side and back lobes and the beam width depend on the frequency range, among other factors. For that reason, the union expressions leading to Equation (3.24) are critical in deciding if a sector can be used or not. A simple decision approach would be to consider that the neighboring sectors and the sector at 180° may also emit spectrum in the elimination matrix in Equation (3.25). Another factor to consider is the power emission. If the secondary user has to always consider emitting a signal at relatively low energy to the primary user signal such that the side and back lobes impact in Figure 3.9 is minimal, consideration of neighboring sectors would differ and the number of elements with 1 in the matrix in Equation (3.25) would increase.
Figure 3.9 Example of a single‐sector radiation pattern corresponding to the multi‐sector antenna in Figure 3.8.
Now that we have shown cases for further local decision fusion concepts building on the ROC models, let us move to distributed and centralized decsion fusion that can make the decision fusion results more accurate.
