Dynamic Spectrum Access Decisions. George F. Elmasry

the antenna sectors can be expressed as a matrix as follows:

      (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, S_1,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.

      3.3.2 Distributed and Centralized Decision Fusion

      Depending on the DSA design, local decision fusion can be communicated to distributed peer nodes or to a centralized arbitrator. Distributed and centralized techniques can estimate a more comprehensive spectrum map of the area of operation. Spectrum awareness can be local (node‐based), distributed (net‐based), or centralized (area‐of‐operation‐based).²³ Spectrum awareness can be expressed as a spatial map showing areas of interference per each frequency band used in the area of operation or can be potentially used.

Let us consider the local interference estimation exemplified in Figure 3.7 for a local node. Let us also consider that this type of directional interference estimation is shared between peer nodes in a distributed cooperative MANET. Each node can fuse the directional spectrum interference estimation communicated from multiple peer nodes to produce a cooperative spectrum map of the area of interference as shown in Figure 3.10. Notice how the estimated interference area can be larger than the actual interference area as spectrum directional fusion may draw a circle around the estimated overlaid triangles.²⁴ If this sensed frequency is the same frequency used by the MANET, cooperative decisions can be made to continue to use the frequency band or switch to a different frequency band based on the results of the decision fusion.

Figure 3.10 Cooperative distributed estimation of area of interference.

Figure 3.11 shows a case where a distributed cooperative MANET DSA technique estimated the interference area of the frequency band in use by the MANET, f₁. The same DSA technique also estimated the (probed) frequency band f₂, which is a potential frequency band to be used by the MANET. If the MANET trajectory²⁵ is as shown in Figure 3.11, the distributed cooperative decision may continue to use f₁ as the MANET will move away from the area where interference of f₁ is detected and avoid using f₂. This decision will occur because probing f₂ as a potential frequency to use informed the DSA technique that the MANET will encounter interference if it is to switch to f₂. The key point here is for the distributed cooperative MANET to overlay estimated interference areas of the frequency band in use with the estimated spatial areas of use of potential frequency bands and consider other factors such as trajectory to make the best spectrum use decision, which may include avoiding f₂ and switching to a third frequency f₃ or staying with f₁. Recall that a good DSA design will attempt to avoid the rippling of DSA decisions.

Figure 3.11 Cooperative estimation of overlay spatial use of different frequency bands.

A centralized arbitrator can start by using a pool of frequency bands to assign to different heterogeneous networks in a spatially separated manner, as shown in the previous chapter in Figure 2.15. Recall that the goal of the centralized arbitrator is to optimize the spatial use of spectrum resources. The challenge a centralized arbitrator faces with a case like Figure 2.15 is when a certain frequency is interfered with in a certain area, which may require tapping into a larger pool of frequency bands. Figure 3.12 shows how the frequency band f₃ can suffer from interference, as illustrated with the background large circle indicating