# Energy Efficient Multicast Communication in Cognitive Radio Wireless Mesh Network
## 4 Proposed Technique  
The overall energy consumption \(E[k]\) for a multicast session \(k\) is the sum of energy consumed by the different local forwarding operations belonging to the multicast tree constructed for that session. Each forwarding operation can be represented by a hyperlink. Thus, \(E[k]\) for a multicast session \(k\) can be reduced by minimizing the number of local forwarding operations/hyperlinks. In multicast CR-WMNs, the hyperlinks for a multicast session can be minimized by covering more receiving nodes in a hyperlink, either by assigning a suitable multicast channel or selecting the forwarding nodes. Figure 1a illustrates how channel assignment can help to reduce hyperlinks. Node A has four available channels, i.e., CA = {1, 2, 3, 4} and three neighboring nodes, i.e., B, C, and D. The available channels at nodes B, C, and D are {2, 3}, {3, 4}, and {1, 2}, respectively. The distance between node A and nodes B, C, and D means a single channel cannot be used to cover them because of channel heterogeneity. It can be observed that there does not exist a single channel that node A has in common with all three nodes. Thus, node A must use multiple channels to achieve this one hop multicast. Several different realizations are possible, among them, two are shown in Figure 1a,b. In Figure 1a, node A uses three channels (1, 2, 3), thus there are three hyperlinks, i.e., {{A, 3, {B}, {A, 2, {C,}, {A, 1, {D}}}. However, Figure 1b uses two channels to cover all three nodes resulting in two hyperlinks, i.e., C\({}_{\text{A}}\) = {1, 2, 3}; C\({}_{\text{B}}\) = {2, 3}; C\({}_{\text{C}}\) = {3, 4}; C\({}_{\text{D}}\) = {1,2}. According to the energy consumption model presented in (1), the energy consumed for a one hop multicast in Figure 1a is \(3(E^{t}+E^{c})+4E^{r}\), whereas the energy consumed for the second case is \(2(E^{t}+E^{c})+4E^{r}\). Hence, by assigning the appropriate channel, the number of hyperlinks can be reduced resulting in a reduction of overall energy consumption. The example given in Figure 2 illustrates how the selection of forwarding nodes can help reduce hyperlinks in multicasts in CR-WMNs. Here, assume the same channels are available at each node and ignore spectrum heterogeneity. A multicast session with source node A and destination nodes E, F, and G is used. Assume that, based on distance, node B neighbors nodes E and F, node C neighbors nodes E, F, and G, node D neighbors nodes F and G, and vice versa. Any node neighbor to nodes E, F, and G can be a forwarding node for them based on which different realizations of hyperlinks are possible, out of which two are shown in Figure 2a,b. In Figure 2a, nodes B, C, and D are forwarding nodes for nodes E, F, and G, respectively, which results in three overall hyperlinks, i.e., {[B, 1, {E}, {C, 2, {F}, {D, 3, {G}}}, whereas there is only one hyperlink {[C, 1, {E, F, G} in Figure 2b for this one hop multicast. According to the energy consumption model presented in (1), the energy consumed for a one hop multicast in Figure 1a is \(3(E^{t}+E^{c})+4E^{r}\), whereas the energy consumed in the second case is \(2(E^{t}+E^{c})+4E^{r}\). Hence, by selecting the appropriate forwarding node, the number of hyperlinks can be reduced resulting in a reduction of overall energy consumption. Figure 1: (**a**) Node A uses three channels {1, 2, 3}. (**b**) Node A uses two channels {1, 2}. In this work, based on the joint consideration of the illustrated concepts, we proposed a heuristic algorithm to construct a minimum energy consumption-based multicast tree in CR-WMNs. For each session \(k\), a node level is defined initially. Each node level is the least number of hops it has from the source node ranging from 0 to L, where level 0 is assigned to the source node and level L to the leaf nodes. For example, in Figure 3, node level is defined as ranging from L = 0 to L = 3. A is the source node and is assigned a level L = 0 and E and F are the leaf nodes and are assigned level L = 3.