A Rendezvous Protocol with the Heterogeneous Spectrum Availability Analysis for Cognitive Radio Ad Hoc Networks

Figure 3

Example of mirror torus QS: 𝐴 and 𝐵 initiate their tail selection in a backward manner; that is, the first element of node A is selected from column 𝐶₅ (a mirror of 𝐶₇), and the one of node 𝐵 is selected from column 𝐶₃ (a mirror of 𝐶₅). Then, both nodes select the next tail element in a forward manner, thus from 𝐶_𝑗+2 column, which is 𝐶₈ in case of node 𝐴, and 𝐶₆ in case of node B. The third tail element is selected in a backward manner, which is 𝐶₃ in case of node 𝐴, and 𝐶₁ in case of node 𝐵. The last element of nodes 𝐴 and 𝐵 falls in the same (mirror) column. Nodes meet at slot 5 (they would meet in one element of column 𝐶₆ anyway) and additionally in slot 18. Hence, nodes can always alternate the manner, either forward or backward, while picking up elements; however, they need to have the same 𝑘_𝑖, in this example 𝑘_𝑖={−1,1,−1,{1∣−1}}, where 𝑖=1⋯⌊8/2⌋.