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These results take into account the point-to-point connections between all the nodes of the network.
Perfect synchronization between all the nodes is assumed so the cross correlation between the sensor nodes is almost zero because the spreading sequences is totally orthogonal.
The basic idea is to pre-compute the shortest distances between all the nodes and selected landmarks and then apply the triangle inequality to help estimate the shortest path distance.
If we now compare the hop count for all the point-to-point connections between all the nodes, we notice that the maximum hop count is reduced from 14 to 8 hops.
The first was characterized by the use of AWGN channels between all the nodes: from TS to the RTS and RS nodes, between the RTS nodes, and between the K−1th RTS node and the RS node.
The cooperative communication between all the nodes (depicted in Figure 1 for N = 4) is performed over a total of 2N time slots and is split into two phases (N time slots each): (a) the broadcasting phase (BP) and (b) the cooperation phase (CP).
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We randomly generate the channel matrices between all the node pairs with each of their entries being i.i.d.i.d
We assume that the traffic flow between all the node pairs in the network is uniform and that the processes of new packet arrival at the different nodes are independent.
The comparison between such distribution and the distribution of distances between all the node pairs in the network (Figure 5, left) reveals that the process of social partner selection is biased towards the topological vicinity of the user.
Accordingly, the sink node will collect position data and compute distances between all the pairs of nodes.
Also, those links are not directly established because its impossible to find a shared key between all the pairs of nodes.
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