The Benefit of Co-Locating Groups of Nodes in Cooperative Line Networks

We consider two topologies for the deployment of nodes in a one-dimensional network. The first deployment scenario considers nodes equally spaced on a line, while the second topology has groups of co-located nodes, such that the groups are equally spaced on the line, and such that the two networks have equal average density. In both linear topologies, nodes transmit cooperatively, as opportunistic large arrays, in each hop. The difference is only that in the first topology, the cooperators have disparate path loss, while in the second they do not. We study the multi-hop transmission for both cases, where the one hop distance remains the same for both the topologies. We model both the scenarios with a quasi-stationary Markov chain and show that the co-located groups deployment gives better performance, especially for higher path loss exponents.