Joint protocol and relay node selection in collaborative networks

We consider a multi-hopping communication network of users transmitting information on a shared medium with limited resources, e.g., limited time and limited bandwidth. We assume that two users collaborate (one acts as a relay for another) only if, as a result of the collaboration, they gain more capacity, save on resources or save power.We perform optimal resource allocation for three problems: 1) maximizing the capacity given limited resource and energy, 2) minimizing the resource usage given capacity and energy and 3) minimizing energy usage given capacity and resources. By comparing the collaboration gain as a function of the channels and available energies, one may decide either to collaborate or not and select a collaborator among candidates. We show that a significant gain is attained only if the channel energy gain of one of the users is significantly smaller than those of other involved links. Depending on the channel conditions, there is a given capacity gain ratio that may be obtained, where eta is the environment path loss exponent. We show that the energy minimizing problem is the dual of the capacity maximizing problem. Also we show that users requiring low capacity might not gain more resources from possible collaboration.