Energy-efficient relay selection for multicast traffic

We consider the problem of multicasting from a single source to a set of destinations. We assume that the source cannot reach the destinations directly, but must forward its traffic through a set of relays. Under the performance objective of maximizing the common amount of information (number of bits) that the source sends to all destinations per Joule of the total energy spent, we wish to obtain a policy that identifies: a) which subset of the relays should be activated, b) for how long, and c) the respective destinations that each relay has to serve. We consider centralized policies with exact knowledge of the channel conditions. In the special case of a network with two relays we show that for any fixed assignment of destinations to relays the problem of maximizing the number of bits per Joule by choosing the duration that each relay should be activated can be formulated as a convex optimization problem. However, since the problem of assigning destinations to relays remains combinatorially complex, we then present an algorithm with reduced complexity that exploits the knowledge of the underlying channel conditions. Finally, we provide a set of numerical results to illustrate the optimal relay selection and assignment of destinations to relays corresponding to different channel conditions.