Optimal Relay Selection for Energy-Efficient Multicast

Abstract

We consider multicast transmission from a single source to multiple destinations. We assume that the source cannot reach the destinations directly, but must forward its traffic through a set of assisting relay nodes. The performance objective under consideration is to maximize the common amount of information (number of bits) that the source delivers to all destinations per joule of the total energy spent. Our aim is 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 networks employing at most 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. Unfortunately, the problem of assigning destinations to relays is combinatorially complex. Thus, in the sequel we present a method with reduced complexity that exploits the knowledge of the underlying channel conditions to perform this assignment. 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.