Energy efficient relay assisted wireless multicast system

In this paper, the optimization based on energy efficiency in a relay assisted wireless multicast system, where a single source communicates with multiple destinations with the help of an amplify-and-forward relay, is proposed. We assume that the source cannot reach the destinations directly, and thus the relay forwards the signal in two hops. Under the performance objective of maximizing the number of bits that the source sends to all destinations per Joule of the total energy spent, we formulate the optimization problem based on high SNR approximation, and prove that the problem can be extended to a standard Geometric Programming (GP) problem, which is a well-studied class of nonlinear and nonconvex optimization and has regular solutions. Finally, we provide a set of numerical results to illustrate energy efficiency corresponding to different channel conditions.