  Aiming at maximizing the energy efficiency (EE) of multicast multibeam
satellite communications, we consider the precoding design under the total
power and quality of service (QoS) constraints. Since the original EE
maximization problem is nonconvex, it is sequentially converted into a
concave-convex fractional programming problem by introducing some variables and
using the first-order Taylor low bound approximation. Based on the
Charnes-Cooper transformation, it is further converted into a convex problem.
Then an iterative algorithm is presented to design the energy efficient
precoding. To find feasible initialization points for the algorithm and ensure
its convergence, another convex optimization problem with some nonnegative
slack variables and a positive penalty parameter is iteratively solved. In
particular, the algorithm is verified by the measured channel data of multibeam
satellite communications.
