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.

中文翻译：

---

多用户多波束卫星通信的节能组播预编码

为了最大化组播多波束卫星通信的能效（EE），我们考虑了总功率和服务质量（QoS）约束下的预编码设计。由于原始EE最大化问题是非凸的，通过引入一些变量并使用一阶泰勒下界逼近，将其依次转化为凹凸分数规划问题。在Charnes-Cooper变换的基础上，进一步转化为凸问题。然后提出了一种迭代算法来设计节能预编码。为了找到算法的可行初始化点并确保其收敛，迭代求解另一个具有一些非负松弛变量和正惩罚参数的凸优化问题。特别是，