Closed-Form Optimal Power Allocation for Weighted Rate Sum Maximization in Gaussian Broadcast Channel

This paper is motivated by optimal adaptive resource allocation policies at the base station in wireless communication systems, and we particularly study the maximization of the weighted rate sum in Gaussian broadcast channel. The problem of finding the optimal power allocation in Gaussian broadcast channel is non-convex and intractable to solve using traditional methods with low complexity. In this paper, we derive a closed-form optimal solution of the weighted rate sum maximization in Gaussian broadcast channel. The derived closed-form optimal solution can give the optimal power allocation for the weighted rate sum maximization one time and does not need to determine the water level and iterative process. Thus, it is very easy to be implemented with an adaptive power allocation in the real communication systems.