Energy efficiency optimization in MIMO broadcast channels with fairness constraints

We consider the minimization of the energy per bit (or, equivalently, the maximization of the energy efficiency) in multiple-input multiple-output (MIMO) broadcast channels with rate balancing constraints for fairness between users, and we propose a framework to find the globally optimal energy-efficient solution, which relies on dirty paper coding (DPC). The main idea is to introduce a continuous, differentiable, and concave optimal rate function, which transforms the problem into a convex-concave fractional program in one scalar variable. This not only allows an efficient solution, but also an intuitive interpretation of the method as well as the possibility to extend the method to related problems. In numerical simulations, we compare the energy efficiency with and without fairness constraints.