Energy-efficient rate balancing in vector broadcast channels with linear transceivers

We consider the minimization of the energy per bit (or, equivalently, the maximization of the energy efficiency) in a multiple-input single-output (MISO) broadcast channel with rate balancing constraints, i.e., in a multiuser system where certain fixed ratios between the rates of the various users have to be kept. This paper deals with the practically relevant case where the transmit strategy is restricted to simple linear filtering without time-sharing, i.e., sophisticated coding schemes such as dirty paper coding (DPC) are not allowed. Even though the arising optimization problem is non-convex, it can be solved with reasonable complexity in a globally optimal manner using the algorithm proposed in this paper. This globally optimal solution enables us to study the impact of rate balancing constraints on the energy efficiency of a vector broadcast channel in numerical simulations.