Energy-efficient zero-forcing with user selection in parallel vector broadcast channels

We consider the maximization of the energy efficiency (or, equivalently, the minimization of the energy per bit) in a set of parallel multiple-input single-output (MISO) broadcast channels (e.g., in the downlink of a multiuser multicarrier system). For a given allocation of users to subchannels, the problem is strictly-quasiconvex and can be efficiently solved by introducing a continuous, differentiable, and concave waterfilling-rate function. To optimize the user allocation, we adopt successive allocation schemes that have been formerly applied to the problem of sum rate maximization. In numerical simulations, we compare different allocation schemes, and we demonstrate that a fixed sum transmit power can lead to a significant loss in energy efficiency if the fixed value is either too high or too low.