  This letter studies the energy-efficient design in a downlink multi-antenna
multi-user system consisting of a multi-antenna base station (BS) and multiple
single-antenna users, by considering the practical non-linear power amplifier
(PA) efficiency and the on-off power consumption of radio frequency (RF) chain
at each transmit antenna. Under this setup, we jointly optimize the transmit
beamforming and antenna on/off selection at the BS to minimize its total power
consumption while ensuring the individual signal-to-interference-plus-noise
ratio (SINR) constraints at the users. However, due to the non-linear PA
efficiency and the on-off RF chain power consumption, the formulated
SINR-constrained power minimization problem is highly non-convex and difficult
to solve. To tackle this issue, we propose an efficient algorithm to obtain a
high-quality solution based on the technique of sequential convex approximation
(SCA). We provide numerical results to validate the performance of our proposed
design. It is shown that at the optimized solution, the BS tends to activate
fewer antennas and use higher power transmission at each antenna to exploit the
non-linear PA efficiency.
