Energy-efficient uplink training design for closed-loop MISO systems

When the circuit power consumption and the overhead for channel estimation are taken into account, the system designed for maximizing the spectrum efficiency (SE) does not necessarily yield high energy efficiency (EE). In this paper, we strive to optimize the uplink training length towards maximizing the EE of closed-loop multi-antenna systems under the constraint of the SE. The upper bounds of the system EE and the net downlink SE with channel estimation errors are derived, based on which the optimization problem is proved as convex, and the impacts of signal-to-noise ratio (SNR) and circuit power consumption on the optimal training length are analyzed. Analytical and simulation results show that in general the EE-oriented optimization leads to a longer training length than the SE-oriented optimization, and it will reduce to the SE-oriented optimization at high SNR and very low SNR regime, or with very high circuit power consumption.