Energy-efficient uplink training for downlink multi-antenna transmission

The design of uplink training aimed at maximizing the energy efficiency (EE) for time division duplex (TDD) multi-antenna systems was investigated. It was proved that when the channel estimation errors are taken into account, both the upper bounds of EE and spectrum efficiency (SE) are concave functions of the uplink training length, based on which the impacts of signal-to-noise ratio (SNR) and circuit power consumption on the optimal training length were analyzed. Analytical and simulation results show that the EE-oriented optimization reduces to the SE-oriented optimization at high SNR regime. Yet in general scenarios, a longer training signal is necessary to maximize EE compared to that maximizing SE.