Energy efficient multi-pair transmission in large-scale multi-antenna relay systems

A multi-pair large-scale multi-antenna relaying system is considered in this paper. We investigate the energy efficiency (EE) performance by taking the circuit power consumption into account when maximum ratio combining/maximum ratio transmission is explored at the relay station (RS). By utilizing the law of large numbers, an analytical expression of EE is derived. Based on this, we characterize the trend of EE with regard to the transmit power of the users and the RS, and the number of RS antennas. Regarding to the transmit power at users and RS, it is shown that the optimal EE can be always achieved by an unique globally transmit power set. Furthermore, an iterative algorithm is proposed to obtain the globally optimal solution. The analysis also demonstrates that the EE function is quasiconcave with respect to the RS antenna number when the circuit power is comparable to the transmit power, based on which we obtain the optimal solution in closed form to the number of antennas for RS. When the circuit power is negligible compared with high transmit power, the EE has a nearly logarithmic increase with the number of RS antennas. All the analytical results are verified by the numerical simulations.