Energy-spectral efficiency trade-off for a massive SU-MIMO system with transceiver power consumption

We consider a single user (SU) massive MIMO system with multiple antennas at the transmitter (base station) and a single antenna at the user terminal (UT). Taking transceiver power consumption into consideration, for a given spectral efficiency (SE) we maximize the energy efficiency (EE) as a function of the number of base station (BS) antennasM, resulting in a closed-form expression for the optimal SE-EE trade-off. It is observed that in contrast to the classical SE-EE trade-off (which considers only the radiated power), with transceiver power consumption taken into account, the EE increases with increasing SE when SE is sufficiently small. Further, for a fixed SE we analyze the impact of varying cell size (i.e., equivalently average channel gain Gc) on the optimal EE. We show the interesting result that for sufficiently small Gc, the optimal EE decreases as O(√Gc) with decreasing Gc. Our analysis also reveals that for sufficiently small SE (or large Gc), the EE is insensitive to the power amplifier efficiency.