On the Energy-Spectral Efficiency Trade-off of the MRC Receiver in   Massive MIMO Systems with Transceiver Power Consumption
  We consider the uplink of a multiuser massive MIMO system wherein a base station (BS) having $M$ antennas communicates coherently with $K$ single antenna user terminals (UTs). We study the energy efficiency of this system while taking the transceiver power consumption at the UTs and the BS into consideration. For a given spectral efficiency $R$ and fixed transceiver power consumption parameters, we propose and analyze the problem of maximizing the energy efficiency as a function of $(M,K)$. For the maximum ratio combining (MRC) detector at the BS we show that with increasing $R$, $(M,K)$ can be adaptively increased in such a way that the energy efficiency converges to a positive constant as $R \rightarrow \infty$ ($(M,K)$ is increased in such a way that a constant per-user spectral efficiency $R/K$ is maintained). This is in contrast to the fixed $(M,K)$ scenario where the energy efficiency is known to converge to zero as $R \rightarrow \infty$. We also observe that for large $R$, the optimal $(M,K)$ maximizing the energy efficiency is such that, the total power consumed by the power amplifiers (PA) in all the $K$ UTs is a small fraction of the total system power consumption. 
Sudarshan Mukherjee and Saif Khan Mohammed
cs.IT math.IT