Energy Efficient Design of Massive MIMO: How Many Antennas?

We provide explicit formulas for the optimal number of antennas per base station to maximize the cell total energy efficiency of a power- controlled multi-cell Massive MIMO. Furthermore, we show that equipping the same number of antennas in each base station results in virtually no loss in energy efficiency due to the flatness of energy efficiency function. Conjugate beamforming compares very competitively with zero-forcing and in fact, due to the loss in effective array gain and the additional computational cost in zero-forcing, conjugate beamforming can achieve better energy efficiency when per user throughput demand is moderate. In single cell case, we provide explicit algebraic formulas for the optimal number of antennas and optimal radiated power when a target per user throughput is given.