Energy Efficiency Scaling Law of Massive MIMO Systems

Massive multi-input multi-output (MIMO) can support high spectral efficiency with simple linear transceivers, and is expected to provide high energy efficiency (EE). In this paper, we analyze the scaling laws of EE with respect to the number of antennas M at each base station of downlink multi-cell massive MIMO systems under spatially correlated channel, where both transmit and circuit power consumptions, channel estimation errors, and pilot contamination (PC) are taken into account. We obtain the maximal EE for the systems with maximum-ratio transmission and zero-forcing beamforming for given numbers of antennas and users by optimizing the transmit power subject to the minimal data rate requirement and maximal transmit power constraint. The closed-form expressions of approximated EE-maximal transmit power and maximal EE, and their scaling laws with M are derived. Our analysis shows that the maximal EE scales with M in O(log₂ M/M) for the system without PC, and in O(1/M) for the system with PC. The EE-maximal transmit V power scales up with M in O(√(M/ln M)) until reaching the maximal transmit power for the system without PC, and in O(1) for the system with PC. The analytical results are validated by simulations under a more realistic 3D channel model.