Energy-efficient multi-cell massive MIMO: How many antennas should we use?

In this paper, we investigate resource optimization for energy-efficient data transmissions in a multi-cell massive multiple-input multiple-output (MIMO) system with zero-forcing (ZF) detectors. We optimize the number of active antennas per BS so as to maximize the energy efficiency (EE) of uplink data transmissions. To model the bit-per-joule EE objective, we consider throughput rate and power expenditure expressions which incorporate the effect of pilot contamination and non-zero circuit power consumption at the BS and the users. The resulting optimization problem is an integer fractional programming problem, which is non-convex and is difficult to solve in its original form. Therefore, a novel solution methodology is proposed, wherein principles from fractional programming are used to transform the original problem into a parametric form and then, to derive an iterative EE-maximization algorithm. During each iteration, the problem in parametric form is transformed into a discrete monotonic optimization problem, which is then solved using polyblock outer approximation. For a wide range of traffic loads, simulation results show that the proposed EE-maximization scheme achieves significantly higher EE levels when compared to conventional schemes with full antenna activation, particularly if the number of antennas deployed per BS is excessively large.