Performance Analysis of Large Multiuser MIMO Systems With Space-Constrained 2-D Antenna Arrays

Massive multiple-input-multiple-output (MIMO) systems deploying a large number of antennas at the base station (BS) have been shown to produce high spectral and energy efficiency (EE) under the assumptions of increasing BS physical space and critical antenna spacing. We examine the deployment of massive MIMO systems and resulting EE with a more realistic scenario considering a 2-D rectangular array with increasing antenna elements within a fixed physical space. Mutual coupling and correlation among the BS antennas are incorporated by deriving a practical mutual coupling matrix which considers coupling among all antenna elements within a BS. We also provide a realistic analysis of the energy consumption using a model, which takes into account the circuit power consumptions as a function of the number of BS antennas and then present a performance analysis of two practical low complexity detectors/receivers keeping EE into consideration. The simulation results obtained show that EE does not monotonically increase with the number of BS antennas. On the contrary, it is a decreasing concave or quasi-concave function of the number of BS antennas depending on the detection technique used at the receiver. We also show that with decreasing spacing between the antennas, mutual coupling increases, contributing toward reduction in EE. Our analysis thus shows that EE does not increase infinitely in a massive MIMO system when the increasing number of antennas are to be accommodated within a fixed physical space and the total power consumed is considered to be a function of the antennas. Accordingly, closed-form expressions for the optimum number of antennas to attain maximum EE for zero forcing (ZF) are obtained.