Massive MIMO With Antenna Selection: Fundamental Limits and Applications

Antenna selection is an effective means to address the cost and complexity issues in massive MIMO systems. This paper studies the performance limits of massive MIMO systems under practical antenna selection algorithms. A massive MIMO system is considered in which the transmitter employs only a fixed-size subset of the available antennas with the strongest channel gains. For this setup, the input-output mutual information of the system is shown to be well-approximated by a normal random variable when the number of transmit antennas is large. The mean of this random variable grows proportional to the number of antennas and its variance vanishes in the large-system limit. This behavior of the mutual information generalizes the well-known channel hardening property in massive MIMO systems to the cases with antenna selection. Our investigations show that 90% of the ergodic rate achieved by full antenna selection can be achieved by selecting less than 30% of the transmit antennas. Using large-system analysis, we drive an analytical expression for the number of selected antennas that maximizes the energy efficiency. This number is also derived for the case where a certain fraction of the totally achievable rate is aimed to be achieved. Our numerical investigations demonstrate a close match between the analytical and simulation results even for scenarios with not-so-large dimensions.