How Many Antenna Arrays Are Dense Enough in Massive MIMO Systems

In this paper, we study multiple-input multiple-output (MIMO) systems with a large number of antennas at a base station serving a number of users in a cell. The antennas at the base station are assembled into multiple antenna arrays (MAA), which are well separated to keep independence between the arrays, but in each array, antennas are densely installed. The MAA can be viewed as a flexible configuration of multiple antennas to reduce the space for installing the antennas and benefit from beamforming. In order to determine how dense the MAA can be designed, we define antenna area efficiency, that is the ratio of the achievable rate and the 2-D space required for installing the antennas. Then, we analyze the achievable rate of the massive MIMO system with
$K$
uplink users and
$NM$
antenna elements at the base station placed in
$N$
square arrays and each array having
$\sqrt{M}\times \sqrt{M}$
antennas densely deployed. Specifically, the analytical uplink sum rate is first derived. Then, the sum rate in the low-SNR and high-SNR regimes is studied. A case study is provided to show how dense MAA can be designed in a massive MIMO system. Our analytical and simulations results show that, for ten users in low SNR, a single dense antenna array with
$11\times 11$
antennas in a square requires only
$1/200$
of the area of conventional 100 independent antennas to achieve the same rate. For ten users in high SNR, we find that two
$8\times 8$
square arrays can achieve the highest antenna area efficiency in comparison with one
$16\times 16$
antenna array, four
$5\times 5$
antenna arrays, and 100 independent antennas.