3D Massive MIMO Systems: Modeling and Performance Analysis
  Multiple-input-multiple-output (MIMO) systems of current LTE releases are capable of adaptation in the azimuth only. Recently, the trend is to enhance system performance by exploiting the channel's degrees of freedom in the elevation, which necessitates the characterization of 3D channels. We present an information-theoretic channel model for MIMO systems that supports the elevation dimension. The model is based on the principle of maximum entropy, which enables us to determine the distribution of the channel matrix consistent with the prior information on the angles. Based on this model, we provide analytical expression for the cumulative density function (CDF) of the mutual information (MI) for systems with a single receive and finite number of transmit antennas in the general signal-to-interference-plus-noise-ratio (SINR) regime. The result is extended to systems with finite receive antennas in the low SINR regime. A Gaussian approximation to the asymptotic behavior of MI distribution is derived for the large number of transmit antennas and paths regime. We corroborate our analysis with simulations that study the performance gains realizable through meticulous selection of the transmit antenna downtilt angles, confirming the potential of elevation beamforming to enhance system performance. The results are directly applicable to the analysis of 5G 3D-Massive MIMO-systems. 
Qurrat-Ul-Ain Nadeem, Abla Kammoun, Merouane Debbah, and Mohamed-Slim   Alouini
cs.IT math.IT