Closed-form ASE of downlink massive MIMO system with uplink and downlink training

Massive multi-input multi-output (MIMO) is one of the key technologies for the fifth generation (5G) cellular system. To reveal the potential of massive MIMO systems, it is important to quantify the achievable performance. Spectral efficiency (SE) is an important performance metric for cellular systems, and area spectral efficiency (ASE) is one of the metric of the cell-average SE. This paper considers the ASE for the multiuser downlink massive MIMO system. Both the base station (BS) and the users obtain imperfect channel state information (CSI) through pilot training. We first give the expression of ASE for this system. With the number of antennas at the BS goes to infinity in the massive MIMO system, we apply random matrix theory derive a closed-form lower bound of the ASE. Numerical results show that our lower bound is very close to the simulation results.