On Achievable Rates in Massive MIMO-Based Hexagonal Cellular System with Pilot Contamination

In this paper, a pilot reuse scheme is considered for the uplink of a massive multiple input multiple output (MIMO) system and a lower bound on the throughput of the system is derived, which is applicable for any number of antennas. A hexagonal geometry of the system is considered where each cell contains uniformly distributed users and a conventional frequency reuse pattern. The derived lower bound is shown to be limited by three types of interferences: inter-cell interference, intra- cell interference and pilot contamination. A set of conditions including the number of users, antennas, pilot reuse factor and coherence period is analyzed for which the lower bound of throughput is achieved. The results indicate that the reuse factor plays a critical role in the least achievable throughput. A minimum reuse factor is quantified for a given user density and coherence period.