User Association with Maximizing Sum Energy Efficiency for Massive MIMO   Enabled Heterogeneous Cellular Networks
  In this paper, we design an association scheme to maximize the sum energy efficiency for massive multiple-input and multiple-output (MIMO) enabled heterogeneous cellular networks (HCNs). Considering that the final formulated problem is in a sum-of-ratio form, we first need to transform it into a parametric nonfractional form, by which we can achieve its solution through a two-layer iterative algorithm. The outer layer searches the energy efficiency parameters and multipliers associated with signal-interference-plus-noise-ratio (SINR) constraints using Newton-like method, and the inner layer optimizes the association indices using Lagrange multiplier method. In fact, the inner layer doesn't need iterative steps when the SINR constraints are not involved in the original problem, and then the whole algorithm should be a one-layer iterative one. As for the two-layer iterative algorithm, we also give the corresponding convergence proof. Numerical results show that the proposed scheme significantly outperforms the existing one in system throughput and network energy efficiency. In addition, we also investigate the impacts of the number of massive antennas and the transmit power of each pico base station on these association performances. 
Tianqing Zhou
cs.IT math.IT