  Millimeter wave (mmWave) communication technologies have recently emerged as
an attractive solution to meet the exponentially increasing demand on mobile
data traffic. Moreover, ultra dense networks (UDNs) combined with mmWave
technology are expected to increase both energy efficiency and spectral
efficiency. In this paper, user association and power allocation in mmWave
based UDNs is considered with attention to load balance constraints, energy
harvesting by base stations, user quality of service requirements, energy
efficiency, and cross-tier interference limits. The joint user association and
power optimization problem is modeled as a mixed-integer programming problem,
which is then transformed into a convex optimization problem by relaxing the
user association indicator and solved by Lagrangian dual decomposition. An
iterative gradient user association and power allocation algorithm is proposed
and shown to converge rapidly to an optimal point. The complexity of the
proposed algorithm is analyzed and the effectiveness of the proposed scheme
compared with existing methods is verified by simulations.
