  To keep pace with the rapid growth of mobile traffic demands, dense
deployment of small cells in millimeter wave (mmWave) bands has become a
promising candidate for next generation wireless communication systems. With a
greatly increased data rate from huge bandwidth of mmWave communications,
energy consumption should be mitigated for higher energy efficiency. Due to
content popularity, many content-based mobile applications can be supported by
the multicast service. mmWave communications exploit directional antennas to
overcome high path loss, and concurrent transmissions can be enabled for better
multicast service. On the other hand, device-to-device (D2D) communications in
physical proximity should be exploited to improve multicast performance. In
this paper, we propose an energy efficient multicast scheduling scheme,
referred to as EMS, which utilizes both D2D communications and concurrent
transmissions to achieve high energy efficiency. In EMS, a D2D path planning
algorithm establishes multi-hop D2D transmission paths, and a concurrent
scheduling algorithm allocates the links on the D2D paths into different
pairings. Then the transmission power of links is adjusted by the power control
algorithm. Furthermore, we theoretically analyze the roles of D2D
communications and concurrent transmissions in reducing energy consumption.
Extensive simulations under various system parameters demonstrate the superior
performance of EMS in terms of energy consumption compared with the
state-of-the-art schemes. Furthermore, we also investigate the choice of the
interference threshold to optimize network performance.
