  Emerging applications involving device-to-device communication among wearable
electronics require Gbps throughput, which can be achieved by utilizing
millimeter wave (mmWave) frequency bands. When many such communicating devices
are indoors in close proximity, like in a train car or airplane cabin,
interference can be a serious impairment. This paper uses stochastic geometry
to analyze the performance of mmWave networks with a finite number of
interferers in a finite network region. Prior work considered either lower
carrier frequencies with different antenna and channel assumptions, or a
network with an infinite spatial extent. In this paper, human users not only
carry potentially interfering devices, but also act to block interfering
signals. Using a sequence of simplifying assumptions, accurate expressions for
coverage and rate are developed that capture the effects of key antenna
characteristics like directivity and gain, and are a function of the finite
area and number of users. The assumptions are validated through a combination
of analysis and simulation. The main conclusions are that mmWave frequencies
can provide Gbps throughput even with omni-directional transceiver antennas,
and larger, more directive antenna arrays give better system performance.
