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.
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