As an intrinsic part of the Internet of Things (IoT) ecosystem, machine-to-machine (M2M) communications are expected to provide ubiquitous connectivity between machines. Millimeter-wave (mmWave) communication is another promising technology for the future communication systems to alleviate the pressure of scarce spectrum resources. For this reason, in this paper, we consider multi-hop M2M communications, where a machine-type communication (MTC) device with the limited transmit power relays to help other devices using mmWave. To be specific, we focus on hop distance statistics and their impacts on system performances in multi-hop wireless networks (MWNs) with directional antenna arrays in mmWave for M2M communications. Different from microwave systems, in mmWave communications, wireless channel suffers from blockage by obstacles that heavily attenuate line-of-sight signals, which may result in limited per-hop progress in MWNs. We consider two routing strategies aiming at different types of applications and derive the probability distributions of their hop distances. Moreover, we provide their baseline statistics assuming the blockage-free scenario to quantify the impact of blockages. Based on the hop distance analysis, we propose a method to estimate the end-to-end performances (e.g., outage probability, hop count, and transmit energy) of the mmWave MWNs, which provides important insights into mmWave MWN design without time-consuming and repetitive end-to-end simulation.
Keywords: Internet-of-Things (IoT); hop distance; machine-to-machine (M2M) communications; multi-hop networks.