Connectivity of Millimeter Wave Networks with Multi-hop Relaying
  This paper presents a novel stochastic geometry approach to the connectivity of milimeter wave (mmWave) networks with multi-hop relaying. The random positions and shapes of obstacles in the radio environment are modeled as a Boolean model, whose germs are distributed according to a Poisson point process and grains are random rectangles. The derived analytical results shed light on how the connectivity of mmWave networks depends on key system parameters such as the density and size of obstacles as well as relaying route window -- the range of distances in which routing relays are selected. We find that multi-hop relaying can greatly improve the connectivity versus single hop mmWave transmission. We show that to obtain near-optimal connectivity the relaying route window should be about the size of the obstacles. 
Xingqin Lin and Jeffrey G. Andrews
cs.IT cs.NI math.IT