The Connectivity of Millimeter-Wave Networks in Manhattan-Type Regions

The millimeter-wave (mmWave) communication exploits tens-of-GHz of available spectrum in the mmWave band for solving the problem of spectrum scarcity in next-generation wireless networks. Maintaining connectivity in urban mmWave networks is one key design challenge because of the blockage effect characterizing mmWave propagation. Specifically, mmWave signals can be blocked by buildings and other large urban objects. Thus, the type of urban model affects the performance of mmWave networks. In this paper, we make the first attempt to study the connectivity of mmWave networks in a Manhattan-type region modeled using a random lattice while base stations (BSS) are Poisson distributed in the plane. In particular, we define and analyze the connectivity probability that a typical user is within the transmission range of a BS and connected by a line-of-sight. By jointly applying random-lattice and stochastic-geometry theories, different lower bounds on the connectivity probability are derived as functions of the buildings' size and distribution as well as the BSS' transmission range and density. We also investigate the asymptotic connectivity probability for the case of dense buildings. Our study yields closed-form relations between the parameters of the building process and the BS process, providing useful guidelines for practical mmWave network deployment and opening up many directions for future extensions.