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Millimeter-wave (mm-wave) communication opens up tens of giga-hertz spectrum in the mm-wave band for use by next-generation wireless systems, thereby solving the problem of spectrum scarcity. Maintaining connectivity stands out as a key design challenge for mm-wave networks deployed in urban regions due to the blockage effect characterizing mm-wave propagation. In this paper, we set out to investigate the blockage effect on the connectivity of mm-wave networks in a Manhattan-type urban region modeled using a random regular lattice, while base stations (BSs) are Poisson distributed in the plane. In particular, we analyze the connectivity probability that a typical user is within the transmission range of a BS and connected by a line-of-sight. First, we consider a single-tier network. By jointly applying the random lattice and stochastic geometry theories, a lower bound on the connectivity probability is derived as a function of building parameters (e.g., size and site occupancy probability) and BS parameters (e.g., transmission range and BS density). For the case of dense buildings, the bound is derived in a simpler form. Next, the preceding lower bounds are tightened based on the geometric technique of partitioning the irregular blockage-free region around the typical user. Moreover, the analysis is generalized to mm-wave channels with both LoS and NLoS paths. Finally, the results are extended to a K-tier heterogeneous network (HetNet), where building heights are random, and depending on its height, a building can block the signals transmitted by a subset of BS tiers but not all. The analysis shows that the connectivity probability of the K-tier HetNet increases linearly with the number of tiers. In general, our work quantifies the relation between the coverage of an mmwave network and the parameters of building and BS processes, providing useful guidelines for deploying practical networks in a Manhattan-type region.

The Connectivity of Millimeter Wave Networks in Urban Environments Modeled Using Random Lattices