Coverage in Downlink Heterogeneous mmWave Cellular Networks with User-Centric Small Cell Deployment

A K-tier heterogeneous downlink millimeter wave (mmWave) cellular network with user-centric small cell deployments is studied in this paper. In particular, we consider a heterogeneous network model with user equipments (UEs) being distributed according to a Poisson cluster process (PCP). Distinguishing features of mmWave communications including directional beamforming and a sophisticated path loss model incorporating both line-of-sight and non-line-of-sight transmissions, are taken into account. Initially, we determine general expressions for the association probabilities of different tier BSs. Using tools from stochastic geometry, we then characterize the Laplace transform of the interference and derive a general expression for the signal-to-interference-plus-noise ratio coverage probability. While these expressions are applicable to any PCP, we later specialize the results to two popular PCPs, namely, first, Thomas cluster process, where the UEs are clustered around the base stations (BSs) according to a Gaussian distribution, and second, Matérn cluster process, where the UEs are scattered according to a uniform distribution. Subsequently, upper and lower bounds for the coverage probability are provided. Special cases are also addressed, providing the insight that when the cluster size grows without bound, our PCP-based model specializes to a Poisson point process-based model. Area spectral efficiency is investigated as well. Moreover, we have discussed extensions to cases in which more practical antenna gain patterns are taken into account and also the shadowing is considered. Via numerical and simulation results, we explore the effects of the beamwidth of the main lobe, the main lobe directivity gain, the biasing factor and the transmit power of the small-cell BSs to get insight on the performance in practical scenarios. Performance in dense networks is also analyzed numerically.