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Millimeter wave (mmWave) communications which essentially employ directionalantennas find applications spanning from indoor short range wireless personalarea networks to outdoor cellular networks. A thorough understanding of mmWavesignal propagation through the wireless channel provides valuable insights forthe design of such networks which in turn dictates the achievable performancelimits. High path loss, penetration loss, and negligible signal scattering arecertain distinctive features of the mmWave channel which necessitates thedevelopment of new mathematical models. Importantly, the impact of directionalantennas which spatially filter multi-path components needs to be embodied asan integral part of the channel model. In this paper, we model outdoordirectional non-line-of-sight mmWave channels using a combination of stochasticgeometry and image theory by expressing channel parameters as joint functionsof transmitter-receiver separation distance, antenna half power beamwidth, andantenna beam pointing direction. By approximating the signal propagation pathdue to first and second order reflections from buildings, closed formanalytical expressions for average number of first order reflection components,path loss, and root-mean square delay spread of channel are derived. Theaccuracy of the model is verified by comparing numerically obtained resultswith experimental data reported by various urban outdoor peer-to-peer mmWavemeasurements, thus demonstrating the usefulness of the proposed analyticalmodel for performance evaluation of mmWave communication networks.

A Novel Geometry-based Stochastic Double Directional Analytical Model for Millimeter Wave Outdoor NLOS Channels