Downlink cellular network analysis with a dual-slope path loss model

Existing cellular network analyses are based on the standard power law path loss model. If the base stations are modeled by a Poisson point process, this leads to a tractable analysis of coverage probability and other metrics for downlink cellular networks. Yet, it is also well-known that the standard path loss model is idealized and does not capture the distance-dependence of the path loss exponent. This paper considers a more precise and general model, the dual-slope path loss model, where the path loss exponents are different for short links and long links differentiated by a critical distance. We derive compact expressions on the coverage probability and its tight closed-form estimate under this model. The analytical results show that the SINR does not monotonically increase with network density (as under the standard path loss model). Rather, ultra-densification leads to worse or even zero coverage when the near-field path loss exponent is 2 or less.