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Multi-tier architecture improves the spatial reuse of radio spectrum incellular networks, but it introduces complicated heterogeneity in the spatialdistribution of transmitters, which brings new challenges in interferenceanalysis. In this work, we present a stochastic geometric model to evaluate theuplink interference in a two-tier network considering multi-type users and basestations. Each type of tier-1 users and tier-2 base stations are modeled asindependent homogeneous Poisson point processes, and tier-2 users are modeledas locally non-homogeneous clustered Poisson point processes centered at tier-2base stations. By applying a superposition-aggregation-superposition approach,we quantify the interference at both tiers. Our model is also able to capturethe impact of two types of exclusion regions, where either tier-2 base stationsor tier-2 users are restricted in order to avoid cross-tier interference. As animportant application of this analytical model, an intensity planning scenariois investigated, in which we aim to maximize the total income of the networkoperator with respect to the intensities of tier-2 cells, under constraints onthe outage probabilities of tier-1 and tier-2 users. The result of ourinterference analysis suggests that this maximization can be converted to astandard convex optimization problem. Finally, numerical studies furtherdemonstrate the correctness of our analysis.

Uplink Interference Analysis for Two-tier Cellular Networks with Diverse Users under Random Spatial Patterns