Performance Analysis for Heterogeneous Cellular Systems with Range Expansion

In this paper, the uplink coverage probability for heterogeneous cellular systems with range expansion is analyzed and derived in closed-form. Unlike most of the previous analyses of heterogeneous systems, the randomness of not only the number of mobile users but also their locations is taken into account in the analysis based on the theory of stochastic geometry. With the derived analytical results, the impacts of various system parameters on the uplink performance are investigated in detail. The correctness of the analytical results is also verified by simulations. These analytical results can thus serve as a guidance for the design of the heterogeneous systems.