Cellular systems are becoming more heterogeneous with the introduction of lowpower nodes including femtocells, relays, and distributed antennas.Unfortunately, the resulting interference environment is also becoming morecomplicated, making evaluation of different communication strategieschallenging in both analysis and simulation. Leveraging recent applications ofstochastic geometry to analyze cellular systems, this paper proposes to analyzedownlink performance in a fixed-size cell, which is inscribed within a weightedVoronoi cell in a Poisson field of interferers. A nearest out-of-cellinterferer, out-of-cell interferers outside a guard region, and cross-tierinterference are included in the interference calculations. Bounding theinterference power as a function of distance from the cell center, the totalinterference is characterized through its Laplace transform. An equivalentmarked process is proposed for the out-of-cell interference under additionalassumptions. To facilitate simplified calculations, the interferencedistribution is approximated using the Gamma distribution with second ordermoment matching. The Gamma approximation simplifies calculation of the successprobability and average rate, incorporates small-scale and large-scale fading,and works with co-tier and cross-tier interference. Simulations show that theproposed model provides a flexible way to characterize outage probability andrate as a function of the distance to the cell edge.
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