Generalized Carrier to Interference Ratio Analysis for the Shotgun Cellular System

In this paper, the performance of cellular systems in which the base-stations (BS) are randomly placed (so-called shotgun cellular system, SCS) is studied. Previous results for a uniform 2-dimensional distribution of BS are generalized to non-uniform placement of BS in any dimension. The carrier-tointerference ratio (CIR) and the carrier-to-interference-plus-noise ratio (CINR) are analyzed for dense and sparse BS density cellular systems, respectively. A semi-analytical expression for the tail probability of the CIR is derived. Additionally, a tool for comparing the CIR performances of two SCSs based on BS densities is presented. With these results, we completely characterize the performance of a SCS with an arbitrary BS density function. Next, a SCS affected by random shadow fading is shown to be equivalent to another SCS without shadow fading and a different BS density function, and hence the performance of a uniform l-D SCS is independent of shadow fading. Thus, for a sparse uniform l-D SCS, the effect of all the variations introduced to the SCS is captured in the noise-power term. Also, the effect of random transmission gains, power control, multiple channel reuse groups on the performance of a uniform l-D SCS is analyzed. Index Terms Cellular Radio, Co-channel Interference, Fading channels, Stochastic ordering.