Carrier to interference ratio, rate and coverage analysis in shotgun cellular systems over composite fading channels

Wireless communication performance in shotgun cellular system (SCS: wireless communication system with randomly placed base stations) is analysed. Aiming at this analysis, (i) the carrier to interference ratio (CIR), as an important measure in a cellular network, is considered in the downlink (path-loss, shadowing and multi-path) fading channel. Since direct calculating of the distribution of CIR is complicated, a related mathematical equation is determined through which the probability density function (PDF) of CIR can be calculated. And then, as a special case, the tail probability of CIR is obtained. (ii) A normal approximation for inverse of CIR is proposed which is applicable for calculating a tractable PDF for the downlink CIR. The analytically calculated and the approximate PDFs of CIR are compared with numerical PDFs. (iii) The distribution of the downlink rate and a lower bound for the average rate; the analytical expression for coverage of a user in an SCS based on its received CIR, and an average value for coverage are calculated. (iv) Simulation results show that the closed form and approximate PDFs over different models are close to numerical ones.