Exact Solution for Probability Density Function of Signal to Interference Ratio in a Circular Cell

Signal to interference ratio (SIR) is a key factor to measure the quality of the received signal. In a wireless system parameters such as cell size, coverage, quality of service (QoS), and etc are controlled using SIR. In this paper, exact solution of probability density function (PDF) for SIR is evaluated analytically in a circular cell taking into consideration the randomness of users and channel characteristics. PDF of SIR is evaluated in the presence of large scale fading characterized by loss propagation and shadowing, when there is one interferer base station. This result is a solid foundation to evaluate SIR for multiple interferers. Finally, simulation performed shows good agreement with analytical results obtained.