Analytical SIR for Self-Organizing Wireless Networks

The signal to interference ratio (SIR) in the presence of multipath fading, shadowing and path loss is a valuable parameter for studying the capacity of a wireless system. This paper presents a new generalized path loss equation that takes into account the large-scale path loss as well as the small-scale multipath fading. The probability density function (pdf) of the SIR for selforganising wireless networks with Nakagami-m channel model is analytically derived using the new path loss equation. We chose the Nakagami-m channel fading model because it encompasses a large class of fading channels. The results presented show good agreement between the analytical and Monte Carlobased methods. Furthermore, the pdf of the signal to interference plus noise ratio (SINR) is provided as an extension to the SIR derivation. The analytical derivation of the pdf for a single interferer in this paper lays a solid foundation to calculate the statistics for multiple interferers.