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 self-organising wireless networks with Nakagami-[inline-graphic not available: see fulltext] channel model is analytically derived using the new path loss equation. We chose the Nakagami-[inline-graphic not available: see fulltext] channel fading model because it encompasses a large class of fading channels. The results presented show good agreement between the analytical and Monte Carlo- based 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.