Derivation of the closed-form PDF of the downlink SIR for coexisting LTE systems

Recently, as a variety of cellular systems are coexisted and the use of mobiles in a confined space increases, interference problems between terminals become more important. In this paper, we derive the closed-form probability density function (PDF) of the downlink signal-to-interference ratio (SIR) due to uplink transmission of the adjacent terminal station of the other system for the coexistence environment of two cellular systems. And it is shown that the formula of the PDF is exactly the same with Monte-Carlo simulation. This probability distribution model of the SIR is useful in that it is very simple and can be applicable to general propagation models including shadow fading. With this model, interference analysis for coexisting LTE systems in 900 MHz band of South Korea is suggested.