On the Location-Dependent SIR Gain in Cellular Networks

In wireless networks, the distances from a user to its desired transmitters and undesired interferers play a critical role in its channel quality. In this letter, we study this location-dependence in a cellular network, where a user is always served by its nearest base station. For any stationary and ergodic base station process, we partition its associated Voronoi cells into the cell centers and the cell boundaries. We show that in Poisson networks, the top fraction <inline-formula> <tex-math notation="LaTeX">${x}$ </tex-math></inline-formula> of users enjoy a signal-to-interference ratio (SIR) gain of <inline-formula> <tex-math notation="LaTeX">${-}{5}{\alpha }\text {log}_{{10}}{x}$ </tex-math></inline-formula> dB relative to the typical user for Rayleigh fading and the power-law path loss with the exponent <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>. For the cell boundary users, we give both the exact and asymptotic form of the SIR distribution. As such, this letter permits the grouping of users and the analysis of different groups of users.