The SINR Meta Distribution in Poisson Cellular Networks

Abstract

This work studies the signal-to-interference-plus-noise ratio (SINR) meta distribution (MD) in cellular networks with a focus on the Poisson model. Firstly, we show that for stationary base station point processes, arbitrary fading, and power-law path loss with exponent α, the base station density λ and the noise power σ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> impact the SINR MD only through η\pmb \triangleq λ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α/2</sup> /σ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , termed the network signal-to-noise ratio (NSNR). Next, we show that for Poisson cellular networks, the SINR MD can be written as g(x)θ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2/α</sup> when the target SINR θ and the target reliability x jointly satisfy a constraint. We derive this constraint and the integral of g(x). Lastly, we discuss several extensions of the results to more general models and architectures.