Separability, Asymptotics, and Applications of the SIR Meta Distribution in Cellular Networks

Abstract

The signal-to-interference-ratio (SIR) meta distribution (MD) characterizes the link performance in interference-limited wireless networks: it evaluates the fraction of links that achieve an SIR threshold θ with a reliability above x. In this work, we show that in Poisson networks, for any independent fading and power-law path loss with exponent α, the SIR MD can be expressed as the product of θ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2/α</sup> and a function of x when (θ, x) is in the so-called “separable region”. We show by simulation that the separable form serves as a good approximation of the SIR MD in Ginibre and triangular lattice networks when θ is chosen large enough. Given the quest for ultra-reliable transmission, we study the asymptotics of the SIR MD as x → 1 for general cellular networks with Rayleigh fading. Finally, we apply our results to characterize the distribution of the link rate, where each link transmits with a rate satisfying a given reliability x, and the asymptotic distribution of the local delay, defined as the number of transmissions needed for a message to be received successfully.