WLC02-1: Bounds on the SIR Distribution for a Class of Channel Models in Ad Hoc Networks

We provide closed form upper and lower bounds on the distribution of the signal to interference ratio (SIR) seen by a typical receiver in an ad hoc network where transmitter locations form a Poisson process. The aggregate co-channel interference in such a network is known to be a power law shot noise process and the distribution is known to be symmetric stable; we will show the same is true of the SIR. Stable distributions are unwieldy in that there is no closed form expression for their PDF and CDF; this is the motivation behind seeking simple bounds on the SIR. We consider a broad class of channel models that have a deterministic, distance dependent path-loss component and a random, distance-independent component. This class of channel models includes lognormal shadowing, Rayleigh fading, the Nakagami model, and others. We show that the lower bound on SIR is tight and that the upper bound has a bounded error that depends on the path loss exponent but not on the random channel variation. Numerical plots of the SIR distribution for a variety of common channel models are provided to illustrate the bounds. The bounds are useful for computing common network performance metrics like outage probability and BER.