Diversity Polynomials for the Analysis of Temporal Correlations in Wireless Networks

The interference in wireless networks is temporally correlated, since the node or user locations are correlated over time and the interfering transmitters are a subset of these nodes. For a wireless network where (potential) interferers form a Poisson point process and use ALOHA for channel access, we calculate the joint success and outage probabilities of n transmissions over a reference link. The results are based on the diversity polynomial, which captures the temporal interference correlation. The joint outage probability is used to determine the diversity gain (as the SIR goes to infinity), and it turns out that there is no diversity gain in simple retransmission schemes, even with independent Rayleigh fading over all links. We also determine the complete joint SIR distribution for two transmissions and the distribution of the local delay, which is the time until a repeated transmission over the reference link succeeds.