The Diversity Gain of Retransmissions in Poisson 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. This correlation impacts the diversity achievable with multiple transmissions over a link. In this paper, we focus on a link in a Poisson field of interferers and show that there is no diversity gain in using retransmissions, even with independent Rayleigh fading on all channels, in stark contrast to what the diversity would be if interference was independent from time slot to time slot. To show this, we first derive the joint success probability of n transmissions in closed-form, which is based on the so-called diversity polynomial, which captures the degree of dependence of the transmission success events. The main conclusion is that ignoring interference correlation can lead to significant errors in the network performance evaluation.