Secrecy outage in random wireless networks subjected to fading

We investigated the secrecy outage of unicast channels in random networks exposed to unknown numbers of randomly located eavesdroppers, obtaining original expressions which include uncertainty in terms of the location of legitimate nodes relative to eavesdroppers, the number of eavesdroppers, and fading. Under such conditions, we derive the path gain distributions of legitimate and eavesdropper nodes, as well as the corresponding secrecy non-outage. Two interesting conclusions can be drawn from our analysis. The first is that the uncertainty on the number of eavesdropper does not play a significant role in quantifying secrecy outage; and the second is that secret communication at a given rate is possible (albeit subjected to outage), with very low power. Specifically, it is found that the for a given fading figure and network density (which fundamentally determines the secrecy outage) similar secrecy outage is experience by the k-th furthest legitimate node, independent on the source's transmit power.