Outage probability for multi-hop D2D communications with shortest Path routing

In this letter, we provide a tractable theoretical framework for analysing the performance of device-to-device (D2D) communications in the presence of co-channel interference from other D2D and conventional cellular (CC) transmissions. In particular, we consider multi-hop D2D using the shortestpath- routing (SPR) algorithm in both the uplink (UL) and the downlink (DL) channels. Closed-form expressions for the number of hops and the outage probability are presented. Our analytical and numerical results both show that while the D2D links are reasonably reliable (outage probability <5%), they can severely degrade the performance of CC transmissions (outage probability >25%). Accordingly, we exploit and provide insights into the trade-off between D2D and CC transmission reliability.