Analysis of Multi-Hop Device-To-Device Networks with Half-Duplex Relays

In this paper, we analyze a multi-hop device-to-device (D2D) communication network operating in a region of cellular outage, e.g., in case of a natural disaster. In particular, we assume that the D2D devices operate in a half-duplex manner and can receive signals from or transmit to a single D2D relay. For this system, we characterize a multi-hop D2D transmission protocol wherein we divide the transmission area into multiple regions based on the D2D transmission range. In contrast to the other works present in literature, we have taken into account the probability of a relay being used by another D2D source at the instant when the typical D2D source attempts to connect to it. Then, we derive the signal to interference and noise ratio (SINR) coverage probability for a typical device. Based on this, we define and characterize a performance metric called the availability-coverage product (ACP) to jointly take into account the coverage performance of the devices and the probability of them being used as relays by the other devices in outage. Our analysis highlights several system design insights in terms of the D2D communication range and the optimal number of active devices in the network in terms of the ACP.