| Summary: | IEEE With the development of wireless communications and the intellectualization of machines, the Internet of things (IoT) has been of interest to both industry and academia. Multi-hop routing and relaying are key technologies that will underpin IoT mesh networks in the future. This paper investigates optimal routing based on the trusted connectivity probability (T-CP) for multi-hop, underlay, device-to-device (D2D) communications with decode-and-forward (DF) relaying. Both random and fixed locations for base stations (BSs) are considered, where the former case assumes that the locations of the BSs are modeled as a Poisson point process (PPP). First, we derive two expressions for the connectivity probability (CP): a tight lower bound and an exact closed-form. Analysis is carried out for the cases where the channel state information (CSI) between BSs and the D2D transmitter is known (CSI-aware) and unknown (no-CSI). Interference from active cellular users (CUEs) is characterized by modeling CUE locations as a PPP. Moreover, motivated by results that have shown that social behavior leads to D2D devices communicating with nearby neighbours, we derive the trust probability (TP) for D2D connections by using a rank-based model. Finally, we propose a novel routing algorithm that can achieve the highest T-CP for any pair of D2D devices in a distributed manner. The derived analytical results are verified by Monte Carlo simulations. We show that the proposed routing algorithm achieves almost the same performance as that attained through an exhaustive search. When BSs are located randomly, the optimal path based on the CP is the shortest path between the D2D transmitter and receiver. However, for fixed BSs, the optimal path selection depends on the locations of the BSs, which provides a very useful insight in designing the multi-hop D2D system for 5G IoT.
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