Full-duplex relay (FDR) has attracted considerable interest in enhancing the performance of relay networks by utilizing resources more efficiently. In this paper, we propose a framework for full-duplex random relay networks (FDRRNs), where relay nodes equipped with full-duplex (FD) capability are randomly distributed within a finite two-dimensional region. We first derive the outage probability of an FDRRN and then identify the potential relay location that minimizes the outage probability. Furthermore, we introduce a low-complexity relay selection algorithm that selects the relay node nearest to the potential relay location. Finally, simulation results show that the proposed relay selection algorithm achieves performance comparable to that of the max-min relay selection algorithm.
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