Device-to-Device (D2D) communication underlaying cellular networks enhances the system capacity by efficient spectrum utilization, which significantly benefits local area services. On the other hand, physical layer network coding (PNC) can achieve more efficient two-way transmission. Thus, PNC aided two-way D2D communications have the potential to further increase the system capacity, where joint resource allocation and relay selection is a challenging problem. In this paper, we first present the PNC aided two-way D2D communication scheme over two or three time slots, and derive the corresponding achievable rate under the interferences between the relays and D2D pairs that are sharing the spectrum resource. Then, we formulate the problem of joint resource spectrum and relay selection as an optimization problem, which is NP-hard. Finally, to solve the formulated problem, we propose a distributed algorithm based on coalition game, which deceases the computation complexity significantly. Through extensive simulations, we demonstrate the effective of system performance of different transmission schemes in the two-way D2D communication underlaying cellular networks.
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