The device-to-device (D2D) communication is envisioned as the solution to the bandwidth scarcity problem in the era of exponentially growing smart handheld devices. Although D2D communication in high frequency millimeter wave (mmWave) band offers high data rate, it requires obstacle free line-of-sight (LOS) communication path due to high propagation and penetration losses. The relay selection problem in D2D communication deals with careful selection of relay devices in order to establish a communication link when the direct LOS path is blocked or suffers from high interference from neighboring devices. With the limited number of available frequency channels, the channel allocation problem aims to judicially allocate the frequency channels to the activated D2D communication links. Due to the interdependence of the aforesaid two problems, it is a challenging task to optimally allocate frequency channels to the requesting D2D pairs along with proper selection of relay devices, specially in the presence of obstacles and user mobility. In this paper, we have proposed a mobility and obstacle aware base-station controlled centralized framework which jointly deals the channel allocation and relay selection problems for mmWave D2D communication. After proving the hardness of this joint problem, we provide a greedy solution along with its approximation bound. Our proposed algorithm has been shown to outperform an existing work through extensive simulations.
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