5G networks are expected to provide gigabit data rate to users via the millimeter-wave (mmWave) communication technology. One of the major problems faced by mmWaves is that they cannot penetrate buildings. In this paper, we utilize multihop relaying to overcome the signal blockage problem in an mmWave band. The multihop relay network comprises a source device, several relay devices, and a destination device and uses device-to-device communication. Relay devices redirect the source signal to

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... d the obstacles existing in the propagation environment. Each device amplifies and forwards the signal to the next device, such that a multihop link ensures the connectivity between the source device and the destination device. We consider that the relay devices and the destination device are affected by external interference and investigate the bit error probability (BEP) of this multihop mmWave system. Note that the study of the BEP allows quantifying the quality of communication and identifying the impact of different parameters on the system reliability. In this way, the system parameters, such as the powers allocated to different devices, can be tuned to maximize the link reliability. We derive exact expressions for the BEP of M -ary quadrature amplitude modulation and M -ary phase-shift keying in terms of multivariate Meijer's G-function. Due to the complicated expression of the exact BEP, a tight lower bound expression for the BEP is derived using a novel Mellin-approach. Moreover, an asymptotic expression for the BEP at high SIR regime is derived and used to determine the diversity and the coding gain of the system. In addition, we optimize the power allocation at different devices subject to a sum power constraint such that the BEP is minimized. Our analysis reveals that optimal power allocation allows achieving more than 3-dB gain compared with the equal power allocation. This paper can serve as a framework for designing and optimizing mmWave multihop relaying systems to ensure link reliability. INDEX TERMS Millimeter wave, device-to-device communication, bit error probability, multihop relaying, Nakagami-m fading. 3794 2169-3536 2018 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. VOLUME 6, 2018 A. Chelli et al.: On BEP and Power Optimization in Multihop mmWave Relay Systems communication to work properly. One of the major challenges faced by mmWave is that they cannot penetrate buildings and walls. Measurement results in [3] have shown that for a brick wall mmWave suffer a 178 dB attenuation. For two devices to communicate using mmWaves, they need to rely on a line-of-sight (LOS) link or reflection from buildings. If none of these conditions is satisfied, the mmWave signal is blocked due to shadowing and an outage event occurs [6], [7] . Signal outage may represent the bottleneck for mmWave communication in delivering uniform capacity for all users in the network. In order to deal with this problem, relaying techniques represent a promising solution to mmWave signal blockage [8] . We consider a typical device-to-device (D2D) communication scenario, where a source device sends data to a destination device over mmWave band without using the network infrastructure. In a real-world scenario, the propagation path of the signal between these two devices contains building walls, trees, and other types of objects. Bearing in mind that mmWaves cannot penetrate these objects, it is highly probable that the LOS link, between the source and the destination devices, is blocked. To overcome this problem, other devices laying in the propagation path between the transmitting and the receiving devices can be utilized to redirect the signal around the obstacles in the environment, such that a multihop communication link is created. The multihop link comprises the source device, the destination device, and multiple relay devices. Each of the relay devices amplifies and forwards the signal to the next device until it reaches the destination device. The data exchange between devices takes place using mmWave D2D communication.