Energy-Efficient mmWave IoT Communications with Multihop IRS-Assisted Systems

In this article, we investigate the energy efficiency (EE) maximization problem of the multihop intelligent reflecting surfaces (IRSs) assisted millimeter-wave (mmWave) Internet of Things (IoT) system. In this system, the base station (BS) provides services to IoT devices through the visible link established by the cascaded reflection of multihop IRSs. We aim to maximize the EE by jointly optimizing the active beamforming vector (ABV) at the BS, the number of active reflect elements (REs), the BS's transmit power, and the phase shift (PS) at the multihop IRSs. To achieve this target, we formulate a nonlinear fractional programming problem. However, the formulated problem is nonconvex and all the variables are deeply coupled. To solve this problem, by using the sparse scattering property of the mmWave channels and the maximum ratio transmission method, we first transform the optimization of ABV at the BS into the optimization of the BS's transmit power. We then propose an alternating optimization-based method to decouple all variables iteratively. Specifically, for the PS at multihop IRSs, we employ the sparse scattering property of the mmWave channels to divide it into multiple convex problems and obtain the optimal solution. For the number of active REs, we use the successive convex approximation method to obtain a suboptimal solution. For the BS's transmit power, we employ the Dinkelbach method iteratively solving it and obtaining an optimal solution. Finally, we obtain an iterative suboptimal solution. The simulation results show that the EE of the proposed scheme outperforms the conventional schemes.