Abstract
This paper considers a cellular system with multihop device-to-device (D2D) communications to extend the coverage of a cell, for user equipments (UEs) experiencing service outage. The D2D system is an inband underlay system. The aim is to satisfy the signal-to-noise-ratio (SNR) requirements on the downlink connections on every pre-allocated resource block, signal-to-interference-plus-noise-ratio (SINR) requirements for every D2D sidelink connection on each of their pre-allocated resource blocks, and a maximum allowable interference at the base station receiver on all uplink frame resource blocks. It is desired to perform joint power control and routing to minimize the expended D2D UE energy in the system while meeting these requirements. An optimization problem is formulated that turns out to be a mixed integer non-linear program. For that, we use a generalized Bender's decomposition approach, which breaks down the problem formulation into a master sub-problem, an auxiliary sub-problem and a feasibility sub-problem. In this paper, we focus on developing an efficient solution method for the relaxed version of the master sub-problem that is responsible for generating lower bounds on the optimal objective function value. A benchmark sub-optimal disjoint scheme for the same problem is also proposed, which performs routing and power control separately. Simulations are conducted to compare the performance of both schemes and results show that the joint scheme is superior when compared with the disjoint scheme in terms of the expended UE energy, the expended base station power and success in satisfying the SINR, SNR, and interference bound requirements.