Using Bender’s Decomposition for Optimal Power Control and Routing in Multihop D2D Cellular Systems

In this paper, multihop device-to-device (D2D) communications for cell coverage extension are studied. An in-band underlay D2D mode is considered, and the aim is to satisfy the signal-to-noise-ratio requirements for pre-allocated resource blocks (RBs) on the downlink connections, the signal-to-interference-plus-noise-ratio requirements on pre-allocated RBs for every D2D sidelink connection, and a maximum allowable interference at the base station receiver on all uplink RBs. Power control and routing are performed to minimize the expended user equipment energy in the system while meeting these requirements. An optimization problem is formulated that turns out to be a mixed-integer nonlinear program, which is solved using the generalized Benders decomposition (GBD). The GBD breaks down the formulation into a master sub-problem, an auxiliary sub-problem, and a feasibility sub-problem. In this paper, we focus on finding efficient solution methods for the relaxed version of the master sub-problem that is responsible for generating lower bounds on the optimal objective function. Also, an efficient solution technique for the feasibility sub-problem is proposed. Furthermore, a benchmark disjoint scheme for the same problem is proposed, which performs routing and power control separately. The simulations are conducted to compare the performance of both schemes, which show the superiority of joint routing and power control scheme.