Optimal Resource Allocation via Unified Closed-Form Solutions for SWIPT Multi-Hop DF Relay Networks

Multi-hop relaying can solve the problems of limited single-hop wireless communication distance, poor signal quality, or the inability to communicate directly by "relaying" data transmission through multiple intermediate nodes. It serves as the cornerstone for building large-scale, highly reliable, and self-adapting wireless networks, especially for the Internet of Things (IoT) and future 6G. This paper focuses on a decode-and-forward (DF) multi-hop relay network that employs simultaneous wireless information and power transfer (SWIPT) technology, with relays operating in a passive state. We first investigate the optimization of the power splitting (PS) ratio at each relay, given the source node transmit power, to maximize end-to-end network throughput. Subsequently, we jointly optimized the PS ratios and the source transmit power to minimize the source transmit power while satisfying the system's minimum quality of service (QoS) requirement. Although both problems are non-convex, they can be reformulated as convex optimization problems. Closed-form optimal solutions are then derived based on the Karush-Kuhn-Tucker (KKT) conditions and a recursive method, respectively. Moreover, we find that the closed-form optimal solutions for the PS ratios corresponding to the two problems are identical. Through simulations, we validate that the performance of the two proposed schemes based on the closed-form solutions is optimal, while also demonstrating their extremely fast algorithm execution speeds, thereby proving the deployment value of the two proposed schemes in practical communication scenarios.