# An Energy-Efficient Two-Stage Cooperative Routing Scheme in Wireless Multi-Hop Networks
## 1 Introduction
These studies suggest that the network lifetime reflects the energy balance of the whole network and is generally defined as the time when the energy of the first node becomes depleted. The flow augmentation (FA) [18] designed the link cost considering the residual energy of node which avoided the low-power node in the best route and prolonged the network lifetime. Referring to CAN-\(l\), the flow augmentation cooperative routing (FACR) [19] further combined the cooperative \(l\)-to-\(1\) communication case and residual energy of transmitters to formulate the cooperative link cost, but the selection of cooperative transmitters should be extended from the best route to their neighbors. The energy-balanced cooperative routing (EBCR) [20] assumed that each node can estimate its lifetime based on the expected energy consumption during each end-to-end transmission, and the transmitter of single-hop communication could greedily pick those nodes with larger remaining lifetime to be helpers of the current link, which would balance every helper's remaining lifetime after the transmission. In fact, the estimation of expected energy cost of each node is not accurate for ignoring the shadowing fading of wireless channel. In [21], the maximization of network lifetime was investigated by designing a weighted sum-power minimization strategy, and the multihop transmission was modeled in a amplify-and-forward manner which will result in the problem of noise propagation and be unfavorable to designing the cooperative routing. The lifetime maximization cooperative routing with truncated automatic repeat request (LMCRTA) [22] predefined a possible relay for each link, and the link cost was designed considering the cooperative link and the retransmission. In the virtual multiple-input-multiple-output-based cooperative routing (VMIMOCR) [23], the virtual node and virtual link were defined respectively by taking the cooperation of two neighbors into consideration, and based on these definitions, the cooperative routing algorithm was designed to maximize the network lifetime. However, the number of cooperative nodes in LMCRTA and VMIMOCR schemes should not be fixed. Motivated by these, this paper proposes an energy-efficient two-stage cooperative routing (TSCR) scheme to simultaneously improve the energy efficiency and prolong the network lifetime. In contrast with the existing schemes, the _importance and originality_ of this study are that it firstly explores a two-stage cooperative (TSC) transmission model where the core helper is introduced to determine the helper set for cooperation. Then, the two-stage link cost is formulated where the effect of cooperative transmission is considered, and the weighting coefficient of residual energy, \(x\), is introduced to accommodate the different design goals. By selecting the optimal helper set, the two-stage link cost of each link can be optimized. Finally, based on the optimized two-stage link cost, a distributed TSCR scheme is further designed to minimize the end-to-end route cost and establish the shortest path between source and destination, then the source packet is delivered to the destination via this path with the proposed TSC transmission model. The proposed TSCR scheme can adapt to the fading environment and meet different performance requirements. The benefits of TSCR protocol in network residual energy, network lifetime, average end-to-end transmission delay and energy efficiency are investigated in comparison with the existing schemes through simulation results. The rest of the paper is organized as the following. In Section 2, we describe the system model as well as the existing schemes. Section 3 introduces our proposed TSCR scheme. The performance evaluation results of TSCR scheme are presented in Section 4. Finally, the paper is concluded in Section 5.