# An Energy-Efficient Two-Stage Cooperative Routing Scheme in Wireless Multi-Hop Networks
## 1 Introduction  
In recent years, the development of wireless multiple-hop technology provides a promising direction for the wireless sensor network or ad hoc network [1] where each node is equipped with a wireless transceiver to exchange data with other neighboring nodes and route packets via neighboring nodes to destinations that are not within direct communications if necessary [2; 3]. However, the majority of nodes in the wireless sensor network or ad hoc network are usually power-constraint and deployed in unattended environment where people have difficulty in replacing or recharging the depleted devices. For this reason, it is especially important to save the energy cost and keep the network energy-balanced [4] for the end-to-end packet transmission schemes. To address these problems, the cooperative communication [5; 6; 7] was introduced to increase the energy efficiency of end-to-end transmission by allowing several single-antenna nodes to collaborate with each other and forward the packet to the destination. Furthermore, cooperative routing is a cross-layer routing scheme by combining cooperative communication in the physical layer and routing technology [8] in the network layer to select a cooperative route and allocate power for nodes in the route. According to the different design goals, the previous works can be mainly classified into two categories: the first oneis to maximize the end-to-end performance of wireless multi-hop transmission, the other is designed to maximize the network lifetime. Several attempts [9; 10; 11; 12; 13; 14; 15] have been made to maximize the end-to-end performance of wireless multi-hop transmission, such as minimizing total energy routing (MTE) [9], cooperation along the minimum energy non-cooperative path (CAN) [10], progressive cooperative routing (PC) [10], cooperative cluster-based routing (CwR) [11], cooperative shortest path algorithm (CSP) [12], relay selection-based cooperative routing (CC-OPT) [13], power efficient location-based cooperative routing (PELCR) [14] and minimum-energy cooperative routing (MECR) [15]. MTE [9] aimed at finding a minimum total energy non-cooperative route and can be achieved by a standard shortest path algorithm [16] such as Dijkstra and Bellman-Ford. In CAN-\(l\)[10], the last \(l\) nodes along the above non-cooperative route cooperatively transmit the packet to the next-hop node. Similar to CAN-\(l\), PC-\(l\)[10] combined the last \(l\) nodes into a single node and then updated the shortest path from the combined node to the destination node. CwR [11] introduced the'recruiting-and-transmitting' phase based on the non-cooperative path, and the cooperative model was similar to the multiple-input-single-output (MISO) case. The above schemes were designed based on the minimum energy non-cooperative path. In fact, the effect of cooperation on the performance should be considered in searching the optimal end-to-end route. Based on CAN-\(l\), CSP [12] was designed to find an optimal cooperative shortest path considering the gains of \(l\)-to-\(1\) cooperative transmission. However, the channel model of this scheme only considered the effect of distance and ignored the fading of wireless environment. In CC-OPT [13] and PELCR [14], a relay node of each cooperative link was elaborately selected from the nodes located in the middle area between the transmitter and the receiver. However, the number of cooperative nodes should be adaptive to the actual neighbors instead of a predefined number. MECR [15] designed the cooperative link cost subject to a constraint on link reliability and proposed a probabilistic cooperative routing to find the minimum-energy route in the network, but it is executed in a centralized manner and has a high computational complexity. A considerable amount of literature [17; 18; 19; 20; 21; 22; 23] has been published on maximizing the network lifetime.