# La-CTP: Loop-Aware Routing for Energy-Harvesting Wireless Sensor Networks
## 1 Introduction  
Energy resource is a dominant constraint in wireless sensor networks (WSNs), so prolonging the system lifetime is always an important topic for real-world applications [1; 2]. Recently researchers have attempted to employ the environmental (ambient) energy to drive the wireless sensor nodes. A variety of environmental energy sources exist in nature, such as solar energy, wind energy, RF energy, vibration energy, and hydrokinetic energy [3; 4; 5; 6; 7]; some of them are renewable and can be easily captured and stored in rechargeable battery. By harvesting such renewable environmental energy to power wireless sensor nodes, the users do not need to frequently replace (or manually charge) the battery modules of their nodes, and then they could achieve longer or even perpetual system operation [8; 9; 10; 11]. In a WSN, if all the nodes or a part of them are driven by environmental energy, it is usually called an energy-harvesting wireless sensor network (EH-WSN, in short). EH-WSNs have recently attracted increasing attention from academia and industry. For the energy-harvesting node in EH-WSNs, its energy consumption rate is far higher than its energy charging rate. An immediate, unavoidable consequence is that the energy-harvesting node cannot afford to keep active all the time, because it must stop working--leaving the network--to replenish its energy. The absence of recharging nodes, even temporary sometimes, is very likely toresult in a segmented network topology, which could be recovered only until some of those recharging nodes return to the network with sufficient energy capacity. In such an intermittently-connected network, a node will lose its current forwarder (also called next-hop or parent node), if the recharging process comes on at that forwarder. If the parent-losing node cannot reestablish valid routing paths, its packet will have to be dropped after many failed retries, wasting the scarce resources of energy and bandwidth. Though unreliable, low-power wireless channels and energy-harvesting processes are both likely to break off forwarding paths in EH-WSNs, the latter will impact the network performance and efficiency more severely than the former does. Therefore, recovering or re-determining valid forwarding path is an urgent and challenging mission for EH-WSN applications due to their intermittent and random nature in connectivity. In the designs of practical EH-WSN routing protocols, the control of routing loops is a crux of establishing and maintaining throughput-high and cost-aware forwarding paths. Loops are most likely to occur during the routing path re-establishment of various networks, whether the routing protocols in use are designed based on the link state, the distance vector, or the application-specific gradient information [12; 13; 14; 15; 16; 17]. A loop will come into network if a node chooses one of its upstreaming nodes as forwarder. Figure 1a shows a loop-free network. For the two cases shown in Figure 1b,c, however, the packets generated by nodes \(A\) and \(D\) will be locked in the network, never arriving at the destination, because node \(C\) mistakenly chooses \(B\) and \(D\) as its forwarders in the two cases, respectively. Basically, the unwise forwarder selection is due to the local network status changes that cannot be timely shared within the neighborhood after they happen. The 2-node loop shown in Figure 1b is easy to be identified and corrected by forcing each node not to send packets to its previous-hop node. However, the \(n\)-node (\(n\geq 3\)) loops are hard to be shunned or removed, unless each node can exactly know all its upstreaming nodes in a way of taking no account of the demand for more network resources and the risk of performance deterioration. In contrast to traditional duty-cycled WSN [18; 19], EH-WSNs are more prone to experiencing long-term loops, because the recharging periods of energy-harvesting nodes are usually heterogeneous and random, and because the unreliability of low-power wireless links will also compound the bad situation.