###### Abstract  
Underwater wireless sensor networks (UWSNs) are featured by long propagation delay, limited energy, narrow bandwidth, high BER (Bit Error Rate) and variable topology structure. These features make it very difficult to design a short delay and high energy-efficiency routing protocol for UWSNs. In this paper, a routing protocol independent of location information is proposed based on received signal strength (RSS), which is called RRSS. In RRSS, a sensor node firstly establishes a vector from the node to a sink node; the length of the vector indicates the RSS of the beacon signal (RSSB) from the sink node. A node selects the next-hop along the vector according to RSSB and the RSS of a hello packet (RSSH). The node nearer to the vector has higher priority to be a candidate next-hop. To avoid data packets being delivered to the neighbor nodes in a void area, a void-avoiding algorithm is introduced. In addition, residual energy is considered when selecting the next-hop. Meanwhile, we establish mathematic models to analyze the robustness and energy efficiency of RRSS. Lastly, we conduct extensive simulations, and the simulation results show RRSS can save energy consumption and decrease end-to-end delay.  
UWSNs; routing protocol; received signal strength; energy consumption; void-avoiding algorithm +
Footnote †: journal: Information Informationproposed some routing protocols for UWSNs which are applied to certain scenarios. However, these protocols have some defects, which are detailed in Section 2.  
In this paper, in order to decrease energy consumption and shorten delay, we propose a routing protocol for UWSNs based on received signal strength (RRSS). In RRSS, each node maintains a vector from itself to a sink node. After receiving a data packet, the receiving node selects the neighbor nearest to the RSS vector as the best next-hop. In our protocol, there are two kinds of control messages. One is the control message from a sink node, which is called a beacon message, and another is a \"hello\" message from a neighbor sensor node. The RSS of a hello packet (RSSH) indicates the distance from itself to its neighbor as well as the link quality. The RSS of the beacon signal (RSSB) is used to reflect the link quality and the distance to the sink node. Candidate next-hop nodes are those neighbor nodes with stronger RSSB. When the RSSB of neighbor nodes is the same, the sender determines the priority of the neighbor nodes according to RSSH: the stronger RSSH, the higher priority to be the next-hop. However, data packets may be delivered to a node in a void area or without enough residual energy. Therefore, we introduce a residual energy threshold as well as a void-avoiding algorithm when selecting the best next-hop node.  
Our contributions are summarized as follows:  
* We provide a method to construct the vector with the least energy consumption from the source node to a sink node independent of location information, and this is suitable for networks with both a single sink node and multiple sink nodes.
* We propose RSS as the parameter to select next-hop. RSS can not only reflect propagation distance but also noise power, which decreases delay and saves on energy consumption.
* We consider void node and energy threshold in our protocol to avoid data packets being delivered to the nodes in a void area or without sufficient residual energy.
* We establish mathematical models to analyze the energy-efficiency and robustness of RRSS.  
The paper is organized as follows: In Section 2, we introduce related work. In Section 3, we describe the RRSS routing protocol. In Section 4, we build a mathematical model to analyze the performance of RRSS. In Section 5, we conduct extensive simulations and evaluate the performance of RRSS. Section 6 concludes the paper.