## 3 RRSS Protocol  
### Motivation  
Decreasing energy-consumption is a major objective for designing protocols for UWSNs. On the one hand, the energy of sensor nodes underwater is limited. Nodes are powered by batteries, which are hard to recharge and replace. On the other hand, an acoustic signal consumes more energy than a radio signal during communication. Shortening the delay is another major objective in UWSNs. The propagation speed of acoustic signals underwater is 1500 m/s, which is five orders of magnitude lower than the speed of RF signals in the air, so the propagation delay is the main part of system delay in UWSNs. Therefore, shortening the propagation distance in the path from source node to destination node is an effective way to decrease system delay [22]. The propagation distance affects directly the signal attenuation. The relation between propagation distance and attenuation is shown as Equation (1). \[A(d,f)=A_{0}d^{k}\alpha(f)^{d} \tag{1}\]  
Here, \(A_{0}\) is the unit-normalizing constant; \(A(d,f)\) is path loss or attenuation over distance \(d\) when communication frequency is \(f\); \(k\) is constant 1.5 for a practical scenario [17]. From Equation (1) we can see that the signal attenuation increases with increasing of communication distance. So, shortening the propagation distance can decrease energy consumption. Therefore, the path with the least energy consumption is the path with the least propagation distance. In addition, the underwater environment is harsh, and communication quality is affected by diversified noises, including waves, shipping, wind and thermal noises [23]. Among all the routing protocols proposed, DBR and VBF are the most popular. Both are greedy broadcasting routing protocols. VBF is based on location information, which is another unsolved problem. DBR is half independent on geographical location information. However, because of the nature of broadcasting in a densely distributed network, DBR consumes a lot of energy. For example, in Figure 1, there is only one sink node \(S\) on the water surface, and the data packet from node A can be delivered by two paths. The path 1 is \(\mathrm{A}\rightarrow\mathrm{C}\rightarrow\mathrm{S}\). The path 2 is \(\mathrm{A}\rightarrow\mathrm{B}\rightarrow\mathrm{S}\). Node A, B and S are on a straight line. According to triangle relation, \(|\mathrm{AC}|\;+\;|\mathrm{CS}|\;>\;|\mathrm{AS}|\), clearly, the propagation distance of path 2 is shorter than path 1. However, according to DBR, path 1 should be selected as the forwarding path, which consumes more energy and increases delay clearly. To solve the problems in VBF and DBR as mentioned above, a routing protocol with higher energy efficiency, shorter delay and independent of locations should be proposed for UWSNs. In our algorithm, each node firstly establishes a vector from itself to a sink node according to RSSB. The RSS depends on the transmission power, the attenuation of the signal, and link quality. RSS can be calculated by Equation (2). The attenuation is related to the propagation distance, which can be seen in Equations (3)-(5). Link quality is reflected by the noise power, as in Equation (6). Therefore, RSS can reflect the propagation delay, energy consumption and link quality of the path. So, RSS is used as the main parameter for selecting the best next-hop in the RRSS routing protocol. The realization of our protocol is simple and suitable for the networks with both single sink node and multiple sink nodes. \[\mathrm{RSS}=\frac{P_{R}}{P_{N}} \tag{2}\]  
Combining Equation (1), we get Equation (5):  
\[P_{R}=\alpha P_{S}-A(d,f) \tag{3}\]  
\[\alpha=(rssi-rssi_{min})/(P_{Smax}-P_{Smin}) \tag{4}\]  
\[P_{R}=\alpha P_{S}-A_{0}d^{k}\alpha(f)^{d} \tag{5}\]  
Figure 1: Topology 1.