# Self-Organized Proactive Routing Protocol for Non-Uniformly Deployed Underwater Networks
## 3 Overview of the SPRINT Protocol  
The RSS metric is used to estimate which node is the closest neighbor of the transmitting node. The node selects the node that is closest to it to forward the packet. Along with the distance, two more metrics are used: number of hops between the sender and the sink, and the number of neighbors of the candidate nodes. The minimum distance between the nodes also increases the probability of successful packet delivery. The estimation of the RSS is not very precise due to the path loss, the fading, and the limited mobility of the sensor nodes. The spreading of acoustic signal is an important factor for path loss. Spreading losses depend not only on the transmission range, but also on the propagation model adopted: cylindrical (shallow waters) or spherical (deep waters). The path loss is also due to absorption,The absorption of acoustic channels depends on the frequency of the acoustic signal. Total path loss \(A(l,f)\)[19] due to spreading and absorption can be expressed in decibels by the following equation:  
\[A(l,f)=10\cdot\log(\hat{l}^{k})+\alpha(f)\times l\left(\text{dB}\right), \tag{1}\]  
where \(l\) (km) is the transmission range of the acoustic signal, \(k\) is the spreading factor, \(\alpha(f)\) (in dB/km) is the absorption coefficient, and \(f\) (kHz) is the frequency. The value of \(k=1\) is for cylindrical spreading, and \(k=2\) for spherical spreading. A graph of absorption coefficient versus acoustic signal frequency is depicted in Figure 3[20]. We can see that for frequencies up to 20 kHz, \(\alpha(f)\) is \(<\)4 dB/km (approximately). Figure 4[20] shows that Signal-to-noise ratio (SNR) also depends on the frequency. This figure also shows that the bandwidth of acoustic signal depends on the distance. For 100 km, the bandwidth is about 1 kHz, whereas for 5 km it is about 10 kHz. Fading is more severe in shallow water compared to deep water due to multipath. There are no standard fading models for acoustic communication, and experimental measurements are used to predict the channel behavior [20]. For this protocol, the error in estimation of RSS due to losses, fading, and limited mobility of the nodes is not significant as long as a node successfully forms a path with one of its neighbors that is closer to the gateway. The error in node selection may be corrected later by measuring the RSS value at regular intervals using the data packets. Our proposed protocol assumes that the nodes are deployed randomly in a 3D network. The minimum distance between nodes is 300 m and maximum is 1000 m. The transmission power is adaptable and can be adjusted according to the distance between the transmitter and sender. The nodes  
Figure 4: SNR versus frequency and distance. Figure 3: Absorption coefficient versus frequency. are not stationary and keep moving in all directions, although their movement is limited by the length of the binding lines to the surface buoy or the anchor at the sea bottom (see Figure 1). Lists of the acronyms and symbols used in this paper are shown in Tables 1 and 2, respectively. The process of route formation is initiated by the gateway node. The gateway broadcasts a route request (RR) packet, which will traverse throughout the network. When a node receives the RR packet, it measures the strength of the received signal. Initially, all the nodes will transmit at the same power, which will be enough to cover the maximum distance between the nodes. With the help of RSS, the distance between the RR sending node and receiving node is estimated. The RSS indicates the relative proximity between the sending node the receiving node. This is explained in the following example. Assume that three nodes, B, C, and H, are placed as illustrated in Figure 5.  
Suppose that nodes B and C have received the RR packet from the gateway. Nodes B and C will broadcast the RR packet at randomly selected time slots. Since H is the neighbor of both nodes, it will receive the RR packets from nodes B and C. When H receives the RR packet from B, it measures the