1 Introduction

Recently, underwater sensor networks (UWSNs) [1,2,3] have received a great deal of attention from the wireless communication and networking communities. This technology is expected to mark a new era of scientific and industrial underwater monitoring and exploration applications, such as oceanographic data collection, disaster prevention, and pollutant content monitoring. As communication in a UWSN is through acoustic waves and high frequency radio waves are strongly absorbed in water, underwater communication has high bit errors, limited bandwidth capacity and high energy consumption. Further because GPS does not work underwater as the radio signals on which it depends cannot penetrate into water, it is non-trivial to obtain the exact location of each node in a UWSN. These issues lead to excessive data retransmission, high energy consumption and low packet delivery ratio, which all contribute to the difficulties of designing an efficient and reliable routing protocol for UWSNs.

Routing protocols for UWSNs are divided into active routing, passive routing and geographic routing [4,5,6]. Both active routing and passive routing protocols are not energy-efficient as they rely on flooding to build routing, causing high energy consumption by sensor nodes. In contrast, geographic routing protocols are simple and scalable. They do not require establishing or maintaining complete routes to destinations, or transmitting routing messages to update states. A geographic routing protocol is energy-efficient and thus able to prolong the lifespan of a UWSN as it can reduce flooding by exploiting the location information of sensor nodes, which is getting easier to acquire thanks to the development of localization technology.

In a geographic routing protocol, the current forwarding node selects its local optimal neighbor node as a next-hop forwarder to continue forwarding the packet. The choice of this next-hop node is made from the position or depth information of the current forwarder node, that of its neighbors, and that of the destination node. The idea is to advance the packet as close as possible to the destination at each hop.

This paper presents a novel geographic routing protocol referred to as EEL (Energy Efficient Localization-based), which integrates localization and energy-awareness in each routing process of an underwater sensor network. EEL uses location information and residual energy of sensor nodes to greedily forward data packets to sink nodes with the aim to reduce the energy consumption by sensor nodes and ultimately extend the lifespan of the entire network. Selection of a forwarding node is based on its NADV (Normalized Advancement) determined by its depth difference relative to the sending node and the residual energy of the node. Candidate nodes are sorted according to their NADV, and the node with the highest NADV is selected first to forward data packets. The protocol can periodically update the location information of the nodes in an UWSN and effectively adapt to the dynamic topological changes of the network. Simulation results show that EEL outperforms other well-known geographic routing protocols proposed for UWSNs.

The rest of this paper is organized as follows. Section 2 introduces some related work including representative geographical routing protocols and localization algorithms. Section 3 presents a localization model and a NADV link metric model. Section 4 describes the EEL routing algorithm, followed by its performance evaluation in Section 5. Finally, Section 6 concludes the paper with a summary of major contributions and future work.

2 Related work

In this section, we review some of the important existing geographic information routing protocols and localization schemes for UWSNs.

2.1 Geographic information routing protocols

Geographic information routing, which is also known as position-based routing, uses the position information to route packets towards the destination. Each node knows its own geographical location and consequently forwards packets to a locally optimal next-hop node closest to the destination. A geographic routing protocol does not require the establishment or maintenance of complete routes to the destination, thus making it simple and scalable.

The VBF (Vector Based Forwarding) [7] protocol defines the source node to the destination node vector as the route vector. During a routing process, each node does not need to save status information; instead it uses a forwarding factor to calculate the suppression time before forwarding is carried out in order to increase network energy efficiency by avoiding unnecessary forwarding, while the routing information is included in each data packet. The data forwarding of VBF is limited to a “virtual pipe”. A node, upon receiving a packet, forwards it if its distance to the forwarding vector is less than a predefined threshold. To avoid unnecessary transmissions, node transmissions are prioritized by a packet holding time, which is locally computed as a function of its desirableness factor. The desirableness factor of each node is based on its projection to the routing vector. The closer the node is to the routing vector, the higher its desirableness factor will be and the lower its packet holding time will be. VBF can take full advantage of the location information for both the source and destination nodes to improve the efficiency of routing and forwarding as well as to save energy. However, VBF may cause local nodes to undertake excessive forwarding tasks, which results in fast energy consumption of these nodes and reduces the lifespan of the sensor network. In addition, the radius of pipe may significantly influence the routing performance.

In DBR (Depth Based Routing) [8], sink nodes are deployed on the surface of the water, while the source and routing nodes are deployed underwater. Through specialized sensor nodes (such as pressure sensors) that can obtain their own depth information, packets are forwarded from bottom to top with a threshold depth defined to control the efficiency of packet forwarding. The DBR protocol can achieve good performance in dense networks but may cause long transmission delay and high energy consumption in sparse networks.

In the Hydrocast routing protocol [9, 10], when a node determines that it is located at a local maximum, it searches for a node whose depth is lower than its depth and explicitly maintains a path to the node as such. VAPR (Void-Aware Pressure Routing) [11] uses the depth information of the nodes to forward data packets towards the destination, where the next-hop is selected by matching the forwarding direction. However, a drawback of this approach is that it has to discover and maintain an explicit path.

2.2 Localization schemes

The localization technology has been intensively studied in the past decades. In [12, 13], the researchers proposed location services for wireless networks with mobile sinks. Han et al. proposed automatic precision control positioning for wireless sensor networks [14, 15]. Clearly the acquisition of location information on sensor nodes is indispensable to geographical routing algorithms. For static networks, nodes are usually deployed at fixed locations and as such the location information is known. However, an UWSN is usually deployed in a dynamic environment where the location information of the nodes has to be provided by a localization algorithm. The nodes on the surface can usually have their position information measured by means of GPS, but the underwater nodes have to be located using measurement algorithms. Teymorian et al. [16] proposed transforming the three-dimensional underwater sensor network localization problem into its two-dimensional counterpart by employing sensor depth information. Cheng et al. [17] proposed TDOA (Time Difference of Arrival), a positioning scheme based on the time difference of arrival that does not require time synchronization among the nodes. However, a drawback of this scheme is that it can not locate nodes residing outside an enclosed area by four anchor nodes.

Han et al. [18] combined localization and routing to design a localization-based VBF routing protocol for dynamic UWSNs. The protocol can effectively route data from the source nodes to the sink nodes in a dynamic environment. However, a drawback of this algorithm is its high energy consumption. Liu et al.’s work [19] dealt with large-scale mobility by utilizing an adaptive estimation approach known as interactive multiple mode (IMM) filter in their localization scheme. Zhou et al. [20] proposed a distributed hierarchical localization scheme for stationary nodes in large-scale UWSNs. However, high energy consumption is also a major drawback.

Salwa et al. [21] used probabilistic graphs to capture node location information and proposed the Probabilistic Localization Problem (P-LOC) that computes the probability that a target node in a given probabilistic graph can localize itself within a time interval. They devised an iterative algorithm that can deliver an exact solution to the problem if allowed to execute a sufficient number of iterations and otherwise would provide a lower bound of the solution.

The AUV-based methods use AUVs (Autonomous Underwater Vehicles) instead of anchor nodes as the beacon provider [22, 23]. However, some of them incur extra overhead in communication or high latency in localization. In addition, some of them assume that sensor nodes are stationary or cabled with anchors and buoys, which is however not applicable to some UWSNs.

The major issues in the aforementioned work have motivated us to propose a novel energy-efficient localization-based geographic routing protocol that considers both the location information of neighbors and the residual energy of sensor nodes when determining candidate forwarding nodes and their transmission priority level so as to achieve balanced energy consumption and extended network lifespan.

3 Localization and link metric models

3.1 TOA (time of arrival) localization model

The TOA localization [18] method has been widely adopted for the positioning of underwater sensor nodes. It measures distance between nodes and can usually achieve higher positioning accuracy than other methods do. TOA ranging is a simple form of communication between two nodes, where a timestamp is placed in each frame. The distance between two nodes is obtained by multiplying the signal transmission time by the average propagation speed of the signal. Because of the need to measure the transmission time of the signal, it is usually assumed that the clock of each node is synchronized. When the clock drift between sensor nodes is small, its impact on TOA positioning can be neglected. Moreover, the speed of underwater acoustic signal transmission is 5 orders of magnitude lower than that of terrestrial electromagnetic wave. In addition, TOA positioning is affected by multipath effects, especially for shallow seas. For the sake of simplicity in presenting our solution in this paper, we assume a deep sea, where the influence of multipath effects is not considered.

Considering the beacon nodes A, B, C, and D, their position coordinates are denoted (xa, ya, za), (xb, yb, zb), (xc, yc, zc) and (xd, yd, zd) respectively and their underwater acoustic signal transmission times are denoted Δta, Δtb, Δtc and Δtd respectively. Assume that U whose coordinate is denoted (xu, yu, zu) is the node to be located, which can receive the signals from beacon nodes A, B, C, and D. The underwater acoustic signal transmission time Δt is subject to time measurement errors, signal reflection, anti-radiation and other unknown factors. For the sake of simplicity yet without losing generality, we assume that the time measurement error follows a Gauss distribution of zero mean, that is \( {t}_n\sim N\left(0,{\sigma}_t^2\right) \) and that the time measurement errors of nodes A, B, C, and D are denoted tna, tnc and tnd respectively. Further assuming that nodes are synchronous, the location of node U can be solved by Eq. (1):

$$ \left\{\begin{array}{c}\sqrt{{\left({x}_u-{x}_a\right)}^2+{\left({y}_u-{y}_a\right)}^2+{\left({z}_u-{z}_a\right)}^2}=v\left(\varDelta {t}_a+{t}_{na}\right)\\ {}\sqrt{{\left({x}_u-{x}_b\right)}^2+{\left({y}_u-{y}_b\right)}^2+{\left({z}_u-{z}_b\right)}^2}=v\left(\varDelta {t}_b+{t}_{nb}\right)\\ {}\sqrt{{\left({x}_u-{x}_c\right)}^2+{\left({y}_u-{y}_c\right)}^2+{\left({z}_u-{z}_c\right)}^2}=v\left(\varDelta {t}_c+{t}_{nc}\right)\\ {}\sqrt{{\left({x}_u-{x}_d\right)}^2+{\left({y}_u-{y}_d\right)}^2+\left({z}_u-{z}_d\right)}=v\left(\varDelta {t}_d+{t}_{nd}\right)\end{array}\right. $$
(1)

where v is the propagation speed of acoustical signals in water.

We also assume that the depth information of sensor nodes can be obtained through auxiliary means, such as pressure sensors and as such the three-dimensional underwater sensor node localization problem is reduced to a two-dimensional positioning problem. Only three beacon nodes A, B, and C are required to complete a localization process [18]. In particular, zu is known through pressure sensors and its location is derived through Eq. (2):

$$ \left\{\begin{array}{c}\sqrt{{\left({x}_u-{x}_a\right)}^2+{\left({y}_u-{y}_a\right)}^2}=v\left(\varDelta {t}_a+{t}_{na}\right)\\ {}\sqrt{{\left({x}_u-{x}_b\right)}^2+{\left({y}_u-{y}_b\right)}^2}=v\left(\varDelta {t}_b+{t}_{nb}\right)\\ {}\sqrt{{\left({x}_u-{x}_c\right)}^2+{\left({y}_u-{y}_c\right)}^2}=v\left(\varDelta {t}_c+{t}_{nc}\right)\end{array}\right. $$
(2)

3.2 Packet delivery probability

In this subsection, we estimate the underwater packet delivery probability p(m, d) for transmitting m bits between any pair of nodes with distance d, which is used in the next-hop subset forwarding selection procedure of the proposed EEL routing protocol. Details of the underwater acoustic channel model [24, 25] are given as follows.

First, the attenuation model of underwater acoustic signal of frequency f over a distance of d due to large scale fading is given as:

$$ A\left(d,f\right)={d}^ka{(f)}^d $$
(3)

where k is the spreading factor and a(f) is the absorption coefficient. The geometry of signal propagation is described using spreading factor k with commonly used values k = 1 for cylindrical spreading, k = 2 for spherical spreading, and k = 1.5 for a practical scenario. The absorption coefficient a(f), in dB/km for f in kHz, is describe by the Thorp’s formula given by:

$$ 10\log a(f)=\frac{0.11\times {f}^2}{1+{f}^2}+\frac{44\times {f}^2}{4100+f}+2.75\times {10}^{-4}{f}^2+0.003 $$
(4)

Second, the average Signal-to-Noise Ratio (SNR) over distance d is thus given as:

$$ \Gamma (d)=\frac{E_b/A\left(d,f\right)}{N_0}=\frac{E_b}{N_0{d}^ka{(f)}^d} $$
(5)

where Eb and N0 are constants that represent the average transmission energy per bit and noise power density respectively in a non-fading additive white Gaussian noise (AWGN) channel. We further use Rayleigh fading to model small-scale fading where SNR has the following probability distribution:

$$ {p}_d(x)={\int}_0^{\infty}\frac{1}{\Gamma (d)}{e}^{\frac{-x}{\Gamma (d)}} $$
(6)

The probability of error can be evaluated as:

$$ {p}_e(d)={\int}_0^{\infty }{p}_e(x){p}_d(x) dx $$
(7)

where Pe(X) is the probability of error for an arbitrary modulation at a specific SNR value of X. If symbol carries a bit, the probability of bit error over distance d is calculated by:

$$ {p}_e(d)=\frac{1}{2}\left(1-\sqrt{\frac{\Gamma (d)}{1+\Gamma (d)}}\right) $$
(8)

Finally, for any pair of nodes with the distance of d, the delivery probability of a packet with the size of m bits is given by:

$$ p\left(d,m\right)={\left(1-{p}_e(d)\right)}^m $$
(9)

3.3 NADV link metric model

NADV (Normalized Advancement) [24,25,26,27] is a link metric model used in multi-hop wireless networks. The purpose of the NADV model is to find an optimal balance between the proximity of the destination and the cost of the link. In this paper, the link cost is the energy consumed by a node to transmit data, while the proximity to the destination is the distance from a transmitting node to the sink node on the surface.

As shown in Fig. 1, node B has a packet to send to node S, which however is not within B’s communication range. Therefore B has to rely on its neighboring nodes to relay the packet. Neighboring nodes A and C are both within B’s communication range, so the same energy is consumed by B to send data to A or C. However, as the distance from A to S is shorter than that from C to S, B would choose node A to relay data to destination S in order to reduce the number of data forwarding and thereby minimize the energy consumption in the whole data transmission process. Nonetheless, if node A has a higher transmission error rate than C does, node B would be more likely to retransmit lost data, resulting in additional power consumption and consequently high link cost. This scenario particularly illustrates the importance of striking a balance between the proximity of the next hop and the link cost.

Fig. 1
figure 1

NADV model diagram

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In the NADV model [28], the distance between the source node B and the neighboring node n relative to the destination node is defined by Eq. (10):

$$ ADV(n)=D(B)-D(n) $$
(10)

where D(B) and D(n) respectively represent the distance from node B and node n to destination node S. The larger ADV(n) is, the closer node n can forward the packet to the target node. Assuming that the link cost from node B to node n is denoted Cost(n), NADV of the neighboring node n represents the distance of transmitting data from node n with a unit of energy consumption, which is defined by Eq. (11):

$$ NADV(n)=\frac{ADV(n)}{Cost(n)} $$
(11)

Suppose the probability that the m bits of data will be successfully passed on to the neighboring node n is P(D(n), m) [24,25,26,27]. The value of P(D(n), m) can be calculated by Eq. (9). If the link cost is expressed by 1/P(D(n), m), then NADV(n) is defined by Eq. (12):

$$ NADV(n)= ADV(n)\ast P\left(D(n),m\right) $$
(12)

4 The EEL routing algorithm

Suppose that each node has its own clock that is synchronous or quasi-synchronous. The EEL routing algorithm consists of the two phases of localization and routing. The routing phase is based on the node location information acquired during the localization phase.

4.1 Localization process

In the three-dimensional dynamic network architecture adopted in this paper, the beacon nodes are deployed on the water surface, and their location information is obtained through GPS. The position coordinates of the nodes to be located can be obtained by Eq. (2). According to the different depths of working environments, location of nodes needs to consider two cases: shallow sea and deep sea. Figure 2 depicts the localization of underwater sensor nodes.

Fig. 2
figure 2

Schematic diagram of underwater sensor node diffusion localization

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When all nodes of a network are working in a shallow sea, any unknown node in the network can communicate directly with at least three beacon nodes to complete its localization. For a node in a deep sea, it has to rely on diffusion localization. In Fig. 2, the original beacon nodes are deployed on the surface of water and periodically broadcast their location information by sending location packets. For an unknown node near the surface of water, its localization starts with the three-edge location and after that it becomes a “promoted beacon node”. Other unknown nodes carry out localization through original beacon nodes or enhanced beacon nodes before being converted to “promoted beacon nodes”. Each beacon node broadcasts its location information to be obtained by an unknown node in the network, which is subsequently transformed into a “beacon node”. The localization process proceeds as such until all unknown nodes in the network are identified.

The localization process requires a grouping counter with an initial value of zero to count the number of beacon nodes suitable for localization. Each original beacon node is laid out on the water surface, which periodically broadcasts the location grouping. Upon receiving the location grouping, an unknown node extracts information necessary for localization and increments the grouping counter by 1. When the counter reaches 3, localization of the node is carried out using Eq. (2) and at this moment, this unknown node is turned into a “promoted beacon node”, which can generate and broadcast location grouping using its own information. Generally speaking, location grouping generated by an original beacon node or a promoted beacon node is used for the localization of an unknown node. Through this pervasion localization method, all unknown nodes are gradually turned into “promoted beacon nodes”, thereby accomplishing the localization of the entire network. Change of network topology can also be effectively accommodated by adopting the periodical localization method.

4.2 Selection of next-hop node

A sensor node can calculate the relative distances between itself and its neighboring nodes through the TOA localization algorithm to generate the next-hop candidate nodes set from which the next-hop node is selected for forwarding data packets. In this paper, we improve the NADV algorithm by introducing the residual energy of nodes so that nodes with high residual energy are more likely to be selected as the next hop, which can balance the energy consumption and extend the lifespan of nodes in the network.

To avoid consuming energy by data wandering between nodes of similar depth, we also define a depth threshold to control the next-hop selection as defined in Eq. (13): if the depth difference is less than the threshold of the neighboring node, only the depth and the depth difference are considered [28]; however if the depth difference is larger than the threshold value of the neighboring node, the residual energy of the node is factored in.

$$ ADV(n)=\left\{\begin{array}{cc}\mid Depth- Depth(n)\mid /R,& \mid Depth- Depth(n)\mid <\theta \\ {}\mid Depth- Depth(n)\mid /R+ Energy(n)/E,& \mid Depth- Depth(n)\mid \ge \theta \end{array}\right. $$
(13)

where Depth is the depth of the sending node, Depth(n) is the depth of the neighboring node n, R is the communication radius of the node,θis the depth threshold, Energy(n) is the residual energy of the neighbor node n, and E is the initial energy of the node. Thus, candidate nodes with higher residual energy have a higher probability to be selected to relay data when they have similar depths. When the neighboring nodes are close to the sending nodes, the distance difference is used as a reference so that short distance relay of data can be avoided as it would generate unnecessary energy consumption.

We use Eqs. (11) and (13) to calculate the NADV of each candidate forwarding node and create a sorted list Fi(t) ordered by their NADV from high to low at time t. The first node in Fi(t) will be chosen as the next-hop forwarding node to transmit a data packet and only if it fails to do so, the next one in Fi(t) would be chosen. The process continues in that order until the data has been successfully delivered. In EEL, when the kth node receives the packet, it will wait for the 1st to the (k − 1)thnodes to complete their propagation. After that, if the kth node can not confirm the transmission of the packet, it will broadcast it. Thus, its waiting time [25, 26] is defined as:

$$ {T}_w^i={T}_p+\sum \limits_{i=1}^k\frac{D\left({n}_i,{n}_{i+1}\right)}{v}+k\times {T}_{proc} $$
(14)

where TP is the remaining propagation time, Tprocis the packet processing time, D(ni, ni + 1) represents the distance from node ni to node ni + 1, and v is the speed of sound underwater.

After the optimal next-hop node has been selected, the source node forwards the data packet to the selected forwarding node. The routing process continues as such until the data packet has been delivered to the sink node.

5 Simulation results

To evaluate the performance of the proposed EEL routing algorithm, we compare it with the existing protocols of Flood and VBF using Aqua-Sim [29, 30] as the routing protocol simulator. Aqua-Sim was developed based on NS-2, a popular network simulator, and has the ability to simulate UWSNs. Compared with other wireless network simulators, Aqua-Sim offers many distinctive features such as underpinning to discrete-event-driven networks, support for mobile and 3D networks, simulation of high-fidelity underwater acoustic channels, and implementation of a complete protocol stack.

We randomly deploy 800 sensor nodes in a three-dimensional region of 2000 m*2000 m*2000 m and 64 sink nodes at a sea surface region of 2000 m*2000 m. Each sensor node has an initial energyE0 = 100J, a transmission range of R = 600 m, a positioning time of 100 s, and a maximum/minimum movement speed of 3 m/s and 0.2 m/s respectively. Assume that the packet size is 100kB and energy consumption rate of transmitting data is at 60uJ/bit.

This paper evaluates different protocols using the following performance indicators: 1) positioning performance; 2) packet transmission rate: the ratio of the number of packets successfully received by the sink node to the number of packets sent by the source node; and 3) energy consumption: total energy consumed by all nodes per unit of time.

5.1 Localization performance

5.1.1 Effect of the number of sink nodes on positioning accuracy

As shown in Fig. 3, the positioning accuracy is closely related to the number of sink nodes in such a way that the positioning error decreases while the number of sink nodes increases. Figure 4 further shows the effect of the number of underwater nodes on the average positioning error. With diffusion positioning, unknown nodes may be converted into “promoted beacon nodes” in the process of localization, which consequently increases the intensity of beacons in the network. Therefore, increasing the number of unknown nodes can also improve positioning accuracy. It is worth mentioning that node density may have a negative influence on positioning accuracy, which however is relatively low as compared to the positive influence of beacon intensity.

Fig. 3
figure 3

The influence of the number of beacon nodes on the average localization error

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Fig. 4
figure 4

The influence of the number of underwater nodes on the average localization error

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5.1.2 Effect of the standard error of time measurement error on positioning accuracy

Due to the positioning mode of TOA, the standard error of time measurement error affects directly the magnitude of range error in three-side positioning. It can be seen from Fig. 5 that the average location error responds approximately linearly to the standard deviation of the time measurement error under different network density. However, the EEL routing is based on localization, and the performance of EEL can be directly affected by positioning performance in this paper.

Fig. 5
figure 5

Effect of the standard error of time measurement error on average localization error

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5.1.3 Effect of the standard error of time measurement error on packet delivery radio

Figure 6 shows the effect of the standard error of time measurement error on packet delivery rate in EEL routing. With the increase of the effect of the standard error of time, the average location error of network location is gradually increasing, which results in the decrease of packet delivery rate of routing algorithm based on location, that is, the decrease of routing performance of EEL.

Fig. 6
figure 6

Effect of the standard error of time measurement error on packet delivery radio

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From the above research on the positioning performance of the nodes, it can be seen that the average positioning error of the underwater node location is larger than that of the terrestrial wireless sensor networks, generally in the tens of meters to the highest level of 100 m. This is mainly caused by the diffusion of location errors.

The beacon nodes are usually deployed near the surface of water, while the density of beacon nodes is usually not very high in a large-scale underwater sensor network. However, the nodes that have been located are usually involved in the subsequent positioning of unknown nodes over to which their positioning errors will be spread, hence reducing the positioning accuracy of the unknown nodes.

5.2 EEL routing performance

5.2.1 Packet delivery radio

Figure 7 shows the data transfer rate of the three protocols, where the flood routing is optimal, while the packet delivery ratio of EEL is higher than that of the VBF protocol. The outperformance of EEL over VBF is mainly due to the improved positioning accuracy achieved through the proposed positioning technique that converts unknown nodes into “promoted beacon nodes” and hence increases the intensity of beacons in the network. For all the three protocols, with the increase of network nodes, the density of nodes gets higher and as such the distance between nodes becomes shorter, the connectivity rate gets higher, and so does the data delivery rate.

Fig. 7
figure 7

The influence of the number of nodes on packet delivery ratio

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5.2.2 Energy consumption of localization

Localization of nodes is the cornerstone of the proposed EEL routing algorithm, which itself consumes energy. Figure 8 reveals the relationship between the ratio of energy consumed by the localization process and the total consumed energy and the number of unknown nodes in the EEL routing algorithm in which the number of beacon nodes is set to 30 to ensure a high positioning accuracy. It is clear that the ratio of energy consumed by the localization process to the total consumed energy decreases with the number of unknown nodes. It can be seen that energy consumed by routing overtakes the energy consumed by localization when the number of unknown nodes reaches 150 and becomes more predominant with more unknown nodes added to the network.

Fig. 8
figure 8

The influence of the number of underwater nodes on the ratio of energy consumed by the localization process and the total consumed energy

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It can also be seen from the subsequent simulation that compared to the energy consumed by a flooding algorithm, the energy saved by the EEL algorithm is significantly more than that costed during the localization process. In general, the localization-based EEL routing is more suitable for intensive networks.

5.2.3 Average energy consumption

As shown in Fig. 9, flood routing has the highest energy consumption, VBF routing performs better than flood routing, while EEL routing performs the best. The total energy consumption in the network includes the energy consumed by the routing process and the energy consumed by the localization process. When the network is sparse, the average energy consumption of the network would be high as the packet delivery rate is low in the routing process and as such the positioning process would dominate the energy consumption. With the increase of the number of nodes in the network, the packet delivery rate in the routing process increases and consequently the average energy consumption decreases. When the number of nodes reaches a certain level, routing instead of positioning becomes dominant in the energy consumption and as such the average energy consumption starts to increase with the number of nodes.

Fig. 9
figure 9

The influence of the number of nodes on average energy consumption

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6 Conclusions and future work

Localization and routing are two major challenges in UWSNs. In this paper, we propose a novel routing protocol EEL for UWSNs based on geographic and location information of nodes. Considering the three-dimensional dynamic UWSNs, we combine these two aspects together to design the routing protocol. During the localization process, the diffusion localization can effectively locate the nodes in UWSNs. During the routing process, EEL uses a new greedy approach to deliver packets to sink nodes, improving both the data transmission ratio and energy consumption. Simulation results show that EEL can effectively locate the nodes while significantly improving the packet delivery ratio and reducing the energy consumption as compared to VBF and Flooding routing protocols.

In future work, we will explore other important features of geographic routing in order to reduce its energy consumption, such as average end-to-end delay and average number of candidates. The methodology of depth adjustment of nodes is potentially useful for balancing energy consumption in UWSNs. It can be used to move a node that has a high centrality score from hot spots to locations at the edge of the network, when its energy is below a defined threshold.