1. Introduction
In recent years, underwater sensor networks have played an important role in coastal surveillance, environmental monitoring, undersea exploration, disaster prevention, mine exploration, and other fields. Considerable attention has been paid to the research and application of underwater sensor networks. However, because of the characteristics of underwater acoustic channels, the research and application of underwater sensor network communication has suffered from many challenges [
1,
2]. The time synchronization of underwater sensor networks, as one of the supporting technologies, is also very different from the time synchronization of terrestrial wireless sensor networks.
Time among nodes is inconsistent due to the difference of angular frequency of the crystal oscillator and the difference of boot time of the distributed systems, in which nodes go out of synchronization as time elapses. Most applications in networks require that all sensor nodes have a common notion of time. Depending on the time synchronization level required, these applications can be classified into three categories [
3]. Some applications only require the order of events that occur, while other functionalities require the time interval of each of the occurrences. There are also some applications that require an absolute time at which each event occurs, and the implementation of these applications depends on a precisely synchronized time among network nodes. For example, the time-sensitive data with time stamping information from multiple sensor nodes are then aggregated to a cluster head node, and other applications such as node tracking and location require precise timing. In addition, not only would the application layer require time synchronization; other layers, such as the medium access control (MAC) layer, also have considerable functionalities that benefit from time synchronization.
Numerous time synchronization protocols for terrestrial wireless sensor networks have been proposed in various publications, such as the fine-grained network time synchronization using reference broadcasts (RBS) [
4], the timing-sync protocol for sensor networks (TPSN) [
5], the flooding time synchronization protocol (FSTP) [
6] and others [
7,
8,
9,
10]. However, these protocols cannot be directly applied to underwater sensor networks. This is because they assume that the propagation delay among nodes is negligible. However, in underwater acoustic communication, with a propagation speed (roughly 1500 m/s in water) of nearly five orders of magnitude lower than terrestrial radio freqency (RF), assumptions about rapid communication are incorrect. Meanwhile, due to the mobility of the sensor nodes that are not propelled or self-propelled, the propagation delay among nodes in water is a dynamic variation, which should be considered in the new approach. In addition, the terrestrial synchronization algorithms typically allow nodes to perform frequent re-synchronization and are not highly dependent on available bandwidth and energy constraints. In contrast, underwater acoustic communication systems may have a bandwidth of only a few hundred kilohertz, while bandwidth would drop to a few kilohertz if the targeted communication range reaches several tens of kilometers [
1]. So the bandwidth of the system restricts time synchronization overhead that is not sufficient for frequent re-synchronization. Furthermore, nodes restricted by energy constraints and recharging limitations should avoid frequent re-synchronization.
Time synchronization solutions for underwater sensor networks aim to solve the challenges, including the long and dynamic propagation delay, and especially the dynamic propagation delay caused by the mobility among nodes [
11,
12]. This is an important issue on which recent synchronization schemes focus. In this paper, through analyzing the existing protocols, we propose a Doppler-enhanced time synchronization scheme for mobile underwater sensor networks, called DE-Sync. Our new scheme is a novel synchronization solution for the context of the dynamic propagation delay.
Different from the existing time synchronization protocols based on the Doppler effect, DE-Sync has two main distinguishing attributes. First of all, DE-Sync considers the effect of the clock skew during the process of estimating the Doppler scaling factor, which compensates for the estimation error introduced by the clock skew and increases the accuracy of estimation in the Doppler scale that affects the accuracy of time synchronization. Secondly, the Doppler scaling factor, instead of the relative moving speed between nodes, is contained in the exchange messages, which reduces the quantity of division computations. Because the acoustic velocity in water is a function of depth, temperature and salinity, our new approach does not directly involve the calculation of acoustic velocity, which reduces the error of estimating the clock skew and offset during the process of linear regression, and improves the accuracy of time synchronization. In our comparison of simulation results, the performance of DE-Sync protocol is better than that of existing time synchronization protocols for mobile underwater sensor networks, in both accuracy and energy efficiency.
DE-Sync proposed in this paper deals with time synchronization based on Doppler scale estimation. For underwater acoustic communication, Doppler scale estimation is typically a critical research topic. There are two popular methods for Doppler scale estimation [
13]. One method is to send Doppler insensitive signals for Doppler scale estimation [
14,
15,
16,
17]. Another method is to send a Doppler sensitive waveform for Doppler scale estimation [
18,
19,
20,
21]. Both of the two methods have a common application limitation, which is not ideal for real time processing of the estimation algorithm. DE-Sync adopts a combined Doppler scale estimation scheme that involves two steps to enhance the accuracy of the Doppler scale factor acquired in real time [
22,
23,
24]. In the first step, one linear frequency modulation (LFM) and two identical short orthogonal frequency-division multiplexing (OFDM) symbols preceded by a cyclic prefix (CP), are used as a preamble for initial Doppler scale estimation. In the second step, fine Doppler scale estimations can be achieved based on the CP of each CP-OFDM block.
The remainder of this paper is organized as follows. In
Section 2, we review the previous works of the existing time synchronization protocols for underwater sensor networks. We then provide a description of DE-Sync in
Section 3. Simulation results are shown in
Section 4. Finally, we give our conclusions in
Section 5.
2. Related Work
The design of time synchronization protocol for underwater sensor network needs to consider two main factors, one is the long propagation delay during communication between nodes, and the other is the relative mobility between nodes. At present, a few time synchronization protocols for underwater sensor networks have been proposed, such as the time synchronization for high latency acoustic networks (TSHL) [
25], the time synchronization protocol for underwater mobile networks (MU-Sync) [
26], the efficient time synchronization for mobile underwater sensor networks (Mobi-Sync) [
27], the Doppler-based time synchronization for mobile underwater sensor networks (D-Sync) [
28], and the time synchronization scheme for mobile underwater sensor networks (TSMU) [
29]. However, these protocols have their own application scenarios and they all make different assumptions.
TSHL was the first time a synchronization algorithm was designed for high latency networks, networks in which the algorithm is organized in two phases. TSHL assumes the constant propagation delay among sensor nodes and, essentially, they assume a static network; however, nodes typically move with the ocean current (around 0.83–1.67 m/s) [
30], especially in the case of self-propelled vehicles which move faster, such as autonomous underwater vehicles (AUVs); therefore, the protocol cannot handle mobile scenarios.
MU-Sync takes account of time variability in the propagation delay due to the relative motion of nodes using a two-phase operation, namely the skew and offset acquisition phase, and the synchronization phase. MU-Sync assumes that the one-way propagation delay can be calculated as half of the round trip time, which significantly deteriorates the performance of MU-Sync when the nodes move fast, especially when the unsynchronized nodes respond to the cluster head for a long period of time.
Mobi-Sync introduces spatial correlation of the nodes’ velocities to estimate the varying time propagation delay. In the protocol, all nodes are classified into three categories: surface nodes, super nodes and ordinary nodes. Surface nodes are equipped with a global positioning system (GPS) to obtain the global time reference, while super nodes can communicate directly with surface nodes to achieve time synchronization. However, Mobi-Sync applies only to certain special scenarios, which is because they assume that the exact correlation among neighboring nodes is known, which is difficultly obtained for many actual networks such as those with a long distance between nodes or on self-propelled vehicles.
D-Sync leverages the Doppler shift caused by the relative motion of nodes in underwater environments. D-Sync does not consider the effect of the skew during the process of estimating the Doppler scaling factor, which reduces the accuracy of the Doppler shift estimation and affects the accuracy of time synchronization. Therefore, as the initial skew increases, the accuracy of time synchronization deteriorates.
TSMU utilizes the Doppler effects caused by the relative motion between nodes during the process of time synchronization. Meanwhile, they consider the effect of the skew during the process of estimating the Doppler scaling factor from the physical layer. Furthermore, the Kalman filter and calibration process are exploited during the process of time synchronization. However, due to the velocity of sound in water as a function of depth, temperature and salinity, the estimation of sound velocity is directly applied into the computation during the process of synchronization, causing extra errors. In addition, there are three parameters to be adjusted, initial skew, etc., which affect the accuracy of synchronization and efficiency.
The closest work to our proposed solution is D-Sync, and there are two key differences between DE-Sync and D-Sync: one is that DE-Sync considers the effect of the clock skew during the process of estimating the Doppler scaling factor, and the other is that DE-Sync uses the Doppler scaling factor instead of the relative moving speed among nodes when performing linear regression. Therefore, a performance comparison between DE-Sync and D-Sync is given in
Section 4.
3. Protocol Description
3.1. Overview of the DE-Sync
The clock timer inside each node uses a crystal oscillator operating at a certain angular frequency, which determines the rate at which the clock runs [
3]. Typically, the clock inside each node has an intrinsic drift in angular frequency due to the manufacturing process. The numerous synchronization protocols use a common time model that DE-Sync also follows to estimate the skew and offset. The local time of any node is relevant to the reference time by Equation (1).
where
T denotes the local time of nodes at time
t,
t is the reference time, i.e., beacon time.
α and
β are the relative clock skew and the offset, respectively. Moreover,
α is related to the angular frequency of the crystal oscillator and
β is affected by the starting time of the system.
The time synchronization procedure of DE-Sync consists of three phases: data collection, linear regression and calibration. In the data collection phase, the unsynchronized node collects the time stamps from synchronization messages as well as their Doppler scale factors, with two-way synchronization message exchanges. In the linear regression phase, the unsynchronized node performs the first linear regression with LS (least square estimation) to estimate the clock skew and offset. In the calibration phase, the unsynchronized node performs the calibration process by updating the initial skew, and re-performs the synchronization process to obtain the final clock skew and offset. All parameters are listed in
Table 1.
3.2. Impact of the Clock Skew
Let us assume that beacon node
A is used as a reference node which has an ideal clock and node
B is an unsynchronized node which has a drifting time—a skew with respect to an ideal clock. Let node
B be synchronized with node
A. The signal received from the baseband, going from node
A to node
B, is given by Equation (2), which can be formulated as the summation of signals arriving along multiple physical paths [
29,
31].
In this equation,
Np stands for the path number,
aAB denotes the measured Doppler scale factor, and
Ap and
τp denote amplitude and delay of the
pth path, respectively. Based on Equation (1), due to a drift of the skew between the clocks of nodes, when the time in node
A is expressed as
, the basis time in node
B can be written as
.
aAB depends on both relative motion speed and clock skew difference among nodes, and it is expressed as:
where
am denotes the Doppler scale factor induced by the node mobility. Similarly, upon receiving the synchronization message sent from node
B, the basis time in node
A can be written as
, the Doppler scale factor measured by node
A, namely
aBA, is expressed as:
So, based on the measurement of the Doppler scale factor,
am is expressed as:
As a result, since the clock skew α in the initial phase is unknown, α is assigned with an initial value “1”. After the first linear regression, am can be calibrated based on the estimation of α. Moreover, am is used to re-perform the synchronization process to obtain the final clock skew and offset.
3.3. Details of the DE-Sync
In DE-Sync, the synchronization process is initiated by the unsynchronized node. When the unsynchronized node
B moves to the coverage area of the underwater sensor networks, it sends a synchronization request to beacon
A. Meanwhile, node
B records the sending time-stamp
T1 obtained from the MAC layer right before the message departs. Upon receiving the synchronization request, beacon
A marks its local time as the receiving time-stamp
T2 and records the Doppler scale factor
aAB obtained from the physical layer. Then, beacon
A needs to back off a random time, namely
Tbackoff, to avoid message collisions before it transmits a response message back to node
B at time
T3, which contains
T2,
T3 and
aBA. As before, when receiving the synchronization response message, node
B records its receiving time and the Doppler scale factor
aAB. After a few rounds of message exchanges, node
B will collect a set of time-stamps consisting of
T1,
T2,
T3 and
T4, and the measured Doppler scale factor consisting of
aBA and
aAB.
Figure 1 shows the message exchange process between node
A and node
B.
Now, we will derive a set of equations used by DE-Sync to synchronize nodes.
As given by Equation (1), the following set of equations of the node’s local time can hence be derived:
t1,
t2,
t3 and
t4 denote the reference time, and they derive the following relationship:
Hence, the local time of node
A and node
B can be expressed as:
Considering sensor node mobility, propagation delay
τ1 is not essentially equivalent to
τ2, and based on Equation (6), we get:
Let
vm be the average of relative speed among nodes from
t2 to
t4, hence
. Combining with (6), we get:
If we let
, and combine Equations (7) and (8), then
τ1 and
τ2 are solved as:
τ1 and
τ2 are substituted into (6), which give us the following equation:
Node A at t2 measures the Doppler scale factor expressed as , and node B at t4 measures the Doppler scale factor expressed as .
Let the average of
vAB and
vBA, namely interpolation, replace the average of relative speed among nodes. Hence
vm = 0.5 × (
vAB +
vBA) +
εv, i.e.,
vm = 0.5 ×
c × (
aAB +
aBA) +
εv, where
εv denotes error due to random noise and the interpolation error. We get:
and if
θ is substituted into (10), we get:
Based on Equation (12), we perform linear regression to estimate the skew and offset, which is as follows:
As given by (13), after N rounds of message exchanges, Y is a N × 1 vector and H is a matrix with N × 2 entries. The skew and offset can be estimated by the above equation.
As described earlier, we have discussed the impact of clock skew for the Doppler shift factor, and the skew is assigned with an initial value “1”. However, the skew of the unsynchronized node cannot be 1. In the calibration phase, the initial skew is updated with the estimated skew obtained by using the Equation (13). The unsynchronized node carries out the calibration process to correct the measured Doppler scale factor and re-calculate the clock skew and offset. The calibration process will run iteratively until it reaches the final criterion, which is either when the number of runs reach the maximum iteration (for example: 2, according to the later simulation result) or the difference between estimated skews of two runs is less than the set threshold (for example: 50 part per million (ppm)).
3.4. Error Analysis
In DE-Sync, there are two main error sources: the error
εnoise due to random noise in Doppler measurements and the error
εinterp due to the fact that Doppler measurements are not available continuously. In each round of message exchange, the average of the two measured Doppler scale factors, obtained at the end of each message transmission, is used instead of continuous measurements, which lead to the interpolation error. In Equation (11),
εv is expressed as:
In Equation (12),
ε is expressed as:
Combining with (6), where
T4 is substituted into (14), we get:
Combining with Equation (14), where
εv is substituted into (15), we get:
Tbackoff =
T3 −
T2. When considering (17), and the parameters affecting the estimation of error,
εinterp is a main factor. Referring to Equation (7), we get:
Following the derivation in [
28],
,
Amax and
Aavg denote the maximum relative acceleration and average relative acceleration, respectively. Considering equation (18), there is an indication that estimation error in DE-Sync mainly occurs from random noise, i.e.,
εnoise, if nodes move at a constant speed or uniform acceleration.
εnoise is a random variable which is subject to Gaussian distribution [
20].
5. Conclusions and Future Work
In this paper, we present DE-Sync, a novel synchronization scheme developed for mobile underwater sensor networks, which is a Doppler-enhanced time synchronization. Compared to the existing schemes, DE-Sync does not directly use the Doppler scale factor to calculate the relative speed between nodes. Meanwhile, it conducts linear regression without using the estimates of sound propagation speed, which reduces errors. Furthermore, it compensates for the effect of the skew when using a Doppler scale factor, which improves the accuracy of time synchronization. Meanwhile, when the initial skew reaches a certain value, the performance of DE-Sync will be significantly better in those conditions. Our simulation results show that DE-Sync is a high-precision time synchronization approach with a low message overhead.
Moreover, we will also explore other schemes to enhance the accuracy of synchronization and to reduce the message overhead for mobile underwater sensor networks.