The clock or time synchronization problem in wireless sensor networks (WSNs) requires a procedure for providing a common notion of time across the nodes of WSNs. In general, clock synchronization is viewed as a critical factor in maintaining the good functioning of WSNs due mainly to their decentralized organization and timing uncertainties caused by the imperfections in hardware oscillators and message delays at the physical and medium access control (MAC) layers. In addition, synchronization of the nodes of wireless sensor networks is crucial for implementing fundamental operations such as power management, transmission scheduling, data fusion, localization and tracking, and security protocols to name only a few applications.

The aim of this book is to provide an introduction to the clock synchronization problem of WSNs from a statistical signal processing viewpoint. Therefore, most of the topics presented in this book deal with building efficient clock offset estimation algorithms and performance benchmarks for general synchronization approaches that rely on sender–receiver and receiver–receiver timing packet exchange mechanisms. A summary of the key features of the most representative protocols proposed for clock synchronization of WSNs is also presented, together with some interesting open research problems.

Synchronization of WSNs is currently a very active research field with a large number of results and very diverse contributions coming from an equally diverse body of researchers: computer scientists, electrical engineers, mathematicians, statisticians, etc. Despite the deployed efforts, the general problem of building efficient global synchronization protocols for large-scale wireless sensor networks is still open and the proposed results are still introduced in a quite ad-hoc manner, lacking comprehensive design and optimization studies to assess and improve their performance in a systematic fashion.

Developing long-term and network-wide timing-synchronization protocols that are energy-efficient represents one of the key strategies for the successful deployment of long-lived sensor networks. However, most of the existing protocols have focused only on achieving synchronization for short timescales, and are not appropriate for long-term synchronization. In the adaptive-clock synchronization protocols and, optimizing the network synchronization protocol was considered with the aim of achieving a specific synchronization accuracy with minimal energy consumption. The adaptive-clock synchronization protocol represents a probabilistic extension of RBS and proposes a mechanism for determining the minimum number of synchronization beacons and the synchronization rate in order to achieve a preestablished clock synchronization error. Ganeriwal et al. proposed for the first time a measurement-based study for designing an energy-efficient rate-adaptive long-time synchronization protocol (RATS) that adapts the synchronization period, number of beacons, and length of prediction window to achieve an applicationspecific accuracy.

Motivated in part by these preliminary contributions, we propose a more powerful AMTS scheme with the goal of achieving a long-term network-wide synchronization with minimal energy consumption. AMTS exhibits a number of attractive features:

• It represents a significantly enhanced extension of TPSN aiming at minimizing the overall energy consumption in large-scale and long-lived sensor networks.

• It is equipped with flexible mechanisms to adjust the synchronization mode, the period of network-wide timing synchronization (resynchronization rate), and schemes for joint estimation of clock offset and skew in order to achieve long-term reliability of synchronization.

• It employs a sequential message exchange technique and an energy-efficient signaling scheme to further reduce the energy consumption in synchronization procedures.

• […]

Turning our attention in this chapter to a general receiver-receiver protocol, we address the synchronization problem in which a master node sends reference broadcasts to the neighboring nodes (e.g., RBS). As discussed earlier, the main advantage of adopting such an approach is that all the deterministic and non-deterministic delay components on the sender side (such as send time, transmission time, channel access time) are eliminated and hence the clocks of the beacon-receiving nodes can be very tightly synchronized. The importance of RRS increases due to the fact that the channel access time at the MAC layer is the largest source of error in solving a synchronization problem. This chapter applies both classical and Bayesian estimation approaches to synchronize a set of nodes receiving timing messages from a master node.

The main topics in this chapter are as follows. First, the JMLE for clock phase offset and skew under the exponential noise model is formulated and found via a direct algorithm. Second, the Gibbs sampler is proposed for joint clock phase offset and skew estimation and is shown to provide superior performance relative to JMLE. Finally, lower and upper bounds for the MSE of JMLE and Gibbs sampler are introduced in terms of the MSE of the MVUE and the conventional BLUE, respectively.

As discussed in Chapter 2, there are a number of key factors in designing time synchronization protocols for WSNs, such as accuracy, energy consumption, scalability, acquisition time, implementation complexity, and robustness. The most important and crucial factor is the tradeoff between accuracy and energy consumption. Increasing the synchronization accuracy in general requires more energy consumption to transmit the RF timing messages among sensor nodes. But, the energy consumption for synchronization should be kept as small as possible since the power resources of common wireless sensors are strictly limited and are not rechargeable in general. However, for most of the existing synchronization protocols, there is a lack of in-depth analysis to assess the energy-efficiency tradeoff of synchronization algorithms. This chapter describes in detail the characteristics of the PBS protocol which efficiently combines both SRS and ROS approaches (described in Chapter 4) to achieve network-wide synchronization with a significantly reduced number of synchronization messages, i.e., with less energy consumption.

The main topics in this chapter are as follows. First, there is a brief summary of the PBS technique used to achieve network-wide synchronization for singlecluster sensor networks based on ROS, the newly developed approach, described in Chapter 4. Second, the performance of PBS is analyzed and compared with those of other well-known protocols. Third, for the extension to general multicluster sensor networks, use of the network-wide pair selection algorithm and the group-wise pair selection algorithm is proposed to select the best synchronization sequence aiming at minimizing the overall energy consumption, respectively. Fourth, the performance of the proposed pair selection algorithms is analyzed with respect to the number of required synchronization messages (i.e., energy consumption).

Although the MLE derived in the previous chapter is not computationally very complex, WSNs can still benefit from some simplified schemes to estimate the clock parameters specially when the synchronization accuracy constraints are not extremely stringent but the energy conservation constraints are. In addition, to estimate both the clock offset and skew in the Gaussian noise case, knowledge of the fixed portions of delay d was required, which is not usually available beforehand. Therefore, in this chapter, two simple algorithms will be developed to estimate the clock offset and skew regardless of the distribution of the delays, and these are very suitable for the low-power-demanding regime of WSNs. The proposed estimators can be implemented using simple steps and present remarkably low complexity. These estimators and the derived performance bounds are targeting practical applications, and are of much significance due to their robustness to the actual distribution of network delays.

The main topics in this chapter are as follows. In the first proposed estimation scheme, the clock skew is estimated using only the first and the last data samples, since the difference between timestamps is largest between those two samples for any distribution, and then maximum-likelihood-like estimators (MLLEs) and Cramer–Rao-like lower bounds are derived for the clock skew. Subsequently, the data are processed to remove the effect of skew and then the clock offset is estimated, which just requires a few computations. The second proposed clock offset estimation scheme fits a line between two points, the differences between the first and the fourth timestamps, that are at a minimum distance apart, yielding both the clock offset and skew regardless of the underlying actual distribution.

As described in Chapter 3, various protocols targeting clock synchronization in WSNs have been proposed, mainly based on packet synchronization techniques. In general, this family of protocols can be broadly divided into two fundamental approaches: sender–receiver synchronization (SRS), see, e.g., and receiver–receiver synchronization (RRS), see, e.g. SRS relies on the traditional model of two-way message exchanges between a pair of nodes. For RRS, the nodes to be synchronized first receive a beacon packet from a common sender, then compare the receiving times of the beacon packet to compute the relative clock offsets. Most of the existing time synchronization protocols rely on one of these two approaches. For instance, NTP and TPSN adopt SRS since they depend on a series of pairwise synchronizations that assume two-way timing message exchanges. Notice also that the RBS protocol relies on RRS since it requires pairs of message exchanges among children nodes (except the reference) to compensate their relative clock offsets.

A new approach for time synchronization, called receiver-only synchronization (ROS), has also been proposed. The aim of ROS is to minimize the number of required timing messages and energy consumption during synchronization while preserving a high level of accuracy. This approach can be used to achieve network-wide synchronization with many fewer timing messages than other wellknown protocols such as TPSN and RBS.

Next we will present and analyze each of these synchronization approaches and illustrate how the general design considerations can be resolved in these approaches.

Clock synchronization between any two nodes is generally accomplished through message exchanges. Due to the presence of non-deterministic and possibly unbounded message delays, messages can be delayed arbitrarily, which makes the clock synchronization very difficult. The most commonly proposed nondeterministic network delay distributions are the Gaussian, exponential, Gamma, and Wei-bull pdfs, see e.g. In general, it is difficult, if not impossible, to assess which distribution model may be fit to capture the network delay distributions in a given WSN. This is due to the fact that various factors may impact the distribution of network delays differently. The Gaussian pdf and the exponential pdf have also been proposed to model the network delays in WSNs. Here, the ML estimators for clock offset estimation in the presence of Gaussian and exponential network delay distributions will be referred to as the Gaussian ML (GML) and exponential ML (EML), respectively. The simulation results in Figure 6.4 showed that GML and EML are quite sensitive to the network delay distributions. Therefore, one important problem to cope with is the design of clock offset estimation schemes that are robust with respect to the distribution of the unknown network delays.

This chapter deals with the development of clock offset estimators for WSNs that are robust with respect to the possible asymmetries and the unknown or possibly time-varying distributions of the network delays in the uplink and downlink of message exchanges. The two-way message exchange mechanism used in the NTP and TPSN is adopted here as the clock synchronization approach between two nodes of the WSN.