Clock synchronization is a crucial requirement for coordinated activities in distributed networks. As an effective solution, Precision Time Protocol (PTP) is tailored to provide tight synchronization which, however, suffers from packet delay variation (PDV). Therefore, it is a challenging task to mitigate the uncertainties of PDV so that clock skew and offset can be estimated with higher accuracy and robustness. Under the assumption of delay symmetry, PDV is caused by unavailable prior information about the statistical distributions of stochastic delay. This paper investigates a robust estimator that can achieve joint estimation for clock skew and offset under delay with unknown distributions by employing the competitive learning-based rival penalized expectation maximization (RPEM) algorithm to learn the unknown probability density function (pdf) of stochastic delay. Moreover, for the asymmetric delay scenario, besides the unknown delay distributions, delay asymmetry is another important influence on synchronization accuracy. Therefore, the optimal invariant robust estimator is developed to simultaneously handle the performance degradation caused by delay asymmetry and unknown delay distributions. The estimator can even cope with the scenario where the random delays in the uplink and downlink follow different distributions. The effectiveness of the estimation schemes is validated by the computer simulations.

Precise clock synchronization is a critical requirement in industrial networks. To meet this need, the Precision Time Protocol (PTP) has been widely adopted as the standard solution. Nevertheless, the protocol’s accuracy is often compromised by unknown and unmodeled random delays, presenting a significant obstacle to reliable network operation. In this article, we propose a robust clock offset estimation scheme to enable a much higher synchronization accuracy for PTP in the presence of unknown and unmodeled delay distributions. To make this possible, we first derive the probability density function (pdf) of the delays via a maximum entropy approach, which is constrained by fractional moments and an unbiased likelihood estimation. Based on the derived pdfs, we further develop a low computational cost L-estimator for the clock offset, which is a linear function of the order statistics and robust against unknown and unmodeled random queueing delays. Simulation results illustrate that the proposed clock offset estimation scheme has much lower computational complexity and yields much more accurate estimation results than the compared existing methods in the presence of unknown and unmodeled disturbances.

Age of Information (AoI) is a crucial metric for data freshness in 5G ultrareliable low-latency communication systems. It is affected by various factors, such as the channel quality, the energy of the nodes, and so on. To overcome the severe path losses and environmental obstacles, intelligent reconfigurable surface (IRS) is adopted to reconfigure signal propagation environments, thereby mitigating the significant losses and creating additional signal reflection links. Different from the existing research on AoI in IRS-assisted wireless networks, which overlooks the impact of energy consumption on AoI and assumes ideal phase shift models, we investigate the entire process of data generation to arrival and propose a double-IRS cooperative scheme for data transmission with practical phase shift models in blocked wireless networks. The joint optimization problem of the long-term average AoI and node energy consumption is formulated. Given the nonconvexity of the joint optimization problem, we decompose it into an outer data transmission scheduling problem and an inner double-IRS phase shift optimization using a two-layer optimization framework. Then, we use the deep Q-network algorithm to solve the outer problem. For the inner problem, we propose a penalty-based alternating optimization (PB-AO) algorithm to solve the coupling between double-IRS phase shifts and the nonconvex constraints of practical phase shift models. The extensive simulation results verify the effectiveness of the proposed PB-AO algorithm in optimizing double-IRS phase shifts under the practical phase shift model and demonstrate the superiority of our double-IRS cooperative data transmission scheme compared with other benchmark ones.

Timestamp-free synchronization protocol is tailored to provide a global time understanding for resource-limited wireless networks as it eliminates timestamp interaction, thereby minimizing additional resource overheads. However, the existing two-hop based timestamp-free protocols are not suitable for synchronizing all nodes in multi-hop networks, as they necessitate multiple response times to establish the timestamp relationship between each pair of neighboring nodes. To this end, we introduce a novel multi-hop timestamp-free synchronization protocol. The proposed protocol allows any two nodes to be synchronized using only local timestamps and the skew estimates embedded within packets traversing the reverse path. Furthermore, considering that synchronization accuracy suffers from delay variation resulting from packet loss or retransmission in wireless networks, we derive a Pitman estimator to estimate the clock skew under arbitrary delay models, given known information. To further target unknown arbitrary delay distributions, we approximate the probability density function (pdf) of stochastic delays using a Gaussian mixture model, and then learn the pdf using the rival penalized expectation maximization algorithm. With the aid of the learned pdf, the robustness-enhanced Pitman estimator is derived, which is robust against arbitrary distributed delays without known knowledge. The effectiveness and performance enhancement of estimators are validated by simulations.

To measure the freshness of information more accurately and satisfy the timeliness demands for a wide range of time-sensitive applications, Age of Information (AoI) becomes a popular network performance metric. In this paper, we investigate the optimization of real-time performance in an Internet of Things (IoT) system with heterogeneous traffic, where periodic traffic for control and random traffic for update coexist. Generally, the periodically arriving data used for control is strictly deadline-sensitive, while the randomly arriving data used for updates has freshness requirements. Thus, we seek to develop a scheduling scheme that minimizes the long-term average AoI under the delay tolerance constraint, to meet the varying transmission timeliness requirements for different arrival models. The optimization problem is modeled as a constrained Markov decision process, and then it is decoupled into two classes of optimization sub-problems for single-node by relaxing the hard constraint of channel resources with the Lagrange multiplier. On this basis, a multi-node scheduling scheme consisting of a master policy and two sub-policies is designed. Specifically, two sub-policies are built for the two classes of optimization sub-problems, respectively, with Lyapunov and linear programming methods. For the hard constraint, a master policy is designed by introducing deep reinforcement learning for scheduling opportunities allocation, and a truncated sub-policy is proposed based on one of the sub-policies. Numerical results show that the proposed scheme can obtain a smaller long-term average AoI compared to other advanced algorithms while satisfying the delay constraint.

In industrial wireless sensor networks, the existing event-based consensus clock synchronization schemes can achieve network-wide clock synchronization without considering the communication delays. However, communication delays are a significant factor restricting the achievement of clock synchronization in realistic scenarios. Besides, a constraint to be considered in the design of synchronization scheme is the limited communication resources of sensor nodes. Therefore, in this article, we investigate an event-based consensus clock synchronization scheme under delays. On the one hand, a new low-pass filter is used to estimate the relative skew to resist the influence of communication delays. On the other hand, a new event-triggered scheme is utilized to reduce unnecessary information transmission. Finally, we provide the convergence proof and simulation results of the proposed scheme, which further proves that it can achieve clock synchronization under communication delays while decreasing communication overhead.

Wireless sensor networks (WSNs) have a broad range of applications, and time synchronization is essential to ensure their correct operation. In this paper, a clock skew estimation scheme is presented for timestamp-free synchronization, which greatly simplifies computation while economizing energy consumption. Considering that no single delay model can fit all cases in WSNs, a robust estimator with low complexity based on this scheme is developed that can estimate clock skew accurately without prior statistical characteristics of delays. Simulation results demonstrate the effectiveness of the proposed scheme.

In UAV-enabled wireless power transfer (WPT) systems, the UAV is usually planned to fly and charge the ground nodes (GNs), so as to prolong the lifetime of wireless sensor networks. But in fact, the long charging distance between the UAV and the GNs makes the GNs receive less energy. In order to maximize the received energy of GNs, this article focuses on the charging process and proposes a V-shaped WPT scheme, where the UAV descends to the optimal hover position and charges the GNs, so as to transfer more energy to the GNs. Moreover, considering that the GNs far from the hover position receive little energy in the V-shaped WPT scheme, we further develop an Inverted Trapezoidal WPT scheme to improve the fairness of the energy received by the GNs, in which the UAV continuously charges the GNs whether it is hovering or flying horizontally after lowering its altitude. Because the UAV’s flight and maneuvering are strictly constrained by its loading energy, we establish the UAV’s propulsion power consumption model in different flight attitudes and formulate the optimization problems of the GNs’ received energy in two schemes, and then develop two algorithms to solve them. The simulation results show that the performance metrics of UAV’s energy consumption, the efficiency, and fairness of GNs’ received energy are better than the compared schemes.

Unmanned aerial vehicles (UAVs) have been widely used to collect data from ground nodes (GNs) in various applications because of their flexibility and mobility. Some emergency situations pose strict requirements for UAV’s mission completion time. The current research focuses on the design and optimization of UAV’s flight trajectory to shorten the mission completion time. But the data collection process also greatly affects the mission completion time, especially when the uplink throughput is large. This article emphasizes the data collection process and proposes a V-shaped collection trajectory for the first time to shorten UAV’s collection time and then jointly optimizes the flight and collection trajectory to minimize the mission completion time. We formulate the mission completion time under energy constraints to an optimization problem and decompose it into three subproblems: 1) mission allocation of UAVs; 2) collection time minimization; and 3) joint optimization of collection and flight trajectory. 1) We establish the mission allocation model by setting the scaling factors for the flight and collection mission, and then solve it by utilizing the min–max multiple traveling salesman problem (MTSP) algorithm; 2) for the data collection process, we propose a V-shaped trajectory to minimize the data collection time and prove its validity; and 3) since the flight and collection trajectory of the adjacent GNs are deeply coupled, we model the joint optimization of the flight and the collection time as a mixed-integer nonlinear programming problem, and solve it by the joint optimization algorithm for flight trajectory and collection trajectory (JOFC). The simulation results show that our proposal outperforms the compared schemes.

Clock synchronization is crucial for applications in wireless sensor networks, such as event scheduling and data fusion. In practical wireless networks, environmental changes cause the oscillator to be imperfect. Thus, it is necessary to track the nonlinear varying clock dynamically. In this paper, we propose a timestamp-free clock skew (frequency difference) and offset (time difference) joint tracking algorithm based on extended Kalman filter (EKF), which can be embedded into the general network data flow to achieve long-term synchronization without additional communication overhead. To further improve energy efficiency of clock synchronization, this paper develops an EKF clock skew tracking algorithm for silent nodes in receiver-only synchronization. For the situation that silent node overhears synchronization information from multiple active nodes, we present multi-information timestamp-free synchronization and multi-observation clock skew fusion scheme for silent nodes. Simulation results show the effectiveness of the proposed tracking algorithms.

Existing packet-based synchronization approaches take extensive energy for industrial wireless sensor networks due to substantial timing message exchanges. Combined with acknowledgement (ACK), this article proposes an energy-efficient synchronization protocol without exchanging timestamps. Also, a mapping rule of ACK response time is presented for the joint estimation of skew and fixed delay without requiring a following response in each cycle, so that estimation can be implemented in parallel to data transmission. Then, the timestamp-free synchronization technique is extended to the receiver-only synchronization scenario to further reduce communication overhead. Assuming Gaussian variable delays, the maximum likelihood estimators and corresponding lower bounds for slave node and silent node are developed, as well as a low-complexity estimator for silent node. In addition, considering the dynamics of clock, a timestamp-free clock skew tracking algorithm using Kalman filtering is developed. Simulation results validate the efficiency of the proposed estimators.

Time synchronization is indispensable for convenient network management, device monitoring, security, and other fundamental operations in industrial wireless sensor networks (IWSNs). Over the past few decades, a wide variety of highly accurate clock synchronization protocols have been investigated by employing powerful statistical signal processing techniques. However, most two-way exchange estimation schemes do not readjust the node's local clock upon every resynchronization before the clock parameters are estimated. And it may not be appropriate in IWSNs where time synchronization is consistently required. Based on the two-way message exchange mechanism, this paper investigates the clock synchronization schemes of active node and overhearing node with immediate clock readjustment. The maximum-likelihood estimators of the clock skew and the corresponding Cramer–Rao lower bounds are derived assuming Gaussian delays. Simulation and experimental results validate the performance of the proposed estimators.

The clock synchronization problem for wireless sensor networks (WSNs) is inherently related to parameter estimation. Nowadays, extensive studies on time synchronization have been conducted by adopting statistical signal processing methods. However, most estimation schemes do not readjust clock offset during the process of synchronization parameter estimation, and it would lead to unsatisfactory clock accuracy during synchronization. Thus, the applications of these methods are greatly limited in WSNs. This paper analyzes time synchronization of sensor nodes with immediate clock adjustment at every cycle under multihop scenario, and presents an estimator of clock skew under the Gaussian linear delay model and the corresponding algorithms for finding the estimator in detail. Simulation results verify that the proposed estimator is efficient.

The surveillance for data collection in wireless sensor networks (WSNs) setting is recognized as an important application of WSNs. Given an area of interest and a number of wireless sensors, typical problems to be addressed are covering the whole area while prolonging the network lifetime. It is explicitly observed that most existing studies focus on limited case in which the interested area is static. In many WSN applications, however, the areas of interest are dynamic, e.g., deploying sensors to monitor the contaminated area of poisonous material which is fluid or diffusing. Accordingly, this paper turns to solve the Dynamic Area Coverage (DAC) problem. Our work focuses on tackling two key challenges: 1) determine the candidate positions for sensors once the area has evolved, 2) map each sensor to one of the candidate positions to achieve the desirable requirements. Different algorithms are proposed to determine the candidate positions and mappings with constraints. Through extensive simulations, the efficiency and efficacy of the proposed algorithms are well validated.

Selection cooperation is an attractive cooperative strategy for its simplicity and automatic repeat request (ARQ) mechanism can bring additional diversity benefit for wireless networks. In this paper, we combine the distributed selection cooperation protocols with ARQ mechanism to develop more powerful cooperative schemes for delay-tolerant wireless networks and analyze their performance from the perspective of diversity-multiplexing-delay (D-M-D) tradeoff. For small networks where any two nodes have direct links, we investigate the general ARQ scheme which directly extends the selection cooperation protocol with single round of feedback to multiple rounds. We show that the D-M-D tradeoff is determined by the ability of relays in signal combining and demonstrate that allowing relays to perform combining reception can achieve optimal D-M-D tradeoff. Then we propose a simplified scheme which greatly reduces the number of feedbacks and almost achieves the optimal performance. For large networks where direct links are limited in the neighbors of each node, we present a diffusion ARQ protocol which can effectively exploit the channels of nodes that have no direct links with the source. The D-M-D tradeoff analysis and simulation results demonstrate the significant performance improvement of all the proposed schemes.