Diffusion-Based Clock Synchronization for Molecular Communication Under Inverse Gaussian Distribution

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.

Clock synchronization plays a crucial role in Wireless Sensor Networks (WSNs). Assuming that there is no clock skew between sensor nodes, the Maximum Likelihood Estimate (MLE) of clock offset was derived by [1] for clock synchronization protocols assuming exponential random delays and a two-way message exchange mechanism as in TPSN (Timing-sync Protocol for Sensor Networks [2]) or NTP (Network Time Protocol). The MLE is appropriate for the case that the random delays in WSNs are exponentially distributed. However, the performance of the MLE is deteriorated considerably in the case that the underlying distribution is contaminated by or mixed with other distributions. Hence, a robust estimator is needed. In this paper, clock offset estimators based on the robust M-estimation method are proposed and it is shown that the proposed estimators present excellent performance in the mean squared error (MSE) sense under the condition that the underlying distribution is mixed with other distribution.

Molecular communication is a promising nanoscale communication paradigm that enables nanomachines to exchange information by using molecules as communication carrier. Up to now, the molecular communication channel between a transmitter nanomachine (TN) and a receiver nanomachine (RN) has been modeled as either concentration channel or timing channel. However, these channel models necessitate exact time synchronization of the nanomachines and provide a relatively low communication bandwidth. In this paper, the Molecular ARray-based COmmunication (MARCO) scheme is proposed, in which the transmission order of different molecules is used to convey molecular information without any need for time synchronization. The MARCO channel model is first theoretically derived, and the intersymbol interference and error probabilities are obtained. Based on the error probability, achievable communication rates are analytically obtained. Numerical results and performance comparisons reveal that MARCO provides significantly higher communication rate, i.e., on the scale of 100 Kbps, than the previously proposed molecular communication models without any need for synchronization. More specifically, MARCO can provide more than 250 Kbps of molecular communication rate if intersymbol time and internode distance are set to 2 μs and 2 nm, respectively.

Underwater acoustic networks can have large propagation delays as compared to typical packet durations, as a result of the low speed of sound in water. The ill effects of large propagation delay on medium access control (MAC) are well known. Conventional MAC protocol design for such networks focuses on mitigation of the impact of propagation delay. Most proposed protocols to date achieve, at best, a throughput similar to that of the zero propagation delay scenario. We have explored the possibility that propagation delays can be exploited to make throughput far exceed that of networks without propagation delay and shown that the throughput of a N-node wireless network with propagation delay is upper bounded by N/2. In a small set of illustrative network geometries, we can manually determine transmission schedules that allow us to achieve this N/2 bound. However, for a given network, the problem of determining transmission schedules that maximize throughput is as yet unsolved. In this paper, we put forward an algorithm that generates transmission schedules with high throughput for arbitrary network geometries.

Underwater acoustic (UWA) networks are a key form of communications for human exploration and activities in the oceanographic space of the earth. A fundamental issue of UWA communications is large propagation delays due to water medium, which has posed a grand challenge in UWA network protocol design. Conventional wisdom of addressing this issue is to live with this disadvantage by inserting a guard interval to introduce immunity to propagation delays. Recent advances in interference alignment (IA) open up a new direction to address this issue and promise a great potential to improve network throughput by exploiting large propagation delays. In this paper, we investigate propagation delay-based IA (PD-IA) in multi-hop UWA networks. We first develop a set of simple constraints to characterize PD-IA feasible region at the physical layer. Based on the set of PD-IA constraints, we develop a distributed PD-IA scheduling algorithm to greedily maximize interference overlapping possibilities in a multi-hop UWA network. Simulation results show that the proposed PD-IA algorithm yields higher throughput than an idealized benchmark algorithm without propagation delays, indicating that large propagation delays are not adversarial but beneficial for network throughput performance.

Extending the idea of having silent nodes in a Wireless Sensor Network (WSN) overhear the two-way timing message communication between two active (master and slave) nodes, this paper focuses on deriving the Maximum Likelihood Estimator (MLE) and performance lower bounds for the clock offsets of the listening nodes located within the communication range of the active nodes by assuming an exponential link delay modeling. Hence, synchronization with the reference node is achieved at a very low cost. The MLE is also shown to be the minimum variance unbiased estimator of the clock offset when the mean of exponential link delays is known. Since it is attractive to know in advance the extent to which an estimator can perform relative to global performance lower bounds, the Chapman-Robbins and Barankin bounds for the clock offset estimator are derived. It is shown that for an exponential link delay model, the mean square error of the unbiased clock offset estimator is inversely proportional to the square of the number of observations, and hence its performance is on a similar scale, albeit slightly lesser, as compared to the usual sender-receiver clock offset estimator.

In distributed systems like large wireless sensor networks, dense indoor small cell networks, maintaining each node's logical clock synchronized to a common reference is challenging. Increasing data rates and required cooperation among nodes for high spectral efficiency, further exacerbate the required clock synchronization accuracy. Here, we propose a one way timing information distribution mechanism simplifying existing two way information exchange for clock synchronization. We view the problem at the synchronizing node as a Peer-to-Peer (P2P) continuously running process. A node with stable clock (master) transmits regular packets embedded with transmit time stamps. All synchronizing nodes within the master's communication range can listen and apply receive time stamp. Efficient Passive Minimum Variance Unbiased Estimator (PMVUE) or Passive Maximum Likelihood Estimator (PMLE) are applied to jointly estimate clock offset and skew to correct the local clock. Random component of the link delay is assumed to be Gaussian distributed. Cramer-Rao Lower Bound (CRLB) guarantees that PMVUE and PMLE are efficient. We also propose a less accurate PMLE method, Independent PMLE (IPMLE) to remove dependency on random delay distribution parameter and show through simulations the high accuracy of our algorithms.

The use of wireless access networks, particularly IEEE 802.11 wireless access networks, is an economical method for realizing a communication network between a core information network of a smart grid and a rural area network. This paper presents a novel analysis of the throughput performance of the IEEE 802.11 carrier sense multiple access with collision avoidance (CSMA/CA) protocol with a large propagation delay. The throughput analysis is performed by using a real model. A Markov chain model is used to analyze the throughput performance of the IEEE 802.11 CSMA/CA binary exponential backoff algorithm. The results of analysis and computer simulations show that the theoretical throughput is in good agreement with the throughput obtained from computer simulations under the propagation delay less than 20 µs. When the propagation delay is more than 20 µs, the throughput obtained from the simulation results becomes larger than the theoretical throughput because of short-term unfairness. The throughput degradation for a transmission rate of 6 Mb/s and a propagation delay of 40 µs is 16.8 %; this propagation delay corresponds to a transmission distance of 12 km.

Global Navigation Satellite Systems (GNSS) rely on one-way signal travel time measurements from satellites to receivers. To ensure accurate ranging, GNSS must estimate and compensate for clock offsets on at least one end of the transmitter-receiver system. Consequently, clock offsets are highly correlated with GNSS-derived parameters such as station coordinates, tropospheric delay estimates, satellite radial orbit parameters, and apparent geocenter coordinates. Improper handling of clock offsets can lead to their absorption into these parameters, degrading geodetic product accuracy. Traditionally, clocks have been handled within individual techniques without being specially addressed. However, some research efforts and experimental trials have explored using VLBI to synchronize clocks for GNSS and refining clock models to reduce correlations with other estimated parameters in GNSS, thereby improving overall precision.With recent advancements, high-precision optical clocks and fiber-optic time transfer technologies provide new possibilities for enhancing clock synchronization in GNSS. Optical fiber offers a stable, interference-free medium for time and frequency transfer, eliminating atmospheric effects such as ionospheric and tropospheric delays that impact GNSS-based synchronization. Moreover, fiber-optic time transfer is inherently two-way, removing the need for external clock offset estimation. Thus, fiber-optic clock synchronization represents the most precise timing technique currently available. Establishing a common clock by connecting multiple GNSS receivers via optical fiber could significantly reduce the number of estimated clock parameters in GNSS solutions, leading to improved geodetic measurement precision and a more accurate geodetic reference frame.Despite its potential, the approach of implementing a common clock with optical fiber for GNSS receivers remains largely untested. Although optical fiber links have been successfully used in clock synchronization, their integration into GNSS receiver clocking is still in an experimental stage. Notable existing efforts include: (1) the Geodetic Observatory Wettzell, where multiple receivers are connected to a single clock via optical fiber, representing a local baseline setup, and (2) the GFZ experiment, where a receiver is linked to the ultra-stable clock of PTB, representing a regional baseline approach.This study characterizes existing fiber-optic connections among GNSS receivers to identify practical challenges and evaluate their impact on GNSS parameter estimation. We process data from receivers sharing a common clock using Bernese GNSS Software. Initially, PPP will be performed to compare GNSS-derived clock parameters across receivers sharing a common clock, verifying the effectiveness of fiber-optic clock synchronization. Following this validation, we will leverage GNSS-derived clock parameters to evaluate inter-receiver clock differences measured via optical fiber. Subsequently, we will implement a strategy in which only one receiver’s clock parameters are estimated, using fiber-measured clock differences as a priori constraints for other receivers in the PPP solution. This approach reduces the number of estimated clock parameters and serves as a preliminary test of the feasibility of a GNSS common clock framework.Future developments will focus on refining our analysis framework to enable simultaneous estimation of GNSS receivers operating under a common clock. This research contributes to the broader goal of integrating ultra-stable clocks into global GNSS networks, ultimately enhancing the stability of geodetic reference frames and improving GNSS-derived geodetic products.

Clock synchronization is a mechanism for providing a standard time to various devices across a network. This monograph provides a comprehensive overview of recent developments for clock synchronization protocols built on two-way message exchanges. Several clock synchronization protocols are available in the literature for distributing time from high-cost, high-stability clocks (termed masters) to low-cost, low-stability clocks (termed slaves) via an interconnecting network. A number of clock synchronization protocols are built on two-way message exchanges. These include the timing protocol for sensor networks (TPSN), lightweight time synchronization (LTS) protocol, tiny-sync and mini-sync, network time protocol (NTP) and the IEEE 1588 precision time protocol (PTP). The messages traveling between the master and slave nodes can encounter several intermediate switches and routers, accumulating delays at each node. The main factors contributing to the overall delay are the fixed propagation and processing delays at the intermediate nodes along the network path between the master and slave, as well as the stochastic queuing delays at each such node. Popular probability density function (pdf) models for modeling the stochastic delays include Gaussian, exponential, gamma, Weibull, and log-normal. Although these pdf models for the stochastic queuing delays apply to several scenarios, they might not be suitable in specific scenarios such as cellular base station synchronization using mobile backhaul networks and IEEE 1588 in 4G Long Term Evolution (LTE) networks. Further, there could be possibly unknown asymmetries between the fixed path delays in the forward master-to-slave path and the reverse slave-to-master path. These unknown asymmetries could arise from various sources, including delay attacks or incorrect modeling. In this monograph, we present recent developments for clock synchronization protocols built on the two-way message exchange. After an introduction to the basic concepts and mathematical models, the optimum estimators are presented for estimating the clock skew and offset that are applicable for any pdf model of the stochastic delays. Robust algorithms that can also handle unknown path asymmetries are presented next. The focus is on techniques that consider practical, relevant measurement models in order to guide the reader from physical observations to the actual synchronization of the clocks at the slave and master.

The Inverse Gaussian (IG) distribution is widely used in practice and therefore an important issue is to develop a powerful goodness-of-fit test (GOF) for this distribution. In this article, we propose and examine a new GOF test for the IG distribution based on a new estimate of Kullback-Leibler (KL) information. The properties of the test statistic are presented. In order to compute the proposed test statistic, parameters of the IG distribution are estimated by maximum likelihood estimators, which are simple explicit estimators. Critical values and the actual sizes of the proposed test are obtained. Through a simulation study, power values of the proposed test are compared with some prominent existing tests. Finally, two illustrative examples are presented and analyzed.

The extreme conditions under which multi-hop underwater acoustic sensor networks (UASNs) operate constrain the performance of medium access control (MAC) protocols. The MAC protocol employed significantly impacts the operation of the network supported, and such impacts must be carefully considered when developing protocols for networks constrained by both bandwidth and propagation delay. Time-based coordination, such as TDMA, have limited applicability due to the dynamic nature of the water channel used to propagate the sound signals, as well as the significant effect of relatively small changes in propagation distance on the propagation time. These effects cause inaccurate time synchronization and therefore make time-based access protocols less viable. The large propagation delays also diminish the effectiveness of carrier sense protocols as they do not predict with any certainty the status of the intended recipients at the point when the traffic would arrive. Thus, CSMA protocols do not perform well in UASNs, either. Reservation-based protocols have seldom been successful in commercial products over the past 50 years due to many drawbacks, such as limited scalability, relatively low robustness, etc. In particular, the impact of propagation delays in UASNs and other such constrained networks obfuscate the operation of the reservation protocols and diminish, if not completely negate, the benefit of reservations. The efficacy of the well-known RTS-CTS scheme, as a reservation-based enhancement to the CSMA protocol, is also adversely impacted by long propagation delays. An alternative to these MAC protocols is the much less complex ALOHA protocol, or one of its variants. However, the performance of such protocols within the context of multi-hop networks is not well studied. In this paper we identify the challenges of modeling contention-based MAC protocols and present models for analyzing ALOHA and p-persistent ALOHA variants for a simple string topology. As expected, an application of the model suggests that ALOHA variants are very sensitive to traffic loads. Indeed, when the traffic load is small, utilization becomes insensible to p values. A key finding, though, is the significance of the network size on the protocols' performance, in terms of successful delivery of traffic from outlying nodes, indicating that such protocols are only appropriate for very small networks, as measured by hop count.

Transmission algorithms are introduced for use in a single-hop packet switching system with nonuniform traffic and with propagation delay that Is large relative to the packet transmission time. The traffic model allows arbitrary traffic streams subject only to a constraint on the number of data packets which can arrive at any individual source in the system or for any individual destination in the system over time periods of specified length. The algorithms are based primarily on sending transmission schedules to the receivers immediately before transmitting each data packet multiple times so that the receiver can maximize the number of packets it captures. An algorithm based on matchings in a random graph is shown to provide mean total delay divided by mean propagation delay arbitrarily close to one, as the propagation delay tends to infinity.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

With the ever-increasing number of multicast data applications recently, considerable efforts have been focused on the design of flow control schemes for multicast services. The main difficulties in designing a flow controller for multicast service are caused by heterogeneous multicast receivers, especially those with large propagation delays, since the feedback arriving at the source is somewhat outdated, and can be harmful to the control operations. To attack the above problem, the present paper describes a novel multicast flow control scheme, the so-called proportional, integrative, derivative plus neural network (PIDNN) predictive technique, which consists of two components: the proportional integrative plus derivative (PID) controller and the back propagation BP neural network (BPNN). This network-assisted property is different from the existing control schemes, in that the PIDNN controller can release the irresponsiveness of a multicast flow caused by those long propagation delays from the receivers. By using BPNN for the receivers with longer propagation delay, this active scheme makes the control more responsive to network status. Thus the rate adaptation can be performed in a timely manner, for the sender to respond to network congestion quickly. We analyze the theoretical aspects of the proposed algorithm, show how the control mechanism can be used to design a controller to support multi-rate multicast transmission based on feedback of explicit rates, and verify this matching using simulations. Simulation results demonstrate the efficiency of our scheme in terms of high link utilization, quick response, scalability, high unitary throughput, intra-session fairness and inter-session fairness.

The large-scale mobile Underwater Wireless Sensor Network (UWSN) is a useful networking paradigm to explore underwater environments. The characteristics of mobile UWSNs, such as low communication bandwidth, large propagation delay, and floating node mobility are significantly different from wireless sensor networks. In this paper, we propose a new efficient routing protocol, called multi-path routing (MPR) protocol, for UWSNs to improve the transmission delay. Multi-path is utilized during the path construction from the source node to the destination node, which is composed of a series of multi-subpaths. Each multi-subpath is a sub-path from a sending node to its two-hop neighboring node, called receiving node, by one more relay nodes, where these relay nodes simultaneously are neighboring nodes of sending and receiving nodes. Due to the different propagation delay of UWSN, the packet arrival time along the different sub-path is different; thus it may avoid the data collision in the receiving node when receiving different packets from different relay nodes. It surely sends the different packet along different sub-path to significantly improve delay time and packet delivery ratio. Finally, simulation results illustrate the performance achievements of the MPR protocol in improving delay time, packet delivery ratio, throughput and reducing overhead ratio.