Industry 5.0 envisions the seamless integration of automation, human-machine collaboration, and intelligent systems to enable highly flexible and adaptive manufacturing. However, this puts stringent requirements on the communication systems extending beyond the capabilities of current 5G technologies. This gap motivates the adoption of the digital twin (DT) paradigm, where a digital replica of physical assets and networks enables continuous monitoring, simulation, and optimization of industrial processes. This paper investigates the optimization of network access protocols, which are critical to maintaining uninterrupted industrial production. Specifically, we develop a reinforcement learning (RL) algorithm embedded within the DT framework to ensure reliable communication and production flow continuity. In a congested factory environment, an autonomous guided vehicle (AGV) must transmit data to a base station (BS) using an ALOHA-like protocol at terahertz (THz) frequencies. The DT-enabled RL model dynamically learns traffic patterns and adaptively selects backoff (BO) times for network access, maximizing reliability without requiring prior knowledge of system topology. Extensive evaluations across diverse operating scenarios–ranging from static to mobile settings, varying traffic loads, and different data and action space sizes–confirm the robustness, scalability, and adaptability of the proposed solution in highly dynamic industrial environments against conventional and advanced baselines.

This paper highlights the value of Digital Twins (DTs) in optimizing and maintaining Cyber-Physical Systems (CPSs) across domains like manufacturing and communication. It proposes the interaction between an industry DT and a 6G DT and identifies Situational Awareness (SA) as a key step toward supporting critical services. A use case involving 6G communication with mobile User Equipment (UE) in manufacturing is analyzed to identify critical operating scenarios and how SA can predict and mitigate the risk of failure in these scenarios. Based on this use case, relevant parameters for improving the SA of the entire CPS are identified in both DTs and an example of interaction is given for optimizing the joint task planning and execution. Additionally, the benefits of cross-domain SA are demonstrated through 5G testbed measurements. The use case illustrates the broader applicability of our proposal.

Reliable time synchronization is of utmost importance within 6G networks, particularly when envisioning their role in future industrial automation scenarios that demand deterministic communication. In particular, we focus on the integration of 6G with time-sensitive networking (TSN). Traditionally, the best timeTransmitter clock algorithm (BTCA) is used to dynamically select a grandmaster (GM) for TSN nodes in a 6G-TSN network. However, BTCA’s performance in case of link or device failures is categorized to be slow. The IEEE 802.1ASdm standard addresses this limitation by introducing a hot standby GM in the network. In this paper, we extend the hot standby amendment to 6G-TSN networks to support continuous time synchronization. For the analysis, we develop a simulation framework in OMNeT++. We analyze the performance in terms of clock drift and out-of-sync time for different time synchronization scenarios in case of failures. Having two synchronized GMs in the network reduces the out-of-sync time in case of failure when compared to BTCA.

We demonstrate a private 5G network integration with precise ultra-wideband (UWB)-based localization for enabling a collaborative robots use case in an industrial environment. The results confirm 5G’s ability to provide high throughput, low latency, and reliable connectivity, even in complex industrial environments. UWB provides real-time decimeter-level wireless localization accuracy, critical for reliable and precise object localization. These combined capabilities are essential for real-time monitoring, automation, and operational efficiency. The developed demonstrator serves as proof of concept, showcasing how 5G, when coupled with advanced localization technologies, can optimize industrial processes and improve safety. This study offers a valuable system performance evaluation under real-world conditions for researchers and industry, underscoring the transformative potential of 5G in future industrial systems and its integration with precise wireless localization technology.

Digital Twin (DT) technology has emerged as a transformative paradigm across various domains, offering powerful capabilities to monitor and optimize processes prior to real-world deployment. DTs are well-suited for next-generation deployment, as well as industrial applications, in which the dynamicity and complexity of processes pose significant challenges. This study proposes a novel DT-based framework that integrates network infrastructure with shop-floor industrial operations, where robotic arms execute pick-and-place tasks and communicate with a base station (BS) using a contention-based medium access control (MAC) protocol (i.e., ALOHA and carrier sense multiple access (CSMA)) at THz frequencies. The framework aims to optimize closed-loop production systems by enabling continuous and bidirectional data exchange between the robotic arms and the BS. A centralized reinforcement learning (RL) model enables joint optimization of backoff (BO) selection and task allocation, enhancing production efficiency while preserving workflow continuity. The results prove that the proposed framework significantly outperforms state-of-the-art (SoTA) solutions for network and industrial operation performance, achieving a 55.2% reduction in average latency, a 9.8% improvement in success probability, and a 27.96% increase in processed product rate. These findings highlight the robustness and effectiveness of the proposed framework across varying operational scenarios and MAC protocols.

Industry 5.0 marks a transition from the digitalization focus of Industry 4.0 to a paradigm emphasizing resilience, sustainability, and human-centric processes. In such dynamic networks, reinforcement learning (RL) algorithms can play a crucial role in enhancing performance. The paper proposes a novel approach using a centralized RL algorithm to optimize the medium access control for a moving autonomous guided vehicle (AGV) on an industrial shop floor. This ensures uninterrupted production flow by dynamically managing the network traffic. The use case scenario considers a mobile AGV transmitting data to a base station (BS) within a harsh industrial environment. It uses the RL algorithm to dynamically select an optimal backoff (BO) time for an ALOHA-like channel access protocol. This enables accurate data transmission without prior knowledge of the industrial environment. The results show an improvement of up to 34.6% in success probability compared to traditional BO design approaches. The RL model achieves outstanding performance, guaranteeing a minimum success probability of 99.46%.

The rise of industrial applications such as autonomous systems, industrial automation, and precision manufacturing has increased the need for resilient and continuous time synchronization. Time-sensitive networking (TSN) addresses these requirements using the IEEE 802.1AS standard, which implements the generalized precision time protocol (gPTP) for sub-microsecond accuracy. However, best timeTransmitter clock algorithm (BTCA) used for grandmaster (GM) selection is slow to recover from failures and cannot detect transient faults, resulting in unstable synchronization. The IEEE 802.1ASdm standard addresses these limitations by disabling BTCA and introducing a static configuration with a hot standby GM. This paper presents a first analysis of time synchronization in TSN networks with hot standby. Using OMNeT++, we compare BTCA and hot standby performance in terms of out-of-sync time and clock offset during failures. The results demonstrate a close to zero out-of-sync time with hot standby as compared to BTCA.

In wireless communications, trustworthiness computation has emerged as a crucial aspect of safeguarding modern systems against cybersecurity threats, ensuring reliable data transmission and upholding user trust. However, there is no unified definition of trustworthiness computation in the literature, and it is often presented as a specifically tailored adaptation of attack detection mechanisms. In contrast, this work introduces a general method for trustworthiness computation in wireless networks. It leverages key system characteristics, such as the channel, timing, and packet information to identify measurable Quality of Service (QoS) features with sufficient sensitivity across varying operational conditions. Building on these features, a novel three-step approach is applied. It employs changepoint detection to identify potential trustworthiness issues, calculates indicators based on the observed features, and finally combines them into a quantitative representation of trustworthiness. This systematic method effectively distinguishes between regular statistical variations in QoS features and actual trustworthiness issues. The applicability of the presented approach is demonstrated using a typical IEEE 802.11 wireless link, where different QoS features and scenarios are defined. These scenarios include network attacks, system malfunctions, and typical operational conditions. Our trustworthiness computation method correctly alerts the system to all trustworthiness issues that we challenge it with.

6G networks will play a crucial role in Industry 4.0 advancing further smart manufacturing and trustworthy communication. This paper introduces a reinforcement learning scheduler that considers environmental knowledge designed to improve reliability and security aspects of trustworthiness by favoring to serve nodes when in line-of-sight. We evaluate the performance in a factory floor scenario for two different heights of remote-radio heads and various blockage densities. The results show that the proposed method outperforms traditional schedulers such as round robin and proportional fair in terms of reliability, availability and fairness enhancing thus reliability and security aspects of trustworthiness when the environment is prone to a mixture of line-of-sight and non-line-of-sight.

Wireless Sensor Networks (WSNs) play a pivotal role in diverse domains such as environmental sensing, industrial monitoring, and entertainment. This paper focuses on modeling the connectivity of the link considering the quality of service (QoS) criterion. This is a baseline for considering the probability density function (PDF) of the node’s distance from the base station (BS) to form a multi-hop wireless sensor networks (WSNs) structure. We delve into modeling the connectivity behavior in multi-hop networks, addressing scenarios involving non-homogeneous Poison Point Process (NHPPP) and homogeneous Poison Point Process (HPPP). Furthermore, we introduce closed-form expressions with reduced computational complexity. This contribution establishes a comprehensive framework for understanding and enhancing the performance of multi-hop wireless sensor networks.

Industry 4.0 promises the increase of productivity and efficiency within manufacturing and industrial processes. A key milestone in this evolution is the 3GPP specification on time-sensitive communication and integration of 5G with time-sensitive networking (TSN), thus enabling the required flexibility for future time-sensitive industrial applications. Although 3GPP introduces ultra-reliable low latency communication (URLLC) features to meet stringent timing requirements, the notable challenge persists in resource overprovisioning, limiting the capacity of the next-generation radio access network (NG-RAN). Our work addresses this by focusing on the sources of packet delay and packet delay variation within the 6G system. Through analysis and proposed enhancements, supported by simulation and measurement results, we aim to minimize queuing delay and optimize 6GS capacity. Our study not only explores standardized 5GS features but also proposes extensions to support periodic deterministic traffic, offering insights to enhance 6GS performance and capacity in real-world scenarios.

The third generation partnership project (3GPP) has outlined ultra-reliable low latency communication (URLLC) essential to ensure enhanced network dependability under stringent latency constraints. A transmission scheme known as configured grant (CG) transmission, defined in 3GPP Release 15, allows devices to compete for resources and transmit their data without explicit permission in a specified time budget. In this study, we introduce an enhanced modeling approach for CG transmission that takes into account the repetition and retransmission, allowing a thorough evaluation of network performance. The numerical results shed light on configuring CG transmission settings to achieve a predetermined probability of success for successful packet decoding. Importantly, the system model in the paper closely follows 3GPP-based Transmission Time Interval (TTI) models, which helps to map the observed results to real system performance.

The third generation partnership project (3GPP) has defined ultra-reliable low latency communication (URLLC) as one of the key 5G competencies to provide high network reliability and low latency. The configured grant (CG) transmission, defined in 3GPP Release-15, is a technique that automatically transmits a URLLC packet with a configured number of repetitions to increase reliability. In this paper, we propose enhanced modeling for CG transmission considering the communication channel state to evaluate the network performance. The results show how to configure CG transmission to reach a defined probability of success for decoding the packets.

Bluetooth Low Energy (BLE) is one of the key enablers for low-power and low-cost applications in consumer electronics and the Internet of Things. The latest features such as audio and direction finding will introduce more and more devices that rely on BLE for communication. However, like many other wireless standards, BLE relies on the unlicensed 2.4 GHz frequency band where the spectrum is already very crowded and a channel access without collisions with other devices is difficult to guarantee. For applications with high reliability requirements, it will be beneficial to actively consider channel access from other devices or standards. In this work, we present an approach to estimate the connection parameters of multiple BLE connections outside our control and knowledge by passively listening to the channel. With this, we are able to predict future channel access of these BLE connections which can be used by other wireless networks to avoid collisions. We show the applicability of our algorithm with measurements from which we can identify unknown BLE connections, reconstruct their specific connection parameters, and predict their future channel access.

5G is considered a promising wireless communication technology to fulfill the high-demanding communication requirements of many Industry 4.0 applications. This work evaluates a 5G campus network for indoor factory floor scenarios using the latest commercially available 3GPP release-16 developments. The measurement campaign is conducted to obtain detailed coverage maps with reference signal received power, channel quality indicators, and downlink and uplink throughput (TP). Moreover, end-to-end delay measurements with varying channel conditions, 5G quality of service (QoS) priorities, and traffic loads were evaluated. It was concluded that even without ultra-reliable low-latency features, the TP and latency performance could be controlled by configuring QoS parameters. The evaluations suggest scenarios where QoS allocation and retention priority levels can be used in order to ensure the required performance of a specific QoS flow within the 5G system.

5G, the latest generation of cellular technology, targets not only enhanced data rates but also new applications which require, e.g., ultra-reliable low latency communication. Verticals like industrial automation or automotive, which want to make use of this type of wireless services, need experimental deployments to test the performance of 5G in various modes and environments for their use cases. Due to the ongoing stan-dardization process, experimental 5G networks based on open-source frameworks are especially well suited, as they provide the possibility to easily implement new features introduced by the yearly 5G standard releases. We thus present an experimental 5G standalone deployment, based on the OpenAirInterface, which is an open-source framework, that is being used both, commercially and for academic purposes. We evaluate coverage parameters including reference signal received power, reference signal received quality, and signal to interference and noise ratio both for single user and multiple user scenarios. The measured downlink data rate reaches up to 390 Mbps at a bandwidth of 60 MHz, which is close to the achievable theoretical value. The average latency both for uplink and downlink was measured to be 19 ms for the round trip time, while the minimum latency value was 6 ms, which is acceptable for many application.

Nowadays Internet of Things and Industry 4.0 devices are often connected wirelessly. Current wireless sensor network (WSN) deployments are relying in most cases on the industrial, scientific, and medical (ISM) bands without centralized resource scheduling. Thus, each device is a potential source of interference to other devices, both within its own WSN but also to devices in other collocated WSNs. If the transmission behavior of devices from other WSNs is not random, we are able to find patterns in the time domain in their channel access. This is, for example, possible for periodic channel access, which is quite common for WSNs with demanding low-power and reliability requirements. The main goal of this work is to detect multiple sources of periodic interference in time slotted signal-level measurements and estimate the time windows of future transmissions. This gives a WSN a certain understanding of the radio surrounding and can be used to adapt the transmission behavior to thus avoid collisions. For this, the multihypothesis tracking algorithm is adapted and used together with timeslot-based interference measurements on low-cost sensor nodes. The applicability of the algorithm is shown with extensive simulations and the performance is demonstrated with measurements on a time-division multiple access-based WSN built upon the Bluetooth low-energy physical layer.

Functional safety protocols provide automatic protection against system failures. Safety will be of critical importance for future industrial systems since they are undergoing automation and digital transformation under the Industry 4.0 revolution. However, functional safety depends on the underlying communication system employed in the manufacturing area. An extensive evaluation of the communication system and the functional safety protocol is needed before deploying it to the production environment. To facilitate the evaluation process of a fail-safe communication protocol, we integrate openSAFETY in the OMNeT++ simulation framework. We validate its integration by comparing the simulation results with an existing experimental work where the results show similar trends. Furthermore, we simulate an industrial closed-loop control use case with IEEE 802.11n being the communication technology. The results obtained in terms of safe-state duration and packet error rate demonstrate that 802.11n with its default configuration is not suitable for a high demanding industrial application.

Minimized and nearly deterministic end-to-end latency facilitates real-time data acquisition and actuator control. In addition, defined latency is an integral part of quality-oriented service in order to get closer to the reliability of wired networks and at the same time takes advantage of wireless networking. This article introduces a QoS routing protocol capable of balancing power consumption between wireless sensor and actuator nodes while minimizing end-to-end latency. We introduce a time-division multiple access scheme in the routed wireless network to enable defined latency, and in addition, it improves the energy efficiency by avoiding collisions, which eliminates time and energy consuming retries. Our novel routing method allows latency and round-trip times to be calculated in advance. We implement a demonstrator and show experimental results of a wireless sensor network with our proposed routing scheme.

Advanced industrial communication systems are fundamental pillars of the ongoing digital transformation of industrial systems. Initiatives like the Industry 4.0 and the Industrial Internet Consortium aim at increasing the overall production efficiency leveraging on fast, reliable, and deterministic communication technologies. The improvements of information and communication technologies (ICT), driven by the tremendous influence of the consumer market, result in positive relapse for the industrial ICT, allowing an ever-increasing amount of data and information to be gathered from systems, machines, and devices. On the other hand, the availability of low-cost computational capabilities permitted to easily process these “Big Data,” generating on-the-fly trend forecasts for the management systems, which, in turn, allow to issue actions for controlling the manufacturing processes in real time. The ensemble of all these technologies is generally addressed with the term industrial Internet of Things (IIoT).

Functional safety has become a crucial part of industrial automation. With industry environments being connected more than ever, achieving required functional safety depends on establishing safety-critical communication. Numerous application layer safety protocols have been developed to ensure compliance with functional safety standards for wired communications. However, with all the benefits wireless communications entails, wireless communication is pushing for an important place in the future of industrial automation. It is important that safety protocols also follow this transition and are able to operate as intended using a wireless channel. By default, openSAFETY frames are exchanged using UDP broadcast, whereas TCP provides additional reliability features. Thus, the aim of this paper is to analyze if safety-critical communication using a wireless channel can benefit from the additional reliability features provided by TCP. To answer this, we experimentally analyze the performance of openSAFETY protocol providing functional safety over the IEEE 802.11 standard for three different test cases. We analyze the performance in terms of median end-to-end delay and time spent by a safety node in a safe state for both protocol stacks. Results show that UDP provides lower median end-to-end delay, whereas TCP is able to achieve less time spent in a safe state under bounded delay constraint.

For Cyper-Physical Production Systems (CPPS), localization is becoming increasingly important as wireless and mobile devices are considered an integral part. While localizing targets in a wireless communication system based on the Received Signal Strength Indicators (RSSIs) is a usual solution, it is limited by sensor quality. We consider the scenario of a car moving in and out of a chamber and propose to use a particle filter for sensor fusion, allowing us to incorporate non-idealities in our model and achieve a high-quality position estimate. Then, we use Machine Learning (ML) to classify the vehicle position. Our results show that the location output of the particle filter is a better input to the classifiers than the raw RSSI data, and we achieve improved accuracy while simultaneously reducing the number of features that the ML has to consider. We also compare the performance of multiple ML algorithms and show that SVMs provide the overall best performance for the given task.

Interoperability is one of the important characteristics of the cyber-physical system (CPS) based automation system. Engineers connecting field devices and control applications in an automation system regularly encounter interoperability problems. ISO/IEC/IEEE 21451 is a series of standard, which provide the building blocks to enable interoperability among field devices and control applications. transducer electronic datasheets (TEDS) are provided as a standard transducer description format by ISO/IEC/IEEE 21450. This format provisions the syntactic interoperability among heterogeneous field devices. However, open platform communication unified architecture (OPCUA) is a key enabling technology to achieve semantic and network interoperability. Therefore, the aim of this paper is to provide an integration approach for ISO/IEC/IEEE 21450 TEDS and devices in the OPCUA semantic model. We propose an ISO/IEC/IEEE 21450 based device integration concept with service oriented architecture.

Industrial Internet-of-Things (IIoT) applications require reliable and efficient wireless communication. Assuming dense wireless sensor networks (WSNs) operating in a harsh environment, a concept of a time-division multiple access (TDMA)-based WSN enriched with electronically steerable parasitic array radiator (ESPAR) antennas is proposed and examined in this work. The utilized antenna provides one omnidirectional and 12 directional radiation patterns that can be electronically switched by the sensor node. We introduce a relay discovery algorithm, which selects those sensor nodes with an ESPAR antenna capable to act as relay. The selection of the relay nodes is based on a certain link quality threshold that algorithm uses as input. The outcome is a reduction in the number of layers or hops with a guaranteed Quality of Service (QoS). To emphasize the physical aspect of the wireless propagation, we introduce the measured antenna radiation patterns and consider two different path-loss propagation models representing blockage-free and blockage-prone industrial environments. A number of network simulations were performed and signal-to-noise ratio (SNR) as a link quality measure was examined with respect to the network density and different measured radiation pattern settings. The main outcomes show a tradeoff between SNR per link and the percentage of nodes that can serve as relays. As a result, we propose network design guidelines that take under consideration the QoS range with respect to SNR together with an optimal number of antenna radiation patterns that should be selected as a tradeoff between latency, energy consumption, and reliability in a network.

Electronic data-sheets that are stored within and provided by a transducer such as ISO/IEC/IEEE 21450 Transducer Electronic Data-sheets are currently intended to ease the utilization of transducers. This is achieved as the data-sheets provide information about sensing and actuation as well as communication capabilities, data formats, calibration information and more. However, so far it can not be ensured that the provided information is trustworthy. Consequently, we propose a concept based on ISO/IEC/IEEE 21450 Transducer Electronic Data-sheets in which signatures and secure elements are used to validate the information in the data-sheets, the manufacturer and calibration labs. Furthermore, this information can be utilised for secure key exchange mechanisms and permission management. This approach ensures that the low-power consumption expected of transducers is still met while providing security and trust.

Communication systems have to cope with a variety of non-idealities. Among those, carrier frequency offset (CFO) induced impairments denote a challenging task for any system, but especially for multi-carrier schemes such as orthogonal frequency division multiplexing (OFDM). Unique Word-OFDM (UW-OFDM) is a known variant, which provides various performance benefits over conventional cyclic prefix (CP) based OFDM. In particular, UW-OFDM features excellent spectral sidelobe suppression properties and an outstanding bit error ratio performance. In this work, we expand the investigations to CFO impairments, analyze the varying effects experienced by different UW-OFDM realizations and compare it against conventional OFDM as well as single-carrier systems. Through an error analysis it is shown that compared to CP-OFDM, UW-OFDM has a significantly higher robustness against CFO. This advantage becomes even more dominant with an increasing CFO.

We propose to add a monitoring system consisting of so-called path-and guard nodes to industrial wireless sensor networks (IWSNs), to increase the security level by using receive signal strength indicator (RSSI) measurements. Via these measurements, the monitoring system determines the presence of a mobile sensor node in a predefined area, which can be used to handle access rights and to increase automation capabilities in industrial applications. We add this monitoring system to an IWSN based on the EPhESOS protocol, which has a high degree of flexibility to meet industrial requirements in different applications throughout the lifetime of a sensor node while enabling energy-autonomous operation. Two practical machine learning algorithms for RSSI-based presence detection are presented, namely a support vector machine and a neural network algorithm. They are evaluated in an automotive example and tested for their robustness against malicious attacks. Additionally, a method to find the best node locations of the monitoring system is presented.

Secure wireless communication is essential for most industrial applications. The secure and reliable control of processes as well as the data integrity of measured values are key targets in these applications. The industrial Internet-of-Things (IIoT) tries to connect an increasing number of sensors wirelessly. The wireless sensors form wireless sensor networks (WSNs). However, wireless sensor nodes are exposed to various security threats ranging from physical modification on the device itself to remote attacks via the communication channel. It is important to secure the complete lifetime of the wireless sensor nodes and other system components. This includes the production phase, shipping, preparation phase and operational phase. This paper presents a lifetime security concept for a wireless sensor network applied in automotive test beds. In this application scenario, the wireless sensor nodes are used to capture various temperatures in an automotive unit under test. In order to indicate the current state of trustworthiness of the system, a trustworthiness indicator is implemented which is shown to the user. An evaluation of the impact of encrypted communication on power consumption shows that the increase is negligible, and can be expected to be provided by the wireless sensor node's power supply without reducing the node lifetime.

The time-sensitive network paradigm envisions the integration of operation technology and information technology in the same network. One of the requirements for building time-sensitive networks is sharing a global time along the network. This requirement is especially critical in wireless systems, where there are few robust methods to perform accurate time transfer. In this article, the problem of time transfer over realistic wireless channels is studied, and a time distribution scheme is proposed. The time distribution scheme has three components: Precision time protocol, a novel timestamping method (enhanced timestamps) and an algorithm to implement the enhanced timestamps. The performance of the proposed scheme has been evaluated in MATLAB using the IEEE 802.11n Standard under several standard wireless local area network channel models. The results show that the system can reach subnanosecond time transfer accuracy under non-line-of-sight and time-variant conditions, but its performance greatly depends on the signal-to-noise ratio and on the channel variation rate.

The paper presents a sampling method that dramatically improves the measurement accuracy of the round trip time (RTT) measurement in digital communication systems. For state of the art methods, the accuracy of time measurements in discrete time systems and low noise scenarios is limited to the sampling period T. If the measurement is repeated m-times, the upper bound of the quantization mean square error (MSE) is ~1/m. The proposed sampling scheme reduces the upper bound of the MSE to ~1/m2. This exceptional feature is enabled by applying a prime relation between sampling rate and bit rate of the communication system.

In industrial applications synchronized sensor nodes are vital for many tasks like multi parameter sampling of complex machinery behavior. The wirelessly connected nodes are usually synchronized to a base station. Therefore, frequency or period estimation of the reference clock is a key issue for all connected tasks like sampling, localization or applying energy optimized communication protocols. In wireless systems and especially in harsh industrial environments, it is likely to miss one or more synchronization events. The available data for clock estimations is therefore sparse and periodogramm estimators, at a complexity of at least O(N log N), are commonly used for accurate clock estimation. We introduce a period estimator for sparse clock signals with O(N) complexity. Furthermore, we present an equation for the observation time necessary to estimate the clock period at a certain quality. Mostly due to temperature influences, the crystal frequency at the nodes are varying. Our iterative period estimator follows those changes with a given estimation accuracy. We analyze an equation, which allows to calculate the accuracy of the estimator given a certain change rate of time variant system clock. The work is concluded with simulations considering sparse and time varying processes, including a discussion of the application of the method.

In this paper a novel synchronization method for wireless sensor networks with star topology is presented. We address timing synchronization using low frequency real-time clocks in all nodes. A beacon-driven TDMA-protocol for bidirectional node/base communication is used. Between the beacons, which are sent by the base station, lie the superframe time intervals to handle data transmission from node to base. We discuss the protocol and its energy saving advantages including the challenges of synchronization. We reduce the required communication for synchronization based on long term synchronicity of the node to save energy. Due to the individual node clock, the accurate superframe time interval usually will consist of a rational number of clock ticks. We propose to use a ΔΣ-converter to generate a sequence of superframes with different time durations, but each consisting of integer multiples of clock ticks, which - on average - achieve the accurate superframe duration for any rational number of clock ticks. We show by theory and measurements that our novel approach leads to a variance of the synchronization error which is constant at a value of 0.25 clock cycles. The variance is independent of the rate at which the nodes listen to the beacon of the base station.

We analyse the use of a ΔΣ-modulator in the nodes of a wireless sensor network, which is a new method to achieve long term synchronization. We consider star topology WSNs (Wireless Sensor Networks) with a central base station and address timing synchronization using low frequency realtime clocks. The WSN uses a beacon driven TDMA-protocol for bidirectional node/base communication. Between the beacons, which are sent by the base station, lie the superframe time intervals to handle data transmission from node to base. The ΔΣ-modulator is used to generate - at average - the accurate superframe duration for any rational number of clock ticks, by generating a sequence of superframes with different time durations, but each consisting of integer multiples of clock ticks. We discuss the synchronization accuracy based on the internal arithmetic of the ΔΣ-modulator and show by theory a relation between synchronization accuracy and word length of the internal arithmetic. Additionally the fractional part of a crystal clock module is responsible for variations in the synchronization quality. We present an equation that allows us to interpret measurements showing periodic variations of synchronization quality.

Nonlinear signal processing is now well established both in theory and applications. Nevertheless, very few tools are available for the analysis of nonlinear systems. We introduce the mutual information function (MIF) as a nonlinear correlation function and describe the practicalities of estimating it from data. Even if an estimator is consistent, it is of great interest to check what the bias and variance are with a finite sample. We discuss these questions, as well as the computational efficiency, for two estimators. Both algorithms are of complexity Nlog/sub 2/N, where N is the sample length, but they use different methods to find the histogram for the estimation of the mutual information. An efficient implementation makes it possible to apply the algorithm on real time signal processing problems where the linear correlation analysis breaks down. Examples involving linear and nonlinear channels are discussed.

This paper presents an in-depth study of nonlinear long-term prediction of speech signals. While previous studies of nonlinear prediction focused on short-term prediction (with only moderate performance advantage over adaptive linear prediction in most cases), successful long-term prediction strongly depends on the nonlinear oscillator framework for speech modeling. This hypothesis has been confirmed in a series of experiments run on a voiced speech database. We provide results for the prediction gain as a function of the prediction delay using two methods. One is based on an extended form of radial basis function networks and is intended to show what performance can be reached using a nonlinear predictor. The other relies on calculating the mutual information between multiple signal samples. We explain the role of this mutual information function as the upper bound on the achievable prediction gain. We show that with matching memory and dimension, the two methods yield nearly the same value for the achievable prediction gain. We try to make a fair comparison of these values against those obtained using optimized linear predictors of various orders. It turns out that the nonlinear predictor's gain is significantly higher than that for a linear predictor using the same parameters.