Bernhard Etzlinger

Cooperative Synchronization in Wireless Networks

Synchronization is a key functionality in wireless networks, enabling a wide variety of services. We consider a Bayesian inference framework whereby network nodes can achieve phase and skew synchronization in a fully distributed way. In particular, under the assumption of Gaussian measurement noise, we derive two message passing methods (belief propagation and mean field), analyze their convergence behavior, and perform a qualitative and quantitative comparison with a number of competing algorithms. We also show that both methods can be applied in networks with and without master nodes. Our performance results are complemented by, and compared with, the relevant Bayesian Cramér-Rao bounds.

A distributed particle-based belief propagation algorithm for cooperative simultaneous localization and synchronization

We present a factor graph framework and a particle-based belief propagation algorithm for distributed cooperative simultaneous localization and synchronization (CoSLAS) in decentralized sensor networks. The proposed algorithm jointly estimates the locations and clock parameters of the network nodes in a fully decentralized fashion. This estimation is based on time measurements and communications only between neighboring nodes, and makes only minimal assumptions about the network topology. A significant reduction of computational complexity can be achieved by a novel particle-based scheme for message multiplication. Simulation results demonstrate the good performance of the proposed CoSLAS algorithm.

Cooperative Joint Localization and Clock Synchronization Based on Gaussian Message Passing in Asynchronous Wireless Networks

Localization and synchronization are very important in many wireless applications such as monitoring and vehicle tracking. Utilizing the same time of arrival (TOA) measurements for simultaneous localization and synchronization is challenging. In this paper, we present a factor graph (FG) representation of the joint localization and time synchronization problem based on TOA measurements, in which the non-line-of-sight (NLOS) measurements are also taken into consideration. On this FG, belief propagation (BP) message passing and variational message passing (VMP) are applied to derive two fully distributed cooperative algorithms with low computational requirements. Due to the nonlinearity in the observation function, it is intractable to compute the messages in closed form, and most existing solutions rely on Monte Carlo methods, e.g., particle filtering. We linearize a specific nonlinear term in the expressions of messages, which enables us to use a Gaussian representation for all messages. Accordingly, only the mean and variance have to be updated and transmitted between neighboring nodes, which significantly reduces the communication overhead and computational complexity. A message passing schedule scheme is proposed to trade off between estimation performance and communication overhead. Simulation results show that the proposed algorithms perform very close to particle-based methods with much lower complexity, particularly in densely connected networks.

Cooperative simultaneous localization and synchronization: A distributed hybrid message passing algorithm

Localization and synchronization in wireless networks are strongly related when they are based on internode time measurements. We leverage this relation by presenting a message passing algorithm for cooperative simultaneous localization and synchronization (CoSLAS). The proposed algorithm jointly estimates the locations and clock parameters of the network nodes in a fully decentralized manner while requiring time measurements and communications only between neighboring nodes and making only minimal assumptions about the network topology. Low computation and communication requirements are achieved by a hybrid use of sample-based and Gaussian belief propagation. Our simulations demonstrate performance advantages of the proposed CoSLAS algorithm over separate state-of-the-art localization and synchronization algorithms.

Cooperative simultaneous localization and synchronization: Toward a low-cost hardware implementation

Cooperative sensor self-localization (CSL) in wireless networks usually requires the nodes to be equipped with specific ranging hardware including ultra-wideband or ultrasonic distance sensors. Such designs are not suitable for application in low-cost, low-power sensor networks. Here, we demonstrate how low-cost, low-power, asynchronous sensor nodes can be used to perform CSL (and, simultaneously, distributed synchronization) by means of time-stamped communication without additional ranging hardware. Our method combines a belief propagation message passing algorithm for cooperative simultaneous localization and synchronization (CoSLAS) with a MAC-layer time stamping scheme.We validate the models underlying the CoSLAS algorithm by means of measurements, and we demonstrate that the localization accuracy achieved by our hardware implementation is far better than that corresponding to the time resolution and measurement errors of the hardware.

Factor-Graph-Based Soft-Input Soft-Output Detection for Frequency-Selective MIMO Channels

In this letter we consider a MIMO communication system with iterative detection over a frequency-selective MIMO channel. We present a soft-input soft-output MIMO detector based on a cyclic factor graph representation and the sum-product algorithm with two different message schedules (serial and parallel). Computer simulations show that both schedules provide near-optimum performance in terms of bit error rate, while achieving a remarkable reduction in complexity compared to the optimal MAP detector.

Cooperative Simultaneous Localization and Synchronization in Mobile Agent Networks

Cooperative localization in agent networks based on interagent time-of-flight measurements is closely related to synchronization. To leverage this relation, we propose a Bayesian factor graph framework for cooperative simultaneous localization and synchronization (CoSLAS). This framework is suited to mobile agents and time-varying local clock parameters. Building on the CoSLAS factor graph, we develop a distributed (decentralized) belief propagation algorithm for CoSLAS in the practically important case of an affine clock model and asymmetric time stamping. Our algorithm is compatible with real-time operation and a time-varying network connectivity. To achieve high accuracy at reduced complexity and communication cost, the algorithm combines particle implementations with parametric message representations and takes advantage of a conditional independence property. Simulation results demonstrate the good performance of the proposed algorithm in a challenging scenario with time-varying network connectivity.

Equalization Algorithms for MIMO Communication Systems Based on Factor Graphs

In this paper, we consider a bit-interleaved coded spatial multiplexing MIMO communication system over a frequency-selective MIMO channel. We present a factor-graph-based derivation of two different equalization algorithms. To this end, we propose a cycle-free factor graph representation of the equalizer, to which we apply the sum-product algorithm (SPA). By using different message representations in the SPA, it is shown that the resulting equalization algorithms correspond to the optimal MAP equalizer and the low-complexity LMMSE equalizer, respectively. Both algorithms can be used in turbo processing and we demonstrate that after 3 iterations the BER performance of the LMMSE equalizer is similar to that of the MAP equalizer.

Mean field message passing for cooperative simultaneous ranging and synchronization

Many emerging technologies for wireless networks (WNs) require decentralized synchronization and ranging, i.e., distance estimation between neighboring pairs of nodes. Both tasks are related to each other when they are based on time measurements between nodes. Revealing this connection, we present a mean field (MF) message passing algorithm for cooperative simultaneous ranging and synchronization (CoSRAS), which jointly estimates the internode distances and clock parameters in a fully distributed way. It is shown that the use of the MF method reduces the computation and communication efforts compared to other message passing methods. For MF message exchange between nodes, only broadcast communication is required. Our simulation results demonstrate the equivalence in performance with centralized state-of-the-art joint ranging and synchronization algorithms.

Synchronization and delay estimation with sub-tick resolution

We consider the problem of clock synchronization between a pair of nodes using round-trip communication where only the initiating node collects time stamps, and where no time stamps are exchanged. These time stamps are the current timer values at the event of transmission or reception of a signal. Traditionally, the timer is modeled by a continuous function, i.e. as affine clock in case of asynchronism in clock skew and clock phase. In this work we deviate from the traditional model and propose a discrete-valued clock model, which is motivated by observations from real hardware. Employing the clock model allows us to find a new signaling model for round-trip time measurements, which enables us to simultaneously estimate clock skew, clock phase and propagation delay with a resolution below one clock tick period. Hence, we set a first step towards enabling high timing resolution with limited clock hardware.