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Vibration injury in the hand-arm system from hand-held machines is one of the most common occupational health injuries and causes severe and often chronic nerve and vascular injury to the operator. Machines emitting shock vibrations, e.g., impact wrenches have since long been identified as a special risk factor. In legislative and standard texts the terms shock, impact, and transient vibration are frequently used to underline the special risk associated with these kinds of vibrations. In spite of this, there is no mathematically stringent definition what a shock vibration is or how the amplitude of the shock is defined. This lack of definitions is the subject of this article. This document discusses a number of candidate definitions for a vibration shock index (VSI) that quantifies different vibration signals in terms of how localized they are in the time domain. The VSI is intended to be used to classify and compare different vibration sources. The VSI is independent of the vibration level, i.e., it is unchanged if the vibration signal is rescaled. The traditional root mean square method to determine the vibration level will not produce a value representative for the shocks occurring in a signal with high VSI. Thus, there is a need for a complementing quantification method for the localized signal parts. Possible definitions for such a vibration shock level (VSL) are suggested. A problem formulation is first stated together with a description of the approach used for designing the VSI and the VSL. After this, model signals are defined, which are used to discuss and evaluate the different candidate definitions. Then, a number of candidate definitions are discussed, leading up to a conclusion on which candidate definitions that are promising for experimental evaluation.

Accurate and ubiquitous localization is crucial for a variety of applications such as logistics, navigation, intelligent transport, monitoring, control, and also for the benefit of communications. Exploiting millimeter-wave (mmWave) signals in 5G and Beyond 5G systems can provide accurate localization with limited infrastructure. We consider the single base station (BS) localization problem and extend it to 3D position and 3D orientation estimation of an unsynchronized multi-antenna user equipment (UE), using downlink multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) signals. Through a Fisher information analysis, we show that the problem is often identifiable, provided that there is at least one multipath component in addition to the line-of-sight (LoS), even if the position of corresponding incidence point (IP) is a priori unknown. Subsequently, we pose a maximum likelihood (ML) estimation problem, to jointly estimate the 3D position and 3D orientation of the UE as well as several nuisance parameters (the UE clock offset and the positions of IPs corresponding to the multipath). The ML problem is a high-dimensional non-convex optimization problem over a product of Euclidean and non-Euclidean manifolds. To avoid complex exhaustive search procedures, we propose a geometric initial estimate of all parameters, which reduces the problem to a 1-dimensional search over a finite interval. Numerical results show the efficiency of the proposed ad-hoc estimation, whose gap to the Cram\'er-Rao bound (CRB) is tightened using the ML estimation.

We consider the problem of estimating the 3D orientation of a user, using the downlink mmWave signals received from multiple base stations. We show that the received signals from several base stations, having known positions, can be used to estimate the unknown orientation of the user. We formulate the estimation problem as a maximum likelihood estimation problem in the the manifold of rotation matrices. In order to provide an initial estimate to solve the non-linear non-convex optimization problem, we resort to a least squares estimation problem that exploits the underlying geometry. Our numerical results show that the problem of orientation estimation can be solved when the signals from at least two base stations are received. We also provide the orientation lower error bound, showing a narrow gap between the performance of the proposed estimators and the bound.

In fiber-optic communications, evaluation of mutual information (MI) is still an open issue due to the unavailability of an exact and mathematically tractable channel model. Traditionally, lower bounds on MI are computed by approximating the (original) channel with an auxiliary forward channel. In this paper, lower bounds are computed using an auxiliary backward channel, which has not been previously considered in the context of fiber-optic communications. Distributions obtained through two variations of the stochastic digital backpropagation (SDBP) algorithm are used as auxiliary backward channels and these bounds are compared with bounds obtained through the conventional digital backpropagation (DBP). Through simulations, higher information rates were achieved with SDBP, {which can be explained by the ability of SDBP to account for nonlinear signal--noise interactions, Comment: 8 pages, 5 figures, accepted for publication in Journal of Lightwave Technology

The state of polarization and the carrier phase drift dynamically during transmission in a random fashion in coherent optical fiber communications. The typical digital signal processing solution to mitigate these impairments consists of two separate blocks that track each phenomenon independently. Such algorithms have been developed without taking into account mathematical models describing the impairments. We study a blind, model-based tracking algorithm to compensate for these impairments. The algorithm dynamically recovers the carrier phase and state of polarization jointly for an arbitrary modulation format. Simulation results show the effectiveness of the proposed algorithm, having a fast convergence rate and an excellent tolerance to phase noise and dynamic drift of the polarization. The computational complexity of the algorithm is lower compared to state-of-the-art algorithms at similar or better performance, which makes it a strong candidate for future optical systems.

A theoretical framework is introduced to model the dynamical changes of the state of polarization during transmission in coherent fibre-optic systems. The model generalizes the one-dimensional phase noise random walk to higher dimensions, accounting for random polarization drifts, emulating a random walk on the Poincar\'e sphere, which has been successfully verified using experimental data. The model is described in the Jones, Stokes and real four-dimensional formalisms, and the mapping between them is derived. Such a model will be increasingly important in simulating and optimizing future systems, where polarization-multiplexed transmission and sophisticated digital signal processing will be natural parts. The proposed polarization drift model is the first of its kind as prior work either models polarization drift as a deterministic process or focuses on polarization-mode dispersion in systems where the state of polarization does not affect the receiver performance. We expect the model to be useful in a wide-range of photonics applications where stochastic polarization fluctuation is an issue., Comment: 15 pages, 4 figures

Stochastic digital backpropagation (SDBP) is an extension of digital backpropagation (DBP) and is based on the maximum a posteriori principle. SDBP takes into account noise from the optical amplifiers in addition to handling deterministic linear and nonlinear impairments. The decisions in SDBP are taken on a symbol-by-symbol (SBS) basis, ignoring any residual memory, which may be present due to non-optimal processing in SDBP. In this paper, we extend SDBP to account for memory between symbols. In particular, two different methods are proposed: a Viterbi algorithm (VA) and a decision directed approach. Symbol error rate (SER) for memory-based SDBP is significantly lower than the previously proposed SBS-SDBP. For inline dispersion-managed links, the VA-SDBP has up to 10 and 14 times lower SER than DBP for QPSK and 16-QAM, respectively., Comment: 7 pages, accepted to publication in 'Journal of Lightwave Technology (JLT)'

A low-complexity detector is introduced for polarization-multiplexed M-ary phase shift keying modulation in a fiber-optical channel impaired by nonlinear phase noise, generalizing a previous result by Lau and Kahn for single-polarization signals. The proposed detector uses phase compensation based on both received signal amplitudes in conjunction with simple straight-line rather than four-dimensional maximum-likelihood decision boundaries., Comment: accepted for publication in IEEE Comm. Lett

A low-complexity model for signal quality prediction in a nonlinear fiber-optical network is developed. The model, which builds on the Gaussian noise model, takes into account the signal degradation caused by a combination of chromatic dispersion, nonlinear signal distortion, and amplifier noise. The center frequencies, bandwidths, and transmit powers can be chosen independently for each channel, which makes the model suitable for analysis and optimization of resource allocation, routing, and scheduling in large-scale optical networks applying flexible-grid wavelength-division multiplexing.

Recently an analytical model was presented that treats the nonlinear signal distortion from the Kerr nonlinearity in optical transmission systems as additive white Gaussian noise. This important model predicts the impact of the Kerr nonlinearity in systems operating at a high symbol rate and where the accumulated dispersion at the receiver is large. Starting from the suggested model for the propagating signal, we here give an independent and different calculation of the main result. The analysis is based on the Manakov equation with attenuation included and a complete and detailed derivation is given using a perturbation analysis. As in the case with the published model, in addition to assuming that the input signal can be written on a specific form, two further assumptions are necessary; the nonlinearity is weak and the signal-noise interaction is neglected. The result is then found without any further approximations., Comment: Results are unchanged, but the relation to the results in Ref. [4] is made clear

Within the framework of the thermal wave model, an investigation is made of the longitudinal dynamics of high energy charged particle beams. The model includes the self-consistent interaction between the beam and its surroundings in terms of a nonlinear coupling impedance, and when resistive as well as reactive parts are included, the evolution equation becomes a generalised nonlinear Schroedinger equation including a nonlocal nonlinear term. The consequences of the resistive part on the propagation of particle bunches are examined using analytical as well as numerical methods., Comment: 6 pages, 6 figures, uses RevTeX4

The effect of the Kerr nonlinearity on linear non-diffractive Bessel beams is investigated analytically and numerically using the nonlinear Schr\"odinger equation. The nonlinearity is shown to primarily affect the central parts of the Bessel beam, giving rise to radial compression or decompression depending on whether the nonlinearity is focusing or defocusing, respectively. The dynamical properties of Gaussian-truncated Bessel beams are also analysed in the presence of a Kerr nonlinearity. It is found that although a condition for width balance in the root-mean-square sense exists, the beam profile becomes strongly deformed during propagation and may exhibit the phenomena of global and partial collapse., Comment: 15 pages, 7 figures