Digital nonlinear equalization for optical transmission systems

This thesis focuses on digital equalization of nonlinear fiber impairments for coherent optical transmission systems. Building from well-known physical models of signal propagation in single-mode optical fibers, novel nonlinear equalization techniques are proposed, numerically assessed and experimentally demonstrated. The structure of the proposed algorithms is strongly driven by the optimization of the performance versus complexity tradeoff, envisioning the near-future practical application in commercial real-time transceivers. The work is initially focused on the mitigation of intra-channel nonlinear impairments relying on the concept of digital backpropagation (DBP) associated with Volterra-based filtering. After a comprehensive analysis of the third-order Volterra kernel, a set of critical simplifications are identified, culminating in the development of reduced complexity nonlinear equalization algorithms formulated both in time and frequency domains. The implementation complexity of the proposed techniques is analytically described in terms of computational effort and processing latency, by determining the number of real multiplications per processed sample and the number of serial multiplications, respectively. The equalization performance is numerically and experimentally assessed through bit error rate (BER) measurements. Finally, the problem of inter-channel nonlinear compensation is addressed within the context of 400 Gb/s (400G) superchannels for long-haul and ultra-long-haul transmission. Different superchannel configurations and nonlinear equalization strategies are experimentally assessed, demonstrating that inter-subcarrier nonlinear equalization can provide an enhanced signal reach while requiring only marginal added complexity.

Signal Transceiver Transit Times and Propagation Delay Corrections for Ranging and Georeferencing Applications

The accuracy of ranging measurements depends critically on the knowledge of time delays undergone by signals when retransmitted by a remote transponder and due to propagation effects. A new method determines these delays for every single pulsed signal transmission. It utilizes four ground-based reference stations, synchronized in time and installed at well-known geodesic coordinates and a repeater in space, carried by a satellite, balloon, aircraft, and so forth. Signal transmitted by one of the reference bases is retransmitted by the transponder, received back by the four bases, producing four ranging measurements which are processed to determine uniquely the time delays undergone in every retransmission process. A minimization function is derived comparing repeater's positions referred to at least two groups of three reference bases, providing the signal transit time at the repeater and propagation delays, providing the correct repeater position. The method is applicable to the transponder platform positioning and navigation, time synchronization of remote clocks, and location of targets. The algorithm has been demonstrated by simulations adopting a practical example with the transponder carried by an aircraft moving over bases on the ground.

Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems

Limitations in the performance of coherent transmission systems employing digital back-propagation due to four-wave mixing impairments are reported for the first time. A significant performance constraint is identified, originating from four-wave mixing between signals and amplified spontaneous emission noise which induces a linear increase in the standard deviation of the received field with signal power, and linear dependence on transmission distance.

Propagation of low power low divergence Gaussian fields in unbiased self-defocusing photorefractive media and their interactions

Many optical networks are limited in speed and processing capability due to the necessity for the optical signal to be converted to an electrical signal and back again. In addition, electronically manipulated interconnects in an otherwise optical network lead to overly complicated systems. Optical spatial solitons are optical beams that propagate without spatial divergence. They are capable of phase dependent interactions, and have therefore been extensively researched as suitable all optical interconnects for over 20 years. However, they require additional external components, initially high voltage power sources were required, several years later, high power background illumination had replaced the high voltage. However, these additional components have always remained as the greatest hurdle in realising the applications of the interactions of spatial optical solitons as all optical interconnects. Recently however, self-focusing was observed in an otherwise self-defocusing photorefractive crystal. This observation raises the possibility of the formation of soliton-like fields in unbiased self-defocusing media, without the need for an applied electrical field or background illumination. This thesis will present an examination of the possibility of the formation of soliton-like low divergence fields in unbiased self-defocusing photorefractive media. The optimal incident beam and photorefractive media parameters for the formation of these fields will be presented, together with an analytical and numerical study of the effect of these parameters. In addition, preliminary examination of the interactions of two of these fields will be presented. In order to complete an analytical examination of the field propagating through the photorefractive medium, the spatial profile of the beam after propagation through the medium was determined. For a low power solution, it was found that an incident Gaussian field maintains its Gaussian profile as it propagates. This allowed the beam at all times to be described by an individual complex beam parameter, while also allowing simple analytical solutions to the appropriate wave equation. An analytical model was developed to describe the effect of the photorefractive medium on the Gaussian beam. Using this model, expressions for the required intensity dependent change in both the real and imaginary components of the refractive index were found. Numerical investigation showed that under certain conditions, a low powered Gaussian field could propagate in self-defocusing photorefractive media with divergence of approximately 0.1 % per metre. An investigation into the parameters of a Ce:BaTiO3 crystal showed that the intensity dependent absorption is wavelength dependent, and can in fact transition to intensity dependent transparency. Thus, with careful wavelength selection, the required intensity dependent change in both the real and imaginary components of the refractive index for the formation of a low divergence Gaussian field are physically realisable. A theoretical model incorporating the dependence of the change in real and imaginary components of the refractive index on propagation distance was developed. Analytical and numerical results from this model are congruent with the results from the previous model, showing low divergence fields with divergence less than 0.003 % over the propagation length of the photorefractive medium. In addition, this approach also confirmed the previously mentioned self-focusing effect of the self-defocusing media, and provided an analogy to a negative index GRIN lens with an intensity dependent focal length. Experimental results supported the findings of the numerical analysis. Two low divergence fields were found to possess the ability to interact in a Ce:BaTiO3 crystal in a soliton-like fashion. The strength of these interactions was found to be dependent on the degree of divergence of the individual beams. This research found that low-divergence fields are possible in unbiased self-defocusing photorefractive media, and that soliton-like interactions between two of these fields are possible. However, in order for these types of fields to be used in future all optical interconnects, the manipulation of these interactions, together with the ability for these fields to guide a second beam at a different wavelength, must be investigated.

A deconvolution method for deriving the transit time spectrum for ultrasound propagation through cancellous bone replica models

The acceptance of broadband ultrasound attenuation for the assessment of osteoporosis suffers from a limited understanding of ultrasound wave propagation through cancellous bone. It has recently been proposed that the ultrasound wave propagation can be described by a concept of parallel sonic rays. This concept approximates the detected transmission signal to be the superposition of all sonic rays that travel directly from transmitting to receiving transducer. The transit time of each ray is defined by the proportion of bone and marrow propagated. An ultrasound transit time spectrum describes the proportion of sonic rays having a particular transit time, effectively describing lateral inhomogeneity of transit times over the surface of the receiving ultrasound transducer. The aim of this study was to provide a proof of concept that a transit time spectrum may be derived from digital deconvolution of input and output ultrasound signals. We have applied the active-set method deconvolution algorithm to determine the ultrasound transit time spectra in the three orthogonal directions of four cancellous bone replica samples and have compared experimental data with the prediction from the computer simulation. The agreement between experimental and predicted ultrasound transit time spectrum analyses derived from Bland–Altman analysis ranged from 92% to 99%, thereby supporting the concept of parallel sonic rays for ultrasound propagation in cancellous bone. In addition to further validation of the parallel sonic ray concept, this technique offers the opportunity to consider quantitative characterisation of the material and structural properties of cancellous bone, not previously available utilising ultrasound.

Experimental Study of crack propagation in carbon steel using acoustic emission

Acoustic emission technique has become a significant and powerful structural health monitoring tool for structures. Researches to date have been done on crack location, fatigue crack propagation in materials and severity assessment of failure using acoustic emission technique. Determining severity of failure in steel structures using acoustic emission technique is still a challenge to accurately determine the relationship between the severity of crack propagation and acoustic emission activities. In this study three point bending test on low carbon steel samples along with acoustic emission technique have been used to determine crack propagation and severity. A notch is introduced at the tension face of the loading point to the samples to initiate the crack. The results show that the percentage of load drop of the steel specimen has a reciprocal relationship with the crack opening i.e. crack opening zones are influenced by the loading rate. In post yielding region, common acoustic emission signal parameters such as, signal strength, energy and amplitudes are found to be higher than those at pre-yielding and at yielding.

Wave propagation in elastic solids undergoing damage and growth process

Modeling and analysis of wave propagation in elastic solids undergoing damage and growth process are reported in this paper. Two types of diagnostic problems, (1) the propagation of waves in the presence of a slow growth process and (2) the propagation of waves in the presence of a fast growth process, are considered. The proposed model employs a slow and a fast time scale and a homogenization technique in the wavelength scale. A detailed analysis of wave dispersion is carried out. A spectral analysis reveals certain low-frequency bands, where the interaction between the wave and the growth process produces acoustic metamaterial-like behavior. Various practical issues in designing an efficient method of acousto-ultrasonic wave based diagnostics of the growth process are discussed. Diagnostics of isotropic damage in a ductile or quasi-brittle solid by using a micro-second pulsating signal is considered for computer simulations, which is to illustrate the practical application of the proposed modeling and analysis. The simulated results explain how an estimate of signal spreading can be effectively employed to detect the presence of a steady-state damage or the saturation of a process.

Atrial Electric Signal During Sinus Rhythm in Lone Paroxysmal Atrial Fibrillation

Atrial fibrillation (AF) is the most common tachyarrhythmia and is associated with substantial morbidity, increased mortality and cost. The treatment modalities of AF have increased, but results are still far from optimal. More individualized therapy may be beneficial. Aiming for this calls improved diagnostics. Aim of this study was to find non-invasive parameters obtained during sinus rhythm reflecting electrophysiological patterns related to propensity to AF and particularly to AF occurring without any associated heart disease, lone AF. Overall 240 subjects were enrolled, 136 patients with paroxysmal lone AF and 104 controls (mean age 45 years, 75% males). Signal measurements were performed by non-invasive magnetocardiography (MCG) and by invasive electroanatomic mapping (EAM). High-pass filtering techniques and a new method based on a surface gradient technique were adapted to analyze atrial MCG signal. The EAM was used to elucidate atrial activation in patients and as a reference for MCG. The results showed that MCG mapping is an accurate method to detect atrial electrophysiologic properties. In lone paroxysmal AF, duration of the atrial depolarization complex was marginally prolonged. The difference was more obvious in women and was also related to interatrial conduction patterns. In the focal type of AF (75%), the root mean square (RMS) amplitudes of the atrial signal were normal, but in AF without demonstrable triggers the late atrial RMS amplitudes were reduced. In addition, the atrial characteristics tended to remain similar even when examined several years after the first AF episodes. The intra-atrial recordings confirmed the occurrence of three distinct sites of electrical connection from right to left atrium (LA): the Bachmann bundle (BB), the margin of the fossa ovalis (FO), and the coronary sinus ostial area (CS). The propagation of atrial signal could also be evaluated non-invasively. Three MCG atrial wave types were identified, each of which represented a distinct interatrial activation pattern. In conclusion, in paroxysmal lone AF, active focal triggers are common, atrial depolarization is slightly prolonged, but with a normal amplitude, and the arrhythmia does not necessarily lead to electrical or mechanical dysfunction of the atria. In women the prolongation of atrial depolarization is more obvious. This may be related to gender differences in presentation of AF. A significant minority of patients with lone AF lack frequent focal triggers, and in them, the late atrial signal amplitude is reduced, possibly signifying a wider degenerative process in the LA. In lone AF, natural impulse propagation to LA during sinus rhythm goes through one or more of the principal pathways described. The BB is the most common route, but in one-third, the earliest LA activation occurs outside the BB. Susceptibility to paroxysmal lone AF is associated with propagation of the atrial signal via the margin of the FO or via multiple pathways. When conduction occurs via the BB, it is related with prolonged atrial activation. Thus, altered and alternative conduction pathways may contribute to pathogenesis of lone AF. There is growing evidence of variability in genesis of AF also within lone paroxysmal AF. Present study suggests that this variation may be reflected in cardiac signal pattern. Recognizing the distinct signal profiles may assist in understanding the pathogenesis of AF and identifying subgroups for patient-tailored therapy.

Detection of Tsunami Wave Generation and Propagation Using Fiber Bragg Grating Sensors

This paper describes the design and development of a Fiber Bragg Grating (FBG) sensor system for monitoring tsunami waves generated in the deep ocean. An experimental setup was designed and fabricated to simulate the generation and propagation of a tsunami wave. The characteristics and efficiency of the developed FBG sensor was evaluated with a standard commercial Digiquartz sensor. For real time monitoring of tsunami waves, FBG sensors bonded to a cantilever is used and the wavelength shifts (Delta lambda(B)) in the reflected spectra resulting from the strain/pressure imparted on the FBGs have been recorded using a high-speed Micron Optics FBG interrogation system. The parameters sensed are the signal burst during tsunami generation and pressure variations at different places as the tsunami wave propagates away from the source of generation. The results obtained were compared with the standard commercial sensor used in tsunami detection. The observations suggest that the FBG sensor was highly sensitive and free from many of the constraints associated with the commercial tsunameter.

Wave propagation analysis in carbon nanotube embedded composite using wavelet based spectral finite elements

In this paper, elastic wave propagation is studied in a nanocomposite reinforced with multiwall carbon nanotubes (CNTs). Analysis is performed on a representative volume element of square cross section. The frequency content of the exciting signal is at the terahertz level. Here, the composite is modeled as a higher order shear deformable beam using layerwise theory, to account for partial shear stress transfer between the CNTs and the matrix. The walls of the multiwall CNTs are considered to be connected throughout their length by distributed springs, whose stiffness is governed by the van der Waals force acting between the walls of nanotubes. The analyses in both the frequency and time domains are done using the wavelet-based spectral finite element method (WSFEM). The method uses the Daubechies wavelet basis approximation in time to reduce the governing PDE to a set of ODEs. These transformed ODEs are solved using a finite element (FE) technique by deriving an exact interpolating function in the transformed domain to obtain the exact dynamic stiffness matrix. Numerical analyses are performed to study the spectrum and dispersion relations for different matrix materials and also for different beam models. The effects of partial shear stress transfer between CNTs and matrix on the frequency response function (FRF) and the time response due to broadband impulse loading are investigated for different matrix materials. The simultaneous existence of four coupled propagating modes in a double-walled CNT-composite is also captured using modulated sinusoidal excitation.

Improved large-MIMO detection based on damped belief propagation

In this paper, we consider the application of belief propagation (BP) to achieve near-optimal signal detection in large multiple-input multiple-output (MIMO) systems at low complexities. Large-MIMO architectures based on spatial multiplexing (V-BLAST) as well as non-orthogonal space-time block codes(STBC) from cyclic division algebra (CDA) are considered. We adopt graphical models based on Markov random fields (MRF) and factor graphs (FG). In the MRF based approach, we use pairwise compatibility functions although the graphical models of MIMO systems are fully/densely connected. In the FG approach, we employ a Gaussian approximation (GA) of the multi-antenna interference, which significantly reduces the complexity while achieving very good performance for large dimensions. We show that i) both MRF and FG based BP approaches exhibit large-system behavior, where increasingly closer to optimal performance is achieved with increasing number of dimensions, and ii) damping of messages/beliefs significantly improves the bit error performance.

Guided Ultrasonic Wave Propagation through Inaccessible Damage in a Folded Plate using Sensor-Actuator Network

Rapid diagnostics and virtual imaging of damages in complex structures like folded plate can help reduce the inspection time for guided wave based NDE and integrated SHM. Folded plate or box structure is one of the major structural components for increasing the structural strength. Damage in the folded plate, mostly in the form of surface breaking cracks in the inaccessible zone is a usual problem in aerospace structures. One side of the folded plate is attached (either riveted or bonded) to adjacent structure which is not accessible for immediate inspection. The sensor-actuator network in the form of a circular array is placed on the accessible side of the folded plate. In the present work, a circular array is employed for scanning the entire folded plate type structure for damage diagnosis and wave field visualization of entire structural panel. The method employs guided wave with relatively low frequency bandwidth of 100-300 kHz. Change in the response signal with respect to a baseline signal is used to construct a quantitative relationship with damage size parameters. Detecting damage in the folded plate by using this technique has significant potential for off-line and on-line SHM technologies. By employing this technique, surface breaking cracks on inaccessible face of the folded plate are detected without disassembly of structure in a realistic environment.

Lamb Wave Propagation in Laminated Composite Structures

Damage detection using guided Lamb waves is an important tool in Structural health Monitoring. In this paper, we outline a method of obtaining Lamb wave modes in composite structures using two dimensional Spectral Finite Elements. Using this approach, Lamb wave dispersion curves are obtained for laminated composite structures with different fibre orientation. These propagating Lamb wave modes are pictorially captured using tone burst signal.