Nonlinearity Mitigation in WDM Systems: Models, Strategies, and Achievable Rates

After reviewing models and mitigation strategies for interchannel nonlinear interference (NLI), we focus on the frequency-resolved logarithmic perturbation model to study the coherence properties of NLI. Based on this study, we devise an NLI mitigation strategy which exploits the synergic effect of phase and polarization noise compensation (PPN) and subcarrier multiplexing with symbol-rate optimization. This synergy persists even for high-order modulation alphabets and Gaussian symbols. A particle method for the computation of the resulting achievable information rate and spectral efficiency (SE) is presented and employed to lower-bound the channel capacity. The dependence of the SE on the link length, amplifier spacing, and presence or absence of inline dispersion compensation is studied. Single-polarization and dual-polarization scenarios with either independent or joint processing of the two polarizations are considered. Numerical results show that, in links with ideal distributed amplification, an SE gain of about 1 bit/s/Hz/polarization can be obtained (or, in alternative, the system reach can be doubled at a given SE) with respect to single-carrier systems without PPN mitigation. The gain is lower with lumped amplification, increases with the number of spans, decreases with the span length, and is further reduced by in-line dispersion compensation. For instance, considering a dispersion-unmanaged link with lumped amplification and an amplifier spacing of 60 km, the SE after 80 spans can be be increased from 4.5 to 4.8 bit/s/Hz/polarization, or the reach raised up to 100 spans (+25%) for a fixed SE.Comment: Submitted to Journal of Lightwave Technolog

Information Transmission using the Nonlinear Fourier Transform, Part III: Spectrum Modulation

Motivated by the looming "capacity crunch" in fiber-optic networks, information transmission over such systems is revisited. Among numerous distortions, inter-channel interference in multiuser wavelength-division multiplexing (WDM) is identified as the seemingly intractable factor limiting the achievable rate at high launch power. However, this distortion and similar ones arising from nonlinearity are primarily due to the use of methods suited for linear systems, namely WDM and linear pulse-train transmission, for the nonlinear optical channel. Exploiting the integrability of the nonlinear Schr\"odinger (NLS) equation, a nonlinear frequency-division multiplexing (NFDM) scheme is presented, which directly modulates non-interacting signal degrees-of-freedom under NLS propagation. The main distinction between this and previous methods is that NFDM is able to cope with the nonlinearity, and thus, as the the signal power or transmission distance is increased, the new method does not suffer from the deterministic cross-talk between signal components which has degraded the performance of previous approaches. In this paper, emphasis is placed on modulation of the discrete component of the nonlinear Fourier transform of the signal and some simple examples of achievable spectral efficiencies are provided.Comment: Updated version of IEEE Transactions on Information Theory, vol. 60, no. 7, pp. 4346--4369, July, 201

Theory of remote entanglement via quantum-limited phase-preserving amplification

We show that a quantum-limited phase-preserving amplifier can act as a which-path information eraser when followed by heterodyne detection. This 'beam splitter with gain' implements a continuous joint measurement on the signal sources. As an application, we propose heralded concurrent remote entanglement generation between two qubits coupled dispersively to separate cavities. Dissimilar qubit-cavity pairs can be made indistinguishable by simple engineering of the cavity driving fields providing further experimental flexibility and the prospect for scalability. Additionally, we find an analytic solution for the stochastic master equation, a quantum filter, yielding a thorough physical understanding of the nonlinear measurement process leading to an entangled state of the qubits. We determine the concurrence of the entangled states and analyze its dependence on losses and measurement inefficiencies.Comment: Main text (11 pages, 5 figures), updated to the published versio

Improving the Performance of Dynamic Electromyogram-to-Force Models for the Hand-Wrist and Multiple Fingers

Relating surface electromyogram (EMG) activity to force/torque models is used in many areas including: prosthesis control systems, to regulate direction and speed of movement in reaching and matching tasks; clinical biomechanics, to assess muscle deficiency and effort levels; and ergonomics analysis, to assess risk of work-related injury such as back pain, fatigue and skill tests. This thesis work concentrated on improving the performance of dynamic EMG-to-force models for the hand-wrist and multiple fingers. My contributions include: 1) rapid calibration of dynamic hand-wrist EMG-force models using a minimum number of electrodes, 2) efficiently training two degree of freedom (DoF) hand-wrist EMG-force models, and 3) estimating individual and combined fingertip forces from forearm EMG during constant-pose, force-varying tasks. My calibration approach for hand-wrist EMG-force models optimized three main factors for 1-DoF and 2-DoF tasks: training duration (14, 22, 30, 38, 44, 52, 60, 68, 76 s), number of electrodes (2 through 16), and model forms (subject-specific, DoF-specific, universal). The results show that training duration can be reduced from historical 76 s to 40–60 s without statistically affecting the average error for both 1-DoF and 2-DoF tasks. Reducing the number of electrodes depended on the number of DoFs. One-DoF models can be reduced to 2 electrodes with average test error range of 8.3–9.2% maximum voluntary contraction (MVC), depending on the DoF (e.g., flexion-extension, radial-ulnar deviation, pronation-supination, open-close). Additionally, 2-DoF models can be reduced to 6 electrodes with average error of 7.17–9.21 %MVC. Subject-specific models had the lowest error for 1-DoF tasks while DoF-specific and universal were the lowest for 2-DoF tasks. In the EMG-finger project, we studied independent contraction of one, two, three or four fingers (thumb excluded), as well as contraction of four fingers in unison. Using regression, we found that a pseudo-inverse tolerance (ratio of largest to smallest singular value) of 0.01 was optimal. Lower values produced erratic models and higher values produced models with higher errors. EMG-force errors using one finger ranged from 2.5–3.8 %MVC, using the optimal pseudoinverse tolerance. With additional fingers (two, three or four), the average error ranged from 5–8 %MVC. When four fingers contracted in unison, the average error was 4.3 %MVC. Additionally, I participated in two team projects—EMG-force dynamic models about the elbow and relating forearm muscle EMG to finger force during slowly force varying contractions. This work is also described herein

Mapping the optimal route between two quantum states

A central feature of quantum mechanics is that a measurement is intrinsically probabilistic. As a result, continuously monitoring a quantum system will randomly perturb its natural unitary evolution. The ability to control a quantum system in the presence of these fluctuations is of increasing importance in quantum information processing and finds application in fields ranging from nuclear magnetic resonance to chemical synthesis. A detailed understanding of this stochastic evolution is essential for the development of optimized control methods. Here we reconstruct the individual quantum trajectories of a superconducting circuit that evolves in competition between continuous weak measurement and driven unitary evolution. By tracking individual trajectories that evolve between an arbitrary choice of initial and final states we can deduce the most probable path through quantum state space. These pre- and post-selected quantum trajectories also reveal the optimal detector signal in the form of a smooth time-continuous function that connects the desired boundary conditions. Our investigation reveals the rich interplay between measurement dynamics, typically associated with wave function collapse, and unitary evolution of the quantum state as described by the Schrodinger equation. These results and the underlying theory, based on a principle of least action, reveal the optimal route from initial to final states, and may enable new quantum control methods for state steering and information processing.Comment: 12 pages, 9 figure

Experimental Investigations of EMG-Torque Modeling for the Human Upper Limb

The electrical activity of skeletal muscle—the electromyogram (EMG)—is of value to many different application areas, including ergonomics, clinical biomechanics and prosthesis control. For many applications, the EMG is related to muscular tension, joint torque and/or applied forces. In these cases, a goal is for an EMG-torque model to emulate the natural relationship between the central nervous system (as evidenced in the surface EMG) and peripheral joints and muscles. This thesis work concentrated on experimental investigations of EMG-torque modeling. My contributions include: 1) continuing to evaluate the advantage of advanced EMG amplitude estimators, 2) studying system identification techniques (regularizing the least squares fit and increasing training data duration) to improve EMG-torque model performance, and 3) investigating the influence of joint angle on EMG-torque modeling. Results show that the advanced EMG amplitude estimator reduced the model error by 21%—71% compared to conventional estimators. Use of the regularized least squares fit with 52 seconds of training data reduced the model error by 20% compared to the least squares fit without regulation when using 26 seconds of training data. It is also demonstrated that the influence of joint angle can be modeled as a multiplicative factor in slowly force-varying and force-varying contractions at various, fixed angles. The performance of the models that account for the joint angle are not statistically different from a model that was trained at each angle separately and thus does not interpolate across angles. The EMG-torque models that account for joint angle and utilize advanced EMG amplitude estimation and system identification techniques achieved an error of 4.06±1.2% MVCF90 (i.e., error referenced to maximum voluntary contraction at 90° flexion), while models without using these advanced techniques and only accounting for a joint angle of 90° generated an error of 19.15±11.2% MVCF90. This thesis also summarizes other collaborative research contributions performed as part of this thesis. (1) EMG-force modeling at the finger tips was studied with the purpose of assessing the ability to determine two or more independent, continuous degrees of freedom of control from the muscles of the forearm [with WPI and Sherbrooke University]. (2) Investigation of EMG bandwidth requirements for whitening for real-time applications of EMG whitening techniques [with WPI colleagues]. (3) Investigation of the ability of surface EMG to estimate joint torque at future times [with WPI colleagues]. (4) Decomposition of needle EMG data was performed as part of a study to characterize motor unit behavior in patients with amyotrophic lateral sclerosis (ALS) [with Spaulding Rehabilitation Hospital, Boston, MA]