Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Digital filters underpin the performance of coherent optical receivers which exploit digital signal processing (DSP) to mitigate transmission impairments. We outline the principles of such receivers and review our experimental investigations into compensation of polarization mode dispersion. We then consider the details of the digital filtering employed and present an analytical solution to the design of a chromatic dispersion compensating filter. Using the analytical solution an upper bound on the number of taps required to compensate chromatic dispersion is obtained, with simulation revealing an improved bound of 2.2 taps per 1000ps/nm for 10.7GBaud data. Finally the principles of digital polarization tracking are outlined and through simulation, it is demonstrated that 100krad/s polarization rotations could be tracked using DSP with a clock frequency of less than 500MHz.

Digital filters for coherent optical receivers.

Optical fiber transmission is impacted by linear and nonlinear impairments. We study the use of digital backpropagation (BP) in conjunction with coherent detection to jointly mitigate dispersion and fiber nonlinearity. We propose a noniterative asymmetric split-step Fourier method (SSFM) for solving the inverse nonlinear Schrodinger equation (NLSE). Using simulation results for RZ-QPSK transmitted over terrestrial systems with inline amplification and dispersion compensation, we obtain heuristics for the step size and sampling rate requirements, as well as the optimal dispersion map.

Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation

This paper presents a novel digital feedforward carrier recovery algorithm for arbitrary M-ary quadrature amplitude modulation (M-QAM) constellations in an intradyne coherent optical receiver. The approach does not contain any feedback loop and is therefore highly tolerant against laser phase noise. This is crucial, especially for higher order QAM constellations, which inherently have a smaller phase noise tolerance due to the lower spacing between adjacent constellation points. In addition to the mathematical description of the proposed carrier recovery algorithm also a possible hardware-efficient implementation in a parallelized system is presented and the performance of the algorithm is evaluated by Monte Carlo simulations for square 4-QAM (QPSK), 16-QAM, 64-QAM, and 256-QAM. For the simulations ASE noise and laser phase noise are considered as well as analog-to-digital converter (ADC) and internal resolution effects. For a 1 dB penalty at BER = 10-3, linewidth times symbol duration products of 4.1 x 10-4 (4-QAM), 1.4 x 10-4 (16-QAM), 4.0 x 10-5 (64-QAM) and 8.0 x 10-6 (256-QAM) are tolerable.

Hardware-Efficient Coherent Digital Receiver Concept With Feedforward Carrier Recovery for $M$ -QAM Constellations

Fiber-optic communication systems form the high-capacity transport infrastructure that enables global broadband data services and advanced Internet applications. The desire for higher per-fiber transport capacities and, at the same time, the drive for lower costs per end-to-end transmitted information bit has led to optically routed networks with high spectral efficiencies. Among other enabling technologies, advanced optical modulation formats have become key to the design of modern wavelength division multiplexed (WDM) fiber systems. In this paper, we review optical modulation formats in the broader context of optically routed WDM networks. We discuss the generation and detection of multigigabit/s intensity- and phase-modulated formats, and highlight their resilience to key impairments found in optical networking, such as optical amplifier noise, multipath interference, chromatic dispersion, polarization-mode dispersion, WDM crosstalk, concatenated optical filtering, and fiber nonlinearity

Advanced Optical Modulation Formats

The emergence of capable semiconductor processes has allowed digital signal processing to extend the application range of high-capacity optical systems. We report the performance of polarization multiplexed (or dual-polarization) quadrature phase-shift keying at 40 and 100 Gb/s.

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Performance of Dual-Polarization QPSK for Optical Transport Systems

We introduce digital precompensation for optical nonlinearities. A 10-Gb/s transmitter subsystem is described. Experimental results, across 320 and 1280 km of standard single-mode fiber (G.652) without any optical compensators, show substantial elimination of self-phase modulation. Some of the limits of this method are explored.

Electronic precompensation of optical nonlinearity

Recent advances in the electrical equalization of optical systems are presented in the context of standard methods. We report 10 Gb/s transmission over 60,000 ps/nm of optical dispersion from 3840 km of NDSF.

Electrical Domain Compensation of Optical Dispersion

We report the longest unregenerated reach achieved for a 10 Gb/s return-to-zero differential phase shift keying (RZ-DPSK) system on standard dispersion fiber (G652) with no optical dispersion compensation.

5120 km RZ-DPSK transmission over G652 fiber at 10 Gb/s with no optical dispersion compensation

An add/drop multiplexer/demultiplexer (ADM) for switching, modulating and attenuating optical signals in a fiber optic network employing wavelength division multiplexing (WDM) is disclosed. The ADM is equipped an optical multiplexer for splitting an input WDM signal into individual optical signals, leading to respective 2×2 switches. Each switch has another input originating from a plurality of "add lines", and selects one of its inputs to be dropped and the other to continue along a main signal path. The retained signals may be modulated and attenuated prior to being tapped and finally multiplexed together by a WDM multiplexer. The tapped signals are optoelectronically converted and fed back to a controller, preferably a digital signal processor running a software algorithm, which controls the switching, modulation and attenuation. This permits remote control of the ADM functions by encoding instructions for the controller into a low-frequency dither signal that is embedded within the individual optical signals. The ADM can accordingly be instructed to reroute traffic, dynamically equalize or otherwise change optical channel power levels, and add or remove dither, all in real time. A specific optical channel may be reserved for control purposes, allowing a network administrator to "log in" to the ADM to override the controller software algorithm. Optionally, the optical signals can be tapped upon entry to the ADM. A bidirectional ADM can be constructed from two unidirectional ADMs, and may share the same controller. Also, a single, general multi-input multi-output switch can be used to provide an arbitrary mapping between individual input and output optical signals.

Maurice O'Sullivan

Papers

Performance of Dual-Polarization QPSK for Optical Transport Systems

Electronic precompensation of optical nonlinearity

Electrical Domain Compensation of Optical Dispersion

5120 km RZ-DPSK transmission over G652 fiber at 10 Gb/s with no optical dispersion compensation

Optical add/drop multiplexer/demultiplexer