There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

Filtering and smoothing methods are used to produce an accurate estimate of the state of a time-varying system based on multiple observational inputs (data). Interest in these methods has exploded in recent years, with numerous applications emerging in fields such as navigation, aerospace engineering, telecommunications, and medicine. This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework. Readers learn what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages. They also discover how state-of-the-art Bayesian parameter estimation methods can be combined with state-of-the-art filtering and smoothing algorithms. The book’s practical and algorithmic approach assumes only modest mathematical prerequisites. Examples include MATLAB computations, and the numerous end-of-chapter exercises include computational assignments. MATLAB/GNU Octave source code is available for download at www.cambridge.org/sarkka, promoting hands-on work with the methods.

贝叶斯滤波与平滑 (Bayesian filtering and smoothing)

Today’s telecommunication networks have become sources of enormous amounts of widely heterogeneous data. This information can be retrieved from network traffic traces, network alarms, signal quality indicators, users’ behavioral data, etc. Advanced mathematical tools are required to extract meaningful information from these data and take decisions pertaining to the proper functioning of the networks from the network-generated data. Among these mathematical tools, machine learning (ML) is regarded as one of the most promising methodological approaches to perform network-data analysis and enable automated network self-configuration and fault management. The adoption of ML techniques in the field of optical communication networks is motivated by the unprecedented growth of network complexity faced by optical networks in the last few years. Such complexity increase is due to the introduction of a huge number of adjustable and interdependent system parameters (e.g., routing configurations, modulation format, symbol rate, coding schemes, etc.) that are enabled by the usage of coherent transmission/reception technologies, advanced digital signal processing, and compensation of nonlinear effects in optical fiber propagation. In this paper we provide an overview of the application of ML to optical communications and networking. We classify and survey relevant literature dealing with the topic, and we also provide an introductory tutorial on ML for researchers and practitioners interested in this field. Although a good number of research papers have recently appeared, the application of ML to optical networks is still in its infancy: to stimulate further work in this area, we conclude this paper proposing new possible research directions.

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An Overview on Application of Machine Learning Techniques in Optical Networks

Short range optical data links are experiencing bandwidth limitations making it very challenging to cope with the growing data transmission capacity demands. Parallel optics appears as a valid short-term solution. It is, however, not a viable solution in the long-term because of its complex optical packaging. Therefore, increasing effort is now put into the possibility of exploiting higher order modulation formats with increased spectral efficiency and reduced optical transceiver complexity. As these type of links are based on intensity modulation and direct detection, modulation formats relying on optical coherent detection can not be straight forwardly employed. As an alternative and more viable solution, this paper proposes the use of carrierless amplitude phase (CAP) in a novel multiband approach (MultiCAP) that achieves record spectral efficiency, increases tolerance towards dispersion and bandwidth limitations, and reduces the complexity of the transceiver. We report on numerical simulations and experimental demonstrations with capacity beyond 100 Gb/s transmission using a single externally modulated laser. In addition, an extensive comparison with conventional CAP is also provided. The reported experiment uses MultiCAP to achieve 102.4 Gb/s transmission, corresponding to a data payload of 95.2 Gb/s error free transmission by using a 7% forward error correction code. The signal is successfully recovered after 15 km of standard single mode fiber in a system limited by a 3 dB bandwidth of 14 GHz.

/pdf/multiband-carrierless-amplitude-phase-modulation-for-high-mo3n3zbmwr.pdf

Multiband Carrierless Amplitude Phase Modulation for High Capacity Optical Data Links

Polarization-diverse coherent demodulation allows to compensate large values of accumulated linear distortion by digital signal processing. In particular, in uncompensated links without optical dispersion compensation, the parameter of the residual chromatic dispersion (CD) is vital to set the according digital filtering function. We present different non-data-aided (blind) CD estimation methods for single-carrier transmission under implementation constraint conditions such as bandwidth limitation and sampling rate. The estimation performance for various modulation formats is compared with respect to precision and robustness for a wide range of combined channel impairments.

Chromatic Dispersion Estimation in Digital Coherent Receivers

In this paper, tools from machine learning community, such as Bayesian filtering and expectation maximization parameter estimation, are presented and employed for laser amplitude and phase noise characterization. We show that phase noise estimation based on Bayesian filtering outperforms conventional time-domain approach in the presence of moderate measurement noise. Additionally, carrier synchronization based on Bayesian filtering, in combination with expectation maximization, is demonstrated for the first time experimentally.

Application of Machine Learning Techniques for Amplitude and Phase Noise Characterization

A novel cognitive receiver for modulation format recognition with reconfigurable carrier recovery scheme is proposed and experimentally demonstrated for phase modulated radio-over-fibre links. Demodulation of burst-mode mixed modulation formats (PSK and QAM) is demonstrated after 40km of transmission.

Cognitive digital receiver for burst mode phase modulated radio over fiber links

Highest reported bit rate of 2.5 Gb/s for optically phase-modulated radio-over-fiber (RoF) link, employing digital coherent detection, is demonstrated. Demodulation of 3×2.5 Gb/s quadrature phase-shift-keying modulated wavelength-division-multiplexed RoF channels is achieved after 79 km of transmission through deployed fiber. Error-free performance (bit-error rate corresponding to 10-4) is achieved using a digital coherent receiver in combination with a K-means algorithm for radio-frequency phase recovery.

Experimental 2.5-Gb/s QPSK WDM Phase-Modulated Radio-Over-Fiber Link With Digital Demodulation by a $K$ -Means Algorithm

A 3.125 Gb/s photonic impulse radio ultra-wideband signal is created using the incoherent optical field summation resulting from the cross gain modulation of an uncooled distributed feedback laser injected with an external cavity laser. After 50 km of fiber and wireless transmission over 2.9-3.3-m, successful detection using a digital signal processing receiver is achieved.

Neil Guerrero Gonzalez

Papers

Chromatic Dispersion Estimation in Digital Coherent Receivers

Application of Machine Learning Techniques for Amplitude and Phase Noise Characterization

Cognitive digital receiver for burst mode phase modulated radio over fiber links

Experimental 2.5-Gb/s QPSK WDM Phase-Modulated Radio-Over-Fiber Link With Digital Demodulation by a $K$ -Means Algorithm

3.125 Gb/s Impulse Radio Ultra-Wideband Photonic Generation and Distribution Over a 50 km Fiber With Wireless Transmission