Machine Learning Techniques in Optical Communication

Nowadays, the coherent optical communication system plays an important role in communication field because of large capability and bandwidth. A coherent optical communication, based on high-order modulation and digital signal processing technologies, consists of optical transmitters, optical fiber lines, optical amplifiers and optical receivers. In the high-speed coherent optical communication system, the phase noise from the transmitter laser and the local oscillator laser can significantly degrade the performance of the signal transmission and detection, especially for the systems using high-order modulation format, such as m-ary phase shift keying (mPSK) and m-ary quadrature amplitude modulation (m-QAM). Therefore, investigations on laser phase noise compensation algorithm based on digital signal processing technologies has become more and more significant. In this work, a multi-ring carrier phase recovery algorithm is developed for compensating the laser phase noise in optical fiber communication systems using high-order modulation formats. Degradations on the performance of communication systems due to the laser phase noise have been investigated. The system performance using the proposed algorithm and the conventional Viterbi-Viterbi algorithm were also evaluated in 9-channel and 15- channel, 32-Gbaud, Nyquist-spaced QPSK, 16-QAM, 64-QAM and 256-QAM coherent transmission systems with considering the impact of the laser phase noise. It is found that the phase noise leads to stricter constraints on the linewidths of transmitter-side and receiver-side lasers, and it can greatly degrade the achievable information rates in communication systems. Besides, compared to the conventional Viterbi-Viterbi algorithm, which is usually applied in the QPSK system, our proposed algorithm can also well mitigate the laser phase noise in 16-QAM, 64-QAM and 256-QAM optical communication systems.
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Sequential Monte Carlo (SMC) methods (also known as particle filter) provide a way to solve the state estimation problem in nonlinear non-Gaussian state space models (SSM) through numerical approximation. Particle smoothing is one retrospective state estimation method based on particle filtering. In this paper, we propose a new particle smoother. The basic idea is easy and leads to a forward-backward procedure, where the Metropolis-Hastings algorithm is used to resample the filtering particles. The goodness of the new scheme is assessed using a nonlinear SSM. It is concluded that this new particle smoother is suitable for state estimation in complicated dynamical systems.

Nonlinear mixed-effects state space models with applications to HIV dynamics

As the carrier frequency goes into the terahertz band, the phase noise of the signal source has increasing impacts on the performance of the communication system. Considering a 16QAM high-order digital modulation terahertz communication system (DMTCS), by comparing the influence of two kinds of local oscillator signal sources with different phase noise characteristics on the bit error rate (BER) performance of the system based on theoretical analysis and experimental research, it is found that the near-end phase noise of local oscillator signal source has a great influence on the BER performance of the DMTCS. The suppression of phase noise of the local oscillator signal source based on choosing loop bandwidth of the digital phase-locked loop (DPLL) at the receiving end is also discussed. It is found that the negative impacts of phase noise on BER performance of the system can be efficiently decreased by reasonably selecting the loop bandwidth of the DPLL.

Single frequency fiber laser is the most promising optical source in fibre optic communication, which plays an important role in fibre optic sensor, laser radar and laser range finde. Generally, the performance of the single frequency fiber laser was evaluated by the phase noise. The oscilloscope and dynamic signal analyzer method were adopted to design phase noise of single frequency fiber laser. Using power spectrum and the integral sources of different pump power, seed source power and wavelength of the fiber laser phase noise were analyzed qualitatively, the results show that, the greater pump power can get the low frequency phase noise. For the different seed source powers, phase noise is in the proportion of basic test frequency at the same level. For testing seeds of different wavelengths which is different proportions of high frequency phase noise, the biggest percentage of seed wavelength is 1 560.48 nm.

The presence of laser phase noise (or frequency jitter) limits the resolution of a variety of interferometric sensors ranging from fiber optic acoustic sensors to gravitational wave detectors. At low frequencies, 0 to 100 kHz, the laser phase noise in semiconductor and diode pumped solid-state lasers is dominated by 1/f noise, the source of which is not well understood. We report on phase noise measurements for external cavity semiconductor lasers (ECSLs) utilizing a fiber Bragg grating in a compact butterfly package design produced by K2 Optronics. The results show that the phase noise is dominated by 1/f noise for low frequencies (10 to 100 kHz) transitioning to a white noise due to spontaneous emission for f > 100 kHz. We observed a factor of 40 improvement in the magnitude of the 1/f phase noise as compared to previously published results for a Hitachi HLP 1400 830 nm diode laser. The magnitude of the low frequency phase noise ranges from 100 to 10 microradians per meter per root Hz for frequencies ranging from 10 Hz to 2 kHz. These results are within a factor of 10 for phase noise measurements of the more expensive Lightwave Electronics Nd:YAG laser and a variety of Er-doped fiber lasers in this frequency range. For nominally similar ECSLs, experimental results indicate that the phase noise increases for lasers with larger leakage currents. Linewidth measurement results showed a Schawlow-Townes inverse power dependence for output powers up to 33 mWatts with the observed onset of a linewidth floor of 30 kHz. The RIN of the ECSLs varied from -120 to -155 dB Vrms per root Hz for frequencies ranging from 10 to 500 kHz. These RIN results are roughly equal to those observed for the Nd:YAG laser for frequencies less that 100 kHz. In summary, such low phase noise and RIN results make such ECSLs suitable for all but the most sensitive fiber optic sensing applications where the frequency range of interest is below 1 MHz.

In time-series analysis, state-space models (SSMs) have been widely used to estimate the conditional probability distributions of hidden variables and parameter values, as well as to understand structures that can generate the data. For example, the Kalman filter is used to analytically calculate the conditional probability distribution on linear SSMs in terms of minimizing the variance, and several extensions, such as the unscented Kalman filter and particle filter, have been applied to calculate the approximate distribution on nonlinear SSMs. Recently, the approximate Bayesian computation (ABC) has been applied to such time-series filtering to handle intractable likelihoods; however, it remains problematic with respect to consistently achieving a reduction of the estimation bias, evaluating the validity of the models, and dealing with replicated observations. To address these problems, in this paper, we propose a novel method combined with the kernel ABC to perform filtering, parameter estimation, and the model evaluation in SSMs. Simulation studies show that the proposed method produces inference that is comparable to other ABC methods, with the advantage of not requiring a careful calibration of the ABC threshold. In addition, we evaluate the performance of the model-selection capability using true and competitive models on synthetic data from nonlinear SSMs. Finally, we apply the proposed method to real data in rat circadian oscillations, and demonstrated the usefulness in practical situations.

For coherent and direct-detection Orthogonal Frequency Division Multiplexed (OFDM) systems employing radio frequency (RF) pilot tone phase noise cancellation the influence of laser phase noise is evaluated. Novel analytical results for the common phase error and for the (modulation dependent) inter carrier interference are evaluated based upon Gaussian statistics for the laser phase noise. In the evaluation it is accounted for that the laser phase noise is filtered in the correlation signal detection. Numerical results are presented for OFDM systems with 4 and 16 PSK modulation, 200 OFDM bins and baud rate of 1 GS/s. It is found that about 225 km transmission is feasible for the coherent 4PSK-OFDM system over normal (G.652) fiber.

This paper proposes a nonlinear state space model (SSM) to estimate the health degradation and predict the remaining useful life(RUL) of industry asset. Expectation Maximization (EM) algorithm and particle filtering (PF) are introduced to estimate SSM parameters. A case study is utilized to predict RUL of industry asset.

In continuous-variables quantum key distribution with coherent states, the advantage of performing the detection by using standard telecoms components is counterbalanced by the lack of a stable phase reference in homodyne detection due to the complexity of optical phase-locking circuits and to the unavoidable phase noise of lasers, which introduces a degradation on the achievable secure key rate. Pilot-assisted phase-noise estimation and postdetection compensation techniques are used to implement a protocol with coherent states where a local laser is employed and it is not locked to the received signal, but a postdetection phase correction is applied. Here the reduction of the secure key rate determined by the laser phase noise, for both individual and collective attacks, is analytically evaluated and a scheme of pilot-assisted phase estimation proposed, outlining the tradeoff in the system design between phase noise and spectral efficiency. The optimal modulation variance as a function of the phase-noise amount is derived.

A digital phase noise cancellation technique for ring oscillator-based I/Q receivers is presented. Ring oscillator phase noise, including supply-induced phase noise, is extracted from digital phase-locked loop (DPLL) and used to restore the randomly rotated baseband signal in digital domain. The receiver prototype fabricated in 65nm CMOS technology achieves phase noise reduction from −88 to −109dBc/Hz at 1MHz offset, and an integrated phase noise (IPN) reduction from −16.8 to −34.6dBc, when operating at 2.4GHz.

In this note we shall present a new Gaussian approximation based framework for approximate optimal smoothing of non-linear stochastic state space models. The approximation framework can be used for efficiently solving non-linear fixed-interval, fixed-point and fixed-lag optimal smoothing problems. We shall also numerically compare accuracies of approximations, which are based on Taylor series expansion, unscented transformation, central differences and Gauss-Hermite quadrature.

A new algorithm for the prediction, filtering, and smoothing of non-Gaussian nonlinear state space models is shown. The algorithm is based on a Monte Carlo method in which successive prediction, filtering (and subsequently smoothing), conditional probability density functions are approximated by many of their realizations. The particular contribution of this algorithm is that it can be applied to a broad class of nonlinear non-Gaussian higher dimensional state space models on the provision that the dimensions of the system noise and the observation noise are relatively low. Several numerical examples are shown.

Effect of nonlinear gain on the phase noise of modulated grating Y-branch (MGY) lasers is investigated by experiments and simulations. The phase noise is first characterized by measuring the frequency modulation noise spectrum of the MGY laser, and some interesting phenomena are observed. In order to understand the underlying physic mechanism of those phenomena, simulations are performed with taking Langevin noise sources and nonlinear gain terms into account. Simulated results show that, in the presence of the nonlinear gain, fluctuations of side-modes can bring excess phase noise to the lasing mode, especially when the side-modes are on the long-wavelength side of the main mode. Furthermore, it has been found that the phase noise hopping phenomenon can be induced by a bi-stable state of the laser, which is also closely related to the nonlinear gain. The investigation is helpful for explaining the complicated phase noise characteristics of the MGY laser.

Several authors have recently investigated phase noise in semiconductor lasers and the related problems that arise when such lasers are employed in coherent optical communication systems. We report accurate measurements of high-frequency phase noise in single-mode injection lasers that show the presence of a peak in the phase-noise spectrum at the same frequency as that of the amplitude-noise peak. This peculiar phenomenon must be taken into account when one studies the characteristics of coherent optical communication systems.