Nonlinear Noise Power Research Articles

Joint Fiber Nonlinear Noise Estimation, OSNR Estimation and Modulation Format Identification Based on Asynchronous Complex Histograms and Deep Learning for Digital Coherent Receivers.

In this paper, asynchronous complex histogram (ACH)-based multi-task artificial neural networks (MT-ANNs), are proposed to realize modulation format identification (MFI), optical signal-to-noise ratio (OSNR) estimation and fiber nonlinear (NL) noise power estimation simultaneously for coherent optical communication. Optical performance monitoring (OPM) is demonstrated with polarization mode multiplexing (PDM), 16 quadrature amplitude modulation (QAM), PDM-32QAM, as well as PDM-star 16QAM (S-16QAM) for the first time. The range of launched power is −3 to −2 dBm with a fiber link of 160–1600 km. Then, the accuracy of MFI reaches 100%. The average root mean square error (RMSE) of OSNR estimation can reach 0.37 dB. The average RMSE of NL noise power estimation can reach 0.25 dB. The results show that the monitoring scheme is robust to the increase of fiber length, and the solution can monitor more optical network parameters with better performance and fewer training data, simultaneously. The proposed ACH MT-ANN has certain reference significance for the future long-haul coherent OPM system.

A Novel Nonlinear Noise Power Estimation Method Based on Error Vector Correlation Function Using Artificial Neural Networks For Coherent Optical Fiber Transmission Systems

In this paper, we propose a promising nonlinear noise power estimation method based on correlation functions using artificial neural networks (ANN), which is robust against both amplifier spontaneous emission noise and the symbol patterns. Error vector correlation (EVC), together with the amplitude noise correlation (ANC) and the phase noise correlation (PNC), is used as the input of ANN in the proposed method. 378 cases of 224 Gb/s polarization-multiplexed 16-quadrature amplitude modulated (PM-16-QAM) signal transmitted over a wide range of conditions by varying launch power, OSNR and transmission distance are used to train and test the ANN. With the launch power varying from 0 to 8 dBm and the transmission distance as long as 2400 km, the results of tested samples demonstrate that the maximum absolute deviation (MAD), mean absolute error (MAE) and root mean square error (RMSE) of the estimated nonlinear noise power are 0.65 dB, 0.20 dB and 0.27 dB, respectively. In order to verify the independence of symbol patterns, 150 new cases with 30 pseudo-random binary sequence (PRBS) seeds are used to test the trained ANN. The results show that the MAE, MAD and RMSE of estimated nonlinear noise power are 0.86 dB, 0.25 dB and 0.33 dB respectively, meaning that the trained ANN is valid even if the test samples are not covered by the trained process. The results in this work verified that the ANN with EVC, ANC and PNC as input can make the trained model feasible to accurately estimate the nonlinear noise power in high speed optical coherent communication systems.

Discretized Gaussian model for nonlinear noise in elastic optical networks

A discrete nonlinear noise model based on the well-known Gaussian noise model is introduced for nonlinear noise in dispersion uncompensated fiber-optical links of elastic optical networks (EON). This model is used to calculate the nonlinear noise power of EONs links, consisting of channels with arbitrary transmit powers, central frequencies and bandwidths. The proposed model boils down to a low complexity model for fixed-grid wavelength division multiplex networks. The numerical results show higher precision of the proposed model compared to the previously proposed low complexity models. The proposed model formulation is up to 0.5 dB more accurate in computing the nonlinear noise power spectral density or equivalently up to 15 dB more accurate in calculating the nonlinear noise power for a typical optical link containing channels with a bandwidth of 28 GHz at 100 GHz channel spacing. This improvement in accuracy is achieved at the expense of adding computational complexity.Being more precise and providing more clear insight of nonlinear noise behavior respect to channel parameters changes, this model is a great help in network planing problems like power allocation, routing, and spectrum assignment and opens a new horizon for proposing and evaluating heuristic solutions for network planning problems in EONs.

Nonlinear distortion estimation in dual-carrier PM-QPSK signals for uncompensated fiber links

Abstract Kerr nonlinearity is particularly detrimental in coherent optical communications over long-haul, sub-sea and transatlantic links. The correct and accurate determination of the penalty due to fiber nonlinearity is critical for estimating the link capacity and optical signal to noise ratio margins. Two distinct approaches for calculating the power in the nonlinear field are proposed. The first approach utilizes the nonlinear variance at the decision gate after coherent detection, while the second attempts to extract the electrical field of the nonlinear interference noise. Subsequently, the power spectral density of the nonlinear interference noise is integrated to estimate the nonlinear power within a pre-defined signal-to-nose ratio criterion. Based on the assumptions in this study, a temporal resolution of 16 samples per symbol or (6.25 ps) is required to achieve a signal-to-noise ratio sensitivity of 40 dB on the nonlinear power estimate for a 10 Gbaud signal. Furthermore, a minimum pattern length of 128 symbols is required to obtain an adequate estimate of the nonlinear noise power within 30 dB signal-to-noise ratio for two adjacent wavelength-division-multiplexed (WDM) channels. The influence of the pulse shaping roll-off factor and number of WDM channels on the required pattern length and the nonlinear power estimation is also investigated.

Linear and Nonlinear Noise Characterisation of Dual Stage Broadband Discrete Raman Amplifiers

We characterise the linear and nonlinear noise of dual stage broadband discrete Raman amplifiers (DRAs) based on conventional Raman gain fibres. Also, we propose an optimised dual stage DRA setup that lowers the impact of nonlinear noise (generated in the amplifier) on the performance of a transmission link (with 100-km amplifier spacing). We numerically analyse the design of a backward pumped cascaded dual stage 100-nm DRA with high gain (∼20 dB) and high saturated output power (>23 dBm). We show that the noise figure (NF) of the dual stage DRA is mainly dominated by the first stage irrespective of the type of gain fibre chosen in the second stage, and we also demonstrate that optimising the length and the type of Raman gain fibre can have significant impact on the size of inter/intrasignal nonlinearities generated. Here, we report a theoretical model to calculate the nonlinear noise power generated in transmission spans with dual stage DRAs considering piecewise signal power evolution through the Raman gain fibres. The predicted signal-to-noise ratio (SNR) performances are calculated from the combined contributions from NF and nonlinear product power obtained using the proposed analytical model for transmission systems deployed with 100-km transmission span compensated by different dual stage DRAs. Finally, an optimised IDF 6 km–SMF 10 km dual stage configuration has been identified using the theoretical model, which allows maximum SNR of 14.6 dB at 1000 km for 1 THz Nyquist wavelength division multiplexed signal and maximum transmission reach of 3400 km at optimum launch power assuming 8.5 dB HD-FEC limit of the Nyquist PM-QPSK signal.

Impact of Fiber Nonlinearity on the Performance of Mode Division Multiplexing Systems

In this paper, an analytical model is developed to estimate a nonlinear phase noise (NPN) due to Kerr fiber nonlinearity and its interaction with amplifier noise in mode division multiplexing (MDM) systems. Our analysis uses generalized coupled multimode nonlinear Schrödinger equations (MM- NLSE) that describe the propagation of the mode superimposing in the optical fiber. The nonlinear phase noise versus channel power and transmission distance is evaluated by implementing our analytical model for LP01, LP11a, and LP11b spatial modes. Each mode carries a 4-QAM signal at a symbol rate of 20 Gsymbol/s. The results reveal that LP11 mode has a lower phase noise variance than LP01 mode over entire transmission distances. Finally, the error vector magnitude (EVM) versus channel power is quantified using an analytical model.

Transmission Performance Improvement by Non-Linear Distortion Noise Power Control in Multi-Band Systems

This paper proposes a non-linear distortion noise power control method with bandwidth control for multiple frequency band transmission which simultaneously uses plural frequency bands in wireless communication systems. The control method employs clipping and filtering, and generates out-of-band noise reduction signals using a part of used signal bands to reduce harmful interference in a primary existing system which shares frequency bands with the multi-band system. The improvement of Signalto- Noise Ratios (SNRs) in the bands used by the primary system is evaluated by computer simulations. The simulation results show that the proposed method at the band use rate of 50 % can improve them by 15 dB at the receiving power ratio of -30 dB to the spectrum sharing multi-band system.

Experimental investigation of nonlinear operation mode of a DP-QPSK 100G link with co-propagating-pump Raman amplification

The nonlinear interference noise in a coherent single-span fibre-optic communication link (FOCL) with co-propagating Raman amplification is investigated at different levels of input Raman pump and channel powers and dispersion. A simple phenomenological expression for calculating the nonlinear noise power at the output of a single-channel FOCL is presented. The merit of using a distributed Raman amplifier with co-propagating pump up to 1 W in a single-span single-channel FOCL is experimentally investigated.

OSNR and nonlinear noise power estimation for optical fiber communication systems using LSTM based deep learning technique.

The optical signal-to-noise ratio (OSNR) and fiber nonlinearity are critical factors in evaluating the performance of high-speed optical fiber communication systems. Recently, several deep learning based methods have been put forward to monitor OSNR of a fiber communication system. In this work, we propose a long short-term memory (LSTM) network based method to simultaneously estimate OSNR and nonlinear noise power caused by fiber nonlinearity. In the training step, LSTM network extracts the essential features in frequency domain of the input signal. Then, with the built model in the training step, the LSTM output the OSNR and nonlinear noise power of the signal under test. The simulation by VPI software is carried on a 5-channel long haul optical transmission system with the launched optical power of -3.0~ + 3.0dBm per channel. The results show that the test error of OSNR is less than 1.0dB with the reference OSNR from 15 to 30dB for QPSK, 16QAM and 64QAM signal. The test error of nonlinear noise power is less than 1.0dB for QPSK and 16QAM signal when the Laser linewidth is 6 KHz and 100 KHz respectively. The proposed method is a promising candidate for nonlinearity-insensitive OSNR and accurate nonlinear noise power estimation in multi-channel long haul optical fiber communication systems.

Minimizing the Number of Spans for Terrestrial Fiber-Optic Systems Using Quasi-Single-Mode Transmission

We show that quasi-single-mode transmission in few-mode fibers (FMFs) can reduce the number of spans for a fixed transmission distance and, consequently, the cost per bit for terrestrial transmission systems by minimizing both the Capex and Opex. The Gaussian-noise model is employed to estimate the nonlinear noise power spectral density both, which depends on the effective area of the FMF and span length, for Er-doped fiber amplifier (EDFA) and hybrid Raman/EDFA systems. Together with amplified spontaneous emission noise, an optical signal-to-noise ratio (OSNR) for a fixed transmission distance as a function of the effective area of the FMF and span length can be obtained. Given a target OSNR for a particular modulation format, we determine the maximum span length or the minimum number of spans as the effective area of the FMF varies both analytically and through numerical simulations. The effect of multipath interference in the FMF on the minimum number of span has also been investigated.

Accumulation of nonlinear noise in coherent communication lines without dispersion compensation

The nature of accumulation of nonlinear noise in multi-span communication lines with optical amplifiers without dispersion compensation was investigated experimentally and theoretically. It has been established that the dependence of nonlinear noise power on the number of spans is described by a power function with an exponent greater than 1. It has also been established that the nonlinear noise power generated in one span is practically independent on the amount of dispersion accumulated before this span for the values of accumulated dispersion more than 2ns/nm. Since the noise power generated in one span does not depend on number of this span, in order to describe the superlinear dependence of total noise on number of spans we can assume that noises generated in different spans are correlated.

Expressions for the nonlinear transmission performance of multi-mode optical fiber

We develop an analytical theory which allows us to identify the information spectral density limits of multimode optical fiber transmission systems. Our approach takes into account the Kerr-effect induced interactions of the propagating spatial modes and derives closed-form expressions for the spectral density of the corresponding nonlinear distortion. Experimental characterization results have confirmed the accuracy of the proposed models. Application of our theory in different FMF transmission scenarios has predicted a ~10% variation in total system throughput due to changes associated with inter-mode nonlinear interactions, in agreement with an observed 3dB increase in nonlinear noise power spectral density for a graded index four LP mode fiber.

Nonlinear interference noise in communication lines with the DP-QPSK modulation format

The nonlinear interference noise power was measured experimentally as a function of the signal power and the length of the fibre coherent communication line, in which chromatic dispersion is not optically compensated. An expression was derived for the optimal signal power corresponding to a maximal excess of the measured optical signal-to-noise ratio (OSNR) over the OSNR required for conditionally error-free operation. The dependence of signal optimal power measured experimentally well agrees with the theoretical formula derived.

Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise

By assuming the nonlinear noise as a signal-independent circular gaussian noise, a typical case in non-dispersion managed links with coherent multilevel modulation formats, we provide several analytical properties of a new quality parameter--playing the role of the signal to noise ratio (SNR) at the sampling gate in the coherent receiver--which carry over to the Q-factor versus power (or "bell") curves. We show that the maximum Q is reached at an optimal power, the nonlinear threshold, at which the amplified spontaneous emission (ASE) noise power is twice the nonlinear noise power, and the SNR penalty with respect to linear propagation is 10Log(3/2) ≃ 1.76 dB,, although the Q-penalty is somewhat larger and increases at lower Q-factors, as we verify for the polarization-division multiplexing quadrature phase shift keying (PDM-QPSK) format. As we vary the ASE power, the maxima of the SNR vs. power curves are shown to slide along a straight-line with slope ≃-2 dB/dB. A similar behavior is followed by the Q-factor maxima, although for PDM-QPSK the local slope is around -2.7 dB/dB for Q-values of practical interest.

Transition noise model for longitudinal thin-film media

The integrated noise power in longitudinal thin-film media increases with transition density. This behavior has been attributed to transition noise predominating over the more conventional amplitude modulation noise. At low recording densities the total noise power increases linearly with the transition density. At higher recording densities the noise increases more rapidly. The departure from the linear noise power increase with transition density has been attributed to correlation between noise in adjacent transitions. A model is presented for the noise process in longitudinal thin-film media, assuming that each transition's position fluctuation is correlated to the previous transition's position fluctuation by the demagnetization field. The dominant effect of the demagnetization fields is to increase the inherent noise in each transition and broaden the transitions as the recording density increases. It is the inherent noise increase in each transition, rather than the contribution from the adjacent transition correlation noise power term, that explains the experimentally found nonlinear noise power increase at higher transition densities. The frequency dependence of the integrated noise power is shown to be a strong function of the transition shape.

Design factors for the optimization of multichannel radio systems

The satisfactory design of a multichannel radio system requires evaluation of both nonlinear and thermal noise power and the statistical considerations associated with each. It is pointed out that an optimum design can be attained when these noise powers are equal; and since the noise power is greatest in the top channel of the FM (frequency modulation) system, it is sufficient and suitable to establish design criteria based on these premises. It is seen that certain essential performance factors are required for this purpose. These include a measurement of signal/noise ratio using a white-noise test signal, a knowledge of the principal orders of distortion which give rise to the nonlinear noise, and a value for the overload power of the base-band signal. The effect of such factors as carrier power, channel spacing, speech-power distribution, and traffic activity, on the signal/noise ratio is then examined. The basic expressions are also used to establish the total reliability as a function of traffic fluctuations, propagation reliability, and carrier power. Theoretically optimum distributions as well as typically operative distributions are given. In general, systems are of two classes: integrated ? those which must conform to the technical requirements of existing or proposed associated networks, and non-integrated systems ? those which exist, as it were, independently. Standards are suggested for both these systems. The CCIF (Comite Consultatif International Telephonique) fictitious circuit of reference is a special case of the former and it is concluded that the signal/noise ratio suggested for this reference is some 10 db (decibels) too high. System testing by means of multiple tones is also discussed and some basic requirements related to this method are outlined.

The Equalization of Base-Band Noise in Multichannel FM Radio Systems

Pre-emphasis and de-emphasis networks are frequently incorporated in the radio equipment of multichannel systems in order to improve the distribution of noise among the channels. The pre-emphasis network has a rising frequency amplitude characteristic and this produces a redistribution of both signal power and nonlinear noise power over the working spectrum. The improvement in signal-to-noise ratio in any channel which the technique of equalization affords is dependent not only on this effect, but also on the contribution of the multiplex equipment to the total channel noise. This is discussed for typical networks having a maximum slope of attenuation of 6 db per octave and the general case when second-order distortion is predominant. Under practical conditions, the maximum possible improvement is almost entirely obtained when the mean power of the multichannel signal is unchanged by the presence of the networks; a convenient way of establishing this condition with sufficient accuracy is to maintain constant signal energy at a base-band frequency which is 55 per cent of the highest used. Practical considerations usually dictate that the networks do not have a maximum insertion loss exceeding 26 db. With this value and with the multiplex contributing 25 per cent of the total channel noise, an improvement of 3.6 db in the signal-to-noise ratio of the top channel can be expected; provided this loss is not exceeded, the relative noise power, in general, will still be greatest in the top channel.