The calculation of average error probability in a digital fibre optical communication system

This paper deals with the problem of determining the average error probability in a digital fibre optical communication system, in the presence of message dependent inhomogeneous non-stationary shot noise, additive Gaussian noise and intersymbol interference. A zero-forcing equalization receiver filter is considered. Three techniques for error rate evaluation are compared. The Chernoff bound and the Gram-Charlier series expansion methods are compared to the characteristic function technique. The latter predicts a higher receiver sensitivity.     

Timing error tolerant waveforms in optical fibre systems

The problem of pulse shaping and sensitivity to timing errors in optical fibre data communication is considered. The performance of the overall transmission system is the average probability of error, which is computed for intersymbol interference, thermal noise, and shot noise in avalanche photodiodes. An analysis of the immunity to small sampling errors of various Nyquist pulses indicates useful design criteria.     

Accurate sensitivity in optically preamplified direct detection

We present a novel model for calculating the bit error rate in optical communication systems in the case of on-off keying intensity modulation and optically preamplified direct detection. The model accounts for the intersymbol interference and is based on the Laguerre photon-count probability distribution predicted by photodetection theory. For a non-return-to-zero modulation format an accurate value of the sensitivity for a quantum-limited receiver of 33.9 photons/bit is obtained.     

Comparative study of classifiers to mitigate intersymbol interference in diffuse indoor optical wireless communication links

The maximum data rate that can be achieved in diffuse indoor optical wireless communication (OWC) is limited due to the effect of intersymbol interference (ISI). The adverse effect of ISI on the system performance can be minimised using a channel equaliser at the receiver. In this study, digital signal detection is formulated as a classification problem and hence a classifier is adopted at the receiver. The bit error performance of classifiers with non-linear decision boundary including a multilayer perceptron (MLP), a support vector machine (SVM), the radial basis function (RBF), and the Bayesian classifier is studied along with traditional equaliser and reported here. The MLP offers the best performance; however there is trade-off between the performance and complexity especially at highly diffuse channel.     

基于最大值判决及光硬限幅器的光码分多址并行干扰抑制系统

针对光码分多址（OCDMA）的多用户干扰问题,提出一种引入光硬限幅器、基于最大值判决的光码分多址并行干扰抑制系统.该系统在发送端对比特“0”和比特“1”分别使用一个地址码和它的移位变形进行映射,以避免发送比特“0”时无光脉冲通过的问题,实现并行干扰抑制;在接收端光电检测器前引入一个光硬限幅器,判决电路采用最大值判决,以避免门限判决所引起的误判,进一步减小多用户干扰.阐述了其工作原理,系统采用光正交码作为地址码,PIN光电检测器,分析推导了系统的误码率表达式,进而对新型系统的多用户干扰抑制作用进行误码性能仿真.仿真结果表明,当信号光子到达率为25时,新型系统比常规系统的误码性能改善10个数量级以上,比常规并行干扰抑制系统改善2个数量级以上.     

多噪声背景下光码分多址多用户干扰的抑制

针对光码分多址(OCDMA)的多用户干扰问题, 研究采用APD光电检测器的系统中存在多种噪声情况下, 基于最大值判决的光码分多址并行干扰抑制方法的多用户干扰抑制效果。阐述了其工作原理, 即在发送端对比特“0”和比特“1”分别使用一个地址码和它的移位变形进行映射, 以避免发送比特“0”时无光脉冲通过, 实现并行干扰抑制; 接收端判决电路采用最大值判决, 以避免门限判决所引起的误判, 进一步减小多用户干扰。系统采用光正交码作为地址码, 分析推导了系统的误码率表达式。根据所得的误码率表达式, 进行了数值仿真并与其他多用户干扰抑制方法进行比较。仿真结果表明, 本方法对多用户干扰的抑制作用与系统用户数和码重有关; 与引入双硬限幅器方法、多比特传输方法的多用户干扰抑制作用相比, 抑制效果要优于多比特传输的方法; 当接收功率较低时, 该方法优于引入双硬限幅器的方法, 因此可以有效的抑制多用户干扰。     

Measuring temporal fluctuation on femtosecond scale in a random medium

We report an observation of femtosecond optical fluctuations of transmitted light when a coherent femtosecond pulse propagates through a random medium. They are a result of random interference among scattered waves coming from different trajectories in the time domain. Temporal fluctuations are measured by using cross-correlated frequency optical gating. It is shown that a femtosecond pulse will be broadened and distorted in pulse shape while it is propagating in random medium. The real and imaginary components of transmitted electric field are also distorted severely. The average of the fluctuated transmission pulses yields a smooth profile, probability functions show good agreement with Gaussian distribution.     

Error statistics in a high-rate communication line with bit-density optimization

Direct effective numerical simulation is used to determine the tails of probability density functions of marks and spaces and the error statistics in the optical communication line based on a conventional single-mode fiber and a dispersion-compensation fiber with a reduced density of marks in the original bit sequence. Simple analytical approximations for the tails of the probability density function are derived to determine the number of errors in the line with a relatively high accuracy.     

Maximum repeaterless transmission of lightwave systems imposed by stimulated Brillouin scattering in fibres

To aid in designing high-speed optical networks, the fundamental limitations of lightwave transmission systems are investigated from the viewpoint of fibre nonlinearities, particularly of stimulated Brillouin scattering (SBS). When SBS occurs, the fibre launch power is usually restricted; thus, SBS is detrimental to lightwave systems. The effects of SBS on signals transmitted in fibres are clarified for several modulation schemes, especially coherent modulation schemes. A generalized model based on the maximum power spectrum density in the signals is proposed to estimate the degree of SBS generation. The maximum repeaterless transmissions for various bit rates, laser diode linewidths, and Brillouin gains of optical fibres are presented. The degradation of transmission due to SBS is clarified experimentally, focusing on the bit error rate, fibre input power, and spectra of signals transmitted in fibres. In addition, various techniques for suppressing the SBS effects are proposed. A repeaterless transmission experiment conducted over 364.3 km using optical booster amplifiers is presented to verify the effectiveness of the SBS suppression technique.     

Spectral-domain intermodal interference under general measurement conditions

Spectral-domain intermodal interference is analysed theoretically at the output of a few-mode optical fibre alone and at the output of the optical fibre in a tandem configuration with a Michelson interferometer. The theoretical analysis is performed under general measurement conditions when a light source of a given spectral bandwidth and a spectrometer of a given spectral bandpass are considered and when first- and second-order intermodal dispersion effects in the optical fibre are taken into account. Thus, the effect of a variable spectral bandpass of a low-resolution spectrometer on the spectral fringe visibility functions for a two-mode optical fibre of known intermodal dispersion is specified.     

Spectral-domain intermodal interference and the effect of a low-resolution spectrometer

Spectral-domain intermodal interference is analysed theoretically at the output of a few-mode optical fibre alone and at the output of the optical fibre in a tandem configuration with a Michelson interferometer. The theoretical analysis is performed under general measurement conditions when a broadband source and a low-resolution spectrometer of a Gaussian response function are considered and when the first- and second-order intermodal dispersion effects in the optical fibre are taken into account. The theoretical analysis is performed for two different examples of dispersion curves of a two-mode optical fibre and the effect of the limiting factors is specified.     

Influence of satellite vibration on optical communication performance for intersatellite laser links

For intersatellite laser links, vibration-induced pointing jitter severely influences the communication quality as a result of intensity fluctuation. In this paper the probability density function of normalized intensity at the receiver is derived in the presence of pointing jitter taking consideration of bias error. Accordingly, the scintillation index is developed to identify the impact of bias error on intensity fluctuation. Furthermore the bit error rate (BER) is obtained as a function of the beam divergence angle and vibration variance. Qualitative analysis is also given, and the numerical simulation is carried out for demonstration. Results suggested that bias error has a significant detrimental impact on optical terminals which should be considered in system design. This work can benefit the intersatellite optical system design.     

Power penalty in multitone radio-over-fibre system employing direct and external modulation with optical amplifiers

This paper presents a multitone RoF system employing a central station and a remote antenna station to transmit modulated microwave or mm-wave signals. Two configurations of the system employing direct and external modulation are presented. First, at the central station, the modulating signal is directly and externally modulated at 1549.5 and 1550.5 nm, respectively, and the combined signal is then transmitted using wireless mode. In the second configuration, the combined signal is transmitted over 20 km to the remote antenna station using optical fibre connectivity. At the remote antenna station, both channel wavelengths are separated and amplified with an EDFA and SOA and are detected. The demonstration results show that there exists a small power penalty between the direct and the external modulation. But a large power penalty is reported depending upon the choice of optical amplifier viz. EDFA or SOA. Better performance is recorded in later case. The results also show that power is being distributed among the operating frequency and sidebands adjacent to it after transmission over a fibre link.     

SER estimation method for 56 GBaud PAM-4 transmission system

In this Letter, we have proposed a generalized Gaussian probability density function(GGPDF)-based method to estimate the symbol error ratio(SER) for pulse amplitude modulation(PAM-4) in an intensity modulation/direct detection(IM/DD) system. Furthermore, a closed form expression of SERGGDfor PAM-4 has been derived. The performance of the proposed method is evaluated through simulation as well as experimental work.The fitting of probability density functions of the received signal is applied via GGPDF and shape parameters P1 and P2 associated with different PAM-4 levels are determined. The optimum single value of shape parameter P is then calculated to estimate the SER. The mathematical relationship of P with different received optical powers and receiver bandwidths has been determined and verified. The proposed method is a fast and accurate method to estimate SER of a PAM-4 system, which is more reliable and in agreement with the error counting method.     

Relaxation problem with quadratic noise

A linear first-order equation with a quadratic colored noise is considered. An exact one-dimensional probability distribution of the process is obtained from the characteristic function. The characteristic function is calculated by means of special functionals of the noise. An auxiliary set of three ordinary differential equations (which contains a Riccati equation) is solved for all values of parameters of the problem. In peculiar cases, the characteristic function is expressed by elementary functions. Graphs of the probability density function are presented for a few cases. The article is a continuation of the author's previous paper.     

Rate adaptation of convolutional coded optical CDMA systems for improved goodput

Rate adaptation is a technique that enables the selection of the most suitable error-correction coding rate according to the real-time channel quality, therefore increasing the overall throughput. We propose the use of rate adaptive convolutional codes for amplitude encoded, binary on–off keyed optical code-division multiple access (OCDMA) systems. Conventional OCDMA systems have a bit error probability floor due to optical multiple-user interference (OMUI). A convolutional coded OCDMA system (CC-OCDMA) lowers the error floors with increased coding rates but at the expense of reduced goodput (throughput minus the redundancy bits or symbols). However, by exploiting the variation of OMUI with user number, it is shown here that rate adaptation offers larger and consistent goodput improvements compared to fixed coding rate CC-OCDMA systems for various traffic profiles. This advantage is also observed in comparisons with OCDMA systems using improved receiver designs and 2D wavelength/time signatures codes. Based on the analytical results obtained here and the commercial availability of convolutional coding chipsets, rate-adaptive convolutional coding for OCDMA systems is worth to be considered for practical implementation.     

Bragg光纤光栅用作滤波器时的输出光脉冲波形分析

对光纤光栅用作接收端光噪音滤波器进行了详细的理论分析,计算了通信系统中矩形光脉冲信号经“强”、“弱”Bragg光纤光栅滤波器后的输出光脉冲波形,同时也计算了矩形光脉冲信号经匹配光滤波器、现行光通信系统中常用F-P滤波器的输出光脉冲波形,对四种滤波器的输出光脉冲波形进行了分析和比较,并分析了输出信号在抽样判决时的码间干扰情况,从输出波形分析认为,光纤光栅用做接收端噪音滤波器比F-P滤波器具有更大的优越性.     

Relation between vestigial-sideband filtering and pi/2 progressive phase shift

We show that a Gaussian-shaped vestigial-sideband (VSB) return-to-zero (RZ) on-off-keying (OOK) optical signal is essentially a RZ OOK signal with pi/2 progressive phase shift. The reduced intersymbol interference of the VSB signal can be explained as a destructive interference effect. We experimentally demonstrate a method for generating an effective 40-Gbit/s VSB signal without relying on the detuning of an optical filter.     

Estimation of bit error rate for pseudo-linear differential phase shift keyed transmission links

From studying the statistical behaviour of return-to-zero (RZ) differential phase shift keyed (DPSK) transmission links dominated by fibre nonlinearity, we observe strictly non-Gaussian behaviour in the tails of underlying received current probability density functions. Using this analysis, we derive a new statistical estimate of bit error rate (BER) in pseudo-linear transmission regimes under the growing influence of fibre nonlinearity.     

Baseband equalization in fibre optic digital transmission

The problem of baseband equalization in optical p.c.m. fibre systems is considered. Zero-forcing, minimum-mean-square error, and Kaiman equalizers are briefly reviewed and their relative merits discussed. The performance of the overall communication system is the average probability of error, which can be computed by means of the proposed method with high accuracy. A final section presents some diagrams that may be useful in designing the equalizer and in evaluating the degradation affecting the error probability with respect to ideal conditions. A presentation ofadaptive equalization results concludes the paper.