Accurate Evaluation of Bit-Error Rates of Optical Communication Systems Using the Gram–Charlier Series

Accurate Evaluation of Bit-Error Rates of Optical Communication Systems Using the Gram–Charlier Series The probability densities and cumulative distribution functions of decision statistics of optical communications systems are expanded as a Gram–Charlier series, leading to arbitrarily accurate systematic evaluation of bit-error rates and optimal decision thresholds of optical communication systems. The method displays negligible computational complexity, and is applicable whenever the moment or cumulant generating function of the decision statistics are analytically available. We applied the technique to a birth-and-death Markoffian model of a direct-detection receiver with optical preamplifier in a two-level amplitude-shift keying system. The modal expansion series rapidly converged, whereas the alternative saddlepoint approximation method predicted a bit-error rate which deviated by 7% from the Gram–Charlier result.     

Polarization-Dependent Loss-Induced Outage Probabilities in Optical Communication Systems

Polarization-dependent loss (PDL)-induced outage probabilities (OPs) in optical communication systems are investigated using a semi-analytical method, taking into account the different statistics of the noise parallel and orthogonal to the signal. We show that in today's optical communication systems that typically operate at low optical signal-to-noise ratio due to the use of forward-error-correction coding, neglecting the orthogonal noise or the different statistics between the orthogonal and parallel noise significantly underestimates or overestimates PDL impairments. We find that PDL impairments are larger at lower optical signal-to-noise ratio. Required system margins at an OP of 10^-5 for given PDL values are calculated.     

A novel fast approach for estimating error propagation in decisionfeedback detectors

The study of error-burst statistics is important for all detection systems, and more so for the decision feedback class. In data storage applications, many detection systems use decision feedback in one form or another. Fixed-delay tree search with decision feedback (FDTS/DF) and decision feedback equalization (DFE) are the direct forms, whereas the partial response detectors such as the reduced state sequence estimator (RSSE) and noise predictive maximum likelihood (NPML) detectors are the other forms. Although DF reduces the system complexity, it is inevitably linked with error propagation (EP), which can be quantified using error-burst statistics. Analytical evaluation of these statistics is difficult, if not impossible, because of the complexity of the problem. Hence, the usual practice is to use computer simulations. However, the computational time in traditional bit-by-bit simulations can be prohibitive at meaningful signal-to-noise ratios. In this paper, we propose a novel approach for fast estimation of error-burst statistics in FDTS/DF detectors, which is also applicable to other detection systems. In this approach, error events are initiated more frequently than natural by artificially injecting noise samples. These noise samples are generated using a transformation that results in significant reduction in computational complexity. Simulation studies show that the EP performance obtained by the proposed method matches closely with those obtained by bit-by-bit simulations, while saving as much as 99% of simulation time     

A Novel Approach to the Analysis of Diversity Receivers Corrupted by Partial-Band Noise Interference

Bit error rate performance analysis for communications systems with diversity and partial-band interference often yields complicated probability density functions (PDFs) for the decision statistics. The authors calculate these PDFs via a new technique by evaluating the inverse Laplace transform as an integral of a real integrand over a finite range.     

Level Crossing Rate and Average Fade Duration of EGC Systems With Cochannel Interference in Rayleigh Fading

Both the first-order signal statistics (e.g., the outage probability) and the second-order signal statistics [e.g., the average level crossing rate (LCR) and the average fade duration (AFD)] are important design criteria and performance measures for wireless communication systems, including the equal gain combining (EGC) systems in the presence of the cochannel interference (CCI). Although the analytical expressions for the outage probability of the coherent EGC systems are exposed to CCI and various fading channels are already known, the respective expressions for the average LCR and the AFD are not available in the literature. This paper presents such analytical expressions for the Rayleigh fading channel, which are obtained by utilizing a novel analytical approach that does not require the explicit expression for the joint probability density function (pdf) of the instantaneous output signal-to-interference ratio and its time derivative. Applying the characteristic function method and the Beaulieu series, we determined the average LCR and the AFD at the output of an interference-limited EGC system with an arbitrary diversity order and an arbitrary number of cochannel interferers in the form of an infinite integral and infinite series. For the dual diversity case, the respective expressions are derived in closed forms in terms of the gamma and beta functions.     

Error probability evaluation of optical systems disturbed by phasenoise and additive noise

A direct and efficient method for evaluation of the error probability of optical heterodyne receivers in the presence of phase noise is presented. A closed form expression for the statistics of the decision variable, including photodetector shot noise and thermal noise from electronic circuitry, is derived. The analysis assumes simple integrating filters in the receiver and is based on a power series expansion of the filtered phase noise. The error probability is calculated using a saddle point approximation which is numerically simple and gives accurate results. The optimal prefilter bandwidth for best phase noise rejection is easily determined     

Modified feedback ECL gate for Gb/s applications

This paper introduces a modification of the feedback emitter-coupled logic (FECL) gate that makes it suitable for Gb/s applications. The circuit can be used as a single-ended-to-differential signal converter without the need for an external reference voltage and finds application in digital optical links in which data is typically transmitted single ended. The gate is compared with FECL and ECL gates, and its application to realize logic functions is discussed. A 6-Gb/s series gated decision circuit and a 2-Gbaud/s four-channel optical receiver array employing modified FECL gates are also described     

Evaluation of beat noise in OCDMA system with non-Gaussian approximated method

With the development of phase encoding technologies, beat noise becomes one of the most predominant limitations of optical code division multiaccess (OCDMA) systems. In order to analyze beat noises' impact more accurately, a non-Gaussian analysis with consideration of a decision variable's moment generation function is first introduced in this paper to evaluate both the multiaccess interference and the beat noises simultaneously, where prime, secondary, and partial coherent beat noises are discussed in detail. In this paper, the saddle-point approximation (SPA) method is first utilized to investigate beat noise's impact on an OCDMA system. Comparison of probability density functions as well as bit error rates between the proposed method and the traditional Gaussian approximation method is given here. The resultant achievement shows the outstanding performance of SPA on this occasion, which proves the necessity of such a moment generation function-based non-Gaussian analysis.     

Knowledge engineering for medical decision making: A review of computer-based clinical decision aids

Computer-based models of medical decision making account for a large portion of clinical computing efforts. This article reviews representative examples from each of several major medical computing paradigms. These include 1) clinical algorithms, 2) clinical databanks that include analytic functions, 3) mathematical models of physical processes, 4) pattern recognition, 5) Bayesian statistics, 6) decision analysis, and 7) symbolic reasoning or artificial intelligence. Because the techniques used in the various systems cannot be examined exhaustively, the case studies in each category are used as a basis for studying general strengths and limitations. It is noted that no one method is best for all applications. However, emphasis is given to the limitations of early work that have made artificial intelligence techniques and knowledge engineering research particularly attractive. We stress that considerable basic research in medical computing remains to be done and that powerful new approaches may lie in the melding of two or more established techniques.     

A new probability decoding scheme based on genetic algorithm for FEC codes in optical transmission systems

Based on the genetic algorithm(GA),a new genetic probability decoding(GPD) scheme for forward error correction(FEC) codes in optical transmission systems is proposed.The GPD scheme can further offset the quantification error of the hard decision by making use of the channel interference probability and statistics information to restore the maximal likelihood transmission code word.The theoretical performance analysis and the simulation result show that the proposed GPD scheme has the advantages of lower decoding complexity,faster decoding speed and better decoding correction-error performance.Therefore,the proposed GPD algorithm is a better practical decoding algorithm.     

Analog reconstruction methods for transaxial tomography

Transaxial tomography is a radiographic technique that provides an image of an isolated two-dimensional section of a three-dimensional object. The basic principles of this technique are reviewed here and the equivalence of various mathematical formulations is shown. The properties of the resulting image for various filter functions are described and the limitations imposed by the quantum statistics of the radiation source are briefly discussed. Then various optical approaches to implementing the reconstruction process are described. The distortions arising from the use of a diverging beam of X-rays are detailed, and some simple modifications of the optical systems are shown to substantially eliminate them.     

武器系统效能评估方法浅论

从武器系统效能概念入手，概括了效能评估的基本步骤。简要阐述了各种效能评估的方法及其优缺点，主要有试验统计法、专家调查法、指数法、解析法、层次分析法、SEA法等。熟练掌握和理解了这些方法，就可以为武器系统的研制提供可靠准确的数据，避免不必要的浪费和开支。     

Noise-predictive BCJR equalization for suppression of intrachannel nonlinearities

An iterative equalization scheme for suppressing intrachannel nonlinearities in high-speed optical transmission systems operating at 40 Gb/s is presented. The proposed method employs a noise-predictive filter to mitigate the colored noise due to amplified spontaneous emission noise and optical filtering. The maximum a posteriori probability symbol detection implemented as the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is employed to suppress the intrachannel nonlinear effects. Soft decision outputs provided by the noise-predictive BCJR equalizer are processed by an iterative low-density parity-check decoder.     

Volterra series transfer function of single-mode fibers

A nonrecursive Volterra series transfer function (VSTF) approach for solving the nonlinear Schrodinger (NLS) wave equation for a single-mode optical fiber is presented. The derivation of the VSTF is based on expressing the NLS equation In the frequency domain and retaining the most significant terms (Volterra kernels) in the resulting transfer function. Due to its nonrecursive property and closed-form analytic solution, this method can excel as a tool for designing optimal optical communication systems and lumped optical equalizers to compensate for effects such as linear dispersion, fiber nonlinearities and amplified spontaneous emission (ASE) noise from optical amplifiers. We demonstrate that a third-order approximation to the VSTF model compares favorably with the split-step Fourier (recursive) method in accuracy for power levels used in current optical communication systems. For higher power levels, there is a potential for improving the accuracy by including higher-order Volterra kernels at the cost of increased computations. Single-pulse propagation and the interaction between two pulses propagating at two different frequencies are also analyzed with the Volterra method to verify the ability to accurately model nonlinear effects. The analysis can be easily extended to include inter-channel interference in multi-user systems like wavelength-division multiple-access (WDM), time-division multiplexed (TDM), or code-division multiplexed (CDM) systems     

一种新的光码分多址多用户干扰抑制方法

目前光码多分址（OCDMA）系统多采用开关键控（OOK）调制,多用户干扰主要影响发送比特为“0”时的误码率,原因是发送比特“0”时信号中没有光脉冲。据此,提出了一种新的OCDMA多用户干扰抑制方法。研制了一种新型OCDMA系统,通过对比特“0”和比特“1”分别使用同一地址码和它的移位变形,来避免发送比特“0”时无光脉冲的问题,而且接收端采用最大值判决,进一步减小多用户干扰。阐述了其工作原理,系统采用最佳光正交码作为地址码,分析推导了新型系统的误码率表达式,进而对新型系统和常规系统进行误码性能仿真。仿真结果表明,新型系统比常规系统的误码性能改善10个数量级以上。     

分布式检测系统的模糊有序统计融合算法

为提高基于二元局部判决的分布式检测系统的检测性能，研究了基于模糊隶属度函数的分布式检测系统融合算法，提出了模糊有序统计融合准则。通过对肼传感器进行分布式检测系统仿真，结果表明：模糊有序统计融合准则在均匀环境中能获得比基于二元判决准则更好的检测性能，也好于同样采用模糊隶属度函数的求和准则的检测性能，且在多目标环境下获得了较强的适应性。     

非线性光环镜在光通信系统中的新应用

非线性光环镜(NOLM)以其独特的优点,被广泛应用于光通信系统中.文章阐述了非线性光环镜的基本原理,主要介绍了应用NOLM作为光判决单元、多波长可调谐掺铒光纤激光器的增益均衡器以及2R中继器等在高速光通信系统中的新应用,分别分析了它们特点和发展状况.     

Calculation of Achievable Information Rates of Long-Haul Optical Transmission Systems Using Instanton Approach

A method for estimation of achievable information rates of high-speed optical transmission systems is proposed. This method consists of two steps: 1) approximating probability density functions for energy of pulses, which is done by the instanton approach, and 2) estimating achievable information rates by applying a method originally proposed by Arnold and Pfitser. Numerical results for a specific optical transmission system (submarine system at transmission rate 40 Gb/s) are reported     

A nonlinear electrical equalizer with decision feedback for OOK optical communication systems

In this paper we introduce a nonlinear equalizer using the Radial Basis Function (RBF) network with decision feedback equalizer (DFE) for electronic dispersion compensation in optical communication systems with on-off-keying and a direct detection receiver. The RBF method introduces a non-linear equalization technique suitable for optical communication direct detection systems that include nonlinear transformation at the photodetector. A bit error rate performance comparison shows that the RBF with DFE out performs the RBF without DFE and achieves similar results provided by maximum likelihood sequence estimator.