Comparison of bit error rate estimation methods for QPSK CO-OFDM transmission

In this letter, we experimentally study the statistical properties of a received QPSK modulated signal and compare various bit error rate (BER) estimation methods for coherent optical orthogonal frequency division multiplexing transmission. We show that the statistical BER estimation method based on the probability density function of the received QPSK symbols offers the most accurate estimate of the system performance.

Calculation of non-Gaussian statistics and bit error rate degradation due to pulse-to-pulse interaction

We develop a theoretical method to calculate jitter statistics of interacting solitons. Applying this approach, we have derived the non-Gaussian probability density function and calculated the bit-error rate as a function of noise level, initial separation and phase difference between solitons.

Contact time periods in immunological synapse

This paper resolves the long standing debate as to the proper time scale τ of the onset of the immunological synapse bond, the noncovalent chemical bond defining the immune pathways involving T cells and antigen presenting cells. Results from our model calculations show τ to be of the order of seconds instead of minutes. Close to the linearly stable regime, we show that in between the two critical spatial thresholds defined by the integrin:ligand pair (Δ2∼ 40-45 nm) and the T-cell receptor TCR:peptide-major-histocompatibility-complex pMHC bond (Δ1∼ 14-15 nm), τ grows monotonically with increasing coreceptor bond length separation δ (= Δ2-Δ1∼ 26-30 nm) while τ decays with Δ1 for fixed Δ2. The nonuniversal δ-dependent power-law structure of the probability density function further explains why only the TCR:pMHC bond is a likely candidate to form a stable synapse.

Fully probabilistic control for stochastic nonlinear control systems with input dependent noise

Robust controllers for nonlinear stochastic systems with functional uncertainties can be consistently designed using probabilistic control methods. In this paper a generalised probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented emphasising how the uncertainty can be systematically incorporated in the absence of reliable systems models. To achieve this objective all probabilistic models of the system are estimated from process data using mixture density networks (MDNs) where all the parameters of the estimated pdfs are taken to be state and control input dependent. Based on this dependency of the density parameters on the input values, explicit formulations to the construction of optimal generalised probabilistic controllers are obtained through the techniques of dynamic programming and adaptive critic methods. Using the proposed generalised probabilistic controller, the conditional joint pdfs can be made to follow the ideal ones. A simulation example is used to demonstrate the implementation of the algorithm and encouraging results are obtained.

Revealing statistical properties of quasi-CW fibre lasers in bandwidth-limited measurements

We introduce a general technique how to reveal in experiments of limited electrical bandwidth which is lower than the optical bandwidth of the optical signal under study, whether the statistical properties of the light source obey Gaussian distribution or mode correlations do exist. To do that one needs to perform measurements by decreasing the measurement bandwidth. We develop a simple model of bandwidth-limited measurements and predict universal laws how intensity probability density function and intensity auto-correlation function of ideal completely stochastic source of Gaussian statistics depend on limited measurement bandwidth and measurement noise level. Results of experimental investigation are in good agreement with model predictions. In particular, we reveal partial mode correlations in the radiation of quasi-CW Raman fibre laser.

Influence of the generated power, measurement bandwidth, and noise level on intensity statistics of a quasi-CW Raman fiber laser

In the present paper we numerically study instrumental impact on statistical properties of quasi-CW Raman fiber laser using a simple model of multimode laser radiation. Effects, that have the most influence, are limited electrical bandwidth of measurement equipment and noise. To check this influence, we developed a simple model of the multimode quasi- CW generation with exponential statistics (i.e. uncorrelated modes). We found that the area near zero intensity in probability density function (PDF) is strongly affected by both factors, for example both lead to formation of a negative wing of intensity distribution. But far wing slope of PDF is not affected by noise and, for moderate mismatch between optical and electrical bandwidth, is only slightly affected by bandwidth limitation. The generation spectrum often becomes broader at higher power in experiments, so the spectral/electrical bandwidth mismatch factor increases over the power that can lead to artificial dependence of the PDF slope over the power. It was also found that both effects influence the ACF background level: noise impact decreases it, while limited bandwidth leads to its increase. © (2014) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

Generation dynamics of the narrowband Yb-doped fiber laser

We present direct real-time experimental measurements and numerical modeling of temporal and statistical properties for the Ytterbiumdoped fiber laser with spectral bandwidth of ∼2 GHz. The obtained results demonstrate nearly exponential probability density function for intensity fluctuations. A significant decrease below the Gaussian probability has been experimentally observed for intensity fluctuations having value more than 2.5 of average intensity that may be treated as indication of some mode correlations. © 2013 Optical Society of America.

Bit error rate estimation methods for QPSK CO-OFDM transmission

Coherent optical orthogonal frequency division multiplexing (CO-OFDM) is an attractive transmission technique to virtually eliminate intersymbol interference caused by chromatic dispersion and polarization-mode dispersion. Design, development, and operation of CO-OFDM systems require simple, efficient, and reliable methods of their performance evaluation. In this paper, we demonstrate an accurate bit error rate estimation method for QPSK CO-OFDM transmission based on the probability density function of the received QPSK symbols. By comparing with other known approaches, including data-aided and nondata-aided error vector magnitude, we show that the proposed method offers the most accurate estimate of the system performance for both single channel and wavelength division multiplexing QPSK CO-OFDM transmission systems. © 2014 IEEE.

Conditional probability calculations for the nonlinear Schrödinger equation with additive noise

The method for the computation of the conditional probability density function for the nonlinear Schrödinger equation with additive noise is developed. We present in a constructive form the conditional probability density function in the limit of small noise and analytically derive it in a weakly nonlinear case. The general theory results are illustrated using fiber-optic communications as a particular, albeit practically very important, example.

Probabilistic DHP adaptive critic for nonlinear stochastic control systems

Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Kárnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained.

Some Marginal Densities of the Wishart Distribution

Евелина Илиева Велева - Разпределението на Уишарт се среща в практиката като разпределението на извадъчната ковариационна матрица за наблюдения над многомерно нормално разпределение. Изведени са някои маргинални плътности, получени чрез интегриране на плътността на Уишарт разпределението. Доказани са необходими и достатъчни условия за положителна определеност на една матрица, които дават нужните граници за интегрирането.

Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation

An iterative Monte Carlo algorithm for evaluating linear functionals of the solution of integral equations with polynomial non-linearity is proposed and studied. The method uses a simulation of branching stochastic processes. It is proved that the mathematical expectation of the introduced random variable is equal to a linear functional of the solution. The algorithm uses the so-called almost optimal density function. Numerical examples are considered. Parallel implementation of the algorithm is also realized using the package ATHAPASCAN as an environment for parallel realization.The computational results demonstrate high parallel efficiency of the presented algorithm and give a good solution when almost optimal density function is used as a transition density.

Monte Carlo Study of Particle Transport Problem in Air Pollution

2002 Mathematics Subject Classification: 65C05.

Sub- and Super-solutions of a Nonlinear PDE, and Application to a Semilinear SPDE

2010 Mathematics Subject Classification: 35R60, 60H15, 74H35.

Comparison of numerical bit error rate estimation methods in 112Gbs QPSK CO-OFDM transmission

We demonstrate an accurate BER estimation method for QPSK CO-OFDM transmission based on the probability density function of the received QPSK symbols. Using a 112Gbs QPSK CO-OFDM transmission as an example, we show that this method offers the most accurate estimate of the system's performance in comparison with other known approaches.