scholarly journals BER Performance of PDM 4-QAM Optical Transmission System Considering the Effects of PMD and GVD Using Exact Probability Density Function

2018 ◽  
Vol 6 (1) ◽  
pp. 14
Author(s):  
Kazi Abu Taher
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Optical Transmission ◽  
Transmission System ◽  
Exact Probability ◽  
Ber Performance

scholarly journals Statistical analysis of modulated codes for robot positioning: application to BeAMS

2019 ◽  
Author(s):  
Marc Van Droogenbroeck ◽  
Pierlot Vincent
Keyword(s):  
Performance Analysis ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Theoretical Approach ◽  
Upper Bound ◽  
Angle Measurement ◽  
Exact Probability ◽  
Analysis And Design ◽  
Robot Positioning

<div>Positioning is a fundamental issue for mobile robots. Therefore, a performance analysis is suitable to determine the behavior of a system, and to optimize its working. Unfortunately, some systems are only evaluated experimentally, which makes the performance analysis and design decisions very unclear. </div><div>In [4], we have proposed a new angle measurement system, named BeAMS, that is the key element of an algorithm for mobile robot positioning. BeAMS introduces a new mechanism to measure angles: it detects a beacon when it enters and leaves an angular window. A theoretical framework for a thorough performance analysis of BeAMS has been provided to establish the upper bound of the variance, and to validate this bound through experiments and simulations. It has been shown that the estimator derived from the center of this angular window provides an unbiased estimate of the beacon angle. </div><div>This document complements our paper by going into further details related to the code statistics of modulated signals in general, with an emphasis on BeAMS. In particular, the probability density function of the measured angle has been previously established with the assumption that there is no correlation between the times a beacon enters the angular window or leaves it. This assumption is questionable and, in this document, we reconsider this assumption and establish the exact probability density function of the angle estimated by BeAMS (without this assumption). </div><div>The conclusion of this study is that the real variance of the estimator provided by BeAMS was slightly underestimated in our previous work. In addition to this specific result, we also provide a new and extensive theoretical approach that can be used to analyze the statistics of any angle measurement method with beacons whose signal has been modulated. To summarize, this technical document has four purposes: </div><div>(1) to establish the exact probability density function of the angle estimator of BeAMS, </div><div>(2) to calculate a practical upper bound of the variance of this estimator, which is of practical interest for calibration and tracking (see Table 1, on page 13, for a summary), </div><div>(3) to present a new theoretical approach to evaluate the performance of systems that use modulated (coded) signals, and </div><div>(4) to show how the variance evolves exactly as a function of the angular window (while remaining below the upper bound).</div>

scholarly journals Analysis of exceedance probability of displacement response of randomly nonlinear structures

2000 ◽  
Vol 22 (4) ◽  
pp. 212-224 ◽  
Author(s):  
Luu Xuan Hung
Keyword(s):  
Probability Density Function ◽  
Nonlinear Systems ◽  
White Noise ◽  
Probability Density ◽  
Density Function ◽  
Exceedance Probability ◽  
Nonlinear Structures ◽  
Exact Probability ◽  
Displacement Response ◽  
Linearization Techniques

The paper presents the estimation of the exact exceedance probability (EEP) of stationary responses of some white noise-randomly excited nonlinear systems whose exact probability density function can be known. Consequently, the approximate exceedance probabilities (AEPs) are evaluated based on the analysis of equivalent linearized systems using the traditional Caughey method and the extension technique of LOMSEC. Comparisons of the AEPs versus the EEP are demonstrated. The obtained results indicate important characters of the exceedance probability (EP) as well as the influence of nonlinearity over EP. The evaluation of the applied possibility of the proposed linearization techniques for estimating AEPs are made.

Normalized structure factor analysis with theCentroMKprogram

2013 ◽  
Vol 46 (1) ◽  
pp. 88-92 ◽  
Author(s):  
Marcin Kowiel
Keyword(s):  
Factor Analysis ◽  
Probability Density Function ◽  
Probability Density ◽  
Crystal Structures ◽  
Density Function ◽  
Structure Factor ◽  
Probability Density Functions ◽  
Density Functions ◽  
Exact Probability ◽  
Space Group

Statistical analysis of the normalized structure factorEis important during space-group determination. Several approaches to solve this problem have been described in the literature. In this paper, the most popular approach, the ideal asymptotic probability density function developed by Wilson, is compared with the more accurate exact probability density functions described by Shmueli and co-workers. Furthermore, a new computer program,CentroMK, for normalized structure factor analysis, is presented. The program is capable of plotting histograms of the normalized structure factors and exact probability density functions. Moreover, the program calculates five estimators helpful during the space-group determination: 〈|E|〉, 〈|E2 − 1|〉, %E> 2, %E< 0.25 and the discrepancyRfunction. The two approaches and the error rates of the five listed estimators are compared for nearly 30 600 crystal structures obtained fromActa Crystallographica Section E.It is shown that within a space group the means 〈|E|〉 and 〈|E2 − 1|〉 of real crystal structures show high variability. The comparison shows that decisions based on the exact probability density function are more accurate, the computing time is reasonable, and estimators 〈|E|〉, %E< 0.25 andRare the most accurate and should be preferred during space-group determination.

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