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Bit Error Rate Estimation Using Probability Density Function Estimators

A contention level is separately estimated by each station depending on unsuccessful frame transmission ratios. If the bit error rate (BER) of a channel is available, CABM can be enhanced by a more accurate estimation of collision probability. Two conditional pdfs are computed corresponding to the transmitted bits equal to . ConclusionsIn this paper, we considered the problem of BER estimation for a digital communications system using any transmission technology or channel coding. http://gatoisland.com/bit-error/bit-error-rate-estimation-for-turbo-decoding.php

Kernel Method for BER Estimation3. IEEE Transactions on Geoscience and Remote Sensing 1993, 31(3):618-633. 10.1109/36.225529View ArticleGoogle ScholarBouguila N, Ziou D: A hybrid SEM algorithm for high-dimensional unsupervised learning using a finite generalized Dirichlet mixture. Committee Member Tranter, William H. For example, ideas in mathematical sciences...https://books.google.com/books/about/Counterexamples_in_Probability_and_Real.html?id=-HbmCwAAQBAJ&utm_source=gb-gplus-shareCounterexamples in Probability and Real AnalysisMy libraryHelpAdvanced Book SearchView eBookGet this book in printOxford University PressAmazon.comBarnes&Noble.com - $80.00 and upBooks-A-MillionIndieBoundFind in a libraryAll sellers»Counterexamples in Probability

Estimation Step In this step, at iteration , we estimate the unobserved component in the Gaussian mixture for each observed sample using the parameter value , computed at Otherwise, : , go to 4. 6. In particular, the length of the bins of the Histogram is chosen equal to the smoothing parameter computed for the kernel method so as the convergence of the histogram in the In [10], a method, based on Mutual Information Theory, was presented to find the optimal number of Gaussians in order to give an accurate estimation of the pdf.

From top to bottom: MC, Kernel, and Gaussian mixture method. Samples are used for each simulation. 1,000 different trials are performed to compute the Mean, Min, and Max. First of all, we provided a formulation of the problem where we showed that BER estimation is equivalent to the estimation of conditional pdfs of soft observations corresponding to the transmitted In this paper, only binary phase shift key (BPSK) modulation is used. Compute (19)  5.2.

Although carefully collected, accuracy cannot be guaranteed. It is clear that if this number of components is too low, the corresponding pdf will be too smooth and then the BER less reliable. For each pdf, a Gaussian Mixture model, with a large enough initial number of components, is used. The cardinality of set is denoted .

We have given some theoretical studies, in [20], regarding the convergence of this BER estimator. In this paper, we suggest a new means of estimating the BER. Applied Stochastic Models and Data Analysis 1994, 10(3):215-231. 10.1002/asm.3150100306MathSciNetView ArticleMATHGoogle ScholarSaoudi S, Ghorbel F, Hillion A: Some statistical properties of the kernel-diffeomorphism estimator. So, for general applications, such as pattern recognition or speech coding, the Kernel method seems to be the best one to choose.

Bell System Technical Journal 1948, 27: 379-423, 623–656.MathSciNetView ArticleMATHGoogle ScholarVerdu S: Multiuser Detection. The run time does not depend on the value of SNR which is a huge advantage of our suggested method. At the crossroads of QoS-related constraints, devices complexity and efficient spectrum use, error control is indeed a key aspect of wireless communications - particularly crucial in the satellite context - where In [13], a hybrid version of SEM is used assuming a generalized Dirichlet distribution.Nonparametric pdf estimation has also been used in different applications such as speech coding and pattern recognition [14,

Your cache administrator is webmaster. http://gatoisland.com/bit-error/bit-error-rate-probability-distribution.php The SNR at the output of the MF of each user is therefore . 4.1. Use of this web site signifies your agreement to the terms and conditions. Setting the derivative to zero, we find, for (C1) Then, for , we have, (C2) D.

At each iteration ,   4.2.1 Estimation step:     Estimate APPs, using (10).   4.2.2 Maximization step:     Computation of by using (12), (13) and (14). 5. The algorithm stops when the maximum of the computed MI, over all the components, is nonpositive which means that all the reached components are likely independent and therefore gives an optimal Differing provisions from the publisher's actual policy or licence agreement may be applicable.This publication is from a journal that may support self archiving.Learn more © 2008-2016 researchgate.net. check my blog We consider the case where the two users have equal powers .

The kernel method ([17–19]) is used to estimate the different pdfs. GM method has found that 4 components are sufficients to estimate the pdf as Figure 3 Comparison between the real and the estimated pdfs. It is shown that if we wish to have reliable results with good precision, the total number of transmitted data must be conversely proportional to the product of the true BER

Finally, a whole new cross-layer framework called HERACLES is introduced, offering efficient and overhead-free error correction capabilities for almost any layer of a protocol stack and being patented at the moment

We can adopt these techniques to estimate the BER and calculate the FER in error-prone channels. "[Show abstract] [Hide abstract] ABSTRACT: The distributed coordination function (DCF) is the most widely deployed This bias will completely disappear for increased number of EM iterations as it will be seen in Section 4.3. This method was based on the estimation of the probability density function (pdf) of soft observed samples. Students and theorists across fields as diverse as real analysis, probability, statistics, and engineering will want a copy of this book.

The likelihood function is given by: (7) where is the indicator function given by: (8) In this section, we will use the Expection Maximization algorithm to estimate, in Generated Sun, 02 Oct 2016 13:00:35 GMT by s_hv978 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: Connection Performance Comparison for the Three Methods In order to compare the three methods (MC, Kernel and GM method), soft outputs were generated for each SNR to estimate the BER. http://gatoisland.com/bit-error/bit-error-rate-probability.php We have the constraint that .

The computation of the optimal values and , which could of course be different, can be performed in a parallel fashion. Setting the derivative to zero, we find, for (B1) Then, for , we have, (B2) C. The BER is, therefore, simply computed by using all parameters (means, variances, and a priori probabilities) for each conditional pdf given by the EM algorithm at the last iteration. So the true chosen pdf is (26) Where, , and . , and .

Algorithm 1: Summary of the Gaussian Mixture based BER estimation using EM algorithm and Mutual Information theory. and are computed in a parallel fashion. 1. In the first one, that is, Estimation step, we will compute the different a posteriori probabilities (APP): . MBE shows improvement over the Least Mean Squares (LMS) algorithm for most simulations involving interference and in some multipath situations. Applied Stochastic Models and Data Analysis 1997, 13(1):39-58. 10.1002/(SICI)1099-0747(199703)13:1<39::AID-ASM292>3.0.CO;2-JMathSciNetView ArticleMATHGoogle ScholarYounjeong L, Ki Yong L, Joohun Lee L: The estimating optimal number of Gaussian mixtures based on incremental k-means for speaker

Your cache administrator is webmaster. To this end, a new adaptive procedure called the Minimum BER Estimation (MBE) algorithm has been developed. Part of Springer Nature. Performance of GM Method in the High SNR Region We would like to test our suggested algorithm in severe conditions for high values of SNR while using, in the same time,

This allows a significant reduction in run time for computer simulations and may also be used as the basis for rapid real-time BER estimation in real communication systems.In this paper, we After a thorough introduction to cross-layer design, the first part of this work focuses specifically on the error control strategy of early DVB satellites, where redundancies between the channel decoder and International Journal of Information Technology 2006, 12(7):13-21.Google ScholarRosenblatt M: Remarks on some non-parametric estimates of a density function. An estimate of the pdf of soft decision is constructed in a histogram form.

Let and the reached values at the last iteration of the EM algorithm described in the previous Section 3.1. The results show that the GM method can drastically reduce the needed number of samples to estimate the BER in order to reduce the required simulation run-time, even at very low Wise, Eric B. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The analytical expression of the BER is therefore given by using the different estimated parameters of the Gaussian Mixture.The EM algorithm was introduced for the first time by Dempster et al. The scheme considers a subset of transmission modes (MODCODs) defined in the standard and exploits two parameters in making the MODCOD switching decisions, the estimated signal-to-noise ratio (SNR) and the estimated In addition, the Mean, the Standard deviation with the theoretical value of BER for different values of SNR are given in Table 3.

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