Then, we have: (11) Where is the joint likelihood event given by (7). Proof of (14) Proof. We can show that for the chosen Gaussian kernel, a soft BER estimation can be given by the following expression (see proof in ): (5) where denotes the complementary The are assumed to be independent and identically distributed with and , where . More about the author
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 ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.7/ Connection to 0.0.0.7 failed. HallOxford University Press, 1993 - Mathematics - 211 pages 0 Reviewshttps://books.google.com/books/about/Counterexamples_in_Probability_and_Real.html?id=-HbmCwAAQBAJA counterexample is any example or result that is the opposite of one's intuition or to commonly held beliefs. The precision of the estimation, defined as the the standard deviation to the mean of BER ratio, does not decrease with the number of samples.
Our suggested analytical expression of the BER, based on the Gaussian Mixture model, where parameters are jointly estimated by EM algorithm and Mutual Information theory leads to an efficient fast way Many of the examples in this collection are new, and many old ones, previously buried in the literature, are now accessible for the first time. IEEE Journal on Selected Areas in Communications 1984, 2(1):153-170. 10.1109/JSAC.1984.1146031View ArticleGoogle ScholarShanmugam KS, Balaban P: A modified Monte Carlo simulation technique for the evaluation of error rate in digital communication systems. Table 2 shows the mean and the Standard deviation for the three methods.
The choice of the number of Gaussians for each pdf is very important. Let be the missing data which is a sequence of variables that determines the component from which the observations originate. means that is generated by the th Finally, we evaluated the performance of the proposed BER estimation technique in the framework of CDMA systems. Cambridge University Press, Cambridge,UK; 1998.MATHGoogle ScholarCopyright©Samir Saoudi et al.2010 This article is published under license to BioMed Central Ltd.
Wise is at University of Texas, Austin. Adaptive filtering is the usual approach to mitigating this channel distortion. Preview this book » What people are saying-Write a reviewWe haven't found any reviews in the usual places.Selected pagesTitle PageTable of ContentsIndexReferencesOther editions - View allCounterexamples in Probability and Real AnalysisGary That is why, in another simulation, we are interested in estimating the area of the tail delimited between, for example, and .
Consequently, computing time is reduced drastically. Different simulation results are presented in 4. A 1-bit differential demodulator (DD1) is used to demodulate a Gaussian minimum shift keying signal, and Gram-Charlier-based and Parzen (1962) based BER estimations are compared to measured DD1 results. 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: http://0.0.0.9/ Connection
EURASIP Journal on Wireless Communications and Networking 2009, 2009:-9.Google ScholarYang ZR, Zwolinski M: Mutual information theory for adaptive mixture models. We can see that we obtain an unbelievable result, a BER estimate down to has been measured. The SNR at the output of the MF of each user is therefore . 4.1. The computation of the optimal values and , which could of course be different, can be performed in a parallel fashion.
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 my review here For example, a mixture of two Gaussian distributions with different means and different variances results in a density with two modes, which is not a standard parametric distribution model. Let us underline that we need to perform the EM algorithm two times and in independent way. Subscribe Enter Search Term First Name / Given Name Family Name / Last Name / Surname Publication Title Volume Issue Start Page Search Basic Search Author Search Publication Search Advanced Search
Gaussian Mixture for BER Estimation4. The a priori probability represents the probability that , that is, . Your cache administrator is webmaster. http://onlinetvsoftware.net/bit-error/bit-error-rate-probability.php The two conditional pdfs are then estimated, in a parallel fashion, by using the Mutual Information Theory to compute iteratively the optimal number of components and a subiteration for the EM
Interestingly, we showed that while classical MC method fails to perform BER estimation in the region of high SNR, the proposed GM estimator provides reliable estimates and better, in the sense Let us use the conditional Expectation of the log likelihood function given in Appendix A,(A.1). Kernel Method for BER Estimation 2.1.
We then proposed a BER computation technique using Gaussian Mixture-based pdf estimation. At the last iteration T of EM algorithm, reliable estimates of and are reached and the BER is computed using the obtained estimates. 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 This result will be confirmed in the following sub section for BER estimation in the framework of CDMA systems described in the begining of Section 4.Table 1 Mean and Standard deviation
Dev. 0 4 8 Figure 3 plots the true pdf with the estimated pdf for the three cases. samples has been generated for this first simulation. Proceedings of the IEEE International Conference on Communications (ICC '07), June 2007 986-989.Google ScholarCavus E, Haymes CL, Daneshrad B: Low BER performance estimation of LDPC codes via application of importance sampling navigate to this website Dev.Std.
As the pdf of the obseved samples is a mixture of Gaussians, this means (see ) that each is produced by one component of this mixture ( See all ›19 CitationsSee all ›8 ReferencesShare Facebook Twitter Google+ LinkedIn Reddit Request full-text Bit error rate estimation using probability density function estimatorsArticle in IEEE Transactions on Vehicular Technology 52(1):260 - 267 · February 2003 with 48 So, the following quantity, (19) allows us to know if we have to reduce the number of components or not. Let us also assume that we can use all these PCs in a parallel and optimized structure.
Series B 1977, 39(1):1-38.MathSciNetMATHGoogle ScholarMasson P, Pieczynski W: SEM algorithm and unsupervised statistical segmentation of satellite images. This bias will completely disappear for increased number of EM iterations as it will be seen in Section 4.3. GM method has found that 4 components are sufficients to estimate the pdf as Figure 3 Comparison between the real and the estimated pdfs. The BER is performed based on all soft observations and the smoothing parameter value.
The performance evaluation results are provided in terms of suitable internal parameters of the algorithm and as the trade-off analysis between BER and spectral efficiency. In order to estimate the conditional pdf, from (6), we have to estimate the unknown parameters represented by . Counterexamples can have great educational value in illuminating complex topics that are difficult to explain in a rigidly logical, written presentation. A contention level is separately estimated by each station depending on unsuccessful frame transmission ratios.
At the receiver, any kind of detection such as MIMO equalization, multiuser detection, turbo techniques detection, or simply Rake receiver, may be implemented.