# Bit Error Rate Estimation Using Probability Density Function Estimators

The Annals of Mathematical Statistics **1962, 33(3):1065-1076. 10.1214/aoms/1177704472MathSciNetView ArticleMATHGoogle ScholarKronmal** R, Tarter M: The estimation of probability densities and cumulatives by Fourier series methods. The choice of the number of Gaussians for each pdf is very important. The case of other kinds of modulation is left for future work. Figure 1 General transmission scheme for any transmitter and receiver with soft outputs and hard decisions In [4], High-Order Statistics (HOS) of the bit Log-Likelihood-Ratio (LLR) are used for evaluating performance of turbo-like codes. check my blog

The modular approach blurs the dynamics of layers interaction with the wireless medium, hindering the overall system performance with redundancy, inefficient resource handling and suboptimal performances. ISEHistogramKernelGaussian MixtureMean7.44 7.29 8.09 Std5.40 5.40 5.00 Table 2 Mean and Standard deviation of error estimation of using the three methods with 1,000 different Pdf Estimation Based on Kernel Method A brief description of the kernel method simulation will be given in this section. Mixture distributions can model extreme events better than the basic Gaussian ones.

EM algorithm for : 4.1. Consequently, for small BERs, simulation results take excessively long computing time depending on the complexity of the receiver. Institutional Sign In By Topic Aerospace Bioengineering Communication, Networking & Broadcasting Components, Circuits, Devices & Systems Computing & Processing Engineered Materials, Dielectrics & Plasmas Engineering Profession Fields, Waves & Electromagnetics General The reader can easily find them by replacing " " by " ".

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 The criterion we will use is the maximization of the conditional expectation of the joint likelihood of both observed samples, , and missing data, (see [11] for details about This is linked to the observed bias mentioned before.Table 4 Mean, Standard deviation and precision of BER estimation GM method, for SNR = 10 dB, at different number of samples are used Gaussian Mixture method seems to be the worst one in the MISE criterion.

Files Filename Size Approximate Download Time (Hours:Minutes:Seconds) 28.8 Modem 56K Modem ISDN (64 Kb) ISDN (128 Kb) Higher-speed Access KPHILLIPSTHESIS.PDF 2.26 Mb 00:10:27 00:05:22 00:04:42 00:02:21 00:00:12 Browse All Available The Kernel method leads to a smaller bias but has the greatest standard deviation and then less reliable than the GM method.Table 3 Mean and Standard deviation of BER estimation with 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. So the true chosen pdf is (26) Where, , and . , and .

We can easily show that in this case . Classify soft outputs according to their transmitted bits, that is, . Compared to classical Monte Carlo **method, the importance** sampling technique, reduces the sample size requirement by a factor ranging from up to . Setting the derivative to zero, we find, for (B1) Then, for , we have, (B2) C.

Cambridge University Press, Cambridge,UK; 1998.MATHGoogle ScholarCopyright©Samir Saoudi et al.2010 This article is published under license to BioMed Central Ltd. So, for general applications, such as pattern recognition or speech coding, the Kernel method seems to be the best one to choose. By using the expression of the Bit Error Probability(4) and the two conditional pdfs estimates, and , we can express the BER estimate as, (D1) Given the fact In this paper observable variables are simply given by soft output values at the receiver of a digital communications system.

We analyze the performance of the proposed BER estimator in the framework of a multiuser code division multiple access (CDMA) system with single user detection and show that attractive performance is click site For the SNR estimation SNORE algorithm was adopted, while for the BER estimation we propose a new algorithm exploiting the properties of LDPC decoder and compare its performance to the traditional In a wireless environment, the received signal may be corrupted by Gaussian noise and a variety of other channel disturbances: cochannel interference, multiple access interference, large and small-scale fading, etc. 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

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. Laster12.45 · **Institute of Electrical** and Electronics Engineers2nd Jeffrey H. IEEE Transactions on Communications 2009, 57(7):1886-1888.View ArticleGoogle ScholarSakai T, Shibata K: Fast BER estimation of LDPC codes. news Verification of optimality of : 3.1.

We have given some theoretical studies, in [20], regarding the convergence of this BER estimator. The a priori probability represents the probability that , that is, . Committee Member Tranter, William H.

## Committee Member Keywords Bit Error Rate Adaptive Signal Processing Probability Density Function DSP Equalization Interference Rejection Digital Communications Digital Signal Processing PDF Minimum BER Estimation MBE BER Adaptive Filtering Date of

Choose a large enough number of the Gaussian mixture: and . 2. The authors argue convincingly that probability theory cannot be separated from real analysis, and this book contains over 300 examples related to both the theory and application of mathematics. Note that the soft output in (22) contains a mixture of a Gaussian noise. Full-text · Conference Paper · Sep 2008 · Journal of Convergence Information TechnologyMiha SmolnikarTomaz JavornikMihael MohorcicRead full-textCodage multi-couches pour systèmes de communication par satellites"In addition, BER variations in time are expected

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. 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 Otherwise, : , go to 4. 6. http://sovidi.com/bit-error/bit-error-rate-as-a-function-of-snr.php MCKernelGMSNR (dB)Theoretical BERMeanMeanMeanStd.

The different parameters are estimated by using the Maximum Expectation of joint Likelihood criterion. Introduction2. Initialization of 2.2. Then, we have: (11) Where is the joint likelihood event given by (7).

Skip to main content Advertisement Menu Search Search Search Twitter Facebook Login to my account Publisher main menu Get published Explore Journals About Books EURASIP Journal on Wireless Communications and Networking Our suggested GM method has still a huge advantage as the run time does not depend on the value of SNR. 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 If , save go to step 6.