{"title":"Effect of Different BER Performance Comparison of MAP and ML Detection","authors":"Naveed Ur Rehman, Rehan Jamil, Irfan Jamil","volume":93,"journal":"International Journal of Electronics and Communication Engineering","pagesStart":1531,"pagesEnd":1535,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10000773","abstract":"
In this paper, we regard as a coded transmission over a
\r\nfrequency-selective channel. We plan to study analytically the
\r\nconvergence of the turbo-detector using a maximum a posteriori
\r\n(MAP) equalizer and a MAP decoder. We demonstrate that the
\r\ndensities of the maximum likelihood (ML) exchanged during the
\r\niterations are e-symmetric and output-symmetric. Under the Gaussian
\r\napproximation, this property allows to execute a one-dimensional
\r\nscrutiny of the turbo-detector. By deriving the analytical terminology
\r\nof the ML distributions under the Gaussian approximation, we confirm
\r\nthat the bit error rate (BER) performance of the turbo-detector
\r\nconverges to the BER performance of the coded additive white
\r\nGaussian noise (AWGN) channel at high signal to noise ratio (SNR),
\r\nfor any frequency selective channel.<\/p>\r\n","references":"[1] J. H. Winters and R. D. Gitlin, \\Electrical signal processing techniques in\r\nlong-haul ber-optic systems,\" IEEE Trans. Comm., vol. 38, no. 9, pp.\r\n1439{1453, Sep. 1990.\r\n[2] H. Bulow, \\Electronic equalization of transmission impairments,\" in Proc.\r\nOFC 2002, Anaheim, CA, TuF.\r\n[3] T. Adal_, \\Signal processing for optical communications,\" in Proc. 15th\r\nLEOS, Glasgow, Scotland, 2002. [4] H. Bulow and G. Thielecke, \\Electronic PMD mitigation - from linear\r\nequalization to maximum likelihood detection,\" in Proc. OFC 2001,\r\nAnaheim, CA, WAA3. 6\r\n[5] H. F. Haunstein, K. Sticht, A. Dittrich, W. Sauer-Gre, and R. Urbansky,\r\n\\Design of near optimum electrical equalizers for optical transmission in\r\nthe presence of PMD,\" in Proc. OFC 2001, Anaheim, CA, WAA4.\r\n[6] R. Holzlohner,V. S. Grigoryan, C. R. Menyuk, and W. L. Kath, \\Accurate\r\ncalculation of eye diagrams and bit error rates in optical transmission\r\nsystems using linearization,\" J. Lightwave Tech., vol. 20, pp. 389{400,\r\nMarch 2002.\r\n[7] Wenze Xi, T. Adal, and J. Zweck, \\A MAP equalizer for the optical\r\ncommunications channel,\" submitted to J. Lightwave Tech., June 2004.\r\n[8] L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, \u201cOptimal decoding of\r\nlinear codes for minimizing symbol error rate,\u201d IEEE Trans. Inf. Theory,\r\nvol. IT-32, pp. 284\u2013287, Mar. 1974.\r\n[9] S. Benedetto and E. Biglieri, Principles of Digital Transmission With\r\nWireless Applications. New York: Kluwer\/Plenum, 1999.\r\n[10] C. Berrou, A. Glavieux, and P. Thitimajshima, \u201cNear Shannon limit\r\nerror-correcting coding and decoding: Turbo codes,\u201d in Proc. IEEE Int.\r\nConf. Communications, May 1993, pp. 1064\u20131070.\r\n[11] C. Douillardat et al., \u201cIterative correction of intersymbol interference:\r\nTurbo-equalization,\u201d Eur. Trans. Telecommun., vol. 6, no. 5, pp.\r\n507\u2013511, 1995.\r\n[12] G. D. Forney, Jr., \u201cMaximum-likelihood sequence estimation for digital\r\nsequences in the presence of inter symbol interference,\u201d IEEE Trans. Inf.\r\nTheory, vol. 18, pp. 363\u2013378, May 1972.\r\n[13] Bracewell, R. (2000). The Fourier Transform and its applications.\r\nMcGraw-Hill Science\/Engineering\/Math, 3 edition.\r\n[14] Lees, J. M. and Park, J. (1995). Multiple-taper spectral analysis: A\r\nstand-alone C-subroutine. Computers & Geosciences, 21(2):199\u2013236.\r\n[15] Parker, R. L. and Barbour, A. J. (2013). psd: Adaptive, sine-multitaper\r\npower spectral density estimation. R package version 0.4-0.\r\n[16] Percival, D. and Walden, A. (1993). Spectral analysis for physical\r\napplications. Cambridge University Press.\r\n[17] Rahim, K. and Burr, W. (2013). multitaper: Multitaper Spectral Analysis.\r\nR package version 1.0-7.\r\n[18] Denis Cousineau, Sebastien Helie, \u201cImproving maximum likelihood\r\nestimation using prior probabilities: A tutorial on maximum a posteriori\r\nestimation and an examination of the weibull distribution\u201d Tutorials in\r\nQuantitative Methods for Psychology, 2013, Vol. 9(2), p. 61-71.\r\n[19] Bishop, C.M. Neural Networks for Pattern Recognition, NY: Oxford\r\nUniversity Press, Inc. (1995).\r\n[20] Edwards W, Lindman H & Savage L J. Bayesian statistical inference for\r\npsychological research. Psychol. Rev. 70:193-242, 1963\r\n[21] Jeffreys, H. Theory of Probability, Third Edition . Glasgow: Oxford\r\nUniversity Press: 1961;\r\n[22] Hastie, T. Tibshirani, R. and Friedman, J. The elements of statistical\r\nlearning: Data mining, Inference and Prediction, New York: springer,\r\n2001.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 93, 2014"}