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8 - Detection based on MCMC techniques

Published online by Cambridge University Press:  18 December 2013

A. Chockalingam
Affiliation:
Indian Institute of Science, Bangalore
B. Sundar Rajan
Affiliation:
Indian Institute of Science, Bangalore
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Summary

In large systems where the physical laws governing system behavior are inherently probabilistic and complicated, traditional methods of obtaining closed-form analytic solutions may not be adequate for the level of detailed study needed. In such situations, one could simulate the behavior of the system in order to estimate the desired solution. This approach of using randomized simulations on computers, which came to be called the Monte Carlo methods, is powerful, elegant, flexible, and easy to implement. From the early days of their application in simulating neutron diffusion evolution in fissionable material in the late 1940s, Monte Carlo methods have found application in almost every discipline of science and engineering. Central to the Monte Carlo approach is the generation of a series of random numbers, often a sequence of numbers between 0 and 1 sampled from a uniform distribution, or, in several other instances, a sequence of random numbers sampled from other standard distributions (e.g., the normal distribution) or from more general probability distributions that arise in physical models. More sophisticated techniques are needed for sampling from more general distributions, one such technique being acceptance–rejection sampling. These techniques, however, are not well suited for sampling large-dimensional probability distributions. This situation can be alleviated through the use of Markov chains, in which case the approach is referred to as the Markov chain Monte Carlo (MCMC) method [1]. Typically, MCMC methods refer to a collection of related algorithms, namely, the Metropolis–Hastings algorithm, simulated annealing, and Gibbs sampling.

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Large MIMO Systems , pp. 169 - 196
Publisher: Cambridge University Press
Print publication year: 2014

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References

[1] W. R., Gilks, S., Richardson, and D. J., Spiegelhalter, Markov Chain Monte Carlo in Practice. London: Chapman & Hall, 1996.
[2] N., Metropolis and S., Ulam, “The Monte Carlo method,” J. Amer. Statist. Assoc., no. 44, pp. 335–341, 1949.Google Scholar
[3] N., Metropolis, A. W., Rosenbluth, M. N., Rosenbluth, A., Teller, and H., Teller, “Equations of state calculations by fast computing machines,” Journal of Chemical Physics, no. 21, pp. 1087–1091, 1953.Google Scholar
[4] W. K., Hastings, “Monte Carlo sampling methods using Markov chains and their applications,” Biometrika, no. 57, pp. 97–109, 1970.
[5] S., Chib and E., Greenberg, “Understand ing the Metropolis-Hastings algorithm,” American Statistician, no. 49, pp. 327–335, 1995.
[6] J., Geweke, “Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments,” in Bayesian Statistics, J. M., Bernardo, J. O., Berger, A. P., Dawid, and A. F. M., Smith, Eds. Oxford, UK: Oxford University Press, 1992, ch. 4, pp. 169–193.
[7] A. E., Raftery and S., Lewis, “How many iterations in the Gibbs sampler?” in Bayesian Statistics, J. M., Bernardo, J. O., Berger, A. P., Dawid, and A. F. M., Smith, Eds. Oxford, UK: Oxford University Press, 1992, ch. 4, pp. 763–773.
[8] S., Geman and D., Geman, “Stochastic relaxation, Gibbs distribution and Bayesian restoration of images,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. PAMI-6, no. 6, pp. 721–741, Nov. 1984.Google Scholar
[9] R., Chen and T.-H., Li, “Blind restoration of linearly degraded discrete signals by Gibbs sampler,” IEEE Trans. Signal Process., vol. 43, no. 9, pp. 2410–2413, Sep. 1995.Google Scholar
[10] R., Chen, J. S., Liu, and X., Wang, “Convergence analyses and comparisons of Markov chain Monte Carlo algorithms in digital communications,” IEEE Trans. Signal Process., vol. 50, no. 2, pp. 255–270, Feb. 2002.Google Scholar
[11] B., Farhang-Boroujeny, H., Zhu, and Z., Shi, “Markov chain Monte Carlo algorithms for CDMA and MIMO communication systems,” IEEE Trans. Signal Process., vol. 54, no. 5, pp. 1896–1909, May 2006.
[12] S., Henriksen, B., Ninness, and S. R., Weller, “Convergence of Markov-Chain MonteCarlo approaches to multiuser and MIMO detection,” IEEE J. Sel. Areas in Commun., vol. 26, no. 3, pp. 497–505, Apr. 2008.Google Scholar
[13] R., Peng, R.-R., Chen, and B., Farhang-Boroujeny, “Markov chain Monte Carlo detectors for channels with intersymbol interference,” IEEE Trans. Signal Process., vol. 58, no. 4, pp. 2206–2217, Apr. 2010.Google Scholar
[14] R. R., Chen, R., Peng, A., Ashikhmin, and B., Farhang-Boroujeny, “Approaching MIMO capacity using bitwise Markov chain Monte Carlo detection,” IEEE Trans. Commun., vol. 58, no. 2, pp. 423–428, Nov. 2010.Google Scholar
[15] D. J. C., MacKay, Information Theory, Inference and Learning Algorithms. Cambridge, UK: Cambridge University Press, 2003.
[16] M. K., Hanawal and R., Sundaresan, “Rand omised attacks on passwords,” in Technical Report TR-PME-2010-11, DRDO-IISc Programme on Advanced Research in Mathematical Engineering, IISc, Bangalore, 12 February 2010. Online: http://www.pal.ece.iisc.ernet.in/PAM/docs/techreports/tech_rep10/TR-PME-2010-ll.pdf.
[17] M. K., Hanawal and R., Sundaresan, “Guessing revisited: A large deviations approach,” IEEE Trans. Inform. Theory, vol. 57, no. 1, pp. 70–78, Jan. 2011.Google Scholar
[18] E., Arikan, “An inequality on guessing and its application to sequential decoding,” IEEE Trans. Inform. Theory, vol. 42, no. 1, pp. 99–105, Jan. 1996.Google Scholar
[19] M., Hansen, B., Hassibi, A. G., Dimakis, and W., Xu, “Near-optimal detection in MIMO systems using Gibbs sampling,” in IEEE GLOBECOM'2009, Hondulu Nov.-Dec. 2009, pp. 1–6.
[20] T., Datta, N. A., Kumar, A., Chockalingam, and B. S., Rajan, “A novel Monte Carlo sampling based receiver for large-scale uplink multiuser MIMO systems,” IEEE Trans. Veh. Tech., vol. 62, no. 7, pp. 3019–3038, Sep. 2013.Google Scholar
[21] A., Kumar, S., Chandrasekaran, A., Chockalingam, and B. S., Rajan, “Near-optimal large-MIMO detection using rand omized MCMC and rand omized search algorithms,” in IEEE ICC'2011, Kyoto, Jun. 2011, pp. 1–5.
[22] T., Datta, N. A., Kumar, A., Chockalingam, and B. S., Rajan, “A novel MCMC algorithm for near-optimal detection in large-scale uplink mulituser MIMO systems,” in ITA '2012, San Diego, CA, Feb. 2012, pp. 69–77.
[23] X., Mao, P., Amini, and B., Farhang-Boroujeny, “Markov chain Monte Carlo MIMO detection methods for high signal-to-noise ratio regimes,” in IEEE GLOBE-COM'2007, Washington, DC, Nov. 2008, pp. 3979–3983.
[24] S., Akoum, R., Peng, R.-R., Chen, and B., Farhang-Boroujeny, “Markov chain Monte Carlo MIMO detection methods for high SNR regimes,” in IEEE ICC'2009, Glasgow, Jun. 2009, pp. 1–5.

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