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The Distribution of Foschini's Lower Bound for Channel Capacity

Part of: Distribution theory

Published online by Cambridge University Press:  04 January 2016

Christopher S. Withers  and
Saralees Nadarajah
Christopher S. Withers*
Affiliation:
Industrial Research Limited
Saralees Nadarajah*
Affiliation:
University of Manchester
*
∗ Postal address: Applied Mathematics Group, Industrial Research Limited, Lower Hutt, New Zealand.
∗∗ Postal address: School of Mathematics, University of Manchester, Manchester M13 9PL, UK. Email address: mbbsssn2@manchester.ac.uk
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Abstract

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Foschini gave a lower bound for the channel capacity of an N-transmit M-receive antenna system in a Raleigh fading environment with independence at both transmitters and receivers. We show that this bound is approximately normal.

Keywords

Antennacapacitylower boundtransmit receive

MSC classification

Primary: 62E17: Approximations to distributions (nonasymptotic)
Secondary: 62E20: Asymptotic distribution theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 44 , Issue 1 , March 2012 , pp. 260 - 269
Copyright
© Applied Probability Trust 

References

Abramowitz, M. and Stegun, I. A. (1964). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Nat. Bureau Standards Appl. Math. Ser. 55). US Government Printing Office, Washington, DC.Google Scholar
Ariyavisitakul, S. L. (2000). Turbo space-time processing to improve wireless channel capacity. IEEE Trans. Commun. 48, 1347–1359.Google Scholar
Billingsley, P. (1968). Convergence of Probability Measures. John Wiley, New York.Google Scholar
Chiani, M., Win, M. Z. and Zanella, A. (2003). On the capacity of spatially correlated MIMO Rayleigh-fading channels. IEEE Trans. Inf. Theory 49, 2363–2371.CrossRefGoogle Scholar
Cornish, E. A. and Fisher, R. A. (1937). Moments and cumulants in the specification of distributions. Rev. Internat. Statist. Inst. 5, 307–320.CrossRefGoogle Scholar
Fisher, R. A. and Cornish, E. A. (1960). The percentile points of distributions having known cumulants. Technometrics 2, 209–225.CrossRefGoogle Scholar
Foschini, G. J. (1996). Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas. Bell Labs Tech. J. 1, 41–59.CrossRefGoogle Scholar
Foschini, G. J. and Gans, M. J. (1998). On limits of wireless communications in a fading environment when using multiple antennas. Wireless Personal Commun. 6, 311–335.CrossRefGoogle Scholar
Gradshteyn, I. S. and Ryzhik, I. M. (1965). Tables of Integrals, Series, and Products, 4th edn. Academic Press, New York.Google Scholar
Lee, M. and Oh, S. K. (2009). A simple scheduling algorithm capable of controlling throughput-fairness tradeoff performance. In IEEE VTS Vehicular Technology Conf. Proc., pp. 1622–1625.CrossRefGoogle Scholar
Nechiporenko, T., Phan, K. T., Tellambura, C. and Nguyen, H. H. (2008). Performance analysis of adaptive M-QAM for Rayleigh fading cooperative systems. In Proc. 2008 IEEE Internat. Conf. Commun., pp. 3393–3399.CrossRefGoogle Scholar
Nechiporenko, T., Phan, K. T., Tellambura, C. and Nguyen, H. H. (2009). On the capacity of Rayleigh fading cooperative systems under adaptive transmission. IEEE Trans. Wireless Commun. 8, 1626–1631.CrossRefGoogle Scholar
Rui, X. (2009). Capacity and SER analysis of MIMO MRC systems in an interference-limited environment. Wireless Personal Commun. 50, 133–142.CrossRefGoogle Scholar
Salo, J., Suvikunnas, P., El-Sallabi, H. M. and Vainikainen, P. (2004). Approximate distribution of capacity of Rayleigh fading MIMO channels. Electronics Lett. 40, 741–742.CrossRefGoogle Scholar
Smith, P. J. and Shafi, M. (2002). On a Gaussian approximation to the capacity of wireless MIMO systems. In Proc. 2002 IEEE Internat. Conf. Commun., pp. 406–410.CrossRefGoogle Scholar
Smith, P. J., Garth, L. M. and Loyka, S. (2003). Exact capacity distributions for MIMO systems with small numbers of antennas. IEEE Commun. Lett. 7, 481–483.CrossRefGoogle Scholar
Tan, B. S., Li, K. H. and Teh, K. C. (2010). Performance analysis of LDPC codes with selection diversity combining over identical and non-identical Rayleigh fading channels. IEEE Commun. Lett. 14, 333–335.CrossRefGoogle Scholar
Telatar, E. (1999). Capacity of multi-antenna Gaussian channels. Europ. Trans. Telecommun. 10, 585–595.CrossRefGoogle Scholar
Wei, C., Fan, P. and Ben Letaief, K. B. (2008). On channel coding selection in time-slotted ALOHA packetized multiple-access systems over Rayleigh fading channels. IEEE Trans. Wireless Commun. 7, 1699–1707.CrossRefGoogle Scholar
Withers, C. S. (1982). The distribution and quantiles of a function of parameter estimates. Ann. Inst. Statist. Math. 34, 55–68.CrossRefGoogle Scholar
Withers, C. S. (1984). Asymptotic expansions for distributions and quantiles with power series cumulants. J. R. Statist. Soc. B 46, 389–396.Google Scholar
Withers, C. S. (2004). Outage probability for channel capacity for multiple arrays. In Proc. 2004 Austral. Commun. Theory Workshop, pp. 37–41.Google Scholar
Withers, C. S. (2006). Reciprocity for MIMO systems. In Proc. 7th Austral. Commun. Theory Workshop, pp. 175–183.Google Scholar
Withers, C. S. and Nadarajah, S. (2010). Channel capacity for MIMO systems with multiple frequencies and delay spread. Techn. Rep., Applied Mathematics Group, Industrial Research Limited.Google Scholar
Withers, C. S. and Vaughan, R. (2001). The distribution and percentiles of channel capacity for multiple arrays. In Proc. 11th Symp. Wireless Commun., pp. 141–152.Google Scholar