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The Impact of Shadowing and the Severity of Fading on the First and Second Order Statistics of the Capacity of OSTBC MIMO Nakagami-Lognormal Channels

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Abstract

This article presents a thorough statistical analysis of the capacity of orthogonal space-time block coded (OSTBC) multiple-input multiple-output (MIMO) Nakagami- lognormal (NLN) channels. The NLN channel model allows to study the joint effects of fast fading and shadowing on the statistical properties of the channel capacity. We have derived exact analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the capacity of MIMO NLN channels. It is observed that an increase in the MIMO dimension or a decrease in the severity of fading results in an increase in the mean channel capacity, while the variance of the channel capacity decreases. On the other hand, an increase in the shadowing standard deviation increases the spread of the channel capacity, however the shadowing effect has no influence on the mean channel capacity. We have also presented approximation results for the statistical properties of the channel capacity, obtained using the Gauss-Hermite integration method. It is observed that approximation results not only reduce the complexity, but also have a very good fitting with the exact results. The presented results are very useful and general because they provide the flexibility to study the impact of shadowing on the channel capacity under different fading conditions. Moreover, the effects of severity of fading on the channel capacity can also be studied. The correctness of theoretical results is confirmed by simulations.

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Authors and Affiliations

  1. Department of Information and Communication Technology, Faculty of Engineering and Science, University of Agder, Service box 509, 4898, Grimstad, Norway

    Gulzaib Rafiq & Matthias Pätzold

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  1. Gulzaib Rafiq
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  2. Matthias Pätzold
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Correspondence to Gulzaib Rafiq.

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The material in this paper is based on “On the Statistical Properties of the Capacity of OSTBC Nakagami-Lognormal MIMO Channels”, by Gulzaib Rafiq and Matthias Pätzold which appeared in the proceedings of 4th IEEE International Conference on Signal Processing and Communication Systems, ICSPCS 2010, Gold Coast, Australia, December 2010. © 2010 IEEE.

Throughout this paper, we will refer to the MIMO dimension as N R ×  N T , where N R is the number of receive antennas and N T denotes the number of transmit antennas.

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Rafiq, G., Pätzold, M. The Impact of Shadowing and the Severity of Fading on the First and Second Order Statistics of the Capacity of OSTBC MIMO Nakagami-Lognormal Channels. Wireless Pers Commun 65, 601–616 (2012). https://doi.org/10.1007/s11277-011-0275-x

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