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A New Closed-Form Expressions of Channel Capacity with MRC, EGC and SC Over Lognormal Fading Channel

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Abstract

In this work, we derive the closed-form expressions of channel capacity with maximal ratio combining, equal gain combining and selection combining schemes under different transmission policies such as optimal power and rate adaptation, optimal rate adaptation, channel inversion with fixed rate (CIFR) and truncated CIFR. Various approximations to the intractable integrals have been proposed using methods such as Holtzman and Gauss–Hermite approximations and simpler expressions are suggested. Moreover, as an application, the channel capacity of lognormally distributed fading channel in the interference-limited environment is discussed. The obtained closed-form expressions have been validated with the exact numerical results.

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References

  1. Pan, G., Ekici, E., Feng, Q., et al. (2012). Capacity analysis of log-normal channels under various adaptive transmission schemes. IEEE Communication Letter, 16(3), 346–348.

    Article  Google Scholar 

  2. Khandelwal, V., & Karmeshu, (2015). Channel capacity analysis over slow fading environment: Unified truncated moment generating function approach. Wireless Personal Communication, 82, 2377–2390.

    Article  Google Scholar 

  3. Laourine, A., Stephenne, A., Affes, S., et al. (2007). Estimating the ergodic capacity of log-normal channels. IEEE Communication Letter, 11(7), 568–570.

    Article  Google Scholar 

  4. Olabiyi, O., & Annamalai, A. (2012). Inversible exponential-type approximation for the gaussain probability integral Q(x) with application. IEEE Wireless Communication Letter, 1(5), 544–547.

    Article  Google Scholar 

  5. Goldsmith, A. (2005). Wireless communications. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  6. Karagiannidis, G. K., & Lioumpas, A. S. (2007). An improved approximation for the Gaussian Q-function. IEEE Communication Letter, 11(8), 644–646.

    Article  Google Scholar 

  7. Shi, Q. (2013). On the performance of energy detection for spectrum sensing in cognitive radio over nakagami-lognormal composite channels. In Proceedings of IEEE international conference on signal and information processing (pp. 566–569), China.

  8. http://keisan.casio.com/exec/system/1281195844.

  9. Holtzman, J. M. (1992). A simple, accurate method to calculate spread multiple access error probabilities. IEEE Transaction on Communication, 40(3), 461–464.

    Article  Google Scholar 

  10. Karmeshu, & Khandelwal, V. (2012). On the applicability of average channel capacity in lognormal fading environment. Wireless Personal Communication, 68, 1393–1402.

    Article  Google Scholar 

  11. Steen, N. M., Byrne, G. D., Gelbard, E. M. et al. (1969). Gaussian quadratures for the integrals \(\int \limits _{0}^{\infty }\exp (-x^2)f(x)dx\) & \(\int \limits _{0}^{b}\exp (-x^2)f(x)dx\). Mathematics of Computation, 30, 661–671.

    MATH  Google Scholar 

  12. Fenton, L. F. (1960). The sum of log-normal probability distributions in scatter transmission system. IRE Transactions on Communication systems, 8(1), 57–67.

    Article  Google Scholar 

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Authors and Affiliations

  1. G. B. Pant Engineering College, Pauri, India

    Diwaker Tiwari, Sanjay Soni & Puspraj Singh Chauhan

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  1. Diwaker Tiwari
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  2. Sanjay Soni
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  3. Puspraj Singh Chauhan
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Correspondence to Sanjay Soni.

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Tiwari, D., Soni, S. & Chauhan, P.S. A New Closed-Form Expressions of Channel Capacity with MRC, EGC and SC Over Lognormal Fading Channel. Wireless Pers Commun 97, 4183–4197 (2017). https://doi.org/10.1007/s11277-017-4719-9

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  • DOI: https://doi.org/10.1007/s11277-017-4719-9

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