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Error Probability and Capacity Performance Analysis over Composite Cascade Channels of Relay Networks

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Abstract

The application of the relay networks enlarges the communication area and improves the transmission. However, the price is the increasing system complexity, which makes the performance analysis of the corresponding channel a more challenging task. To this end, we develop the probability density function (PDF) of the composite cascade channel, and later analyze the outage probability (OP), the bit error rate (BER), and the ergodic capacity over this channel. Firstly, the exact PDF of the small-scale cascade channel, which is combined by several independent and identically distributed (i.i.d.) Rayleigh/Nakagami-m channels, is derived. Then, considering the large-scale and the lognormal distributed shadow, the PDF of the composite cascade channel, following the OP, the BER, and the ergodic capacity performance under the optimal selection combining (OSC) and the maximal ratio combining (MRC) schemes are also deduced. Furthermore, in order to obtain the asymptotic lines of the BER and the ergodic capacity performance, the mixture gamma distribution is exploited. The closed-form expressions for these two kinds of asymptotic lines, both under the OSC and the MRC schemes, are proposed. The numerical simulations confirm that the proposed expressions fit well with the Monte-Carlo results.

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References

  1. Simon, M. K., & Alouini, M.-S. (2000). Digital communication over fading channels. New York: Wiley.

    Book  Google Scholar 

  2. Talha, B., & Patzold, M. (2011). Channel models for mobile-to-mobile cooperative communication systems: A state of the art review. IEEE Vehicular Technology Magazine, 6(2), 33–43.

    Article  Google Scholar 

  3. Niyato, D., & Wang, P. (2012). Cooperative transmission for meter data collection in smart grid. IEEE Communications Magazine, 50(4), 90–97.

    Article  Google Scholar 

  4. Uysal, M., & Heidarpour, M. R. (2012). Cooperative communication techniques for future-generation hf radios. IEEE Communications Magazine, 50(10), 56–63.

    Article  Google Scholar 

  5. Sheu, J.-S., Lain, J.-K., & Wang, W.-H. (2013). On channel estimation of orthogonal frequency-division multiplexing amplify-and-forward cooperative relaying systems. IET Communications, 7(4), 325–334.

    Article  MathSciNet  MATH  Google Scholar 

  6. Amin, O., Gedik, B., & Uysal, M. (2010). Channel estimation for amplify-and-forward relaying: Cascaded against disintegrated estimators. IET Communications, 4(10), 1207–1216.

    Article  Google Scholar 

  7. Wang, G., Gao, F., Chen, W., & Tellambura, C. (2011). Channel estimation for two-way relay networks under time-selective environment. In IEEE international conference on communications, pp. 1–5

  8. Jing, Y., & Yu, X. (2012). ML-based channel estimations for non-regenerative relay networks with multiple transmit and receive antennas. IEEE Journal on Selected Areas in Communications, 30(8), 1428–1439.

    Article  Google Scholar 

  9. Abdi, A., & Kaveh, M. (1999). On the utility of gamma pdf in modeling shadow fading (slow fading). In 49th IEEE vehicular technology conference (Vol. 3, pp. 2308–2312).

  10. Ermolova, N. Y., & Tirkkonen, O. (2012). Outage probability over composite fading-shadowing radio channels. IET Communications, 6(13), 1898–1902.

    Article  MathSciNet  MATH  Google Scholar 

  11. Liu, H., Ding, H., Xiang, L., Yuan, J., & Zheng, L. (2014). Outage and ber performance analysis of cascade channel in relay networks. In The 9th international conference of the future networking and communication (pp. 23–30).

  12. Al-Ahmadi, S., & Yanikomeroglu, H. (2010). On the approximation of the generalized-k distribution by a gamma distribution for modeling composite fading channels. IEEE Transactions on Wireless Communications, 9(2), 706–713.

    Article  Google Scholar 

  13. Al-Ahmadi, S., & Yanikomeroglu, H. (2010). On the approximation of the pdf of the sum of independent generalized-k rvs by another generalized-k pdf with applications to distributed antenna systems. In IEEE Wireless communications and networking conference (pp. 1–6).

  14. Liu, Y., Zhang, J., & Zheng, Y. R. (2008). Simulation of doubly-selective compound k fading channels for mobile-to-mobile communications. In IEEE wireless communications and networking conference (pp. 1020–1025).

  15. Lewinski, D. (1983). Nonstationary probabilistic target and clutter scattering models. IEEE Transactions on Antennas and Propagation, 31(3), 490–498.

    Article  Google Scholar 

  16. Shankar, P. M. (2006). Performance analysis of diversity combining algorithms in shadowed fading channels. Wireless Personal Communications, 37(1–2), 61–72.

    Article  Google Scholar 

  17. Kostic, I. M. (2005). Analytical approach to performance analysis for channel subject to shadowing and fading. IEE Proceedings of Communications, 152(6), 821–827.

    Article  Google Scholar 

  18. Conti, A., Win, M. Z., Chiani, M., & Winters, J. H. (2003). Bit error outage for diversity reception in shadowing environment. IEEE Communications Letters, 7(1), 15–17.

    Article  Google Scholar 

  19. Shankar, P. M. (2005). Outage probabilities in shadowed fading channels using a compound statistical model. IEE Proceedings of Communications, 152(6), 828–832.

    Article  Google Scholar 

  20. Efthymoglou, G. P., Ermolova, N. Y., & Aalo, V. A. (2010). Channel capacity and average error rates in generalised-k fading channels. IET Communications, 4(11), 1364–1372.

    Article  MathSciNet  MATH  Google Scholar 

  21. Bithas, P. S., Mathiopoulos, P. T., & Kotsopoulos, S. A. (2007). Diversity reception over generalized-k (kg) fading channels. IEEE Transactions on Wireless Communications, 6(12), 4238–4243.

    Article  Google Scholar 

  22. Lindsay, B. G., Pilla, R. S., & Basak, P. (2000). Moment-based approximations of distributions using mixtures: Theory and applications. Annals of the Institute of Statistical Mathematics, 52(2), 215–230.

    Article  MathSciNet  MATH  Google Scholar 

  23. Wiper, M., Insua, D. R., & Ruggeri, F. (2001). Mixtures of gamma distributions with applications. Journal of Computational and Graphical Statistics, 10(3), 440–454.

    Article  MathSciNet  Google Scholar 

  24. Atapattu, S., Tellambura, C., & Hai, Jiang. (2011). A mixture gamma distribution to model the snr of wireless channels. IEEE Transactions on Wireless Communications, 10(12), 4193–-4203.

    Article  Google Scholar 

  25. Jung, J., Lee, S., Park, H., & Lee, I. (2014). Capacity and error probability analysis of diversity reception schemes over generalized-k fading channels using a mixture gamma distribution. IEEE Transactions on Wireless Communications, 13(9), 4721–4730.

    Article  Google Scholar 

  26. Jung, J., Lee, S.-R., Park, H., & Lee, I., (2013). Diversity analysis over composite fading channels using a mixture gamma distribution. In IEEE international conference on communications (pp. 5824–5828).

  27. Di Renzo, M., Graziosi, F., & Santucci, F. (2010). Channel capacity over generalized fading channels: A novel mgf-based approach for performance analysis and design of wireless communication systems. IEEE Transactions on Vehicular Technology, 59(1), 127–149.

    Article  Google Scholar 

  28. Waqar, O., McLernon, D. C., & Ghogho, M. (2010). Exact evaluation of ergodic capacity for multihop variable-gain relay networks: A unified framework for generalized fading channels. IEEE Transactions on Vehicular Technology, 59(8), 4181–4187.

    Article  Google Scholar 

  29. Laourine, A., Alouini, M. S., Affes, S., & Stephenne, A. (2008). On the capacity of generalized-k fading channels. IEEE Transactions on Wireless Communications, 7(7), 2441–2445.

    Article  Google Scholar 

  30. Bithas, P. S., Sagias, N. C., & Mallik, R. K. (2011). On the sum of kappa stochastic variates and applications to equal-gain combining. IEEE Transactions on Communications, 59(9), 2434–2442.

    Article  Google Scholar 

  31. Yilmaz, F., & Alouini, M. S. (2012). A novel unified expression for the capacity and bit error probability of wireless communication systems over generalized fading channels. IEEE Transactions on Communications, 60(7), 1862–1876.

    Article  Google Scholar 

  32. Gradshteyn, I. S., & Ryzhik, I. M. (2007). Tables of integrals, series and products (7th ed.). San Diego: Academic.

    Google Scholar 

  33. O’Donoughue, N., & Moura, J. M. F. (2012). On the product of independent complex gaussians. IEEE Transactions on Signal Processing, 60(3), 1050–1063.

    Article  MathSciNet  Google Scholar 

  34. Peppas, K. P. (2011). Accurate closed-form approximations to generalised-k sum distributions and applications in the performance analysis of equal-gain combining receivers. IET Communications, 5(7), 982–989.

    Article  MathSciNet  Google Scholar 

  35. Jing, Y., & Jafarkhani, H. (2009). Single and multiple relay selection schemes and their achievable diversity orders. IEEE Transactions on Wireless Communications, 8(3), 1414–1423.

    Article  Google Scholar 

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Authors and Affiliations

  1. College of Electric Science and Engineering, National University of Defence Technology, Changsha, 410073, Hunan Province, People’s Republic of China

    Haibin Liu, Liangjun Xiang, Linhua Zheng & Hong Ding

Authors
  1. Haibin Liu
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  2. Liangjun Xiang
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  3. Linhua Zheng
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  4. Hong Ding
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Correspondence to Haibin Liu.

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Liu, H., Xiang, L., Zheng, L. et al. Error Probability and Capacity Performance Analysis over Composite Cascade Channels of Relay Networks. Wireless Pers Commun 85, 1217–1235 (2015). https://doi.org/10.1007/s11277-015-2836-x

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  • DOI: https://doi.org/10.1007/s11277-015-2836-x

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