Asymptotic Performance of Bidirectional Dual-Hop Amplify-and-Forward Systems

  • Katina KralevskaEmail author
  • Zoran Hadzi-Velkov
  • Harald Øverby
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 231)


This paper considers a bidirectional amplify-and-forward (AF) relaying system where two nodes communicate through an intermediate node due to the lack of a direct path. The communication is realized over Rayleigh fading channels in two phases: multiple access and broadcast phase. We derive closed form and asymptotic expressions for the outage probability of two-way wireless relaying system. The validity of our performance analysis for moderate and high signal-to-noise ratio (SNR) is verified with Monte Carlo simulations.


Two-way relaying amplify-and-forward outage probability Rayleigh fading 


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  1. 1.
    Abramowitz, M., Stegun, I.A.: Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover publications (1972)Google Scholar
  2. 2.
    Duong, T.Q., Hoang, L.N., Bao, V.N.Q.: On the performance of two-way amplify-and-forward relay networks. IEICE Transactions 92, 3957–3959 (2009)CrossRefGoogle Scholar
  3. 3.
    Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products. Elsevier Science (2000)Google Scholar
  4. 4.
    Laneman, J.N., Tse, D.N.C., Wornell, G.W.: Cooperative diversity in wireless networks: Efficient protocols and outage behavior. IEEE Transactions on Information Theory 50, 3062–3080 (2004)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Li, Q., Ting, S.H., Pandharipande, A., Han, Y.: Adaptive two-way relaying and outage analysis. IEEE Transactions on Wireless Communications 8, 3288–3299 (2009)CrossRefGoogle Scholar
  6. 6.
    Louie, R.H.Y., Li, Y., Vucetic, B.: Practical physical layer network coding for two-way relay channels: performance analysis and comparison. IEEE Transactions on Wireless Communications 9, 764–777 (2010)CrossRefGoogle Scholar
  7. 7.
    Rankov, B., Wittneben, A.: Spectral efficient protocols for half-duplex fading relay channels. IEEE Journal on Selected Areas in Communications 35, 379–389 (2007)CrossRefGoogle Scholar
  8. 8.
    Sendonaris, A., Erkip, E., Aazhang, B.: User cooperation diversity. part I. system description. IEEE Transactions on Communications 51, 1927–1938 (2003)CrossRefGoogle Scholar
  9. 9.
    Song, L.: Relay selection for two-way relaying with amplify-and-forward protocols. IEEE Transactions on Vehicular Technology 60, 1954–1959 (2011)CrossRefGoogle Scholar
  10. 10.
    Wang, Z., Giannakis, G.B.: A simple and general parameterization quantifying performance in fading channels. IEEE Transactions on Communications 51, 1389–1398 (2003)CrossRefGoogle Scholar
  11. 11.
    Yang, J., Fan, P., Duong, T.Q., Lei, X.: Exact performance of two-way AF relaying in nakagami-m fading environment. IEEE Transactions on Wireless Communications 10, 980–987 (2011)CrossRefGoogle Scholar
  12. 12.
    Zhang, Y., Ma, Y., Tafazolli, R.: Power allocation for bidirec- tional AF relaying over rayleigh fading channels. IEEE Communications Letters 14, 145–147 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Katina Kralevska
    • 1
    Email author
  • Zoran Hadzi-Velkov
    • 2
  • Harald Øverby
    • 1
  1. 1.Department of Telematics, Faculty of Information Technology, Mathematics and Electrical EngineeringNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.Faculty of Electrical Engineering and Information TechnologiesSs. Cyril and Methodius UniversitySkopjeMacedonia

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