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Self-Powered Wireless Two-Way Relaying Networks: Model and Throughput Performance with Three Practical Schemes


In this paper, we analyse the throughput performance for two, three and four time slot transmission schemes, (2TS, 3TS and 4TS) for two-way amplify-and-forward relaying networks, in which we use RF signal for the energy harvesting (EH) enabled relay node to assist the exchange of information. Most importantly, we derive expression for delay-limited throughput and the approximate expressions for outage probability, and we also compare these results in case of EH and non-EH. Additionally, the trade-off between the distance allocation between source to relay, and relay to destination is comprehensively investigated, in which the large scale path loss is considered to obtain the optimal throughput. Thanks to the numerical results, we consider a scenario in each scheme, where the throughput of 2TS is higher regardless of values of power splitting coefficients compared to other two schemes. Numerical results provide an interesting trade-off between the considered EH parameters in the system design, and reveal the improvement of bandwidth and power efficiency. The proposed schemes confirm that the appropriate placement of nodes can help achieve low outage probability and optimal throughput.

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  1. 1.

    Iwamura, M. (2015). NGMN view on 5G architecture. In Proceedings of IEEE 81st vehicular technology conference (VTC Spring), Glasgow, Scotland, pp. 1–5.

  2. 2.

    Droste H., et al. (2015). The METIS 5G architecture: A summary of METIS work on 5G architectures. In Proceedings of IEEE 81st vehicular technology conference (VTC Spring), Glasgow, Scotland, pp. 1–5.

  3. 3.

    Agyapong, P. K., Iwamura, M., Staehle, D., Kiess, W., & Benjebbour, A. (2014). Design considerations for a 5G network architecture. IEEE Communications Magazine, 52(11), 65–75.

    Article  Google Scholar 

  4. 4.

    Hasan, N. U., Ejaz, W., Ejaz, N., Kim, H. S., Anpalagan, A., & Jo, M. (2016). Network selection and channel allocation for spectrum sharing in 5G heterogeneous networks. IEEE Access, 4, 980–992.

    Article  Google Scholar 

  5. 5.

    Do, D. T. (2015). Energy-aware two-way relaying networks under imperfect hardware: Optimal throughput design and analysis. Telecommunication Systems Journal (Springer), 62(2), 449–459.

    Article  Google Scholar 

  6. 6.

    Ejaz, W., Kandeepan, S., & Anpalagan, A. (2015). Optimal placement and number of energy transmitters in wireless sensor networks for RF energy transfer. In Proceedings of IEEE 26th annual international symposium on personal, indoor, and mobile radio communications (PIMRC), Aug./Sep. 2015, pp. 1238–1243.

  7. 7.

    Nguyen, H. S., Bui, A. H., Do, D. T., & Voznak, M. (2016). Imperfect channel state information of AF and DF energy harvesting cooperative networks. China Communications, 13(10), 11–19.

    Article  Google Scholar 

  8. 8.

    Zhao, N., Yu, F. R., & Leung, V. C. M. (2015). Opportunistic communications in interference alignment networks with wireless power transfer. IEEE Wireless Communications, 22(1), 88–95.

    Article  Google Scholar 

  9. 9.

    Do, D. T. (2016). Optimal throughput under time power switching based relaying protocol in energy harvesting cooperative network. Wireless Personal Communications (Springer), 87(2), 551–564.

    Article  Google Scholar 

  10. 10.

    Kim, S. J., Mitran, P., & Tarokh, V. (2008). Performance bounds for bidirectional coded cooperation protocols. IEEE Transactions on Information Theory, 54(11), 5235–5241.

    Article  MATH  MathSciNet  Google Scholar 

  11. 11.

    Kim, S. J., Devroye, N., Mitran, P., & Tarokh, V. (2011). Achievable rate regions and performance comparison of half duplex bi-directional relaying protocols. IEEE Transactions on Information Theory, 57(10), 6405–6418.

    Article  MATH  MathSciNet  Google Scholar 

  12. 12.

    Rankov, B., & Wittneben, A. (2006). Achievable rate regions for the two-way relay channel. In Proceedings of IEEE ISIT, pp. 1668–1672.

  13. 13.

    Nam, W., Chung, S. Y., & Lee, Y. H. (2010). Capacity of the Gaussian two-way relay channel to within 1/2 bit. IEEE Transactions on Information Theory, 56(11), 5488–5494.

    Article  Google Scholar 

  14. 14.

    Chen, Z., Xia, B., & Liu, H. (2014). Wireless information and power transfer in two-way amplify-and-forward relaying channels. In Proceedigs of IEEE global conference on signal and information processing (GlobalSIP), Atlanta, GA, USA, pp. 168–172.

  15. 15.

    Liu, Y., Wang, L., Elkashlan, M., Duong, T. Q., & Nallanathan, A. (2014). Two-way relaying networks with wireless power transfer: Policies design and throughput analysis. In Proceedings of IEEE global communication conference. Austin, TX, USA, pp. 4030–4035

  16. 16.

    Fang, Z., Yuan, X., & Wang, X. (2015). Distributed energy beamforming for simultaneous wireless information and power transfer in the two-way relay channel. IEEE Signal Processing Letters, 22(6), 656–660.

    Article  Google Scholar 

  17. 17.

    Kaya, T., Varan, B., & Yener, A. (2013). Energy harvesting two-way half-duplex relay channel with decode-and-forward relaying: Optimum power policies. In Proceedings of 18th IEEE international conference on digital signal processing (DSP’13), pp. 1–6.

  18. 18.

    Tutuncuoglu, K., Varan, B., & Yener, A. (2013). Optimum transmission policies for energy harvesting two-way relay channels. In Proceedings of IEEE international conference on communicatins workshop (ICC’13), Budapest, Hungary, pp. 1–5.

  19. 19.

    Wang, Z., Chen, Z., Yao, Y., Xia, B., & Liu, H. (2014). Wireless energy harvesting and information transfer in cognitive two-way relay networks. In Proceedings of IEEE Global Communications Conference (pp. 3465–3470).

  20. 20.

    Gradshteyn, I. S., & Ryzhik, I. M. (1980). Table of integrals, series, and products (4th ed.). Cambridge: Academic Press, Inc.

    MATH  Google Scholar 

Download references


This research is funded by Foundation for Science and Technology Development of Ton Duc Thang University (FOSTECT), website:, under Grant FOSTECT.2016.BR.21.

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Correspondence to Dinh-Thuan Do.



A. Proof of Proposition 1

First, the coming up proposition 1 is established to derive the outage probability and then the output SNRs at A and B for 2TS, 3TS (in case of EH and Ideal EH) is rewritten by

$$\begin{aligned} Z = \frac{{{Q_1}XY}}{{{Q_2}X + {Q_3}}}, \end{aligned}$$

where variables X and Y are \({\left| {{h_A}} \right| ^2}\) and \({\left| {{h_B}} \right| ^2}\). Constant \(Q_1^{Non,uTS} \ge 0\), \(Q_2^{Non,uTS} \ge 0\) and \(Q_3^{Non,uTS} \ge 0\) are distinguished factors from X and Y. We have

$$\begin{aligned} {P_{out}}= & {} {P_r}\left( {\frac{{{Q_1}XY}}{{{Q_2}X + {Q_3}}}< {\gamma _0}} \right) = {P_r}\left( {X< \frac{{{\gamma _0}{Q_3}}}{{{Q_1}Y - {\gamma _0}{Q_2}}}} \right) {1_{Y> \frac{{{\gamma _0}{Q_2}}}{{{Q_1}}}}}\nonumber \\&+ {P_r}\left( {X > \frac{{{\gamma _0}{Q_3}}}{{{Q_1}Y - {\gamma _0}{Q_2}}}} \right) {1_{Y < \frac{{{\gamma _0}{Q_2}}}{{{Q_1}}}}}, \end{aligned}$$

where \({\gamma _0} = R_{0,i}^{uTS}\) and \({1_{Y < \frac{{{\gamma _0}{Q_2}}}{{{Q_1}}}}}\):\({P_r}\left( {X > \frac{{{\gamma _0}{Q_3}}}{{{Q_1}Y - {\gamma _0}{Q_2}}}} \right) = 1\) because \({Q_1}Y - {\gamma _0}{Q_2}\) is a negative number and the probability of X is always 1, since X is a positive number. \({P_{out}}\) is given by

$$\begin{aligned} {P_{out}}= & {} \int \limits _0^{{\gamma _0}{Q_2}/{Q_1}} {{f_{{{\left| {{h_B}} \right| }^2}}}\left( z \right) } dz \qquad + \int \limits _{{\gamma _0}{Q_2}/{Q_1}}^\infty {{f_{{{\left| {{h_B}} \right| }^2}}}\left( z \right) } Pr\left( {X < \frac{{{\gamma _0}{Q_3}}}{{{Q_1}z - {\gamma _0}{Q_2}}}} \right) dz \nonumber \\= & {} 1 - \frac{1}{{{\varOmega _B}}}\int \limits _{{\gamma _0}{Q_2}/{Q_1}}^\infty {{e^{ - \left( {\frac{z}{{{\varOmega _B}}} + \frac{{{\gamma _0}{Q_3}}}{{\left( {{Q_1}z - {\gamma _0}{Q_2}} \right) {\varOmega _A}}}} \right) }}} dz . \end{aligned}$$

The cumulative distribution function (CDF) of the exponential random variable is denoted by \({\left| {{h_A}} \right| ^2}\) and we have \(P(X < z) = 1 - {e^{ - z/{\varOmega _A}}}\) and the average of the exponential random variable \({\left| {{h_B}} \right| ^2}\) is designated by the probability density function (PDF) of exponential random variable \({f_{{{\left| {{h_B}} \right| }^2}}}\left( z \right) \buildrel \varDelta \over = \frac{1}{{{\varOmega _B}}}{e^{ - \frac{z}{{{\varOmega _B}}}}}\). The new integration is established: \(x \buildrel \varDelta \over = {Q_1}z - {\gamma _0}{Q_2}\)

$$\begin{aligned} \begin{array}{c} {P_{out}} = 1 - \frac{1}{{{\varOmega _B}}}\int \limits _0^\infty {{e^{ - \left( {\frac{{x + {\gamma _0}{Q_2}}}{{{Q_1}{\varOmega _B}}} + \frac{{{\gamma _0}{Q_3}}}{{x{\varOmega _A}}}} \right) }}} dx = 1 - \frac{{{e^{ - \left( {\frac{{{\gamma _0}{Q_2}}}{{{Q_1}{\varOmega _B}}}} \right) }}}}{{{\varOmega _B}}}\int \limits _0^\infty {{e^{ - \left( {\frac{x}{{{Q_1}{\varOmega _B}}} + \frac{{{\gamma _0}{Q_3}}}{{x{\varOmega _A}}}} \right) }}} dx, \end{array} \end{aligned}$$

To find closed-form expression of this outage performance it need be solve the intergral function by applying \(\int \limits _0^\infty {{e^{ - \frac{\delta }{{4x}} - \lambda x}}} dx = \sqrt{\frac{\delta }{\lambda }} {K_1}\left( {\sqrt{\delta \lambda } } \right)\) thanks to formula ([20], 3.324.1), in which \({K_1}(.)\) is the modified Bessel function of the second kind. Hence, the cumulative density function (CDF) of Z is computed by

$$\begin{aligned} \begin{array}{c} {F_{{\gamma _A}}}\left( {{\gamma _0}} \right) \approx 1 - \exp \left( { - \frac{{{Q_2}{\gamma _0}}}{{{Q_1}{\varOmega _B}}}} \right) \sqrt{\frac{{\left( {4{Q_3}} \right) {\gamma _0}}}{{{Q_1}\left( {{\varOmega _A}{\varOmega _B}} \right) }}} {K_1}\left( {\sqrt{\frac{{\left( {4{Q_3}} \right) {\gamma _0}}}{{{Q_1}\left( {{\varOmega _A}{\varOmega _B}} \right) }}} } \right) , \end{array} \end{aligned}$$

where the average of the exponential random variable \({\left| {{h_A}} \right| ^2}\) is characterized by \({\varOmega _A}\) and \({\left| {{h_B}} \right| ^2}\) is characterized by \({\varOmega _B}\). This ends the proof for Proposition 1.

B. Proof of Proposition 2

In terms of non-EH, a general form for the received SNR gain is given by

$$\begin{aligned} Z = \frac{{{Q_1}XY}}{{{Q_2}X + {Q_3}Y}}. \end{aligned}$$

Based on the proof of Proposition 1, we have

$$\begin{aligned} {P_{out}}= \,& {P_r}\left( {\frac{{{Q_1}XY}}{{{Q_2}X + {Q_3}Y}}< {\gamma _0}} \right) = {P_r}\left( {X< \frac{{{\gamma _0}{Q_3}Y}}{{{Q_1}Y - {\gamma _0}{Q_2}}}} \right) {1_{Y> \frac{{{\gamma _0}{Q_2}}}{{{Q_1}}}}}\nonumber \\&+ {P_r}\left( {X > \frac{{{\gamma _0}{Q_3}Y}}{{{Q_1}Y - {\gamma _0}{Q_2}}}} \right) {1_{Y < \frac{{{\gamma _0}{Q_2}}}{{{Q_1}}}}}. \end{aligned}$$

The \(P_{out}\) is given by

$$\begin{aligned} {P_{out}}= & {} \int \limits _0^{{\gamma _0}{Q_2}/{Q_1}} {{f_{{{\left| {{h_B}} \right| }^2}}}\left( z \right) } dz + \int \limits _{{\gamma _0}{Q_2}/{Q_1}}^\infty {{f_{{{\left| {{h_B}} \right| }^2}}}\left( z \right) } p\left( {X < \frac{{{\gamma _0}{Q_3}z}}{{{Q_1}z - {\gamma _0}{Q_2}}}} \right) dz\nonumber \\= & {} 1 - \frac{1}{{{\varOmega _B}}}\int \limits _{{\gamma _0}{Q_2}/{Q_1}}^\infty {{e^{ - \left( {\frac{z}{{{\varOmega _B}}} + \frac{{{\gamma _0}{Q_3}z}}{{\left( {{Q_1}z - {\gamma _0}{Q_2}} \right) {\varOmega _A}}}} \right) }}} dz. \end{aligned}$$

Then, the CDF of Z is computed by

$$\begin{aligned} {F_{A,{\gamma _0}}}\left( {{\gamma _0}} \right) = 1 - \exp \left( { - \frac{{{\gamma _0}{Q_2}}}{{{\varOmega _B}{Q_1}}} - \frac{{{\gamma _0}{Q_3}}}{{{\varOmega _A}{Q_1}}}} \right) \sqrt{\frac{{4{{\left( {{\gamma _0}} \right) }^2}{Q_2}{Q_3}}}{{{Q_1}^2{\varOmega _B}{\varOmega _A}}}} {K_1}\left( {\sqrt{\frac{{4{{\left( {{\gamma _0}} \right) }^2}{Q_2}{Q_3}}}{{{Q_1}^2{\varOmega _B}{\varOmega _A}}}} } \right) \end{aligned}$$

This ends the proof for Proposition 2.

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Nguyen, HS., Do, DT., Bui, AH. et al. Self-Powered Wireless Two-Way Relaying Networks: Model and Throughput Performance with Three Practical Schemes. Wireless Pers Commun 97, 613–631 (2017).

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  • Two-way
  • Amplify-and-forward
  • Energy harvesting
  • Throughput