Energy harvesting with adaptive transmit power for cognitive radio networks


This article derives the packet error probability (PEP) of different relay selection techniques for cognitive radio networks (CRN). The power of secondary source and relays is adaptive to not cause high interference to primary receiver \(P_R\). Secondary nodes harvest energy from radio frequency signals to be able to communicate. CRN with secondary nodes transmitting with adaptive power was already studied in the literature. However, in all previous studies, secondary nodes use their own batteries to transmit. The main motivation of our paper is to study CRN with energy harvesting and adaptive transmit power (ATP). We derive new expressions of PEP and throughput for CRN with energy harvesting and ATP. Our results are valid for opportunistic relaying, partial relay selection and reactive relay selection. Our main contribution is to optimize harvesting duration to maximize the system throughput.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7


  1. 1.

    Amini, M. R., Mahdavi, M., & Omidi, M. J. (2018). Discrete-time Markov chain analysis of energy efficiency in a CR network regarding primary and secondary traffic with primary user returns. IEEE Access, 6, 22305–22323.

    Article  Google Scholar 

  2. 2.

    Amini, M. R., Mahdavi, M., & Omidi, M. J. (2018). Maximizing dynamic access energy efficiency in multiuser CRNs with primary user return. IEEE Systems Journal, pp. 1–12

  3. 3.

    Haykin, S. (2005). Cognitive radio: Brain-empowered wireless communications. IEEE Journal on Selected Areas in Communications, 23, 201–220.

    Article  Google Scholar 

  4. 4.

    Ibrahim, N. S., Sali, A., Mohamad, M. H., & Hashim, S. J. (2015). Outage performance in relay-assisted overlay cognitive radio networks. In IEEE 12th Malaysia international conference on communications (MICC).

  5. 5.

    Zhan, J., Liu, Y., Tang, X., & Chen, Q. (2018). Relaying protocols for buffer-aided energy harvesting wireless cooperative networks. IET Networks Year, 7(3), 109–118.

    Article  Google Scholar 

  6. 6.

    Xiuping, W., Feng, Y., & Tian, Z. (2018). The DF-AF selection relay transmission based on energy harvesting. In 2018 10th international conference on measuring technology and mechatronics automation (ICMTMA) (pp. 174–177).

  7. 7.

    Nguyen, H. T., Nguyen, S. Quang, & Hwang, W.-J. (2018). Outage probability of energy harvesting relay systems under unreliable backhaul connections. In 2018 2nd international conference on recent advances in signal processing, telecommunications and computing (SigTelCom) (pp: 19–23).

  8. 8.

    Qiu, C., Hu, Y., & Chen, Y. (2018). Lyapunov optimized cooperative communications with stochastic energy harvesting relay. IEEE Internet of Things Journal, 5(2), 1323–1333.

    Article  Google Scholar 

  9. 9.

    Sui, D., Hu, F., Zhou, W., Shao, M., & Chen, M. (2018). Relay selection for radio frequency energy-harvesting wireless body area network with buffer. IEEE Internet of Things Journal, 5(2), 1100–1107.

    Article  Google Scholar 

  10. 10.

    Hoang, T. M., Tran, M., Tan, N. T., & Choi, S.-G. (2018). Analysis of partial relay selection in NOMA systems with RF energy harvesting. In 2018 2nd international conference on recent advances in signal processing, telecommunications and computing (SigTelCom) (pp. 13–18).

  11. 11.

    Le, Q. N., Bao, V. N. Q., & An, B. (2018). Full-duplex distributed switch-and-stay energy harvesting selection relaying networks with imperfect CSI: Design and outage analysis. Journal of Communications and Networks, 20(1), 29–46.

    Article  Google Scholar 

  12. 12.

    Gong, J., Chen, X., & Xia, M. (2018). Transmission optimization for hybrid half/full-duplex relay with energy harvesting. IEEE Transactions on Wireless Communications, 17(5), 3046–3058.

    Article  Google Scholar 

  13. 13.

    Tang, H., Xie, X., & Chen, J. (2018). X-duplex relay with self-interference signal energy harvesting and its hybrid mode selection method. In 2018 27th wireless and optical communication conference (WOCC) (pp. 1–6).

  14. 14.

    Chiu, H.-C., & Huang, W.-J. (2018). Precoding design in two-way cooperative system with energy harvesting relay. In 2018 27th wireless and optical communication conference (WOCC) (pp. 1–5).

  15. 15.

    Gurjar, D. S., Singh, U., & Upadhyay, P. K. (2018). Energy harvesting in hybrid two-way relaying with direct link under Nakagami-m fading. In 2018 IEEE wireless communications and networking conference (WCNC) (pp. 1–6).

  16. 16.

    Singh, K., Ku, M.-L., Lin, J.-C., & Ratnarajah, T. (2018). Toward optimal power control and transfer for energy harvesting amplify-and-forward relay networks. IEEE Transactions on Wireless Communications, 17, 4971–4986.

    Article  Google Scholar 

  17. 17.

    Wu, Y., Qian, L., Huang, L., & Shen, X. (2018). Optimal relay selection and power control for energy-harvesting wireless relay networks. IEEE Transactions on Green Communications and Networking, 2(2), 471–481.

    Article  Google Scholar 

  18. 18.

    Fan, R., Atapattu, S., Chen, W., Zhang, Y., & Evans, J. (2018). Throughput maximization for multi-hop decode-and-forward relay network with wireless energy harvesting. IEEE Access, 6, 24582–24595.

    Article  Google Scholar 

  19. 19.

    Huang, Y., Wang, J., Zhang, P., & Wu, Q. (2018). Performance analysis of energy harvesting multi-antenna relay networks with different antenna selection schemes. IEEE Access, 6, 5654–5665.

    Article  Google Scholar 

  20. 20.

    Babaei, M., Aygölü, Ü., & Basar, E. (2018). BER analysis of dual-hop relaying with energy harvesting in Nakagami-m fading channel. IEEE Transactions on Wireless Communications, 99, 1–1.

    Google Scholar 

  21. 21.

    Kalluri, T., Peer, M., Bohara, V. A., da Costa, D. B., & Dias, U. S. (2018). Cooperative spectrum sharing-based relaying protocols with wireless energy harvesting cognitive user. IET Communications, 12(7), 838–847. IET Journals and Magazines.

    Article  Google Scholar 

  22. 22.

    Xie, D., Lai, X., Lei, X., & Fan, L. (2018). Cognitive multiuser energy harvesting decode-and-forward relaying system with direct links. IEEE Access, 6, 5596–5606.

    Article  Google Scholar 

  23. 23.

    Yan, Z., Chen, S., Zhang, X., & Liu, H.-Li. (2018). Outage performance analysis of wireless energy harvesting relay-assisted random underlay cognitive networks. IEEE Internet of Things Journal pp. 1–1.

  24. 24.

    Nhat, T. T., Duy, T. T., Bao, V. N. Q. (2018). Performance evaluation of cooperative relay networks with one full-energy relay and one energy harvesting relay. In 2018 2nd international conference on recent advances in signal processing, telecommunications and computing (SigTelCom) (pp. 7–12).

  25. 25.

    Vo, V. N., Nguyen, T. G., So-In, C., Baig, Z. A., & Sanguanpong, S. (2018). Secrecy outage performance analysis for energy harvesting sensor networks with a jammer using relay selection strategy. IEEE Access, 6, 23406–23419.

    Article  Google Scholar 

  26. 26.

    Behdad, Z., Mahdavi, M., & Razmi, N. (2018). A new relay policy in RF energy harvesting for IoT networks-a cooperative network approach. IEEE Internet of Things Journal, (Early Access) pp. 1–1.

  27. 27.

    Yao, R., Lu, Y., Tsiftsis, T. A., Qi, N., Mekkawy, T., & Xu, F. (2018). Secrecy rate-optimum energy splitting for an untrusted and energy harvesting relay network. IEEE Access, 6, 19238–19246.

    Article  Google Scholar 

  28. 28.

    Yin, C., Nguyen, H. T., Kundu, C., Kaleem, Z., Garcia-Palacios, E., & Duong, T. Q. (2018). Secure energy harvesting relay networks with unreliable backhaul connections. IEEE Access, 6, 12074–12084.

    Article  Google Scholar 

  29. 29.

    Lei, H., Xu, M., Ansari, I. S., Pan, G., Qaraqe, K. A., & Alouini, M.-S. (2017). On secure underlay MIMO cognitive radio networks with energy harvesting and transmit antenna selection. IEEE Transactions on Green Communications and Networking, (Early Access) pp. 192–203.

  30. 30.

    Ho-Van, K., & Do-Dac, T. (2018). Performance analysis of jamming technique in energy harvesting cognitive radio networks. Springer Telecommunication Systems, Published online 7 June 2018.

  31. 31.

    Huu, P. N., & Ho-Van, K. (2018). Bidirectional relaying with energy harvesting capable relay: Outage analysis for Nakagami-m fading. Springer Telecommunication Systems, Published online 13 March 2018.

  32. 32.

    Bayrakdar, M. E., & Calhan, A. (2018). Artificial bee colony-based spectrum handoff algorithm in wireless cognitive radio networks. International Journal of Communication Systems, 31(5), e3495.

    Article  Google Scholar 

  33. 33.

    Bayrakdar, M. E., & Calhan, A. (2017). Non-preemptive queueing model of spectrum handoff scheme based on prioritized data traffic in cognitive wireless networks. ETRI Journal, 39(4), 558–569.

    Article  Google Scholar 

  34. 34.

    Hasna, M. O., & Alouini, M.-S. (2004). Harmonic mean and end-to-end performance of transmission systems with relays. IEEE Transactions on Communications, 52(1), 130–135.

    Article  Google Scholar 

  35. 35.

    Krikidis, I., Thompson, J., McLaughlin, S., & Goertz, N. (2008). Amplify and for- ward with partial relay selection. IEEE Communications Letters, 12(4), 237–238.

    Article  Google Scholar 

  36. 36.

    Boujemaa, H. (2010). Exact symbol error probability of cooperative systems with partial relay selection. European Transactions on Telecom, 21, 79–85.

    Google Scholar 

  37. 37.

    Hussain, S. I., Alouini, M. S., Qaraqe, K., & Hasna, M. (2012). Reactive relay selection in underlay cognitive networks with fixed gain relays. In IEEE ICC.

  38. 38.

    Xi, Y., Burr, A., Wei, J. B., & Grace, D. (2011). A general upper bound to evaluate packet error rate over quasi-static fading channels. IEEE Transactions on Wireless Communications, 10(5), 1373–1377.

    Article  Google Scholar 

  39. 39.

    Gradshteyn, I. S., & Ryzhik, I. M. (1994). Table of integrals, series and products (5th ed.). San Diego, CA: Academic.

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Nadhir Ben Halima.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Appendix A

The CDF of \(E_S\) is expressed as

$$\begin{aligned} F_{E_S}(x)= & {} P(E_{S}<x)\nonumber \\= & {} P\left( \min \left( E_{available},\frac{I}{|g_{SP_{R}}|^{2}}\right) <x\right) \nonumber \\= & {} 1-P\left( \min \left( \mu |g_{AS}|^2,\frac{I}{|g_{SP_{R}}|^{2}}\right) >x\right) , \end{aligned}$$

Assuming that \(g_{AS}\) and \(g_{SP_{R}}\) are independent, we deduce

$$\begin{aligned} F_{E_S}(x)= & {} 1-P(\mu |g_{AS}|^2>x)P\left( \frac{I}{|g_{SP_{R}}|^{2}}>x\right) \nonumber \\= & {} 1-P(\mu |g_{AS}|^2>x)P\left( |g_{SP_{R}}|^{2}<\frac{I}{x}\right) , \end{aligned}$$

\(|g_{AS}|^2\) and \(|g_{SP_{R}}|^{2}\) follow an exponential distribution with mean \(E(|g_{AS}|^2)=\frac{1}{\alpha _{AS}}\) and \(E(|g_{SP_R}|^2)=\frac{1}{\alpha _{SP_R}}\). Therefore, we have

$$\begin{aligned} F_{E_S}(x)=1-\alpha _{AS}e^{-\alpha _{AS}\frac{x}{\mu }} \left[ 1-\alpha _{SP_R}e^{-\alpha _{SP_R}\frac{I}{x}}\right] , \end{aligned}$$

Appendix B

The SNR at \(R_k\) is the product of two random variables \(E_S\) and \(\frac{|h_{SR_k}|^2}{N_0}\).

$$\begin{aligned} \gamma _{SR_{k}}=E_S \frac{|h_{SR_k}|^2}{N_0}, \end{aligned}$$

Let \(X=\frac{|h_{SR_k}|^2}{N_0}\), the CDF of SNR at relay \(R_k\) is given by

$$\begin{aligned} F_{\gamma _{SR_{k}}}(x)= & {} P(\gamma _{SR_{k}} \le x)=\int _0^{+\infty }f_X(v)P\nonumber \\&\times \left( E_S\le \frac{x}{v}\right) dv=\int _0^{+\infty }f_X(v)F_{E_S}\left( \frac{x}{v}\right) dv,\nonumber \\ \end{aligned}$$

where \(f_X(v)\) is the PDF of \(X=\frac{|h_{SR_k}|^2}{N_0}\):

$$\begin{aligned} f_X(v)=N_0 \alpha _{SR_k} e^{-N_0 \alpha _{SR_k}v}, \forall v \ge 0, \end{aligned}$$

where \(\alpha _{SR_k}=\frac{1}{E(|g_{SR_k}|^2)}\).

Using the expression of CDF of \(E_S\) provided in “Appendix A”, we can write

$$\begin{aligned} F_{\gamma _{SR_{k}}}(x)= & {} 1-\int _0^{+\infty }\alpha _{AS}e^{-\alpha _{AS}\frac{x}{v\mu }}\nonumber \\&\times \left[ 1-\alpha _{SP_R}e^{-\alpha _{SP_R}\frac{Iv}{x}}\right] f_X(v)dv, \end{aligned}$$

We deduce

$$\begin{aligned}&F_{\gamma _{SR_{k}}}(x)=1-N_0 \alpha _{SR_k}\alpha _{AS}\int _0^{+\infty }e^{-\alpha _{AS}\frac{x}{v\mu }} e^{-N_0 \alpha _{SR_k}v} dv\nonumber \\&\quad +\,N_0 \alpha _{SR_k}\alpha _{SP_R}\alpha _{AS}\nonumber \\&\quad \times \int _0^{+\infty }e^{-\alpha _{AS}\frac{x}{v\mu }}e^{-\alpha _{SP_R}\frac{Iv}{x}}e^{-N_0 \alpha _{SR_k}v} dv, \end{aligned}$$

We use the following result [39]

$$\begin{aligned} \int _0^{+\infty }e^{-ax-\frac{b}{x}}dx=2\sqrt{\frac{b}{a}}K_1(2\sqrt{ba}), \forall a>0,b>0 \end{aligned}$$

to write the CDF of SNR as

$$\begin{aligned}&F_{\gamma _{SR_{k}}}(x)=1-2\sqrt{\frac{\alpha _{AS}x}{\mu N_0\alpha _{SR_k}}}K_1\left( 2\sqrt{N_0\alpha _{SR_k}\frac{\alpha _{AS}x}{\mu }}\right) \nonumber \\&\quad +\,2N_0 \alpha _{SR_k}\alpha _{SP_R}\alpha _{AS} \sqrt{\frac{\alpha _{AS}x^2}{\mu (N_0\alpha _{SR_k}x+\alpha _{SP_R}I)}}\nonumber \\&\quad K_1\left( 2\sqrt{N_0\alpha _{SR_k}\alpha _{AS}\frac{x}{\mu }+\frac{\alpha _{AS}}{\mu }\alpha _{SP_R}I}\right) \end{aligned}$$

Appendix C

Using (9) and (10), we have

$$\begin{aligned}&F_{\gamma _{SR_k}}(x)=1-2e^{N_0\frac{\alpha _{P_TR_k}}{E_{P_T}}}\frac{\alpha _{P_TR_k}}{E_{P_T}}\sqrt{\frac{\alpha _{AS}x}{\mu \alpha _{SR_k}}}\int _{N_0}^{+\infty }\nonumber \\&\quad \sqrt{u}e^{-u\frac{\alpha _{P_TR_k}}{E_{P_T}}} K_1\left( 2\sqrt{\alpha _{SR_k}\frac{\alpha _{AS}ux}{\mu }}\right) du,\nonumber \\&\quad +\,2e^{N_0\frac{\alpha _{P_TR_k}}{E_{P_T}}}\frac{\alpha _{P_TR_k}}{E_{P_T}}\alpha _{SR_k}\alpha _{SP_R}\alpha _{AS} x\nonumber \\&\quad \int _{N_0}^{+\infty }\sqrt{\frac{\alpha _{AS}u^2}{\mu (\alpha _{SR_k}xu+\alpha _{SP_R}I)}}e^{-u\frac{\alpha _{P_TR_k}}{E_{P_T}}}\nonumber \\&\quad \times \, K_1\left( 2\sqrt{\alpha _{SR_k}\alpha _{AS}\frac{ux}{\mu }+\frac{\alpha _{AS}}{\mu }\alpha _{SP_R}I}\right) du \end{aligned}$$

We use the following result [39]

$$\begin{aligned} \int _{0}^{+\infty }\sqrt{y}K_{1}(2\beta \sqrt{y})e^{-\alpha _{3}y}dy=\frac{ e^{\frac{\beta ^{2}}{2\alpha _{3}}}}{2\beta \alpha _{3}}W_{-1,0.5}\left( \frac{ \beta ^{2}}{\alpha _{3}}\right) ,\nonumber \\ \end{aligned}$$

where \(W_{\mu ,\nu }(x)\) is the Whittaker function.

$$\begin{aligned}&F_{\gamma _{SR_k}}(x)=1+2e^{N_0\frac{\alpha _{P_TR_k}}{E_{P_T}}}\frac{\alpha _{P_TR_k}}{E_{P_T}}\sqrt{\frac{\alpha _{AS}x}{\mu \alpha _{SR_k}}}\int _{0}^{N_0}\nonumber \\&\quad \sqrt{u}e^{-u\frac{\alpha _{P_TR_k}}{E_{P_T}}}K_1\left( 2\sqrt{\alpha _{SR_k}\frac{\alpha _{AS}ux}{\mu }}\right) du,\nonumber \\&\quad -\,W_{-1,0.5}\left( \frac{\alpha _{SR_k}x\alpha _{AS}E_{P_T}}{\mu \alpha _{P_TR_k}}\right) e^{N_0\frac{\alpha _{P_TR_k}}{E_{P_T}}}e^{\frac{\alpha _{SR_k}x\alpha _{AS}E_{P_T}}{2\mu \alpha _{P_TR_k}}}\nonumber \\&\quad \times \frac{1}{\alpha _{SR_k}}+\,2e^{N_0\frac{\alpha _{P_TR_k}}{E_{P_T}}}\frac{\alpha _{P_TR_k}}{E_{P_T}}\alpha _{SR_k}\alpha _{SP_R}\alpha _{AS} x\nonumber \\&\quad \int _{N_0}^{+\infty }\sqrt{\frac{\alpha _{AS}u^2}{\mu (\alpha _{SR_k}xu+\alpha _{SP_R}I)}}e^{-u\frac{\alpha _{P_TR_k}}{E_{P_T}}}\nonumber \\&\quad \times \, K_1\left( 2\sqrt{\alpha _{SR_k}\alpha _{AS}\frac{ux}{\mu }+\frac{\alpha _{AS}}{\mu }\alpha _{SP_R}I}\right) du \end{aligned}$$

where the two integrals are evaluated numerically using MATLAB.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Halima, N.B., Boujemâa, H. Energy harvesting with adaptive transmit power for cognitive radio networks. Telecommun Syst 72, 41–52 (2019).

Download citation


  • CRN
  • Energy harvesting
  • Adaptive power