Abstract
In this paper, the transmission of confidential messages through single-input multiple-output (SIMO) independent and identically generalized-K (K G) fading channels is considered, where the eavesdropper overhears the transmission from the transmitter to the receiver. Both the receiver and the eavesdropper are equipped with multiple antennas, and both active and passive eavesdroppings are considered where the channel state information of the eavesdropper’s channel is or is not available at the transmitter. The secrecy performance of SIMO K G systems is investigated. Analytical expressions for secrecy outage probability and average secrecy capacity of SIMO systems are derived via two different methods, in which K G distribution is approximated by the Gamma and mixture Gamma distributions, respectively. Numerical results are presented and verified via the Monte-Carlo simulation.
Similar content being viewed by others
References
Abdi, A., Kaveh, M., 1998. K distribution: an appropriate substitute for Rayleigh-lognormal distribution in fading-shadowing wireless channels. Electron. Lett., 34(9): 851–852. http://dx.doi.org/10.1049/el:19980625
Abramowitz, M., Stegun, I.A., 1972. Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables. Dover Press, New York.
Adamchik, V.S., Marichev, O.I., 1990. The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system. Proc. Int. Symp. on Symbolic and Algebraic Computation, p.212–224. http://dx.doi.org/10.1145/96877.96930
Al-Ahmadi, S., Yanikomeroglu, H., 2010a. On the approximation of the generalized-K distribution by a Gamma distribution for modeling composite fading channels. IEEE Trans. Wirel. Commun., 9(2): 706–713. http://dx.doi.org/10.1109/TWC.2010.02.081266
Al-Ahmadi, S., Yanikomeroglu, H., 2010b. 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. Proc. IEEE Wireless Communications and Networking Conf., p.1–6. http://dx.doi.org/10.1109/WCNC.2010.5506178
Ansari, I.S., Al-Ahmadi, S., Yilmaz, F., et al., 2011. A new formula for the BER of binary modulations with dualbranch selection over generalized-K composite fading channels. IEEE Trans. Commun., 59(10): 2654–2658. http://dx.doi.org/10.1109/TCOMM.2011.063011.100303A
Ata, S.Ö., Altunbas, I., 2015. Relay antenna selection for V2V communications using PLNC over cascaded fading channels. Proc. Int. Wireless Communications and Mobile Computing Conf., p.1336–1340. http://dx.doi.org/10.1109/IWCMC.2015.7289276
Atapattu, S., Tellambura, C., Jiang, H., 2011. A mixture Gamma distribution to model the SNR of wireless channels. IEEE Trans. Wirel. Commun., 10(12): 4193–4203. http://dx.doi.org/10.1109/TWC.2011.111210.102115
Bithas, P.S., Rontogiannis, A.A., 2015. Mobile communication systems in the presence of fading/shadowing, noise and interference. IEEE Trans. Commun., 63(3): 724–737. http://dx.doi.org/10.1109/TCOMM.2015.2390625
Bithas, P.S., Sagias, N.C., Mathiopoulos, P.T., et al., 2006. On the performance analysis of digital communications over generalized-K fading channels. IEEE Commun. Lett., 10(5): 353–355. http://dx.doi.org/10.1109/LCOMM.2006.1633320
Bloch, M., Barros, J., Rodrigues, M.R.D., et al., 2008. Wireless information-theoretic security. IEEE Trans. Inform. Theory, 54(6): 2515–2534. http://dx.doi.org/10.1109/TIT.2008.921908
Chatzidiamantis, N.D., Karagiannidis, G.K., 2011. On the distribution of the sum of Gamma-Gamma variates and applications in RF and optical wireless communications. IEEE Trans. Commun., 59(5): 1298–1308. http://dx.doi.org/10.1109/TCOMM.2011.020811.090205
Cheng, W., 2013. Performance analysis and comparison of dual-hop amplify-and-forward relaying over mixture Gamma and generalized-K fading channels. Proc. Int. Conf. on Wireless Communications & Signal Processing, p.1–6. http://dx.doi.org/10.1109/WCSP.2013.6677092
Gradshteyn, I., Ryzhik, I., 2007. Table of Integrals, Series, and Products (7th Ed.) Academic Press, USA.
Jiang, Y., Zhu, J., Zou, Y., 2015. Secrecy outage analysis of multi-user multi-eavesdropper cellular networks in the face of cochannel interference. Dig. Commun. Netw., 1(1): 68–74. http://dx.doi.org/10.1016/j.dcan.2015.02.002
Jung, J., Lee, S.R., Park, H., et al., 2013. Diversity analysis over composite fading channels using a mixture Gamma distribution. Proc. IEEE Int. Conf. on Communications, p.5824–5828. http://dx.doi.org/10.1109/ICC.2013.6655526
Jung, J., Lee, S.R., Park, H., et al., 2014. Capacity and error probability analysis of diversity reception schemes over generalized-K fading channels using a mixture Gamma distribution. IEEE Trans. Wirel. Commun., 13(9): 4721–4730. http://dx.doi.org/10.1109/TWC.2014.2331691
Laourine, A., Alouini, M.S., Affes, S., et al., 2009. On the performance analysis of composite multipath/ shadowing channels using the G-distribution. IEEE Trans. Commun., 57(4): 1162–1170. http://dx.doi.org/10.1109/TCOMM.2009.04.070258
Lei, H., Gao, C., Ansari, I., et al., 2015a. On physical layer security over SIMO generalized-K fading channels. IEEE Trans. Veh. Technol., 65(9): 7780–7785. http://dx.doi.org/10.1109/TVT.2015.2496353
Lei, H., Gao, C., Guo, Y., et al., 2015b. On physical layer security over generalized Gamma fading channels. IEEE Commun. Lett., 19(7): 1257–1260. http://dx.doi.org/10.1109/LCOMM.2015.2426171
Lei, H., Zhang, H., Ansari, I., et al., 2016a. Performance analysis of physical layer security over generalized-K fading channels using a mixture Gamma distribution. IEEE Commun. Lett., 20(2): 408–411. http://dx.doi.org/10.1109/LCOMM.2015.2504580
Lei, H., Zhang, H., Ansari, I., et al., 2016b. Secrecy outage analysis for SIMO underlay cognitive radio networks over generalized-K fading channels. IEEE Signal Process. Lett., 23(8): 1106–1110. http://dx.doi.org/10.1109/LSP.2016.2587323
Liu, H., Zhao, H., Jiang, H., et al., 2016. Physical-layer secrecy outage of spectrum sharing CR systems over fading channels. Sci. China Inform. Sci., 59:102308. http://dx.doi.org/10.1007/s11432-015-5451-2
Liu, X., 2013. Probability of strictly positive secrecy capacity of the Weibull fading channel. Proc. IEEE Global Communications Conf., p.659–664. http://dx.doi.org/10.1109/GLOCOM.2013.6831147
Pan, G., Tang, C., Zhang, X., et al., 2016. Physical-layer security over non-small-scale fading channels. IEEE Trans. Veh. Technol., 65(3): 1326–1339. http://dx.doi.org/10.1109/TVT.2015.2412140
Prudnikov, A.P., Brychkov, Y.A., Marichev, O.I., 1992. Integrals and Series, Volume 2: Special Functions. Gordon and Breach Science Publishers, New York.
Shankar, P.M., 2004. Error rates in generalized shadowed fading channels. Wirel. Pers. Commun., 28(3): 233–238. http://dx.doi.org/10.1023/B:wire.0000032253.68423.86
Stuber, G.L., 2011. Principles of Mobile Communication. Springer Science & Business Media, New York.
Wang, L., Elkashlan, M., Huang, J., et al., 2014. Secure transmission with antenna selection in MIMO Nakagami-m fading channels. IEEE Trans. Wirel. Commun., 13(11): 6054–6067. http://dx.doi.org/10.1109/TWC.2014.2359877
Yadav, S., Upadhyay, P.K., 2013. Performance analysis of two-way A Frelaying systems over cascaded generalized-K fading channels. Proc. National Conf. on Communications, p.1–5. http://dx.doi.org/10.1109/NCC.2013.6487901
Yang, N., Wang, L., Geraci, G., et al., 2015. Safeguarding 5G wireless communication networks using physical layer security. IEEE Commun. Mag., 53(4): 20–27. http://dx.doi.org/10.1109/MCOM.2015.7081071
Zou, Y., Wang, X., Shen, W., 2013. Optimal relay selection for physical-layer security in cooperative wireless networks.
IEEE J. Sel. Areas Commun., 31(10): 2099–2111. http://dx.doi.org/10.1109/JSAC.2013.131011
Zou, Y., Champagne, B., Zhu, W.P., et al., 2015a. Relayselection improves the security-reliability trade-off in cognitive radio systems. IEEE Trans. Commun., 63(1): 215–228. http://dx.doi.org/10.1109/TCOMM.2014.2377239
Zou, Y., Zhu, J., Wang, X., et al., 2015b. Improving physicallayer security in wireless communications using diversity techniques. IEEE Netw., 29(1): 42–48. http://dx.doi.org/10.1109/MNET.2015.7018202
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported in part by the National Natural Science Foundation of China (Nos. 61471076 and 61401372), the Program for Changjiang Scholars and Innovative Research Team in University, China (No. IRT1299), the Natural Science Foundation Project of CQ CSTC (No. cstc2013jcyjA40040), the Project of Fundamental and Frontier Research Plan of Chongqing, China (No. cstc2015jcyjBX0085), the Special Fund of Chongqing Key Laboratory (CSTC), the Scientific and Technological Research Program of Chongqing Municipal Education Commission, China (No. KJ1600413), the Research Fund for the Doctoral Program of Higher Education of China (No. 20130182120017), and the Fundamental Research Funds for the Central Universities, China (No. XDJK2015B023). Parts of this publication, specifically Sections 1, 3, and 4, were made possible by PDRA (Post- Doctoral Research Award) from the Qatar National Research Fund (QNRF) (a member of Qatar Foundation (QF)), Qatar (No. PDRA1-1227-13029)
A preliminary version was presented at the 78th IEEE Vehicular Technology Conference, Montréal, Canada, Sept. 18–21, 2016
ORCID: Chao GAO, http://orcid.org/0000-0002-7256-7167
Rights and permissions
About this article
Cite this article
Lei, Hj., Ansari, I.S., Gao, C. et al. Secrecy performance analysis of single-input multiple-output generalized-K fading channels. Frontiers Inf Technol Electronic Eng 17, 1074–1084 (2016). https://doi.org/10.1631/FITEE.1601070
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/FITEE.1601070
Keywords
- Physical-layer security
- Generalized-K fading
- Average secrecy capacity
- Secrecy outage probability
- Mixture Gamma distribution