First and Second Order Characteristics of a Wireless Three-hop Relay Channel with the Presence of Rayleigh Fading

• Autorzy: Krstic Dragana , Nikolic Petar , Popovic Zoran , Stefanovic Mihajlo

Identyfikatory

DOI

10.26636/jtit.2020.144020

• Języki publikacji: EN

Abstrakty

EN

In this paper, a wireless three-hop relay communication system operating in a Rayleigh multipath fading environment is analyzed. The output signal from such a system is a product of signal envelopes from all sections, meaning that it is actually a product of three random variables (RVs) with Rayleigh distribution. We considered here the first-order characteristics: probability density function (PDF), cumulative distribution function and outage probability (OP). Then, the moments and amount of fading (AoF) were derived in the closed forms. The second order characteristics we present include the following: level crossing rate (LCR) and average fade duration (AFD). A few graphs are given to show the impact of the specific parameters of the wireless three-hop relay system.

Słowa kluczowe

EN

first order performance; Rayleigh fading; second order performance; three-hop relay telecommunication systems

• Wydawca: Instytut Łączności - Państwowy Instytut Badawczy
• Czasopismo: Journal of Telecommunications and Information Technology
• Rocznik: 2020
• Tom: nr 2
• Strony: 36--44
• Opis fizyczny: Bibliogr. 56 poz., rys.

Twórcy

autor

Krstic Dragana

• Faculty of Electronic Engineering, University of Niš, Niš, Aleksandra Medvedeva 14, 18000 Niš, Serbia

autor

Nikolic Petar

• TigarTyres, Pirot, Serbia

autor

Popovic Zoran

• Higher Technical School of Professional Studies, Zvecan, Serbia

autor

Stefanovic Mihajlo

• Faculty of Electronic Engineering, University of Niš, Niš, Aleksandra Medvedeva 14, 18000 Niš, Serbia

Bibliografia

• [1] Y. Chen, G. K. Karagiannidis, H. Lu, and N. Cao, “Novel approximations to the statistics of products of independent random variables and their applications in wireless communications", IEEE Trans. on Veh. Technol., vol. 61, no. 2, pp. 443-454, 2012 (DOI: 10.1109/TVT.2011.2178441).
• [2] S. Nadarajaha and D. K. Dey, “On the product and ratio of t random variables", Appl. Methem. Lett., vol. 19, no. 1, pp. 45-55, 2006 (DOI: 10.1016/j.aml.2005.01.004).
• [3] N. Zlatanov, Z. Hadzi-Velkov, and G. K. Karagiannidis, “Level crossing rate and average fade duration of the double Nakagami-m random process and application in MIMO keyhole fading channels", IEEE Commun. Lett., vol. 12, no. 11, pp. 822-824, 2008 (DOI: 10.1109/LCOMM.2008.081058).
• [4] K. Pearson, “The problem of the random walk", Nature, vol. 72, p. 294, 1905 (DOI: 10.1038/072294b0).
• [5] J. D. Donahue, “Products and quotients of random variables and their applications", ARL 64-115 Report, The Martin Company, Denver, Colorado, July 1964 [Online]. Available: https://apps.dtic.mil/ dtic/tr/fulltext/u2/603667.pdf
• [6] M. D. Springer and W. E. Thompson, “The distribution of products of independent random variables", SIAM J. on Appl. Mathem., vol. 14, pp. 511-526, 1966 (DOI: 10.1137/0114046).
• [7] M. D. Springer and W. E. Thompson, “The distribution of products of beta, gamma and Gaussian random variables", SIAM J. on Appl. Mathem., vol. 18, pp. 721-737, 1970 (DOI: 10.1137/0118065).
• [8] Z. A. Lomnicki, “On the distribution of products of random variables", J. of the Royal Statist. Soc. Series B (Methodological), vol. 29, no. 3, pp. 513-524, 1967 (DOI: 10.1016/j.crma.2015.10.019).
• [9] A. G. Glen, L. M. Leemis, and J. H. Drew, “Computing the distribution of the product of two continuous random variables", Computat. Statist. and Data Anal., vol. 44, pp. 451-464, 2004 (DOI: 10.1016/S0167-9473(02)00234-7).
• [10] T. S. Glickman and F. Xu, “The distribution of the product of two triangular random variables", Statist. & Probab. Lett., vol. 78, no. 16, pp. 2821-2826, 2008 (DOI: 10.1016/j.spl.2008.03.031).
• [11] G. K. Karagiannidis, N. C. Sagias, and P. T. Mathiopoulos, „N*Nakagami: a novel stochastic model for cascaded fading channels", IEEE Trans. Commun., vol. 55, no. 8, pp. 1453-1458, 2007 (DOI: 10.1109/TCOMM.2007.902497).
• [12] Z. Zheng, L. Wei, J. Hamalainen, and O. Tirkkonen, “Approximation to distribution of product of random variables using orthogonal polynomials for lognormal density", IEEE Trans. Commun., vol. 16, no. 12, pp. 2028-2031, 2012 (DOI: 10.1109/LCOMM.2012.101712.122141).
• [13] E. J. Leonardo and M. D. Yacoub, “Statistics of the product of arbitrary a-m variates with applications", in in Proc. 25th Int. Symp. on Pers., Indoor and Mob. Radio Commun. PIMRC 2014, Washington, USA, 2014, pp. 73-76 (DOI: 10.1109/PIMRC.2014.7136135).
• [14] Z. Stojanac, D. Suess, and M. Kliesch, “On products of Gaussian random variables", arXiv:1711.10516 [math.PR], 2018.
• [15] N. Bhargav et al., “On the product of two к-µ random variables and its application to double and composite fading channels", IEEE Trans. on Wirel. Commun., vol. 17, pp. 2457-2470, 2018 2018 (DOI: 10.1109/TWC.2018.2796562).
• [16] D. H. Pavlovic et al., “Statistics for ratios of Rayleigh, Rician, Nakagami-m, and Weibull distributed random variables", Mathem. Problems in Engin., vol. 2013, Article ID 252804, 2013 (DOI: 10.1155/2013/252804).
• [17] S. Ahmed, L. L. Yang, and L. L. Hanzo, “Probability distributions of products of Rayleigh and Nakagami-m variables using Mellin transform", in Proc. IEEE Intern. Conf. on Commun. ICC 2011, Kyoto, Japan, 2011 (DOI: 10.1109/icc.2011.5963344).
• [18] T. Taniguchi, Y. Karasawa, and M. Tsuruta, “An analysis method of double fading MIMO channels including LOS environments", in Proc. IEEE 19th Int. Symp. on Pers., Indoor and Mob. Radio Commun., Cannes, France, 2008 (DOI:10.1109/pimrc.2008.4699512).
• [19] D. Krstic, M. Stefanovic, R. Gerov, and Z. Popovic, “Wireless relay system with two sections in к-µ short term fading channel", in Proc. 12th Int. Conf. on Wirel. and Mob. Commun. ICWMC 2016, Barcelona, Spain, 2016, pp. 110-114 [Online]. Available: https://www.academia.edu/29873047/ICWMC 2016 The Twelfth International Conference on Wireless and Mobile Communications
• [20] N. Bhargav et al., “On the product of two к-µ random variables and its application to double and composite fading channels", IEEE Trans. on Wirel. Commun., vol. 17, no. 4, pp. 2457-2470, 2018 (DOI:10.1109/twc.2018.2796562).
• [21] A. M. Magableh, T. Aldalgamouni, and N. M. Jafreh, “Capacity analysis of dual-hop wireless communication systems over к-µ fading channels", Comp. and Elec. Engin., vol. 40, no. 2, pp. 399-406, 2014 (DOI: 10.1016/j.compeleceng.2013.04.018).
• [22] T. A. Tsiftsis, G. K. Karagiannidis, and S. A. Kotsopoulos, “Dual-hop wireless communications with combined gain relays", IEE Proceedings Communications, vol. 152, no. 5, pp. 528-532, 2005 (DOI: 10.1049/ip-com:200452685).
• [23] M. Delibasic and M. Pejanovic-Djurisic, “Dual-hop amplify-andforward relay system over non-identical Ricean fading channels", Wirel. Pers. Commun., vol. 93, pp. 675-686, 2014 (DOI: 10.1007/s11277-014-2221-1).
• [24] A. M. Magableh, T. Aldalgamouni, S. Mater, and O. Badarneh, “Ergodic capacity and SNR analysis for dual hop amplify and forward cooperative communication systems over α-ƞ-µ channels", IEEE Trans. on Veh. Technol., vol. 67, no. 12, pp. 12384-12388, 2018 (DOI: 10.1109/tvt.2018.2873485).
• [25] S. Panić, S. Mohanchenko, C. Stefanović, and M. Stefanović, “First order outage statistics of asymmetrical RF-OW dual-hop relay communications", University thought, Publication in Natural Sciences, vol. 10, 2020 (DOI: 10.5937/univtho10-23091).
• [26] E. Zedini, I. S. Ansari, and M. Alouini, “Performance analysis of mixed Nakagami-m and gamma-gamma dual-hop FSO transmission systems", IEEE Photonics J., vol. 7, no. 1, pp. 1-20, 2015 (DOI: 10.1109/jphot.2014.2381657).
• [27] N. I. Miridakis, D. D. Vergados, and A. Michalas, “Dual-hop communication over a satellite relay and shadowed Rician channels", IEEE Trans. on Veh. Technol., vol. 64, no. 9, pp. 4031-4040, 2015 (DOI: 10.1109/tvt.2014.2361832).
• [28] Z. Bhutto and W. Yoon, “Dual-hop cooperative relaying with beamforming under adaptive transmission in к-µ shadowed fading environments", Electronics, vol. 8, no. 6, pp. 1-18, 2019 (DOI: 10.3390/electronics8060658).
• [29] H. Shen, Z. Li, and C. Qiu, “A distributed three-hop routing protocol to increase the capacity of hybrid wireless networks", IEEE Trans. on Mob. Comput., vol. 14, no. 10, pp. 1975-1991, 2015 (DOI: 10.1109/tmc.2015.2388476).
• [30] U. Bendre Shital and R. P. Jadhav, “A survey on packet retrieval for three-hop routing protocol in hybrid wireless networks", Int. J. of Sci. and Res., vol. 4, pp. 2165-2168, 2013 [Online]. Available: https://www.ijsr.net/archive/v4i10/NOV151026.pdf
• [31] D.-H. Kim, Y.-C. Ko, and S. Park, “Three-hop MIMO relaying systems in Gaussian broadcast channels", in Proc. 2nd Int. Conf. on Sig. Process. and Commun. Sys., Gold Coast, QLD, Australia, 2008 (DOI: 10.1109/ICSPCS.2008.4813661).
• [32] D. Krstić et al., “Product of three random variables and its application in relay telecommunication systems in the presence of multipath fading", J. of Telecomm. and Informat. Technol. (JTIT), no. 1, pp. 83-92, 2019 (DOI: 10.26636/jtit.2019.130018).
• [33] D. Krstic, M. Stefanovic, and P. Nikolić, “Level crossing rate of product of Nakagami-m random variable, Rician random variable and Rayleigh random variable", in IEICE Inform. and Commun. Technol. Forum, Graz, Austria, 2018.
• [34] D. Aleksić, D. Krstic, Z. Popovic, I. Dinić, and M. Stefanović, „Outage probability of wireless relay communication system with three sections in the presence of Nakagami-m short term fading", Int. J. of Commun., vol. 1, pp. 199-204, 2016 [Online]. Available: https://www.iaras.org/iaras/filedownloads/ijoc/2016/005-0031.pdf
• [35] D. Krstic, M. Stefanovic, P. Nikolić, and S. Minic, “Statistics of the product of three Nakagami-m random variables with applications", in Proc. 26th Int. Conf. on Software, Telecommun. and Com. Netw. SoftCOM 22018, Split, Croatia, 2018, pp. 36-40 (DOI: 10.23919/SOFTCOM.2018.8555819).
• [36] D. Krstic, M. Stefanovic, M. M. Bani Yassein, S. Aljawarneh, and P. Nikolić, “Statistics of the product of three Rician random processes with application", in Proc. of the 1st Int. Conf. on Data Science, E-learn. and Inform. Syst. DATA 2018, Madrit, Spain, 2018 (DOI: 10.1145/3279996.3280015).
• [37] M. Hajiaghayi, M. Dong, and B. Liang, “Jointly optimal channel pairing and power allocation for multichannel multihop relaying", IEEE Trans. on Sig. Process., vol. 59, no. 10, pp. 4998-5012, 2011 (DOI: 10.1109/TSP.2011.2161475).
• [38] I-H. Lee and D. Kim, “Outage probability of multi-hop MIMO relaying with transmit antenna selection and ideal relay gain over Rayleigh fading channels", IEEE Trans. on Commun., vol. 57, no. 2, pp. 357-360, 2009 (DOI: 10.1109/tcomm.2009.02.070058).
• [39] J. Salo, H. M. El-Sallabi, and P. Vainikainen, “The distribution of the product of independent Rayleigh random variables", IEEE Intern. Conf. on Commun., vol. 54, no. 2, pp. 639-643, 2006 (DOI: 10.1109/TAP.2005.863087).
• [40] Z. Hadzi-Velkov, N. Zlatanov, and G. K. Karagiannidis, “Level crossing rate and average fade duration of the multihop Rayleigh fading channel", in Proc. IEEE Int. Conf. on Commun. ICC 2008, Beijing, China, 2008 (DOI: 10.1109/ICC.2008.835).
• [41] G. K. Karagiannidis, S. Nikos, and M. Takis, “N*Nakagami: a novel stochastic model for cascaded fading channels", IEEE Trans. on Commun., vol. 55, no. 8, pp. 1453-1458, 2007 (DOI: 10.1109/TCOMM.2007.902497).
• [42] C. B. Issaid and M. S. Alouini, “Level crossing rate and average outage duration of free space optical links", IEEE Trans. on Commun., vol. 67, no. 9, pp. 6234-6242, 2019 (DOI: 10.1109/tcomm.2019.2918324).
• [43] G. L. Stüber, “Principles of Mobile Communication”, 2nd ed. Kluwer Academic Publ., 2001 (ISBN: 9780792379980).
• [44] D. Krstic, P. Nikolic, and M. Stefanovic, “The performance of threehop wireless relay channel in the presence of Rayleigh fading", in Image Processing and Communications, M. Choraś and R. S. Choraś, Eds. Adv. in Intell. Syst. and Comput. serie, vol. 1062, pp. 222-230. Springer, 2019 (ISBN: 9783030312534).
• [45] P. M. Shankar, “Statistical models for fading and shadowed fading channels in wireless systems: A pedagogical perspective", Wireless Personal Communications, vol. 60, pp. 191-213, 2011 (DOI: 10.1007/s11277-010-9938-2).
• [46] P. M. Shankar, “Fading and shadowing in wireless systems", New York, Dordrecht, Heidelberg, London: Springer, 2012 (ISBN: 9781461403678).
• [47] Z. H. Yang and Y. M. Chu, “On approximating the modified Bessel function of the second kind", J. of Inequalit. and Appl., vol. 41, 2017 (DOI: 10.1186/s13660-017-1317-z).
• [48] D. B. Cheikh, “Outage probability formulas for cellular networks: contributions for MIMO, CoMP and time reversal features", Telecom Paris Tech, 2012, English [Online]. Available: https://pastel.archives-ouvertes.fr/pastel-00790614
• [49] D. S. Krstic, P. B. Nikolic, I. Vulic, S. Minic, and M. C. Stefanovic, „Performance of the product of three Nakagami-m random variables", applied for publication in J. of Commun. Software and Systems (JCOMSS).
• [50] U. Charash, “Reception through Nakagami fading multipath channels with random delays", IEEE Trans. on Commun., vol. 27, no. 4, pp. 657-670, 1979 (DOI: 10.1109/TCOM.1979.1094444).
• [51] M. K. Simon and M. S. Alouini, “Digital Communication over Fading Channels: A Unified Approach to Performance Analysis”. New York: Wiley, 2000 (ISBN: 9780471317791).
• [52] R. Priyadarshi, M. P. Singh, A. Bhardwaj, and P. Sharma, “Amount of fading analysis for composite fading channel using Holtzman approximation", in Proc. 4th Int. Conf. on Image Inform. Process., Himachal Pradesh, India, 2017 (DOI: 10.1109/iciip.2017.8313759).
• [53] W. C. Jakes, “Microwave Mobile Communications”. Piscataway, NJ: IEEE Press, 1994 (ISBN: 978-078031069).
• [54] S. O. Rice, “Mathematical analysis of random noise", Bell Syst. Tech. J., vol. 23,no. 3, pp. 282-332, 1944 (DOI: 10.1002/j.1538-7305.1944.tb00874.x).
• [55] J. L. Lopez and P. J. Pagola, “A simplification of the Laplace method for double integrals. Application to the second Appell function", Electr. Trans. on Numer. Anal., vol. 30, pp. 224-236, 2008 [Online]. Available: https://www.emis.de//journals/ETNA/vol.30.23008/ pp224-236.dir/pp224-236.pdf
• [56] I. K. Eltahir, K. H. Bilal, and S. Taha, “Evaluate comparative of cooperative relaying protocols in wireless communication", Int. J. of Scient. and Engin. Res., vol. 4, no. 8, pp. 112-116, 2013 [Online]. Available: https://www.ijser.org/onlineResearchPaperViewer.aspx? Evaluate-Comparative-of-Cooperative-Relaying-Protocols-inWireless-Communication.pdf

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).