Analysis of Ratio of One and Product of Two Rayleigh Random Variables and its Application in Telecommunications

AUTHOR(S):

Dragana Krstic, Mihajlo Stefanovic, Siniša Minic, Miloš Peric

TITLE

Analysis of Ratio of One and Product of Two Rayleigh Random Variables and its Application in Telecommunications

ABSTRACT

In this paper, the ratio of product of two Rayleigh random variables and Rayleigh random variable (RV) is considered. The level crossing rate (LCR) of ratio of product of two Rayleigh random variables and Rayleigh random variable is evaluated. Using this result, the average fade duration (AFD) of wireless relay communication system with two sections operating over multipath fading channel in the presence of co-channel interference can be calculated. Then, the LCR of the ratio of Rayleigh RV and product of two Rayleigh RVs is determined. The formula is obtained in the closed form. The influence of Rayleigh fading average power on the LCR is analyzed. By using this formula, the AFD of wireless relay system with two sections working over Rayleigh multipath fading channel in the presence of two Rayleigh co-channel interferences could be evaluated.

KEYWORDS

Level crossing rate (LCR), Ratio, Product, Rayleigh random variable, Fading, Co-channel interference

REFERENCES

[1] P. M. Shankar, Fading and Shadowing in Wireless Systems, Springer, New York Dordrecht Heidelberg London, 2012, DOI: 10.1007/978-1-4614-0367-8

[2] G. L. Stuber, Mobile communication, 2nd ed. Dordrecht: Kluwer Academic Publisher, 2003.

[3] S. Panic, M. Stefanovic, J. Anastasov, and P. Spalevic, Fading and Interference Mitigation in Wireless Communications, USA: CRC Press, 2013.

[4] J. Salo, H.M. El-Sallabi, P. Vainikainen, The distribution of the product of independent Rayleigh random variables, IEEE Transactions on Antennas and Propagation, Vol. 54, Issue: 2, Feb. 2006, pp. 639 – 643, DOI: 10.1109/TAP.2005.863087

[5] Y. Chen, G. K. Karagiannidis, Hao Lu, and Ning Cao, “Novel Approximations to the Statistics of Products of Independent Random Variables and Their Applications in Wireless Communications”, IEEE Transactions on Vehicular Technology, Vol. 61, No. 2, February 2012, pp. 443-454.

[6] G. Karagiannidis, S. Nikos, and M. Takis, “N*Nakagami: A Novel Stochastic Model for Cascaded Fading Channels,” IEEE Transactions on Communications, Vol. 55, No. 8, 2007, pp. 1453–1458.

[7] A. Widanagamage, D. Jayalath, “On the Probability Density Function of the Product of Rayleigh Distributed Random Variables”, 6th International Conference on Signal Processing and Communication Systems (ICSPCS), 12-14 Dec. 2012, Gold Coast, QLD, Australia, DOI: 10.1109/ICSPCS.2012.6508017

[8] S. Ahmed, L.L. Yang, and L. Hanzo, “Probability Distributions of Products of Rayleigh and Nakagami-m Variables Using Mellin Transform”, IEEE International Conference on Communications, ICC 2011, 05 Jun - 09 Jun 2011, Kyoto, Japan

[9] F. Yilmaz, and M.S. Alouini, “Product of the Powers of Generalized Nakagami-m Variates and Performance of Cascaded Fading Channels”, IEEE Global Telecommunications Conference, GLOBECOM 2009, 30 Nov.- 4 Dec. 2009, Honolulu, HI, USA, DOI: 10.1109/GLOCOM.2009.5426254

[10] Č. Stefanović, D. Đošić, S. Maričić, M. Matović, A. Matović, “Level Crossing Rate of the Product of Two Random Variables”, Infoteh- Jahorina, Vol. 12, March 2013. pp. 404 -407.

[11] Z. Hadzi-Velkov, N. Zlatanov, and K. G. Karagiannidis, “On the Second Order Statistics of the Multihop Rayleigh Fading Channel,” IEEE Transactions on Communications, Vol. 57, No. 6, June 2009, pp. 1815–1823, DOI: 10.1109/TCOMM.2009.06.070460.

[12] E. Mekić, N. Sekulović, M. Bandjur, M. Stefanović, P. Spalević, “The Distribution of Ratio of Random Variable and Product of Two Random Variables and its Application in Performance Analysis of Multi-hop Relaying Communications over Fading Channels”, Przegląd Elektrotechniczny (Electrical Review), R. 88 NR 7a/2012

[13] D. Krstić, M. Stefanović, Z. Jovanović, R. Gerov, V. Milenković, “Statistical Characteristic of Ratio and Product of Rician Random Variables and its Application in Analysis of Wireless Communication Systems”, International Journal of Mathematical and Computational Methods, Vol. 1, 2016, pp. 79-86.

[14] D. Krstić, M. Stefanović, V. Milenković, Dj. Bandjur, “Level crossing rate of ratio of product of two α-k-μ random variables and α-k-μ random variable“, WSEAS Transaction on Communications, vol. 13, 2014, pp. 622-630.

[15] D. Krstić, M. Stefanović, N. Simić, A. Stevanović, „The level crossing rate of the ratio of product of two k-μ random variables and k-μ random variable“, 13th WSEAS International Conference on Electric Power Systems, High Voltages, Electric Machines (POWER '13), Chania, Crete Island, Greece, August 27-29, 2013, pp. 153-158.

[16] D. Krstić, I. Romdhani, M. Masadeh Bani Yassein, S. Minić, G. Petković, P. Milačić, “Level crossing rate of ratio of product of two k-μ random variables and Nakagami-m random variable”, 2015 International Workshop on Internet of Things and Smart Spaces (IoT-Smart-2015), DOI: 10.1109/CIT/IUCC/DASC/PICOM.2015.244

[17] Y. A. Rahama, M. H. Ismail, M. S. Hassan, “On the distribution of the product and ratio of products of EGK variates with applications”, Telecommunication Systems, September 2017, DOI: 10.1007/s11235-017-0389-x

[18] M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, 1964; reprinted Dover Publications, 1965.

Cite this paper

Dragana Krstic, Mihajlo Stefanovic, Siniša Minic, Miloš Peric. (2018) Analysis of Ratio of One and Product of Two Rayleigh Random Variables and its Application in Telecommunications. International Journal of Communications, 3, 32-38