Analysis of the Impact of Wireless Three-User Multiple Access Channel Coefficients Correlation on Outage Probability: A Copula-Based Approach

Document Type : Original Article


1 Department of Electrical Engineering, Faculty of Engineering, Ferdowsi University, Mashhad, Iran

2 Department of Electrical Engineering Ferdowsi University of Mashhad (FUM) Mashhad


In wireless communication channels, the channel coefficients are dependent on each other. This paper investigates the constructive or destructive effects of fading coefficients correlation of wireless multiple access channels (MAC) on the outage probability (OP) (one of the wireless communications performances). The desired channel in this paper is a wireless Rayleigh fading MAC with three-users, independent sources, and interdependent fading coefficients; The Copula theory is used as the tool to model the dependence structure. A closed-form expression for the channel outage probability is obtained using an important family of Copulas named the Farlie-Gumbel-Morgenstern (FGM) Copula. The results show that the negative dependence structure of the channel coefficients has a constructive effect on the outage probability; in other words, it reduces the outage probability values compared to the independent case. in contrast, the positive dependency has a destructive effect on the outage probability. The efficiency of the analytical results is illustrated numerically, and the numerical illustrations confirm the theoretical results.


[1] Nelsen, R. B., "An introduction to copulas", Springer, 2006.
[2] Lee, R., Kim, G., Hur, J., and Shin, H., "Advanced Probabilistic Power Flow Method Using Vine Copulas for Wind Power Capacity Expansion," IEEE Access, 10, pp. 114929-114941, 2022.
[3] Pambudi, A. D., Ahmad, F., and Zoubir, A. M., "Robust Copula-Based Detection of Shallow-Buried Landmines With Forward-Looking Radar", IEEE Transactions on Aerospace and Electronic Systems, 58, no. 2, pp. 1187-1198, 2022.
[4] Trigui, I., Shahbaztabar, D., Ajib, W., and Zhu, W. P., "Copula-Based Modeling of RIS-Assisted Communications: Outage Probability Analysis", IEEE Communications Letters, 26, no. 7, pp. 1524-1528, 2022.
[5] Wang, T., Yang, X., Ren, X., Yu, W., and Yang, S., "Locally Private High-Dimensional Crowdsourced Data Release Based on Copula Functions," IEEE Transactions on Services Computing, 15, no. 2, pp. 778-792, 2022.
[6] Zhou, N., Xu, X., Yan, Z., and Shahidehpour, M., "Spatio-Temporal Probabilistic Forecasting of Photovoltaic Power Based on Monotone Broad Learning System and Copula Theory", IEEE Transactions on Sustainable Energy, 13, no. 4, pp. 1874-1885, 2022.
[7]    Eyraud, H., "Les principes de la mesure des correlations", Ann. Univ. Lyon, III. Ser., Sect. A, vol. 1, no. 30-47, pp. 111, 1936.
[8]    Farlie, D. J., "The performance of some correlation coefficients for a general bivariate distribution", Biometrika, vol. 47, no. 3/4, pp. 307-323, 1960.
[9]    Gumbel, E. J., "Bivariate exponential distributions," Journal of the American Statistical Association, vol. 55, no. 292, pp. 698-707, 1960.
[10] Morgenstern, D., "Einfache beispiele zweidimensionaler verteilungen", Mitt, Math, Statist., vol. 8, pp. 234-235, 1956.
[11] Bekrizadeh, H., "Generalized FGM copulas: Properties and applications", Communications in Statistics - Simulation and Computation, pp. 1-12, 2022.
[12] Sriboonchitta, S., and Kreinovich, V., "Why Are FGM Copulas Successful? A Simple Explanation", Advances in Fuzzy Systems, vol. 2018, pp. 5872195, 2018/05/14 2018.
[13] Stoica, E., "A stability property of farlie-gumbel-morgenstern distributions", 2013.
[14] Rostamighadi, F., and Abed Hodtani, G., "Copula-based Analysis of Interference Channels: Outage Probability", Iran Workshop on Communication and Information theory, 2022.
[15] Ghadi, F. R., Hodtani, G. A., and López-Martínez, F. J., "The role of correlation in the doubly dirty fading mac with side information at the transmitters", IEEE Wireless Communications Letters, vol. 10, no. 9, pp. 2070-2074, 2021.
[16] Mohsenzadeh, M. S., Hodtani, G. A., "FGM Copula based Analysis of Outage Probability for Wireless Three-User Multiple Access Channel with Correlated Channel Coefficients", 31st Iranian Conference on Electrical Engineering (ICEE), 2023.
[17] Ahlswede, R., "Multi-way communication channels", 1973.
[18] Liao, H. "Multiple Access Channels," Ph.D. dissertation, Department of Electrical Engineering, University of Hawaii, Honolulu, 1972.