The Generalized-Fisher composite fading model for the next generation of mobile communication systems

Abstract

The new generation of communication systems is moving towards using a millimeter-wave spectrum. Since the shadowing effects are undeniable in this type of propagation, the proposed Generalized Fisher (GF) distribution can be useful in modeling shadowed fading channels, considering the non-linearity and the multi-cluster nature of the diffusion medium. After introducing the model, its main statistics, including Probability Density Function (PDF), Cumulative Distribution Function (CDF), Moment Generating Function (MGF), and the distribution of the sum of an arbitrary number of independent and non-identically distributed (i.n.i.d.) random variables with GF distribution are calculated. Subsequently, some wireless communication application criteria such as ergodic and outage capacities, are computed. Finally, considering the classic Wyner's wiretap model and passive eavesdropping scenario, specific security criteria, such as the probability of non-zero secrecy capacity and secrecy outage probability, are also determined. These expressions are measured in terms of either univariate or multivariate Fox's H-function.

Keywords

Composite fading / Ergodic capacity / Generalized-Fisher distribution / Secrecy analysis / Sum of random variables

References

[1] A. Yun, L. Kong, M. Cheffena, Secrecy outage analysis of double shadowed Rician channels, Electronics Letters 55 (13) (2019) 756-767.

[2] S. Bhattacharyya, M. Aradhana, S.K. Kumar, A BCH code assisted modified NCO based LSPF-DPLL topology for Nakagami-m, Rayleigh and Rician fading channels, Digital Communications and Networks 5 (2) (2019) 102-110.

[3] M.K. Simon, M.S. Alouini, Digital Communication over Fading Channels, Wiley, New York, 2001.

[4] B. Wang, G. Cui, W. Yi, L. Kong, X. Yang, Approximation to independent lognormal sum with α-μ distribution and the application, Signal Processing 111 (2015) 165-169.

[5] S. Hur, S. Baek, B. Kim, Proposal on millimeter-wave channel modeling for 5G cellular system, IEEE Journal of Selected Topics in Signal Processing 10 (3) (2016) 454-469.

[6] C.X. Wang, J. Bian, J. Sun, W. Zhang, M. Zhang, A survey of 5G channel measurements and models, IEEE Communications Surveys Tutorials 20 (4) (2018) 3142-3168.

[7] M.D. Laishram, D.S. Aheibam,Performance of dual-branch selection combining receiver over Fluctuating Two-Ray (FTR) fading channels for 5G mmWave communications, AEU - International Journal of Electronics and Communications 117 (2020) 153093.

[8] M. Shafi, A. Molisch, P. Smith, T. Haustein, P. Zhu, P.D. Silva, F. Tufvesson, A. Benjebbour, G. Wunder, 5G: a tutorial overview of standards, trials, challenges, deployment, and practice, IEEE Journal on Selected Areas in Communications 35

[9] S. Collonge, G. Zaharia, G. Zein, Influence of the human activity on wide-band characteristics of the 60 GHz indoor radio channel, IEEE Transactions on Wireless Communications 3 (6) (2004) 2396-2406.

[10] F. Yilmaz, M.S. Alouini, A new simple model for composite fading channels: second order statistics and channel capacity,in: 2010 7th International Symposium on Wireless Communication Systems, 2010, pp. 676-680.

[11] S.K. Yoo, S. Cotton, P. Sofotasios, M. Matthaiou, M. Valkama, G. Karagiannidis, The Fisher-Snedecor F distribution: a simple and accurate composite fading model, IEEE Communications Letters 21 (7) (2017) 1661-1664.

[12] M.K. Shawaqfeh, O.S. Badarneh, Performance of mobile networks under composite F fading channels, Digital Communications and Networks 8 (1) (2022) 25-32, 2021.

[13] O. Badarneh, D. da Costa, P. Sofotasios, S. Muhaidat, S. Cotton, On the sum of Fisher-Snedecor F variates and its application to maximal-ratio combining, IEEE Wireless Communications Letters 7 (6) (2018) 966-969.

[14] T. Aldalgamouni, C.I. Mehmet, O. Badarneh, H. Yanikomeroglu, Performance analysis of Fisher-snedecor F composite fading channels, in: 2018 IEEE Middle East and North Africa Communications Conference, MENACOMM), 2018, pp. 1-5.

[15] I. Trigui, S. Affes, M.R. Di, N.J. Dushantha, Sinr coverage analysis of dense hetnets over Fox's H-fading channels, in: 2020 IEEE Wireless Communications and Networking Conference, WCNC), 2020, pp. 1-6.

[16] Y. Aborahama, M. Ismail, M. Hassan, Novel methods for generating Fox's H-function distributed random variables with application, IEEE Transactions on Vehicular Technology 68 (7) (2019) 7150-7154.

[17] C.D. Bodenschatz, Finding an H-function distribution for the sum of independent H-function variates, Tech. rep., Air Force Inst of Tech Wright-Patterson AFB OH (1992).

[18] J.D.I. Cook, The H-function and probability density functions of certain algebraic combinations of independent random variables with H-function probability distribution, Tech. rep., Air Force Inst of Tech Wright-Patterson AFB OH (1981).

[19] Y. Jeong, W.J. Chong, H. Shin, M. Win, Intervehicle communication: cox-fox modeling, IEEE Journal on Selected Areas in Communications 31 (9) (2013) 418-433.

[20] M. Payami, A. Falahati, Accurate variable-order approximations to the sum of α-μ variates with application to MIMO systems, IEEE Transactions on Wireless Communications 20 (3) (2021) 1612-1623.

[21] A.M. Mathai, R.K. Saxena, H. Haubold, The H-Function:Theory and Applications, Springer Science & Business Media, 2009.

[22] M.D. Yacoub, The α-μ distribution: a physical fading model for the Stacy distribution, IEEE Transactions on Vehicular Technology 56 (1) (2007) 27-34.

[23] A. Jeffrey, D. Zwillinger, Table of Integrals, Series, and Products, Elsevier, 2007.

[24] L. Kong, G. Kaddoum, H. Chergui, On physical layer security over Fox's H-function wiretap fading channels, IEEE Transactions on Vehicular Technology 68 (7) (2019) 6608-6621.

[25] Y.A. Rahama, M. Ismail, M. Hassan, On the sum of independent Fox's H-function variates with applications, IEEE Transactions on Vehicular Technology 67 (8) (2018) 6752-6760.

[26] D.B.L. Debnath,Integral Transforms and Their Applications, third ed.ed., CRC Press, 2015.

[27] F. Salimian Rizi, A. Falahati, Ergodic capacity and symbol error rate analysis of a wireless system with α-μ composite fading channel, Wireless Personal Communications 124 (1) (2022) 103-118.

[28] K.M. Mota, S.W. de Alvarenga, U.S. Dias, J.R. de Sousa, On the capacity analysis of κ-μ and α-μ fading channels for millimeter waves, in: 2015 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference, IMOC), 2015, pp. 1-5.

[29] C.R.N. da Silva, E.J. Leonardo, M.D. Yacoub, Product of two envelopes taken from α-μ κ-μ and η-μ distributions, IEEE Transactions on Communications 66 (3)(2017) 1284-1295.

[30] Y. Isukapalli, B.D. Rao, Packet error probability of a transmit beamforming system with imperfect feedback, IEEE Transactions on Signal Processing 58 (4) (2010) 2298-2314.

[31] K.S. Ahn, S.-W. Choi, J.-M. Ahn, Secrecy performance of maximum ratio diversity with channel estimation error, IEEE Signal Processing Letters 22 (11) (2015) 2167-2171.

[32] M. Bloch, J. Barros, M. Rodrigues, S. McLaughlin, Wireless information-theoretic security, IEEE Transactions on Information Theory 54 (6) (2008) 2515-2534.

[33] H. Lei, H. Zhang, I.S. Ansari, C. Gao, Y. Guo, G. Pan, K. Qaraqe, Performance analysis of physical layer security over generalized-k fading channels using a mixture Gamma distribution, IEEE Communications Letters 20 (2) (2016) 408-411.

[34] A.A. Kilbas, H-Transforms:Theory and Applications, CRC Press, 2004.

[35] F.S. Rizi, A. Falahati, Effective rate analysis of MISO wireless communication systems over EGK fading channels, in: 2021 29th Iranian Conference on Electrical Engineering, ICEE), 2021, pp. 843-846.