On the Estimation of the α-μ Channel Signal Fading Distribution Parameters

Abdel Nasser S.A.A. Hassan¹, Ahmed M. Gad^1, and Wafaa M. Ibrahim¹

¹Department of Statistics, Faculty of Economics and Political Science, Cairo University, Egypt

Cite this paper:
Abdel Nasser S.A.A. Hassan, Ahmed M. Gad and Wafaa M. Ibrahim. On the Estimation of the α-μ Channel Signal Fading Distribution Parameters. American Journal of Applied Mathematics and Statistics. 2020; 8(1):28-38. doi: 10.12691/ajams-8-1-4

Abstract

Radio channel signals are heavily used tool in telecommunications. A suitable probability distribution is needed to model signals. Many probability distributions have been introduced for this purpose. The α-μ probability distribution is a general channel signal fading model that encompasses many applied important distributions as a special case. This distribution is also known as generalized gamma, Stacy distribution. This distribution is used to describe the fading mobile radio signal under a general diffuse scattering. The main advantage of this probability distribution is that it is flexible and mathematically tractable. Also, many other distributions can be considered as a special case of α-μ probability distribution. In this article we discuss the model parameters' estimation. Two new maximum likelihood (ML) and Psi-inverse (PI) estimators for the α-μ channel signal fading distribution have been proposed. Simulation study is finally conducted to evaluate the performance of the proposed estimators. Simulation results show that the proposed methods perform well comparable to the existing estimators. This behavior is valid for limited sample size; n<1000 or large sample size; n≥1000.

Keywords:
fading radio signals α-μ distribution Stacy distribution gamma distribution Erlang distribution chi-squared Nakagami distribution size-biased distributions ML estimators

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References:

[1]	Batista, F.P. and De Souza, R.A. (2015). On the maximum likelihood estimation for the fading channel. Vehicular Technology Conference, VTC, IEEE 81st , 1-5.
[2]	Batista, F.P., De Souza, R.A. and Ribeiro, A.M. (2016). Maximum likelihood estimators for the fading environment. Proc. IEEE Wireless and Networking Conference, WCNC, 1, 1-6.
[3]	Da Costa, D.B., Yacoub, M.D. and Filho, J.C. (2008). Highly accurate closed-form approximations to the sum of variates and applications. IEEE Trans. Wireless Communications, 7(9), 3301-3306.
[4]	Dharmraj and Katiyar, H. (2015). Performance Analysis of Multi-Hop Relay-Network over Fading Channel. URECT, 2(3).
[5]	Magableh, A.M. and Magableh, M.M. (2009). Moment generating function of the generalized distribution with applications. IEEE Commu. Let., 13(6), 411-413.
[6]	Moraes, A.O., De Paula, E.R., Muella, M.T. Perrella, W.J. (2014). On the second order statistics for GPS ionospheric scintillation modeling. Radio Sci., 49, 94-105.
[7]	Rabou, A. S. and Selim, Z. M. (1987) : Estimation of the shape parameters of the Standard Beta Distribution. Proceeding of the 12th international congress for Statistics, Computer Science, Social and Demographic research, Ain Shams University, Cairo, Egypt. 93-112.
[8]	Reig, J. and Rubio, L. (2011). On simple estimators of the fading distribution. IEEE Trans. Commun., 59, 3254-3258.
[9]	Reig, J. , Martinez-Ingles, M.-T. , Rubio, L., Rodrigo-Penarrocha V.-M. and Molina-Garcia-Pardo J.-M. (2014). Fading Evaluation in the 60 GHz Band in Line-of-Sight Condtions. International Journal of Antennas and Propagation, 1-12.
[10]	Reig, J. , Martinez-Ingles, M.-T. , Molina-Garcia-Pardo J.-M., Rubio, L. and Rodrigo-Penarrocha V.-M. (2017). Small-Scale distributions in an indoor environemt at 94 GHz. Radio Sci., 52, 852-861.
[11]	Selim, Z.M. (1979). Two-sample location and scale tests for distributions with the same finite interval support. Unpublished Ph.D. Thesis, University of Iowa, USA.
[12]	Wang, B., Cui, G., Yi, W., Kong, L. and Yang, X. (2015). Approximation to independent lognormal sum with distribution and the application. Signal Process., 111, 165-169.
[13]	Yacoub, M.D. (2000). The distribution: A general fading distribution. Vehicular Technology Conference, 2000. IEEE VTS-Fall VTC 2000. 52nd Volume: 2, 872-877.
[14]	Yacoub, M.D. (2002). The distribution: A general fading distribution. Proc. IEEE Personal, Indoor and Mobile Radio Communications. PIMRC 2002, 629-633.
[15]	Yacoub, M.D. (2007). The distribution: a physical fading model for the Stacy distribution. IEEE Trans. VTC, 56(1), 27-34.