The α − λ − μ and α − η − μ Small-Scale General Fading Distributions: A Unified Approach
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In this paper, a general small-scale fading model for wireless communications, that explores the nonlinearity and at the same time the inhomogeneous nature of the propagation medium, is presented, studied in terms of its first-order statistics of the envelope, and validated by means of field measurements and the Monte Carlo simulation. It is indeed a novel distribution with many advantages such as its generality, its physical interpretation that is directly associated with the propagation channel, and its mathematical tractability due to its simple and closed-form expression. By fitting to measurement data, it has been shown that the proposed distribution outperforms the widely known fading distributions. Namely, the α − λ − μ model, which can be in fact called α − η − μ format 2 model, can also be obtained from the α − η − μ format 1 model by a rotation of the axes. Both formats are combined, in order to result to a unified model in a closed form that may describe the propagation environment in a variety of different fading conditions. Its physical background is hidden behind the names of its parameters. The unified model includes the already known general distributions α − μ′, η − μ, λ − μ (η − μ format 2), and their inclusive ones as special cases.
KeywordsFading channels Correlation α − μ′ Distribution Nakagami-m distribution Weibull distribution
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- 2.Nakagami M. (1960) The m-distribution–a general formula of intensity distribution of rapid fading. In: Hoffman W. C. (eds) Statistical methods in radio wave propagation. Pergamon, Elmsford, NYGoogle Scholar
- 3.Weibull W. (1951) A statistical distribution function of wide applicability. Journal of Applied Mechanics 27: 292–297Google Scholar
- 5.Fraidenraich, G., & Yacoub, M. D. (2003). The λ − μ general fading distribution. In IEEE microwave and optoelectronics Conference, IMOC 2003. Proceedings of the SBMO/IEEE MTT-S international (Vol. 1, pp. 49–54).Google Scholar
- 11.Yacoub, M. D., & Fraidenraich, G. (2006). The α − η − μ and α − κ − μ fading distributions. In IEEE ninth international symposium on spread spectrum techniques and applications (pp. 16–20).Google Scholar
- 13.Asplund, H., Molisch, A. F., Steinbauer, M., & Mehta, N. B. (2002). Clustering of scatterers in mobile radio channels—evaluation and modeling in the COST259 directional channel model. In IEEE international conference on communications, ICC 2002, New York.Google Scholar
- 14.Butterworth, J. S., & Matt, E. E. (1983). The characterization of propagation effects for land mobile satellite services. In International conference on satellite systems for mobile communication and navigations (pp. 51–54).Google Scholar
- 16.Smith, H., Barton, S. K., Gardiner, J. G., & Sforza, M. (1992). Characterization of the land mobile-satellite (LMS) channel at L and S bands: Narrowband measurements. Bradford, ESA AOPs 104 433/114 473.Google Scholar
- 17.Jakes W. C. (1974) Microwave mobile communications. Wiley, New YorkGoogle Scholar