The κ-μ / Inverse Gamma and η-μ / Inverse Gamma Composite Fading Models: Fundamental Statistics and Empirical Validation

• Published in: IEEE transactions on communications Vol. 69; no. 8; pp. 5514 - 5530
• Main Authors: Yoo, Seong Ki, Simmons, Nidhi, Cotton, Simon L., Sofotasios, Paschalis C., Matthaiou, Michail, Valkama, Mikko, Karagiannidis, George K.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">η-μ fading model; <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">κ-μ fading model; Biological system modeling; Channel modeling; Closed-form solutions; composite fading channel; Computational modeling; Distribution functions; Empirical analysis; Exact solutions; Fading; Fading channels; Goodness of fit; Infinite series; inverse gamma distribution; Inverse problems; Line of sight; Mathematical models; Parameters; Probability density function; Probability density functions; Quadratures; resistor-average distance; Shadow mapping; Statistical analysis; Statistical distributions; Wave power
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2017.2780110

The <inline-formula> <tex-math notation="LaTeX">\kappa </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">\mu </tex-math></inline-formula> / inverse gamma and <inline-formula> <tex-math notation="LaTeX">\eta </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">\mu </tex-math></inline-formula> / inverse gamma composite fading models are presented and extensively investigated in this paper. We derive closed-form expressions for the fundamental statistics of the <inline-formula> <tex-math notation="LaTeX">\kappa </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">\mu </tex-math></inline-formula> / inverse gamma composite fading model, such as the probability density function (PDF), cumulative distribution function (CDF). Additionally, we solve the associated integral that is commonly used to obtain the moment generating function (MGF) of statistical distributions to provide an MGF-type function which is valid for performance analysis over the specified parameter space. Analytic expressions for the PDF, higher order moments and AF are also derived for the <inline-formula> <tex-math notation="LaTeX">\eta </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">\mu </tex-math></inline-formula> / inverse gamma composite fading model, while infinite series expressions are obtained for the corresponding CDF and MGF-type function. The suitability of the new models for characterizing composite fading channels is demonstrated through a series of extensive field measurements for wearable, cellular, and vehicular communications. For all of the measurements, two propagation geometry problems with special relevance to the two new composite fading models, namely the line-of-sight (LOS) and non-LOS (NLOS) channel conditions, are considered. It is found that both the <inline-formula> <tex-math notation="LaTeX">\kappa </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">\mu </tex-math></inline-formula> / inverse gamma and <inline-formula> <tex-math notation="LaTeX">\eta </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">\mu </tex-math></inline-formula> / inverse gamma composite fading models provide an excellent fit to fading conditions encountered in the field. The goodness-of-fit of these two composite fading models is also evaluated and compared using the resistor-average distance. As a result, it is shown that the <inline-formula> <tex-math notation="LaTeX">\kappa </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">\mu </tex-math></inline-formula> / inverse gamma composite fading model provides a better fit compared to the <inline-formula> <tex-math notation="LaTeX">\eta </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">\mu </tex-math></inline-formula> / inverse gamma composite fading model when strong dominant signal components exist. On the contrary, the <inline-formula> <tex-math notation="LaTeX">\eta </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">\mu </tex-math></inline-formula> / inverse gamma composite fading model outperforms the <inline-formula> <tex-math notation="LaTeX">\kappa </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">\mu </tex-math></inline-formula> / inverse gamma composite fading model when there is no strong dominant signal component and/or the parameter <inline-formula> <tex-math notation="LaTeX">\eta </tex-math></inline-formula> is not equal to unity, indicating that the scattered wave power of the in-phase and quadrature components of each cluster of multipath are not identical.