## Abstract

The H-transforms are integral transforms that involve Fox's H-functions as kernels. A large variety of integral transforms can be put into particular forms of the H-transform since H-functions subsume most of the known special functions including Meijer's G-functions. In this paper, we embody the H-transform theory into a unifying framework for modeling and analysis in wireless communication. First, we systematize the use of elementary identities and properties of the H-transform by introducing operations on parameter sequences of H-functions. We then put forth H-fading and degree-2 irregular H-fading to model radio propagation under composite, specular, and/or inhomogeneous conditions. The H-fading describes composite effects of multipath fading and shadowing as a single H-variate, including most of typical models such as Rayleigh, Nakagami-m, Weibull, α-μ, N∗ Nakagami-m, (generalized) K-fading, and Weibull/gamma fading as its special cases. As a new class of H-variates (called the degree-ζ irregular H-variate), the degree-2 irregular H-fading characterizes specular and/or inhomogeneous radio propagation in which the multipath component consists of a strong specularly reflected or line-of-sight (LOS) wave as well as unequal-power or correlated in-phase and quadrature scattered waves. This fading includes a variety of typical models such as Rician, Nakagami-q, κ-μ, η-μ, Rician/LOS gamma, and κ-μ/LOS gamma fading as its special cases. Finally, we develop a unifying H-transform analysis for the amount of fading, error probability, channel capacity, and error exponent in wireless communication using the new systematic language of transcendental H-functions. By virtue of two essential operations - called Mellin and convolution operations - involved in the Mellin transform and Mellin convolution of two H-functions, the H-transforms for these performance measures culminate in H-functions. Using the algebraic asymptotic expansions of the H-transform, we further analyze the error probability and capacity at high and low signal-to-noise ratios in a unified fashion.

Original language | English |
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Article number | 7108024 |

Pages (from-to) | 3773-3809 |

Number of pages | 37 |

Journal | IEEE Transactions on Information Theory |

Volume | 61 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1 Jul 2015 |

### Bibliographical note

Publisher Copyright:© 2015 IEEE.

## Keywords

- Amount of fading
- H-distribution
- H-transform
- channel capacity
- error exponent
- error probability
- multipath fading
- shadowing