English

On the Bivariate Nakagami-$m$ Cumulative Distribution Function: Closed-form Expression and Applications

Information Theory 2024-10-30 v1 math.IT

Abstract

In this paper, we derive exact closed-form expressions for the bivariate Nakagami-mm cumulative distribution function (CDF) with positive integer fading severity index mm in terms of a class of hypergeometric functions. Particularly, we show that the bivariate Nakagami-mm CDF can be expressed as a finite sum of elementary functions and bivariate confluent hypergeometric Φ3\Phi_3 functions. Direct applications which arise from the proposed closed-form expression are the outage probability (OP) analysis of a dual-branch selection combiner in correlated Nakagami-mm fading, or the calculation of the level crossing rate (LCR) and average fade duration (AFD) of a sampled Nakagami-mm fading envelope.

Keywords

Cite

@article{arxiv.1206.3965,
  title  = {On the Bivariate Nakagami-$m$ Cumulative Distribution Function: Closed-form Expression and Applications},
  author = {F. J. Lopez-Martinez and D. Morales-Jimenez and E. Martos-Naya and J. F. Paris},
  journal= {arXiv preprint arXiv:1206.3965},
  year   = {2024}
}

Comments

This work has been submitted to the IEEE for possible publication

R2 v1 2026-06-21T21:21:21.478Z