### Abstract

In this paper the exact probability density function of a multivariate α-μ distributed variables with exponentially correlated random variables is derived. Capitalizing on this the joint probability density function (JPDF) is derived for the square ratios of two multivariate exponentially correlated α-μ distributed variables. Closed form expressions are determined for the cumulative distribution function (CDF) and probability density function (PDF) of the maximal and minimal square ratio of two multivariate exponentially correlated α-μ distributions. Using these new formulae, SIR (signal-to-interference) based analysis of selection combining (SC) receiver through standard communication system performance measures can be performed.

Original language | English |
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Pages (from-to) | 152-159 |

Number of pages | 8 |

Journal | Mathematical and Computer Modelling |

Volume | 54 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 1 Jul 2011 |

Externally published | Yes |

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### Keywords

- Maximal and minimal square ratios
- Multivariate distribution
- SIR based SC diversity
- Square ratios of exponentially correlated variables

### ASJC Scopus subject areas

- Modelling and Simulation
- Computer Science Applications

### Cite this

*Mathematical and Computer Modelling*,

*54*(1-2), 152-159. https://doi.org/10.1016/j.mcm.2011.01.046