### Abstract

The problem of finding the distribution of the sum of more than two Rayleigh fading envelopes has never been solved in terms of tabulated functions. In this letter, we present a closed-form union upper-bound for the cumulative distribution function of the weighted sum of N independent Rayleigh fading envelopes. Computer simulation results verify the tightness of the proposed bound for several values of N. The proposed bound can be efficiently applied in various wireless applications, such as satellite communications, equal-gain receivers, and radars.

Original language | English |
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Pages (from-to) | 589-591 |

Number of pages | 3 |

Journal | IEEE Communications Letters |

Volume | 9 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2005 |

Externally published | Yes |

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### Keywords

- Equal-gain diversity
- False alarm probability
- Rayleigh fading
- Sum of fading envelopes

### ASJC Scopus subject areas

- Computer Networks and Communications

### Cite this

*IEEE Communications Letters*,

*9*(7), 589-591. https://doi.org/10.1109/LCOMM.2005.07011

**A closed-form upper-bound for the distribution of the weighted sum of Rayleigh variates.** / Karagiannidis, George K.; Tsiftsis, Theodoros A.; Sagias, Nikos C.

Research output: Contribution to journal › Article

*IEEE Communications Letters*, vol. 9, no. 7, pp. 589-591. https://doi.org/10.1109/LCOMM.2005.07011

}

TY - JOUR

T1 - A closed-form upper-bound for the distribution of the weighted sum of Rayleigh variates

AU - Karagiannidis, George K.

AU - Tsiftsis, Theodoros A.

AU - Sagias, Nikos C.

PY - 2005/7

Y1 - 2005/7

N2 - The problem of finding the distribution of the sum of more than two Rayleigh fading envelopes has never been solved in terms of tabulated functions. In this letter, we present a closed-form union upper-bound for the cumulative distribution function of the weighted sum of N independent Rayleigh fading envelopes. Computer simulation results verify the tightness of the proposed bound for several values of N. The proposed bound can be efficiently applied in various wireless applications, such as satellite communications, equal-gain receivers, and radars.

AB - The problem of finding the distribution of the sum of more than two Rayleigh fading envelopes has never been solved in terms of tabulated functions. In this letter, we present a closed-form union upper-bound for the cumulative distribution function of the weighted sum of N independent Rayleigh fading envelopes. Computer simulation results verify the tightness of the proposed bound for several values of N. The proposed bound can be efficiently applied in various wireless applications, such as satellite communications, equal-gain receivers, and radars.

KW - Equal-gain diversity

KW - False alarm probability

KW - Rayleigh fading

KW - Sum of fading envelopes

UR - http://www.scopus.com/inward/record.url?scp=23144437408&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23144437408&partnerID=8YFLogxK

U2 - 10.1109/LCOMM.2005.07011

DO - 10.1109/LCOMM.2005.07011

M3 - Article

VL - 9

SP - 589

EP - 591

JO - IEEE Communications Letters

JF - IEEE Communications Letters

SN - 1089-7798

IS - 7

ER -