Exact method for the error probability calculation of three-dimensional signal constellations

Majid Khabbazian; Jahangir Hossain; Mohamed Slim Alouini; Vijay K. Bhargava

doi:10.1109/TCOMM.2009.04.070075

Exact method for the error probability calculation of three-dimensional signal constellations

Majid Khabbazian^*, Jahangir Hossain, Mohamed Slim Alouini, Vijay K. Bhargava

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

The contribution of this letter is the computation of exact symbol error probability (SEP) of three-dimensional (3- D) signal constellations over an additive white Gaussian noise (AWGN) channel. The originality of the proposed method is that it can be applied to any arbitrary 3-D constellation whose decision regions may not meet at right angles. We express the SEP in a triple integral form which is further simplified. The simplified form requires a single integral evaluation of standard "erf" function. Using the derived exact SEP formula, we plot SEP for a number of selected 3-D constellations. The SEP obtained using the proposed formula is validated by simulation results. It is also compared with the union bound approximation, an upper bound for SEP.

Original language	English (US)
Pages (from-to)	922-925
Number of pages	4
Journal	IEEE Transactions on Communications
Volume	57
Issue number	4
DOIs	https://doi.org/10.1109/TCOMM.2009.04.070075
State	Published - 2009

Keywords

Additive white Gaussian noise (AWGN)
Multidimensional signal constellation
Symbol error probability

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/TCOMM.2009.04.070075

Cite this

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abstract = "The contribution of this letter is the computation of exact symbol error probability (SEP) of three-dimensional (3- D) signal constellations over an additive white Gaussian noise (AWGN) channel. The originality of the proposed method is that it can be applied to any arbitrary 3-D constellation whose decision regions may not meet at right angles. We express the SEP in a triple integral form which is further simplified. The simplified form requires a single integral evaluation of standard {"}erf{"} function. Using the derived exact SEP formula, we plot SEP for a number of selected 3-D constellations. The SEP obtained using the proposed formula is validated by simulation results. It is also compared with the union bound approximation, an upper bound for SEP.",

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AU - Khabbazian, Majid

AU - Hossain, Jahangir

AU - Alouini, Mohamed Slim

AU - Bhargava, Vijay K.

PY - 2009

Y1 - 2009

N2 - The contribution of this letter is the computation of exact symbol error probability (SEP) of three-dimensional (3- D) signal constellations over an additive white Gaussian noise (AWGN) channel. The originality of the proposed method is that it can be applied to any arbitrary 3-D constellation whose decision regions may not meet at right angles. We express the SEP in a triple integral form which is further simplified. The simplified form requires a single integral evaluation of standard "erf" function. Using the derived exact SEP formula, we plot SEP for a number of selected 3-D constellations. The SEP obtained using the proposed formula is validated by simulation results. It is also compared with the union bound approximation, an upper bound for SEP.

AB - The contribution of this letter is the computation of exact symbol error probability (SEP) of three-dimensional (3- D) signal constellations over an additive white Gaussian noise (AWGN) channel. The originality of the proposed method is that it can be applied to any arbitrary 3-D constellation whose decision regions may not meet at right angles. We express the SEP in a triple integral form which is further simplified. The simplified form requires a single integral evaluation of standard "erf" function. Using the derived exact SEP formula, we plot SEP for a number of selected 3-D constellations. The SEP obtained using the proposed formula is validated by simulation results. It is also compared with the union bound approximation, an upper bound for SEP.

KW - Additive white Gaussian noise (AWGN)

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KW - Symbol error probability

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JO - IEEE Transactions on Communications

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Exact method for the error probability calculation of three-dimensional signal constellations

Abstract

Keywords

ASJC Scopus subject areas

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