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

Author

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

Author_Institution

Dept. of Electr. & Comput. Eng., Univ. of British Columbia, Vancouver, BC

Volume

57

Issue

4

fYear

2009

fDate

4/1/2009 12:00:00 AM

Firstpage

922

Lastpage

925

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.

Keywords

AWGN channels; error statistics; fading channels; AWGN channel; additive white Gaussian noise; arbitrary 3D constellation; decision regions; error probability calculation; fading channel; symbol error probability; three-dimensional signal constellation; AWGN channels; Additive white noise; Biorthogonal modulation; Computational modeling; Constellation diagram; Digital communication; Error probability; Fading; Pulse modulation; Upper bound; Multidimensional signal constellation, symbol error probability, additive white Gaussian noise (AWGN);

fLanguage

English

Journal_Title

Communications, IEEE Transactions on

Publisher

ieee

ISSN

0090-6778

Type

jour

DOI

10.1109/TCOMM.2009.04.070075

Filename

4814356