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 journalArticlepeer-review

22 Scopus citations


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 languageEnglish (US)
Pages (from-to)922-925
Number of pages4
JournalIEEE Transactions on Communications
Issue number4
StatePublished - 2009


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

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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