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

  • Authors:

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

  • Affiliations:

  • Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, British Columbia, Canada;Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, British Columbia, Canada;Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, British Columbia, Canada;Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, British Columbia, Canada

  • Venue:
  • IEEE Transactions on Communications
  • Year:
  • 2009

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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.