ETRI Journal

Electronics and Telecommunications Research Institute (한국전자통신연구원)
권호 표지
DOI QR코드

DOI QR Code

Approximation for the Two-Dimensional Gaussian Q-Function and Its Applications

  • Park, Jin-Ah (Broadcasting & Telecommunications Convergence Research Laboratory, ETRI) ;
  • Park, Seung-Keun (Broadcasting & Telecommunications Convergence Research Laboratory, ETRI)
  • Received : 2009.08.24
  • Accepted : 2009.11.12
  • Published : 2010.02.28
Download PDF
⟨ Previous Next ⟩

Abstract

In this letter, we present a new approximation for the twodimensional (2-D) Gaussian Q-function. The result is represented by only the one-dimensional (1-D) Gaussian Q-function. Unlike the previous 1-D Gaussian-type approximation, the presented approximation can be applied to compute the 2-D Gaussian Q-function with large correlations.

Keywords

References

  1. S. Park and D. Yoon, "An Alternative Expression for the Symbol-Error Probability of MPSK in the Presence of I/Q Unbalance," IEEE Trans. Commun., vol. 52, no. 12, Dec. 2004, pp. 2079-2081. https://doi.org/10.1109/TCOMM.2004.838737
  2. S. Park and S.H. Cho, "Probability of an Arbitrary Wedge-Shaped Region of the MPSK System in the Presence of Quadrature Error," IEEE Commun. Lett., vol. 9, no. 3, Mar. 2005, pp. 196-197. https://doi.org/10.1109/LCOMM.2005.03011
  3. S. Park and S.H. Cho, "SEP Performance of Coherent MPSK over Fading Channels in the Presence of Phase/Quadrature Error and I-Q Gain Mismatch," IEEE Trans. Commun., vol. 53, no. 7, July 2005, pp. 1088-1091. https://doi.org/10.1109/TCOMM.2005.851608
  4. S. Park and S.H. Cho, "Computing the Average Symbol Error Probability of the MPSK System Having Quadrature Error," ETRI J., vol. 28, no. 6, Dec. 2006. pp. 793-795. https://doi.org/10.4218/etrij.06.0206.0137
  5. L. Szczecinski et al., "Exact Evaluation of Bit- and Symbol-Error Rates for Arbitrary 2-D Modulation and Nonuniform Signaling in AWGN Channel," IEEE Trans. Commun., vol. 54, no. 6, June 2006, pp. 1049-1056. https://doi.org/10.1109/TCOMM.2006.876853
  6. M.S. Alouini and M.K. Simon, "Dual Diversity over Correlated Log-Normal Fading Channels," IEEE Trans. Commun., vol. 50, no. 12, Dec. 2002, pp. 1946-1959. https://doi.org/10.1109/TCOMM.2002.806552
  7. M.K. Simon. "A Simpler Form of the Craig Representation for the Two-Dimensional Joint Gaussian Q-Function," IEEE Commun. Lett., vol. 6, no. 2, Feb. 2002, pp. 49-51. https://doi.org/10.1109/4234.984687
  8. S. Park and U.J. Choi, "A Generic Carig Form for the Two-Dimensional Gaussian Q-Function," ETRI J., vol. 29, no. 4, Aug. 2007, pp. 516-517. https://doi.org/10.4218/etrij.07.0206.0040
  9. M. Chiani, D. Dardari, and M.K. Simon, "New Exponential Bounds and Approximations for the Computation of Error Probability in Fading Channels," IEEE Trans. Wireless Commun., vol. 2, no. 4, July 2003, pp. 840-845.
  10. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1970.
  11. N.C. Beaulieu, "A Simple Series for Personal Computer Computation of the Error Function $Q({\bullet})$," IEEE Trans. Commun., vol. 37, no. 9, Sept. 1989, pp. 989-991. https://doi.org/10.1109/26.35381
  12. G.K. Karagiannidis and A.S. Lioumpas, "An Improved Approximation for the Gaussian Q-Function," IEEE Commun. Lett., vol. 11, no. 8, Aug. 2007, pp. 644-646. https://doi.org/10.1109/LCOMM.2007.070470
  13. J.S. Dyer and S.A. Dyer, "Corrections to and Comments on an Improved Approximation for the Gaussian Q-Function," IEEE Commun. Lett., vol. 12, no. 4, Apr. 2008, p. 231. https://doi.org/10.1109/LCOMM.2008.080009
  14. Y. Isukapalli and B. Rao, "An Analytically Tractable Approximation to the Gaussian Q-Function," IEEE Commun. Lett., vol. 12, no. 9, Sept. 2008, pp. 669-671. https://doi.org/10.1109/LCOMM.2008.080815
  15. Y. Chen and N.C. Beaulieu, "A Simple Polynomial Approximation to the Gaussian Q-Function and Its Application," IEEE Commun. Lett., vol. 13, no. 2, Feb. 2009, pp. 124-126. https://doi.org/10.1109/LCOMM.2009.081754
  16. J. Lin, "A Simple Approximation for the Bivariate Normal Integral," Probability in Engineering and Informational Sciences, vol. 9, no. 1, Sept. 1995, pp. 317-321. https://doi.org/10.1017/S0269964800003880
  17. S. Kotz, N. Balakrishnan, and N.L. Johnson, Continuous Multivariate Distributions - Volume1: Models and Applications, 2nd Ed., Wiley and Sons, New York, 2000.

Cited by

  1. On the Distribution Functions of Ratios Involving Gaussian Random Variables vol.32, pp.6, 2010, https://doi.org/10.4218/etrij.10.0210.0201
  2. High-order exponential approximations for the GaussianQ-function obtained by genetic algorithm vol.100, pp.4, 2010, https://doi.org/10.1080/00207217.2012.713024
  3. Proposal of Simple and Accurate Two-Parametric Approximation for the Q-Function vol.2017, pp.None, 2010, https://doi.org/10.1155/2017/8140487