Journal of Communications and Networks

The Korean Institute of Commucations and Information Sciences (한국통신학회)
권호 표지

Performance Analysis of Space-Time Codes in Realistic Propagation Environments: A Moment Generating Function-Based Approach

  • Lamahewa Tharaka A. (Department of Information Engineering, Research School of Information Sciences and Engineering, the Australian National University) ;
  • Simon Marvin K. (Jet Propulsion Laboratory, California Institute of Technology) ;
  • Kennedy Rodney A. (Department of Information Engineering, Research School of Information Sciences and Engineering, the Australian National University) ;
  • Abhayapala Thushara D. (Department of Information Engineering, Research School of Information Sciences and Engineering, the Australian National University)
  • Published : 2005.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we derive analytical expressions for the exact pairwise error probability (PEP) of a space-time coded system operating over spatially correlated fast (constant over the duration of a symbol) and slow (constant over the length of a code word) fad­ing channels using a moment-generating function-based approach. We discuss two analytical techniques that can be used to evaluate the exact-PEPs (and therefore, approximate the average bit error probability (BEP)) in closed form. These analytical expressions are more realistic than previously published PEP expressions as they fully account for antenna spacing, antenna geometries (uniform linear array, uniform grid array, uniform circular array, etc.) and scattering models (uniform, Gaussian, Laplacian, Von-mises, etc.). Inclusion of spatial information in these expressions provides valuable insights into the physical factors determining the performance of a space-time code. Using these new PEP expressions, we investigate the effect of antenna spacing, antenna geometries and azimuth power distribution parameters (angle of arrival/departure and angular spread) on the performance of a four-state QPSK space-time trellis code proposed by Tarokh et al. for two transmit antennas.

Keywords

References

  1. V. Tarokh, N. Seshadri, and A. R. Calderbank, 'Space-time codes for high data rate wireless communication: Performance criterion and code construction,' IEEE Trans. Inform. Theory, vol. 44, no. 1, pp. 744-765, Mar. 1998 https://doi.org/10.1109/18.661517
  2. D. K. Aktas and M. P. Fitz, 'Computing the distance spectrum of spacetime trellis codes,' in Proc. WCNC 2000, vol. 1, 2000, pp. 51-55 https://doi.org/10.1109/WCNC.2000.904599
  3. R. Gozali and B. D. Woerner, 'Upper bounds on the bit-error probability of space-time trellis codes using generating function techniques,' in Proc. VTC 2001 Spring, Rhodes Island, Greece, 2001, pp. 1318-1323 https://doi.org/10.1109/VETECS.2001.944599
  4. M. Uysal and C. N. Georghiades, 'Error performance analysis of spacetime codes over rayleigh fading channels,' J. Commun. Networks, vol. 2, no. 4, pp. 351-355, Dec. 2000
  5. G. L. Turin, 'The characteristic function of hermetian quadratic forms in complex normal random variables,' Biometrika, vol. 47, no. 1/2, pp. 199-201, June 1960 https://doi.org/10.1093/biomet/47.1-2.199
  6. M. K. Simon, 'Evaluation of average bit error probability for space-time coding based on a simpler exact evaluation of pairwise error probability,' Int. J. Commun. Networks, vol. 3, no. 3, pp. 257-264, Sept. 2001
  7. M. Uysal and C. N. Georghiades, 'Effect of spatial fading correlation on performance of space-time codes,' IEEE Electron. Lett., vol. 37, no. 3, pp. 181-183, Feb. 2001 https://doi.org/10.1049/el:20010113
  8. D. Gesbert, H. Bolcskei, D. A. Gore, and A. J. Paulraj, 'Outdoor MIMO wireless channels: Models and performance prediction,' IEEE Trans. Commun., vol. 50, no. 12, pp. 1926-1934, Dec. 2002 https://doi.org/10.1109/TCOMM.2002.806555
  9. T. D. Abhayapala, T. S. Pollock, and R. A. Kennedy, 'Spatial decomposition of MIMO wireless channels,' in Proc. The Seventh Int. Symp. Signal Processing and its Applications, Paris, France, July 2003, vol. 1, pp. 309-312 https://doi.org/10.1109/ISSPA.2003.1224702
  10. T. D. Abhayapala, T. S. Pollock, and R. A. Kennedy, 'Characterization of 3d spatial wireless channels,' in Proc. VTC 2003 Fall, Orlando, Florida, USA, vol. 1, Oct. 2003, pp. 123-127
  11. H. M. Jones, R. A. Kennedy, and T. D. Abhayapala, 'On dimensionality of multipath fields: Spatial extent and richness,' in Proc. ICASSP 2002, Orlando, Florida, vol. 3, May 2002, pp. 2837-2840 https://doi.org/10.1109/ICASSP.2002.1005277
  12. J. W. Craig, 'A new, simple, and exact result for calculating the probability of error for two-dimensional signal constellations,' in Proc. IEEE MILCOM'91, McLean, VA, Nov. 1991, pp. 571-575 https://doi.org/10.1109/MILCOM.1991.258319
  13. G. H. Golub and C. F. Van Loan, Matrix Computations, The Johns Hopkins University Press, Baltimore and London, 3rd ed., 1996
  14. F. D. Neeser and J. L. Massey, 'Proper complex random processes with applications to information theory,' IEEE Trans. Inform. Theory, vol. 39, pp. 1293-1302, July 1993 https://doi.org/10.1109/18.243446
  15. J. P. Kermoal, L. Schumacher, K.I. Pedersen, P. E. Mogensen, and F. Frederiksen, 'A stochastic mimo radio channel model with experimental validation,' IEEE J. Select. Areas Commun., vol. 20, no. 6, pp. 1211-1226, Aug. 2002 https://doi.org/10.1109/JSAC.2002.801223
  16. T. S. Pollock, 'Correlation Modelling in MIMO Systems: When can we Kronecker?,' in Proc. Australian Commun. Theory Workshop, Newcastle, Australia, Feb. 2004, pp. 149-153
  17. V. V. Veeravalli, 'On performance analysis for signaling on correlated fading channels,' IEEE Trans. Commun., vol. 49, no. 11, pp. 1879-1885, Nov. 2001 https://doi.org/10.1109/26.966050
  18. M. K. Simon and M. S. Alouini, Digital Communications over Fading Channels, John Wiley & Sons, 2nd ed., Nov. 2004
  19. T. A. Lamahewa, R. A. Kennedy, and T. D. Abhayapala, 'Upper-bound for the pairwise error probability of space-time codes in physical channel scenarios,' in Proc. 5th Australian Commun. Theory Workshop, Brisbane, Australia, Feb. 2005, pp. 26-32
  20. T. S. Pollock, T. D. Abhayapala, and R. A. Kennedy, 'Introducing space into MIMO capacity calculations,' J. Telecommun. Syst. (Kluwer Academic Publishers), vol. 24, no. 2, pp. 415-436, 2003 https://doi.org/10.1023/A:1026143603179
  21. J. Salz and J. H. Winters, 'Effect of fading correlation on adaptive arrays in digital mobile radio,' IEEE Trans. Veh. Technol., vol. 42, no. 4, pp. 1049-1057, Nov. 1994
  22. J. K. Cavers and P. Ho, 'Analysis of the error performance of trellis coded modulations in Rayleigh fading channels,' IEEE Trans. Commun., vol. 40, no. l, pp. 74-83, Jan. 1992 https://doi.org/10.1109/26.126709
  23. L. Hanlen and M. Fu, 'Wireless communications systems with spatial diversity: A volumetric approach,' in Proc. ICC 2003, vol. 4, 2003, pp. 2673-2677 https://doi.org/10.1109/ICC.2003.1204445