Open Access

Error Probability of Binary and -ary Signals with Spatial Diversity in Nakagami- (Hoyt) Fading Channels

EURASIP Journal on Wireless Communications and Networking20072007:053742

DOI: 10.1155/2007/53742

Received: 21 June 2007

Accepted: 30 October 2007

Published: 17 December 2007


We analyze the exact average symbol error probability (SEP) of binary and -ary signals with spatial diversity in Nakagami- (Hoyt) fading channels. The maximal-ratio combining and orthogonal space-time block coding are considered as diversity techniques for single-input multiple-output and multiple-input multiple-output systems, respectively. We obtain the average SEP in terms of the Lauricella multivariate hypergeometric function . The analysis is verified by comparing with Monte Carlo simulations and we further show that our general SEP expressions particularize to the previously known results for Rayleigh ( = 1) and single-input single-output (SISO) Nakagami- cases.


Authors’ Affiliations

School of Electronics and Information, Kyung Hee University


  1. Simon MK, Alouini M-S: A unified approach to the performance analysis of digital communication over generalized fading channels. Proceedings of the IEEE 1998,86(9):1860-1877. 10.1109/5.705532View ArticleGoogle Scholar
  2. Simon MK, Alouini M-S: Digital Communication over Fading Channels: A Unified Approach to Performance Analysis. Wiley-Interscience, New York, NY, USA; 2000.View ArticleGoogle Scholar
  3. Annamalai A, Tellambura C:Error rates for Nakagami- fading multichannel reception of binary and -ary signals. IEEE Transactions on Communications 2001,49(1):58-68. 10.1109/26.898251MATHView ArticleGoogle Scholar
  4. Shin H, Lee JH:On the error probability of binary and -ary signals in Nakagami- fading channels. IEEE Transactions on Communications 2004,52(4):536-539. 10.1109/TCOMM.2004.826373View ArticleGoogle Scholar
  5. Efthymogloua GP, Piboongungon T, Aalo VA:Error rates of -ary signals with multichannel reception in Nakagami- fading channels. IEEE Communications Letters 2006,10(2):100-102. 10.1109/LCOMM.2006.02022.View ArticleGoogle Scholar
  6. Aalo VA, Piboongungon T, Efthymoglou GP:Another look at the performance of MRC schemes in Nakagami- fading channels with arbitrary parameters. IEEE Transactions on Communications 2005,53(12):2002-2005. 10.1109/TCOMM.2005.860089View ArticleGoogle Scholar
  7. Lu J, Tjhung TT, Chai CC:Error probability performance of -branch diversity reception of MQAM in Rayleigh fading. IEEE Transactions on Communications 1998,46(2):179-181. 10.1109/26.659476View ArticleGoogle Scholar
  8. Tellambura C, Mueller AJ, Bhargava VK:Analysis of -ary phase-shift keying with diversity reception for land-mobile satellite channels. IEEE Transactions on Vehicular Technology 1997,46(4):910-922. 10.1109/25.653065View ArticleGoogle Scholar
  9. Ekanayake N:Performance of -ary PSK signals in slow Rayleigh fading channels. Electronics Letters 1990,26(10):618-619. 10.1049/el:19900405View ArticleGoogle Scholar
  10. Shin H, Lee JH:Performance analysis of space—time block codes over keyhole Nakagami- fading chanels. IEEE Transactions on Vehicular Technology 2004,53(2):351-362. 10.1109/TVT.2004.823540View ArticleGoogle Scholar
  11. Shin H, Lee JH: Effect of keyholes on the symbol error rate of space—time block codes. IEEE Communications Letters 2003,7(1):27-29. 10.1109/LCOMM.2002.807428View ArticleGoogle Scholar
  12. Shin H, Win MZ: MIMO diversity in the presence of double scattering. to appear in IEEE Transactions on Information Theory, to appear in IEEE Transactions on Information Theory,
  13. Alamouti SM: A simple transmit diversity technique for wireless communications. IEEE Journal on Selected Areas in Communications 1998,16(8):1451-1458. 10.1109/49.730453View ArticleGoogle Scholar
  14. Tarokh V, Jafarkhani H, Calderbank AR: Space—time block codes from orthogonal designs. IEEE Transactions on Information Theory 1999,45(5):1456-1467. 10.1109/18.771146MATHMathSciNetView ArticleGoogle Scholar
  15. Zogas DA, Karagiannidis GK, Kotsopoulos SA:Equal gain combining over Nakagami- (Rice) and Nakagami- (Hoyt) generalzied fading channels. IEEE Transactions on Wireless Communications 2005,4(2):374-379.View ArticleGoogle Scholar
  16. Fraidenraich G, Filho JCSS, Yacoub MD: Second-order statistics of maximal-ratio and equal-gain combining in Hoyt fading. IEEE Communications Letters 2005,9(1):19-21.View ArticleGoogle Scholar
  17. Youssef N, Wang C-X, Pätzold M: A study on the second order statistics of Nakagami-Hoyt mobile fading channels. IEEE Transactions on Vehicular Technology 2005,54(4):1259-1265. 10.1109/TVT.2005.851353View ArticleGoogle Scholar
  18. Radaydeh RM:Average error performance of -ary modulation schemes in Nakagami- (Hoyt) fading channels. IEEE Communications Letters 2007,11(3):255-257.View ArticleGoogle Scholar
  19. Exton H: Multiple Hypergeometric Functions and Applications. John Wiley & Sons, New York, NY, USA; 1976.MATHGoogle Scholar
  20. Erdelyi A: Higher Transcendental Functions. Volume 1. McGraw-Hill, New York, NY, USA; 1953.MATHGoogle Scholar
  21. Tirkkonen O, Hottinen A: Square-matrix embeddable space-time block codes for complex signal constellations. IEEE Transactions on Information Theory 2002,48(2):384-395. 10.1109/18.978740MATHMathSciNetView ArticleGoogle Scholar
  22. Fraidenraich G, Yacoub MD:The - general fading distribution. Proceedings of the SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (IMOC '03), September 2003, Foz do Iguacu, Brazil 1: 49-54.Google Scholar


© Trung Q. Duong et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.