Wireless Personal Communications

, Volume 83, Issue 3, pp 1903–1913 | Cite as

MGF Based Approximate SER Calculation of SM MIMO Systems Over Generalized ημ and κμ Fading Channels

  • B. Kumbhani
  • R. S. KshetrimayumEmail author


Spatial modulation (SM) is a multiple input multiple output (MIMO) wireless communication system that gives better spectral efficiency without costing extra bandwith for the same signal constellation size. In an SM MIMO system with \(N_t\) transmitting antennas, spectral efficiency increases by \(log_2(N_t)\). The superior performance of SM systems over other MIMO systems like Alamouti Space-Time Block Codes and Vertical Bell Laboratories Layered Space-Time is already reported in the literature. In this paper, we analyzed the symbol error rate (SER) performance of an SM system in generalized \(\eta-\mu \) and \(\kappa - \mu \) fading channels for several modulation schemes. A closed form expression for approximate SER is derived using moment generating function (MGF) approach and the results are validated using Monte Carlo simulations. The approximate SER expression obtained in this communication is applicable for any fading channels whose MGF is known. The SER analysis over generalized fading channels can be easily deduced to various classical fading channels like Rayleigh, Rician, Nakagami-m and Nakagami-q fading channels by choosing appropriate values of \(\kappa \), \(\mu \) and \(\eta \).


Spatial modulation Fading channels \(\eta-\mu \) distribution \(\kappa - \mu \) distribution BER performance 



First author would like to thank Mr. Kalpant Pathak for his help in simulation of \(\eta-\mu \) fading channel.


  1. 1.
    Foschini, G. J., & Gans, M. J. (1998). On limits of wireless communications in a fading environment when using multiple antennas. Wireless Personal Communications, 6(3), 311–335.CrossRefGoogle Scholar
  2. 2.
    Wolniansky, P. W., Foschini, G. J., Golden, G.D., & Valenzuela, R. (1998). V-BLAST: An architecture for realizing very high data rates over the rich-scattering wireless channel. In: Proceedings URSI International Symposium on Signals, Systems, and Electronics, (pp. 295–300).Google Scholar
  3. 3.
    Sanayei, S., & Nosratinia, A. (2004). Antenna selection in MIMO systems. IEEE Communications Magazine, 42(10), 68–73.CrossRefGoogle Scholar
  4. 4.
    Jeganathan, J., Ghrayeb, A., Szczecinski, L., & Ceron, A. (2009). Space shift keying modulation for MIMO channels. IEEE Transactions on Wireless Communications, 8(7), 3692–3703.CrossRefGoogle Scholar
  5. 5.
    Mesleh, R. Y., Haas, H., Sinanovic, S., Ahn, C. W., & Yun, S. (2008). Spatial modulation. IEEE Transactions on Vehicular Technology, 57(4), 2228–2241.CrossRefGoogle Scholar
  6. 6.
    Mesleh, R., Haas, H., Ahn, C. W., & Sangboh, Y. (2006). Spatial modulation—A new low complexity spectral efficiency enhancing technique. In: Proceedings First International Conference on Communications and Networking in China, (pp. 1–5).Google Scholar
  7. 7.
    Younis, A., Sinanovic, S., Renzo, M. D., Mesleh, R. Y., & Haas, H. (2013). Generalised sphere decoding for spatial modulation. IEEE Transactions on Communications, 61(7), 2805–2815.CrossRefGoogle Scholar
  8. 8.
    Wang, J., Jia, S., & Song, J. (2013). Signal vector based detection scheme for spatial modulation. IEEE Communications Letters, 16(1), 19–21.CrossRefGoogle Scholar
  9. 9.
    Jeganathan, J., Ghrayeb, A., & Szczecinski, L. (2008). Spatial modulation: Optimal detection and performance analysis. IEEE Communications Letters, 12(8), 545–547.CrossRefGoogle Scholar
  10. 10.
    Renzo, M. D., & Haas, H. (2011). Bit error probability of space modulation over Nakagami-m fading: Asymptotic analysis. IEEE Communications Letters, 15(10), 1026–1028.CrossRefGoogle Scholar
  11. 11.
    Younis, A., Serafimovski, N., Mesleh, R., & Haas, H. (2010). Generalised spatial modulation. In: Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers (ASILOMAR), (pp. 1498–1502).Google Scholar
  12. 12.
    Luna-Rivera, J. M., Gonzalez-Perez, M. G., & Campos-Delgado, D. U. (2014). Improving the performance of spatial modulation schemes for MIMO channels. Wireless Personal Communications, 77(3), 2061–2074.CrossRefGoogle Scholar
  13. 13.
    Osamah, B. S., & Raed, M. (2013). Spatial modulation performance analysis over generalized \(\eta-\mu \) fading channels. In: Proceedings 24th International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC), (pp. 886–890).Google Scholar
  14. 14.
    Yacoub, M. D. (2007). The κ–μ distribution and the η–μ distribution. IEEE Antennas and Propagation Magazine, 49(1), 68–81.CrossRefGoogle Scholar
  15. 15.
    Dixit, D., & Sahu, P. R. (2012). Performance of L-branch MRC receiver in η–μ and κ–μ fading channels for QAM signals. IEEE Wireless Communications Letters, 1(4), 316–319.CrossRefGoogle Scholar
  16. 16.
    Di Renzo, M., & Haas, H. (2012). Bit error probability of SM-MIMO over generalized fading channels. IEEE Transactions on Vehicular Technology, 61(3), 1124–1144.CrossRefGoogle Scholar
  17. 17.
    Chen, Y., & Tellambura, C. (2004). Distribution functions of selection combiner output in equally correlated Rayleigh, Rician, and Nakagami-m fading channels. IEEE Transactions on Communications, 52(11), 1948–1956.CrossRefGoogle Scholar
  18. 18.
    Chiani, M., Dardari, D., & Simon, M. K. (2003). New exponential bounds and approximations for the computation of error probability in fading channels. IEEE Transactions on Wireless Communications, 2(4), 840–845.CrossRefGoogle Scholar
  19. 19.
    Ermolova, N. Y. (2008). Moment generating functions of the generalized η–μ and κ–μ distributions and their applications to performance evaluations of communication systems. IEEE Communications Letters, 12(7), 502–504.MathSciNetCrossRefGoogle Scholar
  20. 20.
    Simon, M. K., & Alouini, M. S. (2004). Digital communication over fading channels , 12(7) (pp. 502–504). New York: Wiley.Google Scholar
  21. 21.
    Koca, M., & Sari, H. (2012). Performance analysis of spatial modulation over correlated fading channels. In: Proceedings IEEE Vehicular Technology Conference (VTC Fall), (pp. 1–5).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Electronics and Electrical EngineeringIndian Institute of Technology GuwahatiGuwahatiIndia

Personalised recommendations