Skip to main content

Cooperative decode-and-forward quadrature spatial modulation over correlated and imperfect ημ fading channels


This paper analyzes the performance of quadrature spatial modulation (QSM) multiple-input multiple-output (MIMO) system in cooperative decode and forward (DF) networks over correlated and imperfect \(\eta \)\(\mu \) fading channels. QSM is a recently proposed propitious MIMO technique that promises significant advantages over conventional MIMO schemes including high spectral efficiency with single RF-chain transmitter and very low receiver complexity. In this study, DF cooperative communication system adopting QSM technique is presented and throughly analyzed. Single or multiple DF relays are placed between the source and the destination to cooperate in the transmission process. Only the relays that decode the signal correctly will participate in the retransmission process. The end to end performance of the considered system is analyzed over correlated and imperfect \(\eta \)\(\mu \) fading channels. The \(\eta \)\(\mu \) channel is a general fading distribution that includes some other well-known channels, such as Rayleigh and Nakagami-m, as spacial cases. Monte Carlo simulation results are presented to corroborate the accuracy of the conducted analysis. The impact of spatial correlation, imperfect channel estimation and the fading parameters \(\eta \) and \(\mu \) on the overall performance is investigated and exhaustively discussed.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8


  1. Wang, C. X., Haider, F., Gao, X., You, X. H., Yang, Y., Yuan, D., et al. (2014). Cellular architecture and key technologies for 5G wireless communication networks. IEEE Communications Magazine, 52(2), 122–130.

    Article  Google Scholar 

  2. Mesleh, R., Ikki, S. S., & Aggoune, H. M. (2015). Quadrature spatial modulation. IEEE Transactions on Vehicular Technology, 64(6), 2738–2742.

    Article  Google Scholar 

  3. Mesleh, R. Y., Haas, H., Sinanovic, S., Ahn, C. W., & Yun, S. (2008). Spatial modulation. IEEE Transactions on Vehicular Technology, 57(4), 2228–2241.

    Article  Google Scholar 

  4. Yigit, Z., & Basar, E. (2016). Low-complexity detection of quadrature spatial modulation. Electronics Letters, 52(20), 1729–1731.

    Article  Google Scholar 

  5. Xiao, L., Yang, P., Fan, S., Li, S., Song, L., & Xiao, Y. (2016). Low-complexity signal detection for large-scale quadrature spatial modulation systems. IEEE Communications Letters, 20(11), 2173–2176.

    Article  Google Scholar 

  6. Afana, A., Mahady, I. A., & Ikki, S. (2016). Quadrature spatial modulation in MIMO cognitive radio systems with imperfect channel estimation and limited feedback. IEEE Transactions on Communications.

  7. Mesleh, R., Ikki, S. S., & Badarneh, O. S. (2016). Impact of cochannel interference on the performance of quadrature spatial modulation MIMO systems. IEEE Communications Letters, 20(10), 1927–1930.

    Article  Google Scholar 

  8. Mesleh, R., & Ikki, S. S. (2015, March). On the impact of imperfect channel knowledge on the performance of quadrature spatial modulation. In Wireless Communications and Networking Conference (WCNC), 2015 IEEE (pp. 534–538). IEEE.

  9. Younis, A., Mesleh, R., & Haas, H. (2016). Quadrature spatial modulation performance over Nakagami-\( m \) fading channels. IEEE Transactions on Vehicular Technology, 65(12), 10227–10231.

    Article  Google Scholar 

  10. Badarneh, O. S., & Mesleh, R. (2016). A comprehensive framework for quadrature spatial modulation in generalized fading scenarios. IEEE Transactions on Communications, 64(7), 2961–2970.

    Article  Google Scholar 

  11. Afana, A., Mesleh, R., Ikki, S., & Atawi, I. E. (2016). Performance of quadrature spatial modulation in amplify-and-forward cooperative relaying. IEEE Communications Letters, 20(2), 240–243.

    Article  Google Scholar 

  12. Afana, A., Ikki, S., Mesleh, R., & Atawi, I. (2016). Spectral efficient quadrature spatial modulation cooperative AF spectrum-sharing systems. IEEE Transactions on Vehicular Technology.

  13. Afana, A., Erdogan, E., & Ikki, S. (2016, December). Quadrature spatial modulation for cooperative MIMO 5G wireless networks. In Globecom Workshops (GC Wkshps), 2016 IEEE (pp. 1–5). IEEE.

  14. Yacoub, M. D. (2007). The distribution and the distribution. IEEE Antennas and Propagation Magazine, 49(1), 68–81.

    Article  Google Scholar 

  15. Genc, V., Murphy, S., Yu, Y., & Murphy, J. (2008). IEEE 802.16 J relay-based wireless access networks: An overview. IEEE Wireless Communications, 15(5),

  16. Beaulieu, N. C., & Hu, J. (2006). A closed-form expression for the outage probability of decode-and-forward relaying in dissimilar Rayleigh fading channels. IEEE Communications Letters, 10(12),

  17. Ikki, S. S., & Ahmed, M. H. (2010). Performance analysis of adaptive decode-and-forward cooperative diversity networks with best-relay selection. IEEE Transactions on Communications, 58(1),

  18. Kermoal, J. P., Schumacher, L., Pedersen, K. I., Mogensen, P. E., & Frederiksen, F. (2002). A stochastic MIMO radio channel model with experimental validation. IEEE Journal on Selected Areas in Communications, 20(6), 1211–1226.

    Article  Google Scholar 

  19. Van Zelst, A., & Hammerschmidt, J. S. (2002). A single coefficient spatial correlation model for multiple-input multiple-output (MIMO) radio channels. In 27th general assembly of the International Union of Radio Science (URSI), Maastricht, the Netherlands (1461–1465).

  20. Proakis, J. G. (1995). Digital communications. New York: McGraw Hill.

    MATH  Google Scholar 

  21. Craig, J. W. (1991). A new, simple and exact result for calculating the probability of error for two-dimensional signal constellations. In Military communications conference, 1991. MILCOM’91, conference record, military communications in a changing world,. IEEE (pp. 571–575). IEEE.

  22. Simon, M.K., & Alouini, M., (2005). Digital communication over fading channels (2nd ed.). Wiley series in telecommunications and signal processing. Wiley. ISBN: 978-0-471-64953-3.

  23. Turin, G. L. (1960). The characteristic function of Hermitian quadratic forms in complex normal variables. Biometrika, 47(1/2), 199–201.

    MathSciNet  Article  MATH  Google Scholar 

  24. Yacoub, M. D. (2007). The distribution and the distribution. IEEE Antennas and Propagation Magazine, 49(1), 68–81.

    Article  Google Scholar 

  25. Papazafeiropoulos, A. K., & Kotsopoulos, S. A. (2009, September). The joint envelope-phase fading distribution. In 2009 IEEE 20th international symposium on personal, indoor and mobile radio communications (pp. 919–922). IEEE.

  26. Abramnowitz, M., & Stegun, I. A. (1972). Handbook of mathematical functions. Washington, DC: US Dept. of Commerce, National Bureau of Standards.

    Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Saud Althunibat.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Althunibat, S., Mesleh, R. Cooperative decode-and-forward quadrature spatial modulation over correlated and imperfect ημ fading channels. Wireless Netw 25, 689–698 (2019).

Download citation

  • Published:

  • Issue Date:

  • DOI:


  • MIMO
  • Quadrature spatial modulation (QSM)
  • Cooperative networks
  • Decode and forward relay networks
  • Performance analysis