Skip to main content

Capacity analysis of cooperative amplify and forward–quadrature spatial modulation MIMO system


Quadrature spatial modulation (QSM) multiple-input multiple-output system attracted substantial research interests lately driven by the several promised advantages. As well, cooperative communication is well-known to enhance the diversity gain and the overall system performance. In this paper, the theoretical capacity of amplify and forward (AF)-QSM system is derived and analyzed. In particular, the mutual information is first obtained and used to obtain the capacity. Derived formulas are corroborated through Monte Carlo simulation results over wide range of system and channel parameters. Besides, the impact of various parameters on the capacity and the mutual information of the studied system is investigated. The performance of AF-QSM is compared with AF-spatial modulation system and superior gains are reported. It is revealed that the capacity of AF-QSM is independent of the channel fading distribution where Rayleigh, Rician and Nakagami-m fading channels are considered. It is also reported that increasing the number of transmit antennas enhances the performance whereas increasing the number of relays degrades the performance.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5


  1. 1.

    Mesleh, R., & Alhassi, A. (2018). Space modulation techniques. New York: Wiley.

    Book  Google Scholar 

  2. 2.

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

    Article  Google Scholar 

  3. 3.

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

    Article  Google Scholar 

  4. 4.

    Al-Nahhal, I., Dobre, O. A., & Ikki, S. S. (2017). Quadrature spatial modulation decoding complexity: Study and reduction. IEEE Wireless Communications Letters, 6(3), 378–381.

    Article  Google Scholar 

  5. 5.

    Mesleh, R., Hiari, O., Younis, A., & Alouneh, S. (2017). Transmitter design and hardware considerations for different space modulation techniques. IEEE Transactions on Wireless Communications, 16(11), 7512–7522.

    Article  Google Scholar 

  6. 6.

    Basar, E., Wen, M., Mesleh, R., Di Renzo, M., Xiao, Y., & Haas, H. (2017). Index modulation techniques for next-generation wireless networks. IEEE Access, 5, 16 693-16 746.

    Article  Google Scholar 

  7. 7.

    Wen, M., Zheng, B., Kim, K. J., Di Renzo, M., Tsiftsis, T. A., Chen, K.-C., & Al-Dhahir, N. (2019). A survey on spatial modulation in emerging wireless systems: Research progresses and applications. IEEE Journal on Selected Areas in Communications, 37(9), 1949–1972.

    Article  Google Scholar 

  8. 8.

    Li, Q., Wen, M., Basar, E., Poor, H. V., & Chen, F. (2019). Spatial modulation-aided cooperative noma: Performance analysis and comparative study. IEEE Journal of Selected Topics in Signal Processing, 13(3), 715–728.

    Article  Google Scholar 

  9. 9.

    Zhang, K., Leng, S., He, Y., Maharjan, S., & Zhang, Y. (2018). Cooperative content caching in 5g networks with mobile edge computing. IEEE Wireless Communications, 25(3), 80–87.

    Article  Google Scholar 

  10. 10.

    Asshad, M., Khan, S. A., Kavak, A., Küçük, K., & Msongaleli, D. L. (2019). Cooperative communications using relay nodes for next-generation wireless networks with optimal selection techniques: A review. IEEJ Transactions on Electrical and Electronic Engineering, 14(5), 658–669.

    Article  Google Scholar 

  11. 11.

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

  12. 12.

    Mesleh, R., Ikki, S. S., Tumar, I., & Alouneh, S. (2017). Decode-and-forward with quadrature spatial modulation in the presence of imperfect channel estimation. Physical Communication, 24, 103–111.

    Article  Google Scholar 

  13. 13.

    Liu, K. R., Sadek, A. K., Su, W., & Kwasinski, A. (2009). Cooperative Communications and Networking. Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  14. 14.

    Afana, A., Mesleh, R., Ikki, S., & Atawi, I. E. (2015). Performance of quadrature spatial modulation in amplify-and-forward cooperative relaying. IEEE Communications Letters, 20(2), 240–243.

    Article  Google Scholar 

  15. 15.

    Mesleh, R., & Ikki, S. S. (2013). Performance analysis of spatial modulation with multiple decode and forward relays. IEEE Wireless Communications Letters, 2(4), 423–426.

    Article  Google Scholar 

  16. 16.

    Younis, A., & Mesleh, R. (2018). Information-theoretic treatment of space modulation MIMO systems. IEEE Transactions on Vehicular Technology, 67(8), 6960–6969.

    Article  Google Scholar 

  17. 17.

    Mesleh, R., & Younis, A. (Sep. 2019). Impact of channel estimation errors on the capacity of space modulation techniques. In IEEE 30th annual international symposium on personal, indoor and mobile radio communications (PIMRC) (Vol. 8–11, pp. 1–6). Istanbul, Turkey.

  18. 18.

    Laneman, J. N., Tse, D. N. C., & Wornell, G. W. (2004). Cooperative diversity in wireless networks: Efficient protocols and outage behavior. IEEE Transactions on Information Theory, 50(12), 3062–3080.

    MathSciNet  Article  Google Scholar 

  19. 19.

    Beres, E., & Adve, R. (2008). Selection cooperation in multi-source cooperative networks. IEEE Transactions on Wireless Communications, 7(1), 118–127.

    Article  Google Scholar 

  20. 20.

    Cover, T. M., & Thomas, J. A. (2006). Elements of information theory. New York: Wiley.

    MATH  Google Scholar 

  21. 21.

    Younis, A., Mesleh, R., & Haas, H. (2016). Quadrature spatial modulation performance over nakagami-\(m\) fading channels. IEEE Transactions on Vehicular Technology, 65(12), 10 227-10 231.

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Abdelhamid Younis.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Eltira, K., Younis, A. & Mesleh, R. Capacity analysis of cooperative amplify and forward–quadrature spatial modulation MIMO system. Wireless Netw 27, 5263–5270 (2021).

Download citation


  • Quadrature spatial modulation
  • Amplify and forward
  • Capacity analysis
  • Mutual information