Skip to main content
SpringerLink
Log in

A Simple Analytical Design Approach to Space Time Trellis Codes

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

The space time trellis code (STTC) is a combined design of error-control coding, modulation and transmit-receive diversity that improves data rate and error performance in a wireless channel without any loss in spectral efficiency. It can either be described by a graphical representation, or, in terms of closed analytical forms that lead to a more tractable generator matrix description. However, the main difficulty in generating best code is the long search duration which makes both trellis implementation and generator matrix description difficult, thereby, limiting the use of STTC in wireless links. Since an exhaustive search over all the matrix entries turns out to be impractical if the number of transmitter, encoder states and/or constellation size is very high, some literature provide techniques to reduce the search complexity. Some of them are sub-optimal, some are good. However, none reports any straightforward rule of thumb to design the generator matrix. In this paper, we propose two very simple rules to construct the generator matrix for designing STTC with any arbitrary number of transmit antennas and any memory-less constellation. Mathematical justification behind the rules has been presented. It has been shown that the simplicity of proposed rules reduces the code search complexity to a large extent along with a similar or better coding gain compared to those presented in previous literature. In addition, the STTCs obtained from proposed rules perform no worse than the codes given in previous literature in terms of error rate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

References

  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, 311–335.

    Article  Google Scholar 

  2. Telatar, E. (1999). Capacity of multi-antenna Gaussian channels. European Transactions on Telecommunications, 10(6), 585–595.

    Article  Google Scholar 

  3. Mietzner, J., Schober, R., Lampe, L., Gerstacker, W. H., & Hoeher, P. A. (2009). Multiple-antenna techniques for wireless communications—a comprehensive literature survey. IEEE Communications Surveys & Tutorials, 11(2), 87–105. Second Quarter 2009.

    Google Scholar 

  4. Jafarkhani, H. (2005). Space-time coding: Theory and practice. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  5. Tarokh, V., Seshadri, N., & Calderbank, A. (1998). Space-time codes for high data rate wireless communication: Performance criterion and code construction. IEEE Transactions on Information Theory, 44(2), 744–765.

    Article  MATH  MathSciNet  Google Scholar 

  6. Tarokh, V., Naguib, A., Seshadri, N., & Calderbank, A. (1999). Space-time codes for high data rate wireless communication: Performance criteria in the presence of channel estimation errors, mobility, and multiple paths. IEEE Transactions on Communications, 47(2), 199–207.

    Article  MATH  Google Scholar 

  7. Alamouti, S. (1998). A simple transmit diversity technique for wireless communications. IEEE Journal on Selected Areas in Communications, 16(8), 1451–1458.

    Article  Google Scholar 

  8. Tarokh, V., Jafarkhani, H., & Calderbank, A. (1999). Space-time block codes from orthogonal designs. IEEE Transactions on Information Theory, 45(5), 1456–1467.

    Article  MATH  MathSciNet  Google Scholar 

  9. Garrett, D. C., Davis, L. M., & Woodward, G. K. (2003). 19.2 Mbit/s 4 4 BLAST/MIMO detector with soft ML outputs. Electronics Letters, 39(2), 233–235.

    Article  Google Scholar 

  10. Tyagi, A., & Bose, R. (2007). A new distance notion for PPAM space-time trellis codes for UWB MIMO communications. IEEE Transactions on Communications, 55(7), 1279–1282.

    Article  Google Scholar 

  11. Ilhan, H., Altunbas, I., & Uysal, M. (2010). Novel distributed space-time trellis codes for relay systems over cascaded Rayleigh fading. IEEE Communications Letters, 14(12), 1140–1142.

    Article  Google Scholar 

  12. Basar, E., Aygolu, U., Panayirci, E., & Poor, H. V. (2011). New trellis code design for spatial modulation. IEEE Transactions on Wireless Communications, 10(8), 2670–2680.

    Article  Google Scholar 

  13. Li, M., Zheng, Z.-W., Ma, X.-H., Sun, P.-F., & Yao, Y. (2012). Space-time trellis coding in MIMO-OFDM system. In 2nd International conference on consumer electronics, communications and networks (CECNet) (pp. 1298–1301).

  14. Sandhu, S., & Paulraj, A. (2000). Space-time block codes: A capacity perspective. IEEE Communications Letters, 4(12), 384–386.

    Article  Google Scholar 

  15. Safar, Z., & Liu, K. (2002). Systematic design of space-time trellis codes for diversity and coding advantages. EURASIP Journal on Applied Signal Processing, 2002(3), 221–235.

    Article  MATH  MathSciNet  Google Scholar 

  16. Calderbank, R., & Mazo, J. E. (1984). A new description of trellis codes. IEEE Transactions on Information Theory, 30(6), 784–791.

    Article  MATH  MathSciNet  Google Scholar 

  17. Baro, S., Bauch, G., & Hansmann, A. (2000). Improved codes for space-time trellis coded modulation. IEEE Communications Letters, 4(1), 20–22.

    Article  Google Scholar 

  18. Gozali, R., & Woerner, B. D. (2000). Applying the Calderbank–Mazo algorithm to space-time trellis coding. In Proceedings of the IEEE Southeastcon, 2000 (pp. 309–314).

  19. Chen, Z., Vucetic, B., Yuan, J., & Lo, K. (2002). Space-time trellis codes for 4-PSK with three and four transmit antennas in quasi-static flat fading channels. IEEE Communications Letters, 6(2), 67–69.

    Article  MATH  Google Scholar 

  20. Chen, Z., Vucetic, B., Yuan, J., & Lo, K. L. (2002). Space-time trellis codes with two, three and four transmit antennas in quasi-static flat fading channels. In IEEE international conference on communications, 2002 (ICC 2002) (Vol. 3, pp. 1589–1595).

  21. Yuan, J., Chen, Z., Vucetic, B., & Firmanto, W. (2003). Performance and design of space-time coding in fading channels. IEEE Transactions on Communications, 51(12), 1991–1996.

    Article  Google Scholar 

  22. Liao, C., & Prabhu, V. K. (2005). Improved code design criteria for space-time codes over quasi-static flat fading channels. In 2005 IEEE 6th workshop on signal processing advances in wireless communications (pp. 7–11).

  23. Hong, Y., Guillen, I., & Fabregas, A. (2007). New space-time trellis codes for two-antenna quasi-static channels. IEEE Transactions on Vehicular Technology, 56(6), 3581–3587.

    Article  Google Scholar 

  24. Viland, P., Zaharia, G., & Helard, J. F. (2010). Euclidean distance decomposition to generate new 16-QAM and 64-QAM space-time trellis codes. In IEEE 21st international symposium on in personal indoor and mobile radio communications (PIMRC), 2010 (pp. 385–390).

  25. Harun, H., Dimyati, K., & Ungku Chulan, U. A. (2011). Optimal generator matrix G. Aerospace Science and Technology, 24(1), 136–140.

    Article  Google Scholar 

  26. Tao, M., & Cheng, R. S. (2001). Improved design criteria and new trellis codes for space-time coded modulation in slow flat fading channels. IEEE Communications Letters, 5(7), 313–315.

    Article  Google Scholar 

  27. Yan, Q., & Blum, R. S. (2000). Optimum space-time convolutional codes. In IEEE wireless communications and networking conference, 2000. WCNC. 2000 (Vol. 3, pp. 1351–1355).

  28. Inoue, A., & Ohtsuki, T. (2004). Performance factors for space-time trellis codes in block fading channels. In 15th IEEE international symposium on personal, indoor and mobile radio communications, 2004. PIMRC 2004 (Vol. 4, pp. 2616–2620).

  29. Bernier, D., & Chan, F. (2004). Improved space-time trellis codes with three and four transmit antennas. In IEEE Canadian conference on electrical and computer engineering (Vol. 4, pp. 2089–2093).

  30. Fukuda, T., Otsu, S., Tokunaga, Y., & Zhao, H. (2008). A realization of determinant criterion for STTC design. In Proceedings of the 23rd international technical conference on circuits/systems, computers and communications (ITC-CSCC 2008) (pp. 61–64).

  31. Harun, H., Chulan, U. A. N. U, Chulan, U. A. I. U., & Khazani, K. (2013). Improving the evaluation of generator matrix G by initial upper bound estimation. In Computing communications and IT applications conference (ComComAp), 2013 (pp. 85–89).

  32. Yan, Q., & Blum, R. S. (2002). Improved space-time convolutional codes for quasi-static slow fading channels. IEEE Transactions on Wireless Communications, 1(4), 563–571.

    Article  Google Scholar 

  33. Abdool-Rassool, B., Nakhai, M. R., Heliot, F., Revelly, L., & Aghvami, H. (2004). Search for spacetime trellis codes novel codes: For Rayleigh fading channels. IEE Proceedings-Communications, 151(1), 25–31.

    Article  Google Scholar 

  34. Viland, P., Zaharia, G., & Hlard, J. F. (2011). Optimal generation of spacetime trellis codes via coset partitioning. IEEE Transactions on Vehicular Technology, 60(3), 966–980.

    Article  Google Scholar 

  35. Viterbi, A. (1967). Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Transactions on Information Theory, 13(2), 260–269.

    Article  MATH  Google Scholar 

  36. Mesleh, R., Renzo, M. D., Haas, H., & Grant, P. M. (2010). Trellis coded spatial modulation. IEEE Transactions on Wireless Communications, 9(7), 2349–2361.

    Article  Google Scholar 

  37. Di Renzo, M., Mesleh, R. Y., Haas, H., & Grant, P. M. (2010). Upper bounds for the analysis of trellis coded spatial modulation over correlated fading channels. In IEEE 71st vehicular technology conference (VTC 2010-Spring) (pp. 1–5).

  38. Vladeanu, C. (2012). Turbo trellis-coded spatial modulation. In 2012. IEEE global communications conference (GLOBECOM) (pp. 4024–4029).

Download references

Author information

Authors and Affiliations

  1. Centre for Applied Research in Electronics, Indian Institute of Technology Delhi, New Delhi , 110016, India

    Sharbari Banerjee & Monika Agrawal

Authors
  1. Sharbari Banerjee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Monika Agrawal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sharbari Banerjee.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Banerjee, S., Agrawal, M. A Simple Analytical Design Approach to Space Time Trellis Codes. Wireless Pers Commun 75, 1141–1154 (2014). https://doi.org/10.1007/s11277-013-1412-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-013-1412-5

Keywords

Search

Navigation