Sigma-Delta Modulation Based Adaptive Channel Equalizer Based on Wiener–Hopf Equations

Abstract

Recenlty, short word length DSP systems are proposed and reported that they outperform compared to their counterpart multi-bit systems in the sense of area-performance-power analysis. In this continuation, this paper presents the application of sigma-delta modulation (SDM) in the design of adaptive channel equalizer using the Wiener filter for wireless and underwater acoustic communication (UWA). To validate the application, various aspects of design are taken into consideration and comparison is carried out with contemporary (i.e., multi-bit) approach. Besides, FPGA based implementation of SDM based design and conventional approach is also carried out to endorse the proposed algorithm to be used in hardware based implementation. The results given in terms of area -perfromance analysis show that proposed algorithm works as desired and it opens the way of using the sigma-delta modulation in adaptive signal processing domain for UWA that has remained a quite challenging task ever before.

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References

  1. 1.

    Pham, T. C., Hoang, B. X., Chiem, Q. T., Tran, L. D., & Ho, A.-V. (2018). Implementation of a short word length ternary FIR filter in both FPGA and ASIC. In 2018 2nd International conference on recent advances in signal processing, telecommunications & computing (SigTelCom), pp. 45–50.

  2. 2.

    Memon, T., Beckett, P., & Sadik, A. Z. (2012). Sigma-delta modulation based digital filter design techniques in FPGA. ISRN Electronics, 2012, 1–10.

    Article  Google Scholar 

  3. 3.

    Memon, T. D., Beckett, P., & Sadik, A. Z. (2013). Power-area-performance characteristics of FPGA-based sigma-delta fir filters. Journal of Signal Processing Systems, 70, 275–288.

    Article  Google Scholar 

  4. 4.

    A. C. Thompson, P. J. O'Shea, and Z. Hussain, “Performance of a new single-bit ternary filtering system,” 2003.

  5. 5.

    Thompson, A. C., O'Shea, P., Hussain, Z. M., & Steele, B. R. (2004). Efficient single-bit ternary digital filtering using sigma-delta modulator. IEEE Signal Processing Letters, 11, 164–166.

    Article  Google Scholar 

  6. 6.

    Pfann, E., & Stewart, R. W. (1998). LMS adaptive filtering with/spl Sigma//spl Delta/modulated input signals. IEEE Signal Processing Letters, 5, 95–97.

    Article  Google Scholar 

  7. 7.

    Hussain, Z., O’Shea, P., & Sadik, A. (2006). Adaptive algorithm for ternary filtering. Electronics Letters, 42, 1–2.

    Article  Google Scholar 

  8. 8.

    Memon, T., Beckett, P., Sadik, A., & O’Shea, P. (2011). Single-bit adaptive channel equalization for narrowband signals. In TENCON 2011.

  9. 9.

    Sadik, A., Hussain, Z., & O'Shea, P. (2006). Adaptive algorithm for ternary filtering. Electronics Letters, 42, 420–421.

    Article  Google Scholar 

  10. 10.

    Sadik, A. Z., & Hussain, Z. M. (2007). Short word-length LMS filtering. In 2007 9th International symposium on signal processing and its applications, pp 1–4.

  11. 11.

    Sadik, A. Z., & Hussain, Z. M. (2007) Short word-length LMS filtering. In 2007 9th International symposium on signal processing and its applications, 2007. ISSPA, pp. 1–4.

  12. 12.

    Xerri, B., Cavassilas, J.-F., & Borloz, B. (2002). Passive tracking in underwater acoustic. Signal Processing, 82, 1067–1085.

    Article  Google Scholar 

  13. 13.

    Singer, A. C., Nelson, J. K., & Kozat, S. S. (2009). Signal processing for underwater acoustic communications. IEEE Communications Magazine, 47, 90–96.

    Article  Google Scholar 

  14. 14.

    Kilfoyle, D. B., & Baggeroer, A. B. (2000). The state of the art in underwater acoustic telemetry. IEEE Journal of Oceanic Engineering, 25, 4–27.

    Article  Google Scholar 

  15. 15.

    Kari, D., Vanli, N. D., & Kozat, S. S. (2016). Adaptive and efficient nonlinear channel equalization for underwater acoustic communication. arXiv preprint arXiv:1601.01218.

  16. 16.

    Song, A., & Badiey, M. (2005). Generalized equalization for underwater acoustic communications. In Proceedings of OCEANS 2005 MTS/IEEE, pp. 1522–1527.

  17. 17.

    Yeo, K., Pelekanakis, K. , & Chitre, M. (2011) Time-domain equalization for underwater acoustic ofdm systems with insufficient cyclic prefix. In OCEANS’11 MTS/IEEE KONA, pp. 1–5.

  18. 18.

    Poularikas, A. D., & Ramadan, Z. M. (2006). Adaptive filtering primer with MATLAB. Boca Raton: CRC Press.

    Google Scholar 

  19. 19.

    Haykin, S. S., Widrow, B., & Widrow, B. (2003). Least-mean-square adaptive filters (Vol. 31). New York: Wiley.

    Google Scholar 

  20. 20.

    Widrow, B. (1971). Adaptive filters. In R. E. Kalman, N. DeClaris (Eds.), Aspects of network and system theory, pp. 563–587. Holt, Rinehart and Winston.

  21. 21.

    Hussain, Z. M., Sadik, A. Z., & O’Shea, P. (2011). Digital signal processing: an introduction with MATLAB and applications. Berlin: Springer.

    Google Scholar 

Download references

Acknowledgements

This research work is supported by the Higher Education Commission (HEC), Pakistan under the National Research Program for Universities (NRPU) grant Number 8521 and National Center for Robotics and Automation (NCRA) joint lab titled “Haptics, Human Robotics and Condition Monitoring Systems (HHCMS) Lab” established at Mehran University of Engineering and Technology, Jamshoro.

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Correspondence to Aneela Pathan.

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Pathan, A., Memon, T.D. Sigma-Delta Modulation Based Adaptive Channel Equalizer Based on Wiener–Hopf Equations. Wireless Pers Commun 116, 1123–1135 (2021). https://doi.org/10.1007/s11277-019-06951-5

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Keywords

  • Sigma-delta modulation
  • Short word length systems
  • Acoustic communication
  • Wiener–Hopf
  • FPGA