OFDM Signal Processing and Analysis in the Presence of Noise Using Wavelet Transform for Temporal Synchronization

Introduction. Temporal synchronization is a relevant issue for various radio communication, radio navigation, and radar systems, for determination of time points for impulse signal arrival and positioning. The radio communication problem should ensure an error-free signal transmission via a radio channel at a maximum possible transmission rate. The known solutions of the temporal synchronization problem in the case of orthogonal frequency-division multiplexing (OFDM) signal transmission employ a guard interval for computing the periodic autocorrelation function of the analyzed OFDM-signal, which leads to unproductive costs of the time-frequency resource. In this paper, we discuss the problem of processing and analysis of OFDM-signals in the presence of noise and estimation of the time point of OFDM-signal arrival.

Aim. Development of an algorithm for time synchronization of OFDM signals in the presence of noise in the radio communication channel using fast computing algorithms based on the harmonic wavelet transform.

Materials and methods. The research was conducted using the methods of wavelet transform and wavelet-based signal processing including the harmonic wavelet transform on the basis of the octave filter bank, fast computational algorithms aimed at computing the harmonic wavelet transform.

Results. A new method for OFDM signal processing in the presence of noise based on the octave harmonic wavelet transform is suggested. This method allows determination of boundaries of orthogonality intervals in an OFDM-signal along with the moments of the onset and end of orthogonality intervals. An algorithm for finding the time point of OFDM signal arrival is proposed. It is shown that the increase of the analysis window of an OFDM signal leads to an improvement in the temporal synchronization accuracy, although requiring more time for establishing synchronization. The suggested approach does not employ the guard interval, thus increasing the information transmission rate.

Conclusion. The harmonic wavelet transform is effective for the analysis and processing of OFDM signals. Furthermore, the aforementioned transform works perfectly well both in the absence and in the presence of noise. The harmonic wavelet transform allows determination of boundaries of orthogonality intervals with maximum possible accuracy. Based on complex vectors, which correspond to the boundaries of orthogonality intervals, the time point of OFDM-signal arrival can be found.

1. Bakulin M. G., Kreindelyin V. B., Shloma A. M., Shumov A. P. Technologia OFDM [OFDM Technology]. Moscow, Goryachaya Linia Telecom, 2021, 360 p. (In Russ.)

2. Egorov V. V., Timofeev A. E. Establishing Time-frequency Synchronization in Multi-frequency Short-wave Data Transmission Systems. Electrical Communications. 2013, no. 7, pp. 41–44. (In Russ.)

3. Shakhtarin B. I., Sizykh V. V., Sidorkina Yu. A., Andrianov I. M., Kalashnikov K. S. Synchronizatsia v radiosvyazi I radionavigatsii [Synchronization in Radio Communications and Radio Navigation]. Moscow, Goryachaya Linia Telecom, 2011, 278 p. (In Russ.)

4. Proakis J. Tsifrovsaya svyaz [Digital Communications]. Moscow, Radio I Svyaz, 2000, 800 p. (In Russ.)

5. Egorov V. V., Klionskiy D. M. Application of the Harmonic Wavelet-Transform for OFDM Signal Processing in a Non-Stationary Radio Channel. Digital Signal Processing. 2024, no. 2, pp. 57–63. (In Russ.)

6. Ifeachor E. C., Jervis B. W. Digital Signal Processing: A Practical Approach. 2nd ed. New Jersey, Prentice Hall, 2004, 960 p.

7. Solonina A. I., Arbuzov S. M. Tsifrovaya obrabotka signalov. Modelirovanie v Matlab [Digital Signal Processing. Simulation in MATLAB]. St Petersburg, BHV-Peterburg, 2008, 816 p. (In Russ.)

8. Solonina A. I., Ulakhovich D. A., Arbuzov S. M., Solov'eva E. B. Osnovi tsifrovoy obrabotki signalov : kurs lectsiy [Fundamentals of Digital Signal Processing: a Lecture Course]. 2nd ed. St Petersburg, BHVPeterburg, 2005, 768 p. (In Russ.)

9. Oppenheim A. V., Schafer R. W. Digital Signal Processing. 1st ed. London, Pearson, 1975, 585 p.

10. Rabiner L. R., Gold B. Theory and Application of Digital Signal Processing. 1st ed. New Jersey, Prentice Hall, 1975, 762 p.

11. Solonina A. I., Klionskiy D. M., Merkucheva T. V., Perov S. N. Tsifrovaya obrabotka signalov i MATLAB [Digital Signal Processing and MATLAB]. St Petersburg, BHV-Peterburg, 2013, 512 p. (In Russ.)

12. Solonina A. I. Tsifrovaya obrabotka signalov v zerkale MATLAB [Digital Signal Processing in the Mirror of MATLAB]. St Petersburg, BHV-Peterburg, 2018, 560 p. (In Russ.)

13. Mallat S. G. A Wavelet Tour of Signal Processing. Heidelberg, Academic Press, 1998, 577 p.

14. Smolentsev N. K. Vawelet analiz v Matlab [Wavelet Analysis in MATLAB]. 3rd ed. Moscow, DMK, 2010, 448 p. (In Russ.)

15. Daubechies I. Ten Lectures Of Wavelets. Cham, Springer-Verlag, 1992, 341 p.

16. Chuyi K. Vvedenie v veivleti [Introduction to Wavelets]. Moscow, Mir, 2001, 412 p. (In Russ.)

17. Freiser M. Vvedenie v waveleti v svete lineinoi algebri [Introduction to Wavelets in the Light of Linear Algebra]. Moscow, Laboratoria Znaniy, 2007, 487 p. (In Russ.)

18. Percival D. B., Walden A. T. Wavelet Methods for Time Series Analysis. Cambridge, Cambridge University Press, 2006, 569 p.

19. Newland D. E. Harmonic Wavelet Analysis. Proc. of the Royal society of London, Series A (Mathematical and Physical Sciences). 1993, vol. 443, no. 1917, pp. 203–225. doi: 10.1098/rspa.1993.0140

20. Newland D. E. An Introduction to Random Vibrations, Spectral and Wavelet Analysis. 3rd ed. New York, Prentice Hall, 1996, 503 p.

21. Newland D. E. Harmonic and Musical Wavelets. Proc. of the royal society of London (Mathematical and Physical Sciences). 1994, vol. 444, no. 1922, pp. 605–620. doi: 10.1098/rspa.1994.0042

22. Oreshko N. I., Geppener V. V., Klionskiy D. M. Primenenie garmonicheskih waveletov v zadachah obrabotki oscilliruuchih signalov [Application of Harmonic Wavelets to Oscillating Signal Processing Problems]. Digital Signal Processing. 2012, no. 2, pp. 6–14. (In Russ.)

23. Oreshko N. I, Klionskiy D. M. Characteristiki realnih wavelet-filtrov primenitelno k harmonicheskomu wavelet-preobrazovaniyu [Characteristics of Real Wavelet-filters Relative to Harmonic Wavelet Transform], DSPA’2013: 15th Intern. Conf., Moscow, 27–29 March 2013, pp. 302–306. (In Russ.)