Research Article
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Improving the BER and PAPR performances of conventional OFDM waveform with sequential LLWT-PTS-AC method

Year 2024, Volume: 39 Issue: 3, 1837 - 1848, 20.05.2024

Bekir Tengizler Efe Kaan Çalışkan Alihan Gülbaz Ali Özen

https://doi.org/10.17341/gazimmfd.1142173

Abstract

One of the major disadvantages of multi-carrier (MC) radio communication systems is the high peak-to-average power ratio (PAPR). Orthogonal frequency division multiplexing (OFDM) system, which is accepted by many standards, is also affected by this disadvantage. In the research literature, many methods, such as amplitude clipping (AC) and filtering, coding, interleaving, tone reservation (TR), tone addition (TI), partial transmit sequence (PTS) and selected mapping (SLM) methods, have been presented to decrease the high PAPR values of MC radio communication systems. In addition, transformations such as fast Walsh Hadamard transform (FWHT) and discrete wavelet transform (DWT) applied to systems are proposed in order to increase other performances of MC radio communication systems using these PAPR reduction methods. In this study, it is suggested to combine PTS and AC technique with Lifting wavelet transform (LLWT) using Lazy wavelet to improve both bit error rate (BER) performance and PAPR performance of MC wireless communication systems. In this article, the LLWT-PTS-AC method, which is the combination of PTS and AC technique with LLWT conversion, which is proposed in this study for the first time, has been applied to the classical OFDM waveform to eliminate the disadvantages of MC radio communication systems, and remarkable results have been obtained. When the results are examined, it is seen that the PAPR and BER performances of the classical OFDM system have increased satisfactorily.

Keywords

OFDM waveform PAPR reduction Lifting wavelet transform PTS LLWT-PTS-AC

Supporting Institution

Yok.

Project Number

Yok

Thanks

Cover letter July 07, 2022 Dear Editor of Journal of the Faculty of Engineering and Architecture of Gazi University, We are submitting a manuscript for consideration of publication in Journal of the Faculty of Engineering and Architecture of Gazi University. The manuscript is entitled “Sıralı LLWT-PTS-AC yöntemi ile klasik OFDM dalga formunun BER ve PAPR performanslarının iyileştirilmesi / Improving the BER and PAPR performances of conventional OFDM waveform with sequential LLWT-PTS-AC method”. It has not been published elsewhere and that it has not been submitted simultaneously for publication elsewhere. Thank you very much for your consideration. Yours Sincerely, Bekir Tengizler1, Efe Kaan Çalışkan1, Alihan Gülbaz1 and Ali Özen1 1Nuh Naci Yazgan Universitesi, Mühendislik Fakültesi, Elektrik Elektronik Mühendisliği Bölümü, 38040, Kayseri, Turkiye Bekir Tengizler Orcid ID: https://orcid.org/0000-0002-9017-7672 Efe Kaan Çalışkan Orcid ID: https://orcid.org/0000-0002-2506-5690 Alihan Gülbaz Orcid ID: https://orcid.org/0000-0003-2831-5058 Ali Özen Orcid ID: https://orcid.org/0000-0003-3232-3181 bekirtengizler@gmail.com, efeak6110@gmail.com, alihan.376.38@gmail.com, aozen@nny.edu.tr İletişim yazarı telefon no: +90 352 324 0000-2292

References

  • 1. Singal A. and Kedia D., “Complexity analysis of SLM PAPR reduction schemes in wireless OFDM system”, 2016 International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT), 2016, pp. 2082-2087, doi: 10.1109/ICEEOT.2016.7755055.
  • 2. Cimini L. J. and Sollenberger N. R., “Peak-to-average power ratio reduction of an OFDM signal using partial transmit sequences”, in IEEE Communications Letters, vol. 4, no. 3, pp. 86-88, March 2000, doi: 10.1109/4234.831033.
  • 3. Bai J., Li Y., Cheng W., Du H. and Wang Y., “A novel peak-to-average power ratio reduction scheme via tone reservation in OFDM systems”, in China Communications, vol. 14, no. 11, pp. 279-290, Nov. 2017, doi: 10.1109/CC.2017.8233667.
  • 4. Gu X., Baek S. and Park S., “PAPR reduction of OFDM signal using an efficient SLM technique”, 2010 The 12th International Conference on Advanced Communication Technology (ICACT), 2010, pp. 324-328.
  • 5. Wang L. and Liu J., “PAPR Reduction of OFDM Signals by PTS With Grouping and Recursive Phase Weighting Methods”, in IEEE Transactions on Broadcasting, vol. 57, no. 2, pp. 299-306, June 2011, doi: 10.1109/TBC.2011.2111210.
  • 6. Yoo S., Yoon S., Kim S. Y. and Song I., “A novel PAPR reduction scheme for OFDM systems: selective mapping of partial tones (SMOPT)”, 2006 Digest of Technical Papers International Conference on Consumer Electronics, 2006, pp. 287-288, doi: 10.1109/ICCE.2006.1598423.
  • 7. Bouquet E., Haese S., Drissi M., Moullec C. and Sayegrih K., “An Innovative and Low Complexity PAPR Reduction Technique for Multicarrier Systems”, 2006 European Conference on Wireless Technology, 2006, pp. 162-165, doi: 10.1109/ECWT.2006.280460.
  • 8. Wang C.-L. and Ouyang Y., “Low-complexity selected mapping schemes for peak-to-average power ratio reduction in OFDM systems”, in IEEE Transactions on Signal Processing, vol. 53, no. 12, pp. 4652-4660, Dec. 2005, doi: 10.1109/TSP.2005.859327.
  • 9. Jiao Y. Z., Liu X. J. and Wang X. A., “A Novel Tone Reservation Scheme with Fast Convergence for PAPR Reduction in OFDM Systems”, 2008 5th IEEE Consumer Communications and Networking Conference, 2008, pp. 398-402, doi: 10.1109/ccnc08.2007.95.
  • 10. Armstrong J., “New OFDM peak-to-average power reduction scheme”, IEEE VTS 53rd Vehicular Technology Conference, Spring 2001. Proceedings (Cat. No.01CH37202), 2001, pp. 756-760 vol.1, doi: 10.1109/VETECS.2001.944945.
  • 11. Deumal M., Vilella C., Pijoan J. L. and Bergada P., “Partially clipping (PC) method for the peak-to-average power ratio (PAPR) reduction in OFDM”, 2004 IEEE 15th International Symposium on Personal, Indoor and Mobile Radio Communications (IEEE Cat. No.04TH8754), 2004, pp. 464-468 Vol.1, doi: 10.1109/PIMRC.2004.1370914.
  • 12. Kliks, A., Bogucka, H. Improving Effectiveness of the Active Constellation Extension Method for PAPR Reduction in Generalized Multicarrier Signals. Wireless Personal Communications vol. 61, pp. 323–334, 2011. https://doi.org/10.1007/s11277-010-0025-5.
  • 13. Wang X., Tjhung T. T. and Wu Y., “On the SER and spectral analyses of A-law companded multicarrier modulation”, in IEEE Transactions on Vehicular Technology, vol. 52, no. 5, pp. 1408-1412, Sept. 2003, doi: 10.1109/TVT.2003.816631.
  • 14. Moazzeni T.; Selvaraj H. and Jiang Y., “A Novel Multi-Exponential Function-based Companding Technique for Uniform Signal Compression over Channels with Limited Dynamic Range”, International Journal of Electronics and Telecommunications, Vol. 56, no. 2, Jun 2010. doi:10.2478/v10177-010-0016-1
  • 15. Huang X., Lu J., Zheng J. and Gu J., “Reduction of PAPR of OFDM signals with piecewise-scales transform”, Proceedings IEEE 56th Vehicular Technology Conference, 2002, pp. 1240-1243 vol.2, doi: 10.1109/VETECF.2002.1040803.
  • 16. Cuteanu V. and Isar A., “PAPR reduction of OFDM signals using hybrid clipping-companding scheme with sigmoid functions”, 2011 International Conference on Applied Electronics, 2011, pp. 1-4.
  • 17. Lakshmanan M. K. and Nikookar H., “A review of wavelets for digital wireless communication”, Wireless Personal Communications, vol. 37, no. 10, pp. 387-420, 2006.
  • 18. Negash B. G. and Nikookar H., “Wavelet-based multicarrier transmission over multipath wireless channels”, IEE Electronics Letters, vol. 36, no. 21, pp. 1787-1788, 2000. doi: 10.1049/el:20001263.
  • 19. Sweldens W., “The lifting scheme: A construction of second generation wavelets”, SIAM Journal of Mathematical Analysis, vol. 29, no. 2, pp. 511-546, 1998. https://doi.org/10.1137/S0036141095289051.
  • 20. Baro M. and Ilow J., “PAPR reduction in OFDM using wavelet packet pre-processing”, 5th IEEE Consumer Communications and Networking Conference (CCNC 2008), pp. 195-199, 2008.
  • 21. Taşpınar N. and Bozkurt Y.T., “PAPR reduction using genetic algorithm in lifting-based wavelet packet modulation systems”, Turkish Journal of Electrical Engineering & Computer Sciences, vol. 24, pp. 184-195, 2016. https://doi.org/10.3906/elk-1306-236.
  • 22. Bozkurt Y. T., Peak-to-avarage power ratio reduction techniques in wavelet packet modulation systems, Ph.D. Dissertation, Erciyes University, Graduate School of Natural and Applied Sciences, Kayseri, September 2017.
  • 23. Kulkarni V. M. and Bhalchandra A. S., “An overview of various techniques to reduce the Peak-to-average power ratio in multicarrier transmission systems”, 2012 IEEE International Conference on Computational Intelligence and Computing Research, 2012, pp. 1-5, doi: 10.1109/ICCIC.2012.6510251.
  • 24. Yıldırım M., Peak-to-avarage power ratio reduction by using intelligent optimisation techniques in wireless communication systems, Ph.D. Dissertation, Erciyes University, Graduate School of Natural and Applied Sciences, Kayseri, January 2018.
  • 25. Zhang X., Duan Y. and Tao G., “The research of peak–to–average power ratio performance by optimum combination of partial transmit sequences in MIMO-OFDM system”, 2010 3rd International Congress on Image and Signal Processing, 2010, pp. 4476-4479, doi: 10.1109/CISP.2010.5646770.
  • 26. O’Neill R. and Lopes L. B., “Envelope variations and spectral splatter in clipped multicarrier signals”, Proceedings of 6th International Symposium on Personal, Indoor and Mobile Radio Communications, 1995, pp. 71-75 vol.1, doi: 10.1109/PIMRC.1995.476406.
  • 27. Tek Y. İ., Yaşar S., Sinop H., Karaerik K., Tuna E. B. and Özen A., “PAPR Reduction Method for Next Generation Waveforms”, 2020 28th Signal Processing and Communications Applications Conference (SIU), 2020, pp. 1-4, doi: 10.1109/SIU49456.2020.9302519.
  • 28. Tengizler B., Sequential LWT-PTS-AC-OFDM Waveform for PAPR Reduction, Bachelor Degree Dissertation, Nuh Naci Yazgan University, Kayseri, June 2022.

Sıralı LLWT-PTS-AC yöntemi ile klasik OFDM dalga formunun BER ve PAPR performanslarının iyileştirilmesi

Year 2024, Volume: 39 Issue: 3, 1837 - 1848, 20.05.2024

Bekir Tengizler Efe Kaan Çalışkan Alihan Gülbaz Ali Özen

https://doi.org/10.17341/gazimmfd.1142173

Abstract

Çok taşıyıcılı (MC) telsiz iletişim sistemlerinin en büyük dezavantajlarından birisi yüksek tepe-ortalama güç oranı (PAPR)’dır. Pek çok standartta kabul edilen dikgen frekans bölmeli çoğullama (OFDM) sistemi de bu dezavantajdan etkilenmektedir. Araştırma literatüründe MC telsiz iletişim sistemlerinin yüksek PAPR seviyelerini azaltmak için genlik kırpma (AC) ve filtreleme, kodlama, serpiştirme, ton rezervasyonu (TR), ton ekleme (TI), kısmi iletim dizisi (PTS) ve seçilmiş haritalama (SLM) teknikleri gibi pek çok yöntem sunulmuştur. Bunlara ek olarak, bu PAPR azaltma yöntemlerini kullanan MC telsiz iletişim sistemlerinin diğer performanslarının iyileştirilmesi amacıyla sistemlere uygulanan hızlı Walsh Hadamard dönüşümü (FWHT) ve ayrık dalgacık dönüşümü (DWT) gibi dönüşümlerde sunulmuştur. Bu çalışmada, MC telsiz iletişim sistemlerinin hem bit hata oranı (BER) performansını hem de PAPR başarımını iyileştirmek için PTS ve AC tekniği ile Lazy dalgacığını kullanan Lifting dalgacık dönüşümünün (LLWT) birleştirilmesi önerilmektedir. Bu makalede, ilk defa bu çalışmada önerilen PTS ve AC tekniği ile LLWT dönüşümünün birleşimi olan LLWT-PTS-AC yöntemi, MC telsiz iletişim sistemlerinin dezavantajlarını ortadan kaldırmak için klasik OFDM dalga formuna uygulanmıştır ve kayda değer sonuçlar elde edilmiştir. Sonuçlar incelendiği zaman, klasik OFDM sisteminin PAPR ve BER başarımlarının tatmin edici ölçüde arttığı görülmektedir.

Keywords

OFDM dalga formu PAPR azaltma Lifting dalgacık dönüşümü PTS LLWT-PTS-AC

Project Number

Yok

References

  • 1. Singal A. and Kedia D., “Complexity analysis of SLM PAPR reduction schemes in wireless OFDM system”, 2016 International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT), 2016, pp. 2082-2087, doi: 10.1109/ICEEOT.2016.7755055.
  • 2. Cimini L. J. and Sollenberger N. R., “Peak-to-average power ratio reduction of an OFDM signal using partial transmit sequences”, in IEEE Communications Letters, vol. 4, no. 3, pp. 86-88, March 2000, doi: 10.1109/4234.831033.
  • 3. Bai J., Li Y., Cheng W., Du H. and Wang Y., “A novel peak-to-average power ratio reduction scheme via tone reservation in OFDM systems”, in China Communications, vol. 14, no. 11, pp. 279-290, Nov. 2017, doi: 10.1109/CC.2017.8233667.
  • 4. Gu X., Baek S. and Park S., “PAPR reduction of OFDM signal using an efficient SLM technique”, 2010 The 12th International Conference on Advanced Communication Technology (ICACT), 2010, pp. 324-328.
  • 5. Wang L. and Liu J., “PAPR Reduction of OFDM Signals by PTS With Grouping and Recursive Phase Weighting Methods”, in IEEE Transactions on Broadcasting, vol. 57, no. 2, pp. 299-306, June 2011, doi: 10.1109/TBC.2011.2111210.
  • 6. Yoo S., Yoon S., Kim S. Y. and Song I., “A novel PAPR reduction scheme for OFDM systems: selective mapping of partial tones (SMOPT)”, 2006 Digest of Technical Papers International Conference on Consumer Electronics, 2006, pp. 287-288, doi: 10.1109/ICCE.2006.1598423.
  • 7. Bouquet E., Haese S., Drissi M., Moullec C. and Sayegrih K., “An Innovative and Low Complexity PAPR Reduction Technique for Multicarrier Systems”, 2006 European Conference on Wireless Technology, 2006, pp. 162-165, doi: 10.1109/ECWT.2006.280460.
  • 8. Wang C.-L. and Ouyang Y., “Low-complexity selected mapping schemes for peak-to-average power ratio reduction in OFDM systems”, in IEEE Transactions on Signal Processing, vol. 53, no. 12, pp. 4652-4660, Dec. 2005, doi: 10.1109/TSP.2005.859327.
  • 9. Jiao Y. Z., Liu X. J. and Wang X. A., “A Novel Tone Reservation Scheme with Fast Convergence for PAPR Reduction in OFDM Systems”, 2008 5th IEEE Consumer Communications and Networking Conference, 2008, pp. 398-402, doi: 10.1109/ccnc08.2007.95.
  • 10. Armstrong J., “New OFDM peak-to-average power reduction scheme”, IEEE VTS 53rd Vehicular Technology Conference, Spring 2001. Proceedings (Cat. No.01CH37202), 2001, pp. 756-760 vol.1, doi: 10.1109/VETECS.2001.944945.
  • 11. Deumal M., Vilella C., Pijoan J. L. and Bergada P., “Partially clipping (PC) method for the peak-to-average power ratio (PAPR) reduction in OFDM”, 2004 IEEE 15th International Symposium on Personal, Indoor and Mobile Radio Communications (IEEE Cat. No.04TH8754), 2004, pp. 464-468 Vol.1, doi: 10.1109/PIMRC.2004.1370914.
  • 12. Kliks, A., Bogucka, H. Improving Effectiveness of the Active Constellation Extension Method for PAPR Reduction in Generalized Multicarrier Signals. Wireless Personal Communications vol. 61, pp. 323–334, 2011. https://doi.org/10.1007/s11277-010-0025-5.
  • 13. Wang X., Tjhung T. T. and Wu Y., “On the SER and spectral analyses of A-law companded multicarrier modulation”, in IEEE Transactions on Vehicular Technology, vol. 52, no. 5, pp. 1408-1412, Sept. 2003, doi: 10.1109/TVT.2003.816631.
  • 14. Moazzeni T.; Selvaraj H. and Jiang Y., “A Novel Multi-Exponential Function-based Companding Technique for Uniform Signal Compression over Channels with Limited Dynamic Range”, International Journal of Electronics and Telecommunications, Vol. 56, no. 2, Jun 2010. doi:10.2478/v10177-010-0016-1
  • 15. Huang X., Lu J., Zheng J. and Gu J., “Reduction of PAPR of OFDM signals with piecewise-scales transform”, Proceedings IEEE 56th Vehicular Technology Conference, 2002, pp. 1240-1243 vol.2, doi: 10.1109/VETECF.2002.1040803.
  • 16. Cuteanu V. and Isar A., “PAPR reduction of OFDM signals using hybrid clipping-companding scheme with sigmoid functions”, 2011 International Conference on Applied Electronics, 2011, pp. 1-4.
  • 17. Lakshmanan M. K. and Nikookar H., “A review of wavelets for digital wireless communication”, Wireless Personal Communications, vol. 37, no. 10, pp. 387-420, 2006.
  • 18. Negash B. G. and Nikookar H., “Wavelet-based multicarrier transmission over multipath wireless channels”, IEE Electronics Letters, vol. 36, no. 21, pp. 1787-1788, 2000. doi: 10.1049/el:20001263.
  • 19. Sweldens W., “The lifting scheme: A construction of second generation wavelets”, SIAM Journal of Mathematical Analysis, vol. 29, no. 2, pp. 511-546, 1998. https://doi.org/10.1137/S0036141095289051.
  • 20. Baro M. and Ilow J., “PAPR reduction in OFDM using wavelet packet pre-processing”, 5th IEEE Consumer Communications and Networking Conference (CCNC 2008), pp. 195-199, 2008.
  • 21. Taşpınar N. and Bozkurt Y.T., “PAPR reduction using genetic algorithm in lifting-based wavelet packet modulation systems”, Turkish Journal of Electrical Engineering & Computer Sciences, vol. 24, pp. 184-195, 2016. https://doi.org/10.3906/elk-1306-236.
  • 22. Bozkurt Y. T., Peak-to-avarage power ratio reduction techniques in wavelet packet modulation systems, Ph.D. Dissertation, Erciyes University, Graduate School of Natural and Applied Sciences, Kayseri, September 2017.
  • 23. Kulkarni V. M. and Bhalchandra A. S., “An overview of various techniques to reduce the Peak-to-average power ratio in multicarrier transmission systems”, 2012 IEEE International Conference on Computational Intelligence and Computing Research, 2012, pp. 1-5, doi: 10.1109/ICCIC.2012.6510251.
  • 24. Yıldırım M., Peak-to-avarage power ratio reduction by using intelligent optimisation techniques in wireless communication systems, Ph.D. Dissertation, Erciyes University, Graduate School of Natural and Applied Sciences, Kayseri, January 2018.
  • 25. Zhang X., Duan Y. and Tao G., “The research of peak–to–average power ratio performance by optimum combination of partial transmit sequences in MIMO-OFDM system”, 2010 3rd International Congress on Image and Signal Processing, 2010, pp. 4476-4479, doi: 10.1109/CISP.2010.5646770.
  • 26. O’Neill R. and Lopes L. B., “Envelope variations and spectral splatter in clipped multicarrier signals”, Proceedings of 6th International Symposium on Personal, Indoor and Mobile Radio Communications, 1995, pp. 71-75 vol.1, doi: 10.1109/PIMRC.1995.476406.
  • 27. Tek Y. İ., Yaşar S., Sinop H., Karaerik K., Tuna E. B. and Özen A., “PAPR Reduction Method for Next Generation Waveforms”, 2020 28th Signal Processing and Communications Applications Conference (SIU), 2020, pp. 1-4, doi: 10.1109/SIU49456.2020.9302519.
  • 28. Tengizler B., Sequential LWT-PTS-AC-OFDM Waveform for PAPR Reduction, Bachelor Degree Dissertation, Nuh Naci Yazgan University, Kayseri, June 2022.
There are 28 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Makaleler
Authors

Bekir Tengizler 0000-0002-9017-7672

Efe Kaan Çalışkan 0000-0002-2506-5690

Alihan Gülbaz 0000-0003-2831-5058

Ali Özen 0000-0003-3232-3181

Project Number Yok
Early Pub Date May 16, 2024
Publication Date May 20, 2024
Submission Date July 7, 2022
Acceptance Date September 10, 2023
Published in Issue Year 2024 Volume: 39 Issue: 3

Cite

APA Tengizler, B., Çalışkan, E. K., Gülbaz, A., Özen, A. (2024). Sıralı LLWT-PTS-AC yöntemi ile klasik OFDM dalga formunun BER ve PAPR performanslarının iyileştirilmesi. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 39(3), 1837-1848. https://doi.org/10.17341/gazimmfd.1142173
AMA Tengizler B, Çalışkan EK, Gülbaz A, Özen A. Sıralı LLWT-PTS-AC yöntemi ile klasik OFDM dalga formunun BER ve PAPR performanslarının iyileştirilmesi. GUMMFD. May 2024;39(3):1837-1848. doi:10.17341/gazimmfd.1142173
Chicago Tengizler, Bekir, Efe Kaan Çalışkan, Alihan Gülbaz, and Ali Özen. “Sıralı LLWT-PTS-AC yöntemi Ile Klasik OFDM Dalga Formunun BER Ve PAPR performanslarının iyileştirilmesi”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 39, no. 3 (May 2024): 1837-48. https://doi.org/10.17341/gazimmfd.1142173.
EndNote Tengizler B, Çalışkan EK, Gülbaz A, Özen A (May 1, 2024) Sıralı LLWT-PTS-AC yöntemi ile klasik OFDM dalga formunun BER ve PAPR performanslarının iyileştirilmesi. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 39 3 1837–1848.
IEEE B. Tengizler, E. K. Çalışkan, A. Gülbaz, and A. Özen, “Sıralı LLWT-PTS-AC yöntemi ile klasik OFDM dalga formunun BER ve PAPR performanslarının iyileştirilmesi”, GUMMFD, vol. 39, no. 3, pp. 1837–1848, 2024, doi: 10.17341/gazimmfd.1142173.
ISNAD Tengizler, Bekir et al. “Sıralı LLWT-PTS-AC yöntemi Ile Klasik OFDM Dalga Formunun BER Ve PAPR performanslarının iyileştirilmesi”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 39/3 (May 2024), 1837-1848. https://doi.org/10.17341/gazimmfd.1142173.
JAMA Tengizler B, Çalışkan EK, Gülbaz A, Özen A. Sıralı LLWT-PTS-AC yöntemi ile klasik OFDM dalga formunun BER ve PAPR performanslarının iyileştirilmesi. GUMMFD. 2024;39:1837–1848.
MLA Tengizler, Bekir et al. “Sıralı LLWT-PTS-AC yöntemi Ile Klasik OFDM Dalga Formunun BER Ve PAPR performanslarının iyileştirilmesi”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, vol. 39, no. 3, 2024, pp. 1837-48, doi:10.17341/gazimmfd.1142173.
Vancouver Tengizler B, Çalışkan EK, Gülbaz A, Özen A. Sıralı LLWT-PTS-AC yöntemi ile klasik OFDM dalga formunun BER ve PAPR performanslarının iyileştirilmesi. GUMMFD. 2024;39(3):1837-48.