D.D. Privalov1

1 Omsk Scientific Center SB RAS (Institute of Radiophysics and Physical Electronics)

The sampling rate at a given bit rate is a requirement for the speed of digital signal processors. In this regard, it is necessary to strive to reduce it in the development of electronic devices, especially portable ones. However, this can lead to an increase in the bit error rate during signal detection. Therefore, it is important to determine the degradation of signal detection with decreasing sampling frequency and to develop practical recommendations to ensure the specified quality of communication. 

The aim of the article is to study the influence of sampling frequency and interpolation on the bit error rate of GMSK Signal.

The article considers the incoherent detection of a GMSK signal in a channel with additive white Gaussian noise, taking into account the influence of the clock synchronization error. Numerical results are presented that characterize an increase in the bit error rate with a decrease in the signal sampling frequency. It is shown that when using the cubic Farrow interpolator, there is no significant degradation in the bit error probability. The minimum number of samples per symbol is determined, at which the bit error rate is close to the theoretical values in the absence of synchronization error.

The presented results can be used in development of wireless data transmission systems.

Privalov D.D. The influence of sampling frequency and interpolation on the bit error rate of GMSK signal. Radiotekhnika. 2021. V. 85.

№ 9. P. 108−114. DOI: https://doi.org/10.18127/j00338486-202109-10 (In Russian)

1. Mengali Umberto, D’Andrea Aldo N. Synchronization techniques for digital receivers. Plenum Press, New York. 1997. 529 p.
2. Skljar B. Cifrovaja svjaz'. Teoreticheskie osnovy i prakticheskoe primenenie. Izd. 2-e, ispr. Per. s angl. M.: Izdatel'skij dom «Vil'jams». 2003. 1104 s. (in Russian).
3. Goldsmit A. Besprovodnye kommunikacii. M.: Tehnosfera. 2011. 904 s. (in Russian).
4. Su Y., Zhao J., Wang Z., Xu W., Sun G. Low Complexity Method for Recovering Continuous Phase Modulation Signals with Low Signal-tonoise Ratios. Journal of Communications Technology and Electronics, 2020. V. 65. № 7. P. 843–847. DOI: 10.1134/S1064226920070128.
5. Chin-long Wey, Shin-Yo Lin, Tsung-Han Tsai, Muh-Tian Shiue. Efficient Implementation of Interpolation Technique for Symbol Timing Recovery. Processings of the 2007 WSEAS International Conference on Computer Engineering and Applications. Gold Coast, Australia.  January 17-19. 2007. P. 13–17.
6. Fuyun Ling. Synchronization in Digital Communication Systems. University Printing House, Cambridge. 2017. 380 p.
7. Gardner F. Interpolation in Digital Modems – Part I: Fundamentals. IEEE Transactions on Communications. March 1993. V. 41. № 3.  P. 501–507.
8. Erup L., Gardner F. Interpolation in Digital Modems. Part II: Implementation and Performance. IEEE Transactions on Communications. June 1993. V. 41. № 6. P. 998–1008.
9. D’Andrea Aldo N., Mengali Umberto, Morelli M. Symbol Timing Estimation with CPM Modulation. IEEE Transactions on Communications. 1996. V. 44. № 10. P. 1362–1372. DOI: 10.1109/26.539778.
10. Derecha E.V., Privalov D.D. Issledovanie algoritma taktovoj sinhronizacii GMMS-signala. Tehnika radiosvjazi. 2019. Vyp. 1(40). S. 46–52. DOI: 10.33286/2075-8693-2019-40-46-52 (in Russian).
11. Muhammad Azam, Ezaz Akram, Dr. Jamil Ahmad, Dr. Ismail Shah. An improved, Non-Data Aided Symbol Timing Recovery for GMSK Modulated Signals. Proceeding IEEE INMIC. 2003. P. 107 – 111. DOI: 10.1109/INMIC.2003.1416661
12. Luise M., Reggiannini R. Carrier Frequency Recovery in All-Digital Modems for Burst-Mode Transmissions. IEEE Transactions on Communications. Feb/March/April 1995. Vol. 43. P. 1169–1178. DOI: 10.1109. 26.380149.
13. Morelli M., Mengali U. Carrier-Frequency Estimation for Transmissions over Selective Channels. IEEE Transactions on Communications. September 2000. Vol. 48. No 9. P. 1580–1589. DOI: 10.1109/26.870025
14. Derecha E.V., Privalov D.D. Analysis of the joint functioning of the timing and phase synchronization algorithms of the GMSK-signal. 2020 Dynamics of Systems, Mechanisms and Machines (Dynamics): Conference Paper. Publisher: IEEE. 2020. P. 1–4. DOI: 10.1109/Dynamics50954.2020.9306155
15. Franck A. Efficient Algorithms for Arbitrary Sample Rate Conversion with Application to Wave Field Synthesis. PhD thesis. Universitätsverlag Ilmenau, Ilmenau. 2012. 249 p.
16. Santosh Shah, V. Sinha. GMSK Demodulator Using Costas Loop for Software-Defined Radio. International Conference on Advanced Computer Control. Publisher: IEEE. 2008. P. 757-761. DOI: 10.1109/ICACC.2009.81