Noise-like discrete signals for asynchronous code division radio systems

Authors

DOI:

https://doi.org/10.30837/rt.2021.2.205.19

Keywords:

noise-like discrete signals, spreading sequence, multiple access, direct spreading of the spectrum, asynchronous code division radio system

Abstract

This article discusses noise-like discrete signals (pseudo-random sequences) for asynchronous code division systems for radio channels. Asynchrony implies the use of sequences that are statistically uncorrelated for an arbitrary cyclically shifted copy of the signals, i.e. their cross-correlation coefficient for arbitrarily chosen starting points is close to zero. The fundamental theoretical limit for this characteristic is the well-known Welch boundary. In this paper, we compare the correlation properties of various sets (Gold codes, Kasami sequences, etc.) with this fundamental limit. The parameters of different codes are estimated, the corresponding bound is shown and compared with the real correlation characteristics of the codes. For the approximation, the Laurent series expansion and the Puiseau series were used. The asymptotic properties were also estimated. The paper also considers new ensembles of noise-like discrete signals for asynchronous systems. These codes are statistically uncorrelated, asymptotically the square of their cross-correlation for arbitrary starting points tends to the theoretical Welch bound. Moreover, the cardinality (power of the set) of new signal ensembles is much higher than that of Gold codes and Kasami sets. Consequently, the practical use of such noise-like discrete signals will increase the capacity of asynchronous code division systems for radio channels and reduce the cost of communication services. In addition, new sets of spreading signals will be useful for the implementation of the so-called. soft capacity, i.e. when, if necessary, the base station can increase the subscriber capacity with a slight decrease in the quality of service.

References

Yang S.-M.M. Modern Digital Radio Communication Signals and Systems. Springer International Publishing, 2019.

Torrieri D. Principles of Spread-Spectrum Communication Systems. Springer International Publishing, 2018.

Spread Spectrum and CDMA: Principles and Applications | Wiley [Electronic resource] // Wiley.com. URL: https://www.wiley.com/en-us/Spread+Spectrum+and+CDMA%3A+Principles+and+Applications-p-9780470091784 (accessed: 01.08.2020).

Sklar B., Harris F.J. Digital Communications: Fundamentals and Applications. 3 edition. Hoboken: Prentice Hall, 2020. 1104 p.

Khalife J., Kassas Z.M. Navigation With Cellular CDMA Signals – Part II: Performance Analysis and Experimental Results // IEEE Transactions on Signal Processing. 2018. Vol. 66, № 8. P. 2204–2218.

Sklar B. Digital Communications: Fundamentals and Applications. Edición: 2. Upper Saddle River, NJ: Prentice Hall, 2017. 1104 p.

Kuznetsov A. et al. Formation of Discrete Signals with Special Correlation Properties // 2019 International Conference on Information and Telecommunication Technologies and Radio Electronics (UkrMiCo). Odessa, Ukraine: IEEE, 2019. P. 1–6.

Kuznetsov A. et al. Generators of Pseudorandom Sequence with Multilevel Function of Correlation // 2019 IEEE International Scientific-Practical Conference Problems of Infocommunications, Science and Technology (PIC S T). 2019. P. 517–522.

Kuznetsov A. et al. Formation of Pseudorandom Sequences with Special Correlation Properties // 2019 3rd International Conference on Advanced Information and Communications Technologies (AICT). 2019. P. 395–399.

Kuznetsov A. et al. Discrete Signals with Special Correlation Properties // Proceedings of the Second International Workshop on Computer Modeling and Intelligent Systems (CMIS-2019), Zaporizhzhia, Ukraine, April 15-19, 2019 / ed. Luengo D. et al. CEUR-WS.org, 2019. Vol. 2353. P. 618–629.

Kuznetsov A. et al. Pseudorandom Sequences with Multi-Level Correlation Function for Direct Spectrum Spreading // 2019 IEEE International Conference on Advanced Trends in Information Theory (ATIT). 2019. P. 232–237.

Welch L. Lower bounds on the maximum cross correlation of signals (Corresp.) // IEEE Transactions on Information Theory. 1974. Vol. 20, № 3. P. 397–399.

Ipatov V.P. Spread Spectrum and CDMA: Principles and Applications. Chichester, UK: John Wiley & Sons, Ltd, 2005.

Rao R., Dianat S. Basics of Code Division Multiple Access (CDMA). 1000 20th Street, Bellingham, WA 98227-0010 USA: SPIE, 2005.

Buehrer R.M. Code Division Multiple Access (CDMA). Morgan & Claypool Publishers, 2006. 192 p.

Gold R. Optimal binary sequences for spread spectrum multiplexing (Corresp.) // IEEE Transactions on Information Theory. 1967. Vol. 13, № 4. P. 619–621.

Hamid M., Miller A. Gold Code Generators in Virtex Devices [Electronic resource]. 2000. URL: /paper/Gold-Code-Generators-in-Virtex-Devices-Hamid-Miller/9ce406a10eb3ae90edd8fa20590a0dcd8ed03c86 (accessed: 01.08.2020).

Kasami T. Weight Distribution Formula for Some Class of Cyclic Codes. Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 1966.

Shi M., Krotov D.S., Solé P. A New Approach to the Kasami Codes of Type 2 // IEEE Transactions on Information Theory. 2020. Vol. 66, № 4. P. 2456–2465.

GPS explained: Transmitted GPS Signals [Electronic resource] // archive.is. 2012. URL: http://archive.is/eC7C (accessed: 01.08.2020).

Massey J.L., Mittelholzer T. Welch’s Bound and Sequence Sets for Code-Division Multiple-Access Systems // Sequences II / ed. Capocelli R., De Santis A., Vaccaro U. New York, NY: Springer, 1993. P. 63–78.

Stüber G.L. Spread Spectrum Techniques // Principles of Mobile Communication / ed. Stüber G.L. Cham: Springer International Publishing, 2017. P. 449–499.

Torrieri D. Chapter 7 Code-Division Multiple Access // Principles of Spread-Spectrum Communication Systems / ed. Torrieri D. Cham: Springer International Publishing, 2015. P. 405–460.

Song T., Zhou K., Li T. CDMA System Design and Capacity Analysis Under Disguised Jamming // IEEE Transactions on Information Forensics and Security. 2016. Vol. 11, № 11. P. 2487–2498.

Korhonen J., You J. Peak signal-to-noise ratio revisited: Is simple beautiful? // 2012 Fourth International Workshop on Quality of Multimedia Experience. 2012. P. 37–38.

Kuznetsov A. et al. Adaptive Pseudo-Random Sequence Generation for Spread Spectrum Image Steganography // 2020 IEEE 11th International Conference on Dependable Systems, Services and Technologies (DESSERT). 2020. P. 161–165.

Published

2021-07-02

How to Cite

Kuznetsov, A. ., Smirnov, O. ., & Kuznetsova , T. . (2021). Noise-like discrete signals for asynchronous code division radio systems . Radiotekhnika, 2(205), 175–183. https://doi.org/10.30837/rt.2021.2.205.19

Issue

Section

Articles