Binary Sequences Having Good Correlation and Large Linear Complexity Properties for Satellite Navigation Applications
Dileep Dharmappa1, Mahalinga V Mandi2, S. Ramesh3

1Dileep Dharmappa, Research Scholar, Department of Electronics and Communication Engineering, Sri Siddhartha Academy of Higher Education (SSAHE), Agalakote, Navigation Systems Area, ISTRAC, ISRO, Bengaluru (Karnataka), India.
2Mahalinga V Mandi, Department of Electronics and Communication Engineering, Dr. Ambedkar Institute of Technology, Near Jnana Bharathi, Bengaluru (Karnataka), India.
3S. Ramesh, Department of Electronics and Communication Engineering, Dr. Ambedkar Institute of Technology, Near Jnana Bharathi, Bengaluru (Karnataka), India.
Manuscript received on 05 February 2019 | Revised Manuscript received on 18 February 2019 | Manuscript Published on 04 March 2019 | PP: 61-67 | Volume-7 Issue-5S2 January 2019 | Retrieval Number: ES2008017519/19©BEIESP
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Abstract: LFSR based binary sequences are known to have good correlation and better balance property and hence they are used in Satellite Navigation Applications as signature sequences. However, due to the code length requirements of length being multiple of on-board fundamental frequency 10.23MHz in GNSS systems, often the LFSR based codes have to be truncated (like 10230 bits). Due to the truncation the correlation property and the balance property gets degraded. Apart from the correlation and balance properties of the binary sequences the linear complexity property also plays an important role for GNSS applications where in users need to be protected against unintended or unauthorized access like commercial applications or military applications. In this work the balance property, even correlation, odd correlation and linear complexity property of the state of the art binary sequences of length 10230 bits being used for one of the GNSS system namely Galileo E5b-I primary sequences of length 10230 bits are evaluated. A method for generation of binary sequences having properties better than Galileo E5b-I primary sequences are presented. Binary sequences generated from the proposed method is analyzed for balance, linear complexity and correlation properties. It is found that the proposed sequences have better balance, correlation properties and high linear complexity. Due to the high linear complexity property, the proposed sequences provide inherent security for the system against spoofing and hence make the GNSS system secure.
Keywords: Even Correlation, Odd Correlation, Linear Complexity, Chaotic Map, Binary Sequences, CDMA, GNSS.
Scope of the Article: Large-Scale Cyber Systems