Generation of Binary Sequences of Length 10230 Bits Having Better Odd and Even Correlation with Large Linear Complexity for Use in Global Navigation Satellites Systems (GNSS) Applications Dileep Dharmappa 1* , Mahalinga V. Mandi 2 , Ramesh Siddaiah 3 1 Department of Electronics and Communication Engineering (ECE), Sri Siddhartha Academy of Higher Education (SSAHE), Agalakote, Tumakuru 572107, Karnataka, India 2 Navigation Systems Area, ISRO Telemetry Tracking and Command Network (ISTRAC), ISRO, Bengaluru 560058, Karnataka, India 3 Department of Electronics and Communication Engineering (ECE), Dr. Ambedkar Institute of Technology, Near Jnana Bharathi, Bengaluru 560056, Karnataka, India Corresponding Author Email: dileep@istrac.gov.in https://doi.org/10.18280/mmep.070112 ABSTRACT Received: 2 September 2018 Accepted: 2 January 2020 Binary sequences used in Global Navigation Satellites Systems (GNSS) are found to be easily decoded due to less linear complexity. The correlation properties are extremely important while selecting the sequences for GNSS Applications. Linear Feedback Shift Register (LFSR) based Sequences are being used in GNSS Systems such as Global Positioning System (GPS) L2 CM (L2 frequency band Civil Moderate) Signal. Due to the short cycling of LFSR these sequences result in poor correlation properties. In this work the properties of binary sequences used in the state of the art GPS L2CM Navigation signal is explored. The odd and even correlation properties of GPS L2CM sequences are presented in detail. These sequences are analyzed for their Linear Complexity property. A method is proposed for generation of 10230 bit length binary sequences. A new set of binary sequences with set size of 47 sequences are generated using chaotic real sequences. The generated sequences are analyzed for odd correlation, even correlation and linear complexity properties. The proposed binary sequences are found to have better correlation and excellent linear complexity properties as compared to GPS L2 CM Sequences, which make them suitable for use in GNSS Applications. Keywords: Global Positioning System (GPS), Global Navigation Satellites Systems (GNSS), chaotic logistic map, auto correlation, Cross Correlation, Linear Complexity (LC) 1. INTRODUCTION Binary sequences play vital role in Global Navigation Satellites Systems (GNSS) Systems. GNSS Systems such as Global Positioning System (GPS) by US, European GNSS (GALILEO), Russians Global Navigation Satellite System (GLONASS), Indian Regional Navigation Satellite System (IRNSS) by India, Quasi Zenith Satellite System (QZSS) by Japan and Chinese BeiDou Navigation Satellite System (BEIDOU/COMPASS) use binary sequences for various types of services provided by each GNSS system. User receiver at ground identifies a unique service from a GNSS System using these binary sequences. GPS system is widely used for location services across the world. Towards enhancing the capabilities of GPS system, a new GPS signal namely GPS L2 band Civil Moderate (GPS L2 CM) signal having binary sequences of length 10230 bits was added in L2 frequency. This signal provides one order better accuracy than the existing GPS C/A (Coarse Acquisition) signal having binary sequences of length 1023 bits. Binary spreading sequences provide secure and reliable transmission for GNSS Systems. Binary sequences derived from Linear Feedback Shift Register (LFSR) are the commonly used Pseudo Random Binary Sequences in spread spectrum applications [1]. For GNSS Systems, the property of spreading sequence length plays an important role. It is always designed such that the spreading sequence length should be an integer multiple of chip rate. However binary sequences generated using conventional methods such as Gold Codes, which are based on LFSR are restricted to code length (2 N -1) for ‘N’ stages. The GPS L2 CM sequences are generated using N = 27 stage LFSR. The length of the binary sequence of 27 stage LFSR is 134217727 bits. However to meet the sequence length constraints these binary sequences are short cycled/reset to 10230 bits in state-of-the art GPS Navigation System. The process of short cycling results in poor correlation properties of the truncated sequences [1]. The desirable properties to be considered in the design of the binary sequences for GNSS Systems are described in the literature [1-5]. However in the existing literature, the detailed analysis of the properties namely odd correlation and linear complexity of the new civilian signal GPS L2 CM sequences are not done. The security of the GNSS Systems depends on the linear complexity property of the binary spreading sequences. It is observed from the literature that due to the low linear complexity property binary sequences used in BeiDou System were decoded by Gao et al. [6]. Also similar instance of decoding Galileo In Orbit Validation Element-A (GIOVE-A) codes, was done by Psiaki et al. [7]. Design of binary sequences with high linear complexity is being attempted by many researchers [8-11]. Mathematical Modelling of Engineering Problems Vol. 7, No. 1, March, 2020, pp. 94-102 Journal homepage: http://iieta.org/journals/mmep 94