Study on the cross-correlation of GNSS signals and typical approximations

In global navigation satellite system (GNSS) receivers, the first signal processing stage is the acquisition, which consists of detecting the received GNSS signals and determining the associated code delay and Doppler frequency by means of correlations with a code and carrier replicas. These codes, as part of the GNSS signal, were chosen to have very good correlation properties without considering the effect of a potential received Doppler frequency. In the literature, it is often admitted that the maximum GPS L1 C/A code cross-correlation is about −24 dB. We show that this maximum can be as high as −19.2 dB when considering a Doppler frequency in a typical range of [−5, 5] kHz. We also show the positive impact of the coherent integration time on the cross-correlation and that even a satellite with Doppler outside the frequency search space of a receiver impacts the cross-correlation. In addition, the expression of the correlation is often provided in the continuous time domain, while its implementation is typically made in the discrete domain. It is then legitimate to ask the validity of this approximation. Therefore, the purpose of this research is twofold: First, we discuss typical approximations and evaluate their regions of validity, and second, we provide characteristic values such as maximums and quantiles of the auto- and cross-correlation of the GPS L1 C/A and Galileo E1 OS codes in the presence of Doppler, for frequency ranges up to 50 kHz and for different integration times.

[1]  J. Leclère Resource-efficient parallel acquisition architectures for modernized GNSS signals , 2014 .

[2]  Janina Decker,et al.  Fundamentals Of Global Positioning System Receivers A Software Approach , 2016 .

[3]  Sana Ullah Qaisar,et al.  An Analysis of L 1-C / A Cross Correlation & Acquisition Effort in Weak Signal Environments , 2007 .

[4]  V. Ipatov Spread Spectrum and CDMA: Principles and Applications , 2005 .

[5]  L. Lestarquit,et al.  Determining and measuring the true impact of C/A code cross-correlation on tracking—Application to SBAS georanging , 2012, Proceedings of the 2012 IEEE/ION Position, Location and Navigation Symposium.

[6]  D. Akopian Fast FFT based GPS satellite acquisition methods , 2005 .

[7]  Jack K. Holmes Spread Spectrum Systems for GNSS and Wireless Communications , 2007 .

[8]  Gary McGraw,et al.  Determination of C/A Code Self-Interference Using Cross-Correlation Simulations and Receiver Bench Tests , 2002 .

[9]  Myriam Foucras,et al.  Performance Analysis of the Modernized GNSS Signal Acquisition. (Analyse des Performances de l'Acquisition des Nouveaux Signaux GNSS) , 2015 .

[10]  Srini H. Raghavan,et al.  The CDMA Limits of C/A Codes in GPSApplications - Analysis and Laboratory Test Results , 1999 .

[11]  Per Enge,et al.  Gps Signal Structure And Theoretical Performance , 1996 .

[12]  Fabio Dovis,et al.  On the Impact of Channel Cross-Correlations in High-Sensitivity Receivers for Galileo E1 OS and GPS L1C Signals , 2012 .

[13]  L. L. Presti,et al.  The math of ambiguity: what is the acquisition ambiguity function and how is it expressed mathematically? , 2010 .

[14]  Cyril Botteron,et al.  Comparison Framework of FPGA-Based GNSS Signals Acquisition Architectures , 2013, IEEE Transactions on Aerospace and Electronic Systems.

[15]  Emmanuel Boutillon,et al.  A flexible implementation of a Global Navigation Satellite System (GNSS) receiver for on-board satellite navigation , 2010, 2010 Conference on Design and Architectures for Signal and Image Processing (DASIP).

[16]  Elliott D. Kaplan Understanding GPS : principles and applications , 1996 .

[17]  Frank van Diggelen,et al.  A-GPS: Assisted GPS, GNSS, and SBAS , 2009 .

[18]  Guenter W. Hein,et al.  Galileo E1 OS and GPS L1C Pseudo Random Noise Codes - Requirements, Generation, Optimization and Comparison - , 2007 .

[19]  Andrew G. Dempster,et al.  Cross-correlation performance assessment of global positioning system (GPS) L1 and L2 civil codes for signal acquisition , 2011 .

[20]  Olivier Julien,et al.  A Novel Computationally Efficient Galileo E1 OS Acquisition Method for GNSS Software Receiver , 2012 .

[21]  Daniele Borio,et al.  Reducing Front-End Bandwidth May Improve Digital GNSS Receiver Performance , 2010, IEEE Transactions on Signal Processing.

[22]  Asghar Tabatabaei Balaei,et al.  Cross Correlation Impacts and Observations in GNSS Receivers , 2011 .

[23]  Søren Holdt Jensen,et al.  A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach , 2006 .