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

Abstract

In global navigation satellite system (GNSS) receivers, the first signal processing stage is the acquisition, which consists in detecting the received GNSS signals and determining the associated code delay and Doppler frequency by means of correlations with a code and a 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. 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 presence of Doppler, for frequency ranges up to 50 kHz, and for different integration times.

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Satellite navigation

A satellite navigation or satnav system is a system that uses satellites to provide autonomous geopositioning. A satellite navigation system with global coverage is termed global navigation s

Doppler effect

The Doppler effect or Doppler shift (or simply Doppler, when in context) is the apparent change in frequency of a wave in relation to an observer moving relative to the wave source. It is named afte

GPS signals

GPS signals are broadcast by Global Positioning System satellites to enable satellite navigation. Receivers on or near the Earth's surface can determine location, time, and velocity using this info

Cyril Botteron, Jérôme Leclère

Nowadays, civil Global Navigation Satellite System (GNSS) signals are available in both L1 and L5 bands. A receiver does not need to acquire independently the signals in both bands coming from a same satellite, since their carrier Doppler and code delay are closely related. Therefore, the question of which one to acquire first rises naturally. Although the common thought would tell the L1 band signals which are narrowband, an accurate comparison has never been done, and the decision is not as easy as it seems. Indeed, L5 band signals have several advantages such as stronger power, lower carrier Doppler, or a pilot channel, unlike the Global Positioning System (GPS) L1 C/A signal. The goal of this paper is therefore to compare the acquisition of L1 and L5 bands signals (GPS L1 C/A and L5, Galileo E1 and E5a/b) to determine which one is more complex and by which factor, in terms of processing time and memory, considering hardware receivers and the parallel code search. The results show that overall the L5 band signals are more complex to acquire, but it depends strongly on the conditions. The E5 signal is always more complex to acquire than E1, while the L5 signal can have a complexity close to the L1 C/A in some cases. Moreover, precise assistance providing accurate Doppler could significantly reduce the L5 complexity below the L1 complexity.

2018, ,

The acquisition of global navigation satellite system signals can be performed using a fast Fourier transform (FFT). The FFT-based acquisition performs a circular correlation, and is thus sensitive to potential transitions between consecutive periods of the code. Such transitions are not occurring often for the GPS L1 C/A signal because of the low data rate, but very likely for the new GNSS signals having a secondary code. The straightforward solution consists in using two periods of the incoming primary code and using zero-padding for the local code to perform the correlation. However, this solution increases the complexity, and is moreover not efficient since half of the points calculated are discarded. This has led us to research for a more efficient algorithm, which discards less points by calculating several sub-correlations. It is applied to the GPS L5, Galileo E5a, E5b and E1 signals. Considering the radix-2 FFT, the proposed algorithm is more efficient for the L5, E5a and E5b signals, and possibly for the E1 signal. The theoretical number of operations can be reduced by 21%, the processing time measured on a software implementation is reduced by 39%, and the memory resources are almost halved for an FPGA implementation.

, ,

This paper proposes alternative architectures to perform a circular correlation using the Fast Fourier Transform (FFT) by decomposing the initial circular correlation into several smaller circular correlations. The approach used is similar to the Fast Finite Impulse Response (FIR) Algorithms (FFAs). These architectures improve the performance in terms of reduced processing time or resource usage, and consequently lower the energy consumption. The results can be applied to any system that performs circular convolution or correlation. In this paper, the application is the acquisition of Global Navigation Satellite System (GNSS) signals with the FFT-based Parallel Code-phase Search (PCS), and more precisely on the GPS L1 C/A signal, when the target considered is a Field Programmable Gate Array (FPGA). In this context, it is for example shown that it is possible with one of the proposed architectures to reduce the logic usage by 11 %, the memory usage by 41 %, and the Digital Signal Processing (DSP) block usage by 32 %, while keeping the same processing time. With another architecture, it is shown that the processing time can be halved by increasing the logic usage by only 35 %, while reducing the memory usage and keeping the same DSP usage. Note that the proposed approach is not based on an approximation of the traditional method, but a modified implementation providing the same result. Thus, there is no loss of sensitivity.

2012