Are Carrier-to-Noise Algorithms Equivalent in All Situations?
“GNSS Solutions” is a regular column featuring questions and answers about technical aspects of GNSS. Readers are invited to send their questions to the columnist, Dr. Mark Petovello, Department of Geomatics Engineering, University of Calgary, who will find experts to answer them. firstname.lastname@example.org
Q: Are C/N0 Algorithms Equivalent in All Situations?
A: Fundamental to determining the status of GNSS tracking subsystems and controlling a GNSS receiver, the measure of C/N0 (carrier-to-noise ratio) provides satellite signal health information in addition to the PVT (position, velocity, time) information. For example, tracking loops experience a rapid increase of tracking errors at low C/N0, e.g., below 30 dBHz, until they completely lose lock.
In this column, we present a comparison of C/N0 algorithm performance. In digital receivers several methods may be used to estimate C/N0, but all involve processing samples from the correlator output. Dr. Brad Badke discussed the most intuitive algorithm in the GNSS Solutions column in the September/October 2009 issue of Inside GNSS — the so-called real signal-complex noise (RSCN) method.
Texts on GPS architecture usually include another classic approach, the narrowband-wideband power ratio (NWPR) method. Additionally, literature on digital communication offers many other methods for estimating SNR (signal-to-noise ratio) — which, as discussed in Dr. Badke’s contribution is not the same as C/N0 — of M-PSK (M-phase shift keying) modulations in additive white Gaussian noise (AWGN). However, these SNR algorithms must be adapted before equating them to C/N0.
Since high-performance GNSS software receivers have become a reality in navigation labs worldwide, software engineers must select algorithms capable of maximizing accuracy with minimal implementation complexity. For this reason, in our discussion we will compare the accuracy and implementation complexity of five different C/N0 estimation algorithms.
Computational Complexity of Different Estimators
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The Effect of Phase Noise
When the noise power contribution is very small, some algorithms cannot discriminate additive noise from θn or other factors, while other algorithms are sensitive to the noise power only.
On the other hand, in low SNR conditions the principal limiting phenomenon is that the carrier tracking loop no longer keeps the incoming and the local carriers synchronized. In this case the SNR algorithms use correlator outputs inconsistent with the assumed distribution of θn, thereby invalidating the SNR estimate.
However, as long as the receiver maintains signal lock and the software tracking loops are not broken, the SNR estimators perform equivalently in medium-to-low SNR conditions.
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(For Emanuela Falletti, Marco Pini and Letizia Lo Presti's complete answer to this question, including formulas and tables, please download the full article using the pdf link above.)
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