Measuring GNSS Signal Strength
What is the difference between SNR and C/N0?
“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. email@example.com
Q: What is the difference between SNR and C/N0?
A: GPS receivers built for various applications, such as handhelds, automobiles, mobile phones, and avionics, all have a method for indicating the signal strength of the different satellites they are tracking. Some receivers display the signal strength in the form of vertical bars, some in terms of normalized signal strength, and others in terms of carrier-to-noise density (C/N0) or signal-to-noise ratio (SNR).
The latter two terms are regularly used so interchangeably that their fundamental differences are often overlooked. A full understanding of the differences between SNR and C/N0 is useful both for users of GPS receivers and for GPS receiver designers and testers.
SNR and C/N0
SNR(dB) = S – N
S is the signal power, usually the carrier power expressed in units of decibel/milliwatt (dBm) or decibel/watts (dBW);
C/N0, on the other hand, is usually expressed in decibel-Hertz (dB-Hz) and refers to the ratio of the carrier power and the noise power per unit bandwidth.
For the GPS L1 C/A signal, one can consider the received signal power as the power of the original unmodulated carrier power (at the point of reception in a receiver) that has been spread by the spreading (ranging) codes when transmitted from a satellite. We can express C/N0 as follows:
C/N0 (dB-Hz) = C – (N – BW) = C – N0 = SNR + BW
C is the carrier power in dBm or dBW;
Typical values in an L1 C/A code receiver are as follows:
C/N0: ~ 37 to 45dB-Hz
Receiver front-end bandwidth: ~ 4MHz => BW = 10*log (4,000,000) = 66dB
In order to determine C/N0, then, one clearly needs to determine the carrier power and noise density at the input to the receiver.
Noise and Signal Power
. . .
Signal and Noise Paths from Antenna to Receiver
NF = SNRin / SNRout
and provides an estimate of the amount of noise added by an active component, such as a low-noise amplifier (LNA), or even a passive component, such as a filter or the cable.
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Taking into consideration the noise environment and the receiver front-end components, the C/N0 of a particular tracked satellite will scale relative to the signal power. The signal power of the various satellites being tracked by the receiver will vary in relation to the satellite elevation angle due to differences in path loss and the satellite and receiver antennas’ gain patterns. So, for example, if the signal power varies ±4dB of the nominal signal power of -158.5dBW, the corresponding C/N0 will vary from 38.5dB-Hz to 46.5dB-Hz.
Interpretation and Significance of C/N0
Two different GPS receivers connected to the same antenna and tracking the same GPS satellite at the same time may output different C/N0 values. If one assumes that the C/N0 values are computed accurately by both the receivers, the differences in the C/N0 values can be attributed to differences in the noise figure of the two front-ends and/or the receivers’ respective band-limiting and quantization schemes.
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Receiver Acquisition, Processing Blocks, and SNR
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The improvement in SNR as the result of a longer integration occurs because of the reduction in the noise equivalent bandwidth. Note that the performance of the PLL and FLL in the presence of thermal noise is further affected by the bandwidths of the respective loops themselves. The integration time in this case establishes the input SNR and the loop update time for the respective loops.
Interpretation and Significance of SNR
The SNR is very useful when evaluating the performance of the acquisition and tracking stages in a receiver. For example, when performing Monte Carlo simulations, the SNR needs to be determined at the various stages of the signal processing chain to properly simulate the receiver. In simulations the required C/N0 needs to be first converted to an SNR from which the appropriate noise variance can be readily determined.
Furthermore, the SNR is an indication of the level of noise present in the measurement, whereas C/N0 alone does not provide this information.
In conclusion, we can see that both the C/N0 and SNR are useful quantities that can be used when designing, evaluating or verifying the performance of a GPS receiver. However the use of one quantity over the other very much depends upon the context and the purpose for which the signal quality measurement is being made or is to be used for and this should be carefully considered when choosing between the two.
(For Angelo Joseph’s complete answer to this question, including formulas and tables, please download the full article using the pdf link above.)
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