This paper describes methods to estimate the carrier to noise ratio in GNSS application

Falletti, Emanuela

Lo Presti, Letizia

Pini, Marco

English

This paper describes methods to estimate the carrier to noise ratio in GNSS applications

FALLETTI, EMANUELA

PINI, MARCO

LO PRESTI, Letizia

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

29 November 2022POLITECNICO DI TORINORepository ISTITUZIONALEAre carrier-to-noise algorithms equivalent in all situations? / Falletti, Emanuela; Pini, Marco; LO PRESTI, Letizia. - In:INSIDE GNSS. - ISSN 1559-503X. - STAMPA. - January 2010:(2010), pp. 20-27.OriginalAre carrier-to-noise algorithms equivalent in all situations?Publisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2420564 since:Eugene, Ore. Gibbons Media & Research20      InsideGNSS  j a n u a r y / f e b r u a r y  2 0 1 0 	 www.insidegnssAre	C/N0	Algorithms	Equivalent	in	All	Situations?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, track-ing 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 per-formance. 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-com-plex noise (RSCN) method. Texts on GPS architecture usually include another classic approach, the narrowband-wideband power ratio (NWPR) method. Additionally, litera-ture 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 real-ity in navigation labs worldwide, soft-ware engineers must select algorithms capable of maximizing accuracy with minimal implementation complexity. For this reason, in our discussion we will compare the accuracy and imple-mentation complexity of five different C/N0 estimation algorithms.Computational	Complexity	of	Different	EstimatorsHere we will investigate the following SNR estimation algorithms (See Addi-tional Resources section at the end of this column for more details): • Real Signal-Complex Noise (RSCN)• Beaulieu's method (BL): an “intui-tively motivated” algorithm intro-duced in 2000 by N. C. Beaulieu et alia (see Additional Resources sec-tion at end of this article) • Signal-to-Noise Variance (SNV): squared Signal-to-Noise Vari-ance estimator, based on the first absolute moment and the second moment of the signal samples• Moment Method (MM): employs the second- and fourth-order moments for the separate estima-tion of carrier strength and noise strength• Narrowband-Wideband Power Ratio (NWPR) Method, reported in several books on GPS receivers. Note that this is the only algorithm that estimates C/N0 directly; the others estimate SNR, which can be converted to C/N0 as discussed later.Because we sample the “observable”    GNSS Solutions: Carrier-to-Noise	Algorithms“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. His e-mail address can be found with his biography below.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.Mark	Petovello is an Assistant Professor in the Department of Geomatics  Engineering at the University of Calgary. He has been actively involved in many aspects of positioning and navigation since 1997 including GNSS algorithm development, inertial navigation, sensor integration, and software development. Email: mark.petovello@ucalgary.ca22      InsideGNSS  j a n u a r y / f e b r u a r y  2 0 1 0 	 www.insidegnssGNSS	SOLUTIONSsignal stream from the prompt correla-tor output to compute C/N0, we write the sample stream as a function of the discrete time, n,where D[n] = ±ejθn are the navigation bit samples; θn is the residual carrier phase error due to the carrier tracking loop; Pd and Pn are the powers associ-ated to data and noise, respectively; and η[n] = ηRe[n] + jηIm[n] expresses the complex noise samples.Thus the SNR related to the signal rC[n] is defined as λC = Pd/Pn, so thatwhere Beqn represents the normalized equivalent noise bandwidth of the sys-tem.Table 1 summarizes the algorithms defined by each of the foregoing meth-ods, where we indicate their computa-tional complexity in terms of the num-ber of real (versus complex) sums, real multiplications, and square roots. In Table 1, N is the number of observed samples used to produce one SNR estimate. We assume that we can select a high enough N — typically on the order of a few hundreds of samples — to prevent any additional estimation bias due to an insufficient number of observations. The parameter M introduced in the NWPR estimator is the ratio between the bandwidth associated to the wide-band power measurement WBPk , and the bandwidth associated with the narrowband measurement NBPk. An indicative evaluation of the computa-tional complexity is also reported in figure 1.The	Effect	of	Phase	NoiseIn the presence of a residual phase error (θn) in the carrier tracking loop, the above algorithms experience asymptotic biases for high C/N0 values. Such biases can be theoretically dem-onstrated by computing the asymptotic limit for Pd →∞ of the SNR estimators with non-zero θn. Herein, θn is assumed to be a zero-mean random variable with variance σθ² and uniform distri-bution between [-√3σθ, +√3σθ]. 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 phe-nomenon 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.Table 2 gives expressions for each estimator’s expected asymptotic esti-TABLE 1.  SNR estimation algorithms. A “hat” (ˆ) over a variable indicates an estimate from measured quantities (observables)24      InsideGNSS  j a n u a r y / f e b r u a r y  2 0 1 0 	 www.insidegnssGNSS	SOLUTIONSmation value, λ∞(θ), that is, the SNR estimate for signal power tending to infinity. Note that the limit for SNR as σθ2 approaches zero is the true SNR, thus guaranteeing an unbiased asymptotic estimation capability of all the approaches in absence of residual phase noise.Numerical simulations confirm the asymptotic behavior (for Pd → ∞) foreseen by theoretical analysis. figure 2 shows the estimated C/N0 versus the true C/N0 obtained by simulating the signal using Equation 1, and for both cases where the residual phase noise variance σθ2=(1°)2, as well as for the expected asymptotic limits of σθ2 (computed using the equations given in Table 2).figure 3 shows a comparison of λ(•)∞(θ) as a function of σθ for SNR val-ues of 30, 40, and 50 decibels. The SNR for the RSCN, SNV, and NWPR esti-mators decreases asymptotically with increasing values of the residual phase noise. This inverse relationship indi-cates a bias in the estimated value.Note that, as σθ→0, the estimated SNR, λ(•)∞(θ), for the RSCN, SNV and NWPR methods approaches the true 6005004003002001000N = 100, M=4RSCN Beaulieu SNV MMNWPRMultiplicationsSumsSquare RootsTABLE 2.  Asymptotic behavior of the SNR estimation algorithms for  Pd → ∞FIGURE 1  Relative computational complexity of SNR algorithms Estimated C/N0 [dBHz]C/N0 [dBHz]20 30 40 50 60 70 808070605040302010FIGURE 2  C/N0 estimates for  σθ = 1° The dark dashed line indicates the true  C/N0 values.Asymptoic SNR estimation values λ∞(θ)Phase noise standard deviation: σθ[deg]0 2 4 6 8 10504540353025201510FIGURE 3  Asymptotic SNR estimates vs. the phase noise standard devia-tion.www.insidegnss.com   j a n u a r y / f e b r u a r y  2 0 1 0  InsideGNSS 25SNR. These estimators exhibit fewer errors for decreasing SNR, that is, the bias from the SNR estimate at σθ → 0, is smaller for lower SNR values. This simulation confirms the limits for the RSCN, SNV, and NWPR methods. For high values of C/N0, the esti-mates of SNR provided by these algorithms is valid only for extremely small values of the residual phase noise, θn, while, vice-versa, for an increasing phase noise, their estimates are valid only in medium-to-low C/N0 conditions.As a final note, the bias of the BL estimator is practically negligible for the considered values of phase noise standard deviation. Also, the SNR estimated by the MM estimator, λMM,∞(θ), coincides with the true SNR.As a further verification of these theoretical consider-ations, we consider the performance of each estimator in a real time GPS software receiver with an RF signal supplied by a hardware GPS signal simulator tuned at different levels of power. figure 4 shows the estimated C/N0 with respect to the GPS signal power.As predicted, both the BL and MM methods show a linear trend as the signal power increases. These algorithms are not biased and have the same performance, indeed the difference between the estimated values is always less than 0.1 dB.The RSCN, SNV, and NWPR algorithms perform less reliably. Their estimates vary linearly under normal power conditions, ranging between 35 and 50 dBHz, but as signal power increases to around -120 dBm, their error decreases asymptotically. Moreover these methods tend to underesti-mate C/N0 in comparison with the BL and MM methods. Additionally, we found that the RSCN algorithm under-estimates the C/N0 by more than three decibels at all signal power levels. We attribute this bias to a high sensitivity to residual carrier phase noise. As soon as the signal constella-tion is rotated by θn, a corresponding portion of signal power is interpreted as noise power, proportionally lowering the Estimated C/No vs Signal PowerSignal Power [dBm]-135 -130 -125 -120 -115 -1106560555045403530C/No[dB]FIGURE 4  Estimated C/N0 from a real software receiver.www.insidegnss.com   j a n u a r y / f e b r u a r y  2 0 1 0  InsideGNSS 27GNSS	SOLUTIONSestimated C/N0. Despite its simple algorithm and moderate computational burden, the RSCN method does not yield a suitable solution when accurate C/N0 estimates are required.ConclusionsSeveral algorithms developed for SNR estimation of biphase shift keying/quad phase shift keying (BPSK/QPSK) modula-tions in a noisy environment can be employed to compute the C/N0 ratio in a GNSS digital receiver; however, they expe-rience different estimation performance and implementation complexity. In particular they offer different sensitivities to the residual carrier phase noise, mainly for very high car-rier-to-noise ratios. Receiver designers should select the algo-rithm that best suits their particular needs.Additional	ReadingBeaulieu, N. C., and A. S. Toms, and D. R. Pauluzzi, “Comparison of four SNR estimators for QPSK modulations,” IEEE Communications Letters, vol. 4, no. 2, pp. 43–45, Feb. 2000.Falletti, E., and M. Pini, L. Lo Presti, “Low complexity carrier to noise ratio estimators for GNSS digital receivers,” in publication in the IEEE Transactions on Aerospace and Electronics SystemsFalletti, E., and M. Pini, M. Fantino, “Performance Evaluation of C/N0 Estimators using a Real Time GNSS Software Receiver,” Proceedings of the International Symposium on Spread-Spectrum Technologies and Applications, ISSSTA 2008, Bologna, Italy, August 2008Falletti, E., and M. Pini, L. Lo Presti, D. Margaria, “Assessment on low complexity C/N0 estimators based on a M-PSK signal model for GNSS Receivers,” IEEE/ION PLANS 2008, pp. 167-172, May 2008EMANUELA FALLETTI,  MARCO PINI, AND  LETIZIA LO PRESTIEmaNUEla FallEttI obtained her M.S. and Ph.D. degrees in electronics and communications engineering from Politecnico di Torino, Italy. Currently she is with the Istituto Superiore Mario Boella, in Torino, where she performs the analysis and design of signal processing algorithms in GNSS digital receivers. Her research focuses on array signal processing, wireless channel modeling, communications from high-altitude platforms, and signal processing for digital receivers. maRCo PINI received his Ph.D. in electronics and communication engineering in 2007 from Politecnico di Torino University. Currently, performs research at Istituto Superiore Mario Boella. His major interests cover the field of baseband signal processing on new GNSS signals, multi-frequency RF front end design, and software radio receivers.lEtIzIa lo PREStI is a full professor with the information engineering faculty of Politecnico di Torino. Her research covers the field of digital signal processing, simulation of telecommunica-tion systems, array processing for adaptive antennas, and the technology of navigation and positioning systems. She is the scientific coordinator of the Master on Navigation and Related Applications held by Politecnico di Torino. She actively cooperates with the officers of the United Nations Office for Outer Space Affairs in Vienna, Austria, in the framework of the UN/Italy fellowship program, with the aim of keeping the master program permanently aligned with the UN needs and suggestions. 

Are carrier-to-noise algorithms equivalent in all situations?

PORTO Publications Open Repository TOrino

20      InsideGNSS   january/february 2010	 www.insidegnss
Are	C/N0	Algorithms	
Equivalent	in	All	
Situations?
F
undamental 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, track-
ing 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 per-
formance. 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-com-
plex noise (RSCN) method. 
Texts on GPS architecture usually 
include another classic approach, the 
narrowband-wideband power ratio 
(NWPR) method. Additionally, litera-
ture 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 real-
ity in navigation labs worldwide, soft-
ware engineers must select algorithms 
capable of maximizing accuracy with 
minimal implementation complexity. 
For this reason, in our discussion we 
will compare the accuracy and imple-
mentation complexity of five different 
C/N0 estimation algorithms.
Computational	Complexity	
of	Different	Estimators
Here we will investigate the following 
SNR estimation algorithms (See Addi-
tional Resources section at the end of 
this column for more details): 
•  Real Signal-Complex Noise (RSCN)
•  Beaulieu's method (BL): an “intui-
tively motivated” algorithm intro-
duced in 2000 by N. C. Beaulieu et 
alia (see Additional Resources sec-
tion at end of this article) 
•  Signal-to-Noise Variance (SNV): 
squared Signal-to-Noise Vari-
ance estimator, based on the first 
absolute moment and the second 
moment of the signal samples
•  Moment Method (MM): employs 
the second- and fourth-order 
moments for the separate estima-
tion of carrier strength and noise 
strength
•  Narrowband-Wideband Power 
Ratio (NWPR) Method, reported 
in several books on GPS receivers. 
Note that this is the only algorithm 
that estimates C/N0 directly; the 
others estimate SNR, which can be 
converted to C/N0 as discussed later.
Because we sample the “observable” 
   GNSS 
Solutions: 
Carrier-
to-Noise	
Algorithms
“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. His e-mail address 
can be found with  
his biography below.
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.
Mark	Petovello is an Assistant 
Professor in the Department 
of Geomatics  Engineering at 
the University of Calgary. He 
has been actively involved in 
many aspects of positioning and 
navigation since 1997 including 
GNSS algorithm development, 
inertial navigation, sensor 
integration, and software 
development. 
Email: mark.petovello@ucalgary.
ca22      InsideGNSS   january/february 2010	 www.insidegnss
GNSS	SOLUTIONS
signal stream from the prompt correla-
tor output to compute C/N0, we write 
the sample stream as a function of the 
discrete time, n,
where D[n] = ±ejθn are the navigation 
bit samples; θn is the residual carrier 
phase error due to the carrier tracking 
loop; Pd and Pn are the powers associ-
ated to data and noise, respectively; 
and η[n] = ηRe[n] + jηIm[n] expresses the 
complex noise samples.
Thus the SNR related to the signal 
rC[n] is defined as λC = Pd/Pn, so that
where Beqn represents the normalized 
equivalent noise bandwidth of the sys-
tem.
Table 1 summarizes the algorithms 
defined by each of the foregoing meth-
ods, where we indicate their computa-
tional complexity in terms of the num-
ber of real (versus complex) sums, real 
multiplications, and square roots. 
In Table 1, N is the number of 
observed samples used to produce one 
SNR estimate. We assume that we can 
select a high enough N — typically on 
the order of a few hundreds of samples 
— to prevent any additional estimation 
bias due to an insufficient number of 
observations. 
The parameter M introduced in the 
NWPR estimator is the ratio between 
the bandwidth associated to the wide-
band power measurement WBPk , and 
the bandwidth associated with the 
narrowband measurement NBPk. An 
indicative evaluation of the computa-
tional complexity is also reported in 
figure 1.
The	Effect	of	Phase	Noise
In the presence of a residual phase 
error (θn) in the carrier tracking loop, 
the above algorithms experience 
asymptotic biases for high C/N0 values. 
Such biases can be theoretically dem-
onstrated by computing the asymptotic 
limit for Pd →∞ of the SNR estimators 
with non-zero θn. Herein, θn is assumed 
to be a zero-mean random variable 
with variance σθ² and uniform distri-
bution between [-√3σθ, +√3σθ]. 
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 phe-
nomenon 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.
Table 2 gives expressions for each 
estimator’s expected asymptotic esti-
TABLE 1.  SNR estimation algorithms. A “hat” (ˆ) over a variable indicates an estimate from measured quantities 
(observables)24      InsideGNSS   january/february 2010	 www.insidegnss
GNSS	SOLUTIONS
mation value, λ∞(θ), that is, the SNR 
estimate for signal power tending to 
infinity. Note that the limit for SNR 
as σθ
2 approaches zero is the true 
SNR, thus guaranteeing an unbiased 
asymptotic estimation capability of all 
the approaches in absence of residual 
phase noise.
Numerical simulations confirm 
the asymptotic behavior (for Pd → ∞) 
foreseen by theoretical analysis. figure 
2 shows the estimated C/N0 versus 
the true C/N0 obtained by simulating 
the signal using Equation 1, and for 
both cases where the residual phase 
noise variance σθ
2=(1°)2, as well as for 
the expected asymptotic limits of σθ
2 
(computed using the equations given in 
Table 2).
figure 3 shows a comparison of 
λ(•)∞(θ) as a function of σθ for SNR val-
ues of 30, 40, and 50 decibels. The SNR 
for the RSCN, SNV, and NWPR esti-
mators decreases asymptotically with 
increasing values of the residual phase 
noise. This inverse relationship indi-
cates a bias in the estimated value.
Note that, as σθ→0, the estimated 
SNR, λ(•)∞(θ), for the RSCN, SNV and 
NWPR methods approaches the true 
600
500
400
300
200
100
0
N = 100, M=4
RSCN Beaulieu SNV MM
NWPR
Multiplications
Sums
Square Roots
TABLE 2.  Asymptotic behavior of the SNR estimation algorithms for  Pd → ∞
FIGURE 1  Relative computational complexity of SNR algorithms 
Estimated C/N0 [dBHz]
C/N0 [dBHz]
20 30 40 50 60 70 80
80
70
60
50
40
30
20
10
FIGURE 2  C/N0 estimates for  σθ = 1° The dark dashed line indicates the 
true  C/N0 values.
Asymptoic SNR estimation values λ∞(θ)
Phase noise standard deviation: σθ[deg]
0 2 4 6 8 10
50
45
40
35
30
25
20
15
10
FIGURE 3  Asymptotic SNR estimates vs. the phase noise standard devia-
tion.www.insidegnss.com    january/february 2010  InsideGNSS  25
SNR. These estimators exhibit fewer errors for decreasing 
SNR, that is, the bias from the SNR estimate at σθ → 0, is 
smaller for lower SNR values. 
This simulation confirms the limits for the RSCN, SNV, 
and NWPR methods. For high values of C/N0, the esti-
mates of SNR provided by these algorithms is valid only for 
extremely small values of the residual phase noise, θn, while, 
vice-versa, for an increasing phase noise, their estimates are 
valid only in medium-to-low C/N0 conditions.
As a final note, the bias of the BL estimator is practically 
negligible for the considered values of phase noise standard 
deviation. Also, the SNR estimated by the MM estimator, 
λMM,∞(θ), coincides with the true SNR.
As a further verification of these theoretical consider-
ations, we consider the performance of each estimator in a 
real time GPS software receiver with an RF signal supplied by 
a hardware GPS signal simulator tuned at different levels of 
power. figure 4 shows the estimated C/N0 with respect to the 
GPS signal power.
As predicted, both the BL and MM methods show a linear 
trend as the signal power increases. These algorithms are not 
biased and have the same performance, indeed the difference 
between the estimated values is always less than 0.1 dB.
The RSCN, SNV, and NWPR algorithms perform less 
reliably. Their estimates vary linearly under normal power 
conditions, ranging between 35 and 50 dBHz, but as signal 
power increases to around -120 dBm, their error decreases 
asymptotically. Moreover these methods tend to underesti-
mate C/N0 in comparison with the BL and MM methods. 
Additionally, we found that the RSCN algorithm under-
estimates the C/N0 by more than three decibels at all signal 
power levels. We attribute this bias to a high sensitivity to 
residual carrier phase noise. As soon as the signal constella-
tion is rotated by θn, a corresponding portion of signal power 
is interpreted as noise power, proportionally lowering the 
Estimated C/No vs Signal Power
Signal Power [dBm]
-135 -130 -125 -120 -115 -110
65
60
55
50
45
40
35
30
C
/
N
o
[
d
B
]
FIGURE 4  Estimated C/N0 from a real software receiver.www.insidegnss.com    january/february 2010  InsideGNSS  27
GNSS	SOLUTIONS
estimated C/N0. Despite its simple algorithm and moderate 
computational burden, the RSCN method does not yield a 
suitable solution when accurate C/N0 estimates are required.
Conclusions
Several algorithms developed for SNR estimation of biphase 
shift keying/quad phase shift keying (BPSK/QPSK) modula-
tions in a noisy environment can be employed to compute 
the C/N0 ratio in a GNSS digital receiver; however, they expe-
rience different estimation performance and implementation 
complexity. In particular they offer different sensitivities to 
the residual carrier phase noise, mainly for very high car-
rier-to-noise ratios. Receiver designers should select the algo-
rithm that best suits their particular needs.
Additional	Reading
Beaulieu, N. C., and A. S. Toms, and D. R. Pauluzzi, “Comparison of four SNR 
estimators for QPSK modulations,” IEEE Communications Letters, vol. 4, no. 
2, pp. 43–45, Feb. 2000.
Falletti, E., and M. Pini, L. Lo Presti, “Low complexity carrier to noise 
ratio estimators for GNSS digital receivers,” in publication in the IEEE 
Transactions on Aerospace and Electronics Systems
Falletti, E., and M. Pini, M. Fantino, “Performance Evaluation of C/N0 
Estimators using a Real Time GNSS Software Receiver,” Proceedings of 
the International Symposium on Spread-Spectrum Technologies and 
Applications, ISSSTA 2008, Bologna, Italy, August 2008
Falletti, E., and M. Pini, L. Lo Presti, D. Margaria, “Assessment on low 
complexity C/N0 estimators based on a M-PSK signal model for GNSS 
Receivers,” IEEE/ION PLANS 2008, pp. 167-172, May 2008
EMANUELA FALLETTI,  
MARCO PINI, AND  
LETIZIA LO PRESTI
EmaNUEla FallEttI obtained her M.S. and Ph.D. 
degrees in electronics and communications 
engineering from Politecnico di Torino, Italy. 
Currently she is with the Istituto Superiore Mario 
Boella, in Torino, where she performs the 
analysis and design of signal processing 
algorithms in GNSS digital receivers. Her research focuses on array signal 
processing, wireless channel modeling, communications from high-
altitude platforms, and signal processing for digital receivers. 
maRCo PINI received his Ph.D. in electronics and 
communication engineering in 2007 from 
Politecnico di Torino University. Currently, performs 
research at Istituto Superiore Mario Boella. His 
major interests cover the field of baseband signal 
processing on new GNSS signals, multi-frequency 
RF front end design, and software radio receivers.
lEtIzIa lo PREStI is a full professor with the 
information engineering faculty of Politecnico di 
Torino. Her research covers the field of digital 
signal processing, simulation of telecommunica-
tion systems, array processing for adaptive 
antennas, and the technology of navigation and 
positioning systems. She is the scientific coordinator of the Master on 
Navigation and Related Applications held by Politecnico di Torino. She 
actively cooperates with the officers of the United Nations Office for Outer 
Space Affairs in Vienna, Austria, in the framework of the UN/Italy fellowship 
program, with the aim of keeping the master program permanently aligned 
with the UN needs and suggestions. 

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Are carrier-to-noise algorithms equivalent in all situations?

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