ICES Journal of Marine Science, 62: 123e130 (2005)
doi:10.1016/j.icesjms.2004.09.006
Definition of signal-to-noise ratio and its critical role
in split-beam measurements
Robert Kieser, Pall Reynisson, and Timothy J. Mulligan
Kieser, R., Reynisson, P., and Mulligan, T. J. 2005. Definition of signal-to-noise ratio and
its critical role in split-beam measurements. e ICES Journal of Marine Science, 62:
123e130.
The signal-to-noise ratio (SNR) plays a critical role in any measurement but is particularly
important in fisheries acoustics where both signal and noise can change by orders of
magnitude and may have large variations. ‘‘Textbook situations’’ exist where the SNR is
clearly defined, but fisheries-acoustic measurements are generally not in this category as
signal and noise come from a wide range of sources that change with location, depth, and
ocean conditions. This paper defines the SNR and outlines its measurement using splitbeam data. Its effect on target-strength (TS) measurements is explored. Recommendations
are given for the routine use of the SNR in fisheries-acoustic measurements. This work also
suggests a new equation for TS estimation that is important at low SNR.
Crown Copyright Ó 2004 Published by Elsevier Ltd on behalf of International Council for the Exploration of
the Sea. All rights reserved.
Keywords: digital data, echosounding, noise, reverberation, signal-to-noise ratio, split
beam, target-strength bias.
Received 4 March 2004; accepted 8 September 2004.
R. Kieser and T. J. Mulligan: Pacific Biological Station, 3190 Hammond Bay Road,
Nanaimo, BC V9T 6N7, Canada. P. Reynisson: Marine Research Institute, PO Box 1390,
Skulagata 4, 121 Reykjavik, Iceland. Correspondence to R. Kieser; tel: C1 250 756 7181;
fax: C1 250 756 7053; e-mail: [email protected].
Introduction
The signal-to-noise ratio (SNR) is well defined and
understood in electrical engineering and communications
(Tucker and Gazey, 1966; Carlson, 1968; Haykin, 1994;
Ziemer and Tranter, 1995). It is frequently used in fisheriesacoustic work that is concerned with the measurement
process and instrument design (Ehrenberg and Weimer,
1974; Weimer and Ehrenberg, 1975; Ehrenberg, 1978;
Ehrenberg, 1979; Ehrenberg, 1981; Mitson, 1983, 1995;
Furusawa et al., 1993; Furusawa et al., 2000), but has seen
relatively little use in the application-oriented, fisheriesacoustic literature (MacLennan and Simmonds, 1991). It is
the goal of this paper to introduce the SNR and to
demonstrate its usefulness for fisheries applications.
Communications’ theory tells us that the SNR in its
simplest form is defined as the ratio of signal power to noise
power. We will develop this definition and describe the
practical measurement of the SNR from split-beam data.
The importance of the SNR for TS measurements and splitbeam modelling will be briefly highlighted and the routine
use of the SNR for data-quality assurance will be
1054-3139/$30.00
recommended. Finally we propose an equation for
measuring TS at low signal to noise.
In practice, noise is recognized on the echogram as
a general background of random marks. These can be
removed by choosing a threshold that will provide an
interference-free image but does not significantly reduce
the desired echo signals in the depth range of interest. Foote
(1991) and others have discussed the bias that may arise
from thresholding in echo integration (EI). Split-beam
measurements generally use echo-amplitude and beampattern thresholds (MacLennan and Simmonds, 1991) to
reduce adverse noise effects. Thresholds provide an
intuitive and practical tool, however the SNR is required
to understand, quantify, minimize, and possibly correct for
the bias that cannot be avoided when the SNR is too low.
A distinction can be made between passive- and activenoise measurements. Passive-noise measurements are made
in listening mode with the echosounder transmitter
disabled. Active-noise measurements are made during
normal echosounder operations for the range of interest.
Both measurements will record vessel and environmental
noise, but only active-noise measurements will record
Crown Copyright Ó 2004 Published by Elsevier Ltd on behalf of
International Council for the Exploration of the Sea. All rights reserved.
124
R. Kieser et al.
reverberation, which is the noise-like, volume-backscatter
signal from unwanted, interfering target distributions.
Reverberation may be from bubble, silt, or plankton layers
at the range of the target or from boundaries. Here, we are
concerned with the noise that is observed during active
measurements as it includes all noise sources that occur
during typical echosounder operation.
We use fisheries-acoustic ‘‘standard notation’’ (Craig,
1981; Kieser, 1981; MacLennan et al., 2002) where
possible and will use two or more leading capital letters
for quantities expressed in dB, e.g. TS or SNR. For
consistency we use SV rather than SV for the volumebackscatter coefficient and STE will stand for single-target
echo as it plays a central role in TS and SNR measurements.
Given separate realizations of the filtered signal and
filtered noise, or of their envelopes, an estimate of the SNR
is given by:
Snr S
N
ð1Þ
where Snr is the SNR expressed as a power ratio rather than
in dB, S is the RMS signal power for the echo peak
(Johannesson and Mitson, 1983) and N is the mean RMS
noise power at the echolocation. A different approach is
needed to estimate the SNR from the filtered echo that is
shown at the lower right in Figure 1 as it contains signal
and noise contributions. In this case the SNR is estimated
from:
E NE
;
NE
Definition of signal-to-noise ratio
Snr The SNR is defined as signal power divided by noise power
(Carlson, 1968). Inspired by Mitson (1983) we start with
simulation results to illustrate the application of this
definition to fisheries acoustics (Figure 1). The signal and
noise are received by the transducer and processed in the
echosounder to generate the filtered signal and filtered noise
and their respective envelopes. Superposition of signal and
noise generates a realistic echo; the filtered echo now
clearly resembles a typical single-fish echo which may be
seen on the oscilloscope or plotted from the digital data.
Estimation of the SNR would be trivial if signal and noise
could be observed separately.
This simulation employs a pulse with 1-ms duration,
amplitude 1 and 5-kHz carrier. The pulse envelope is
composed of a flat top (0.5 ms) with cosine-shaped, leading
and trailing edges (Clay and Medwin, 1977). Band-limited,
Gaussian white noise (Kafadar, 1986) with random phase
and an amplitude of 0.5 between 2 and 10 kHz and an
elliptical bandpass filter of order 4 with 4.5 to 5.5 kHz pass
band (Matlab, 1998) are used.
where E is the combined signal and noise power at the
location of the echo peak and NE is noise power that is
estimated from observations on both sides of the peak.
Estimation of E and NE is described in the next section.
With this definition the estimated SNR has the desirable
property of approaching zero as the echo peak is reduced
and becomes masked by the noise.
The echo power at the peak location, E NE, approximates the steady echo signal that would be obtained from
a long, nearly rectangular transmit pulse that could be used
to estimate backscatter cross-section (Foote et al., 1987).
Note that the use of E NE in Equation (2) is in contrast to
the conventional use of E for TS estimation. We
recommend that E NE be used for TS estimation,
especially at low SNR provided that good noise estimates
are available.
This definition of the SNR matches that used for
modelling the split-beam process (Ehrenberg, 1979; Kieser
et al., 2000). Like TS the SNR assumes an on-axis target. It
follows that off-axis targets will have a reduced SNR. For
Input:
Signal
Transducer
Noise
Echo = Signal + Noise
Filtered:
Signal
Echosounder
ð2Þ
Envelop:
Signal
Noise
Noise
Echo
Echo
Figure 1. A simulation of signal and noise and a typical echo that includes signal and noise as they might appear at the transducer and after
the filter and envelop detection that are part of a typical echosounder.
Definition of signal-to-noise ratio and its role in split-beam measurements
example a reduction of 6 dB will occur for targets at the
3 dB beam-pattern contour.
The simple definition of the SNR used here assumes that
signal and noise are measured at the output of the bandpass
filters that are used in typical echosounders and therefore
are limited to the same bandwidth. The definition is useful
for work with a given echosounder both for comparing
identical acoustic systems and for modelling. However,
comparing SNR measurements from acoustic systems with
different pulse duration, bandwidth, beam width, and
transmit level will require a more encompassing definition
of the SNR. This is also required when signal and noise are
measured at the receiver input where noise will have
a much wider frequency spectrum than the signal.
Appropriate definitions are available (Carlson, 1968) but
are beyond the scope of this paper.
Measurement of signal-to-noise ratio
Figure 2 shows a single-target echo (STE) that was
observed with a SIMRAD EK500 echosounder. The cross
and the larger points on either side of the peak highlight the
maximum echo amplitude, emax, and the noise amplitudes,
Ping (#)
25
Range (m)
172.0
2BP (dB)
1.0
E (dB)
31.0
NE (dB)
59.6
nj, respectively. The observed echo and mean noise power,
E and NE, are:
J
1X
EZe2max ; NE Z
n2 ;
J jZ1 j
ð3Þ
where j is summed over the number of measured noise
amplitudes. As stated above the SNR is defined as the ratio
of signal power over noise power when the signal comes
from a target that is on the beam axis (Equation (2)). For
Figure 2. An echo from a single fish at 172-m range. SIMRAD
EK500 sample data (40 log r) with 0.1-m range resolution are used.
Pulselength is 0.75 m (1 ms). The observed signal is defined by the
peak (cross) and the noise by the larger dots on both sides of the peak.
125
a target at any position in the beam, E and NE are obtained
from the echo and the estimate of the SNR is:
E NE
SNRZ10log
2BP;
ð4Þ
NE
where SNR and BP are in dB and BP is the one-way beampattern factor for the target’s location in the beam.
Measurement of the SNR ratio typically starts with splitbeam STE data (echo traces) which provide an estimate of
the beam-pattern factor and give the location of the
detected target in the sample data. The sample data are
then used to estimate the signal and noise power as
described above. Resampling (Lyons, 1997) or curve fitting
may be required when additional data points are needed to
define the peak more accurately. The regions used to
estimate the noise (noise windows) must be well separated
from the peak to avoid contamination from the signal
envelope. A larger separation may be required at the longer
range side of the echo as the echo may be extended due to
‘‘ringing’’ or target size. The noise windows also must be
free of other signals and must include a sufficient number of
sample points to produce reasonable estimates.
The following results are obtained from the STE in
Figure 2.
TSu (dB)
31.0
TSc (dB)
30.0
SNRu (dB)
28.6
SNRc (dB)
29.6
where 2BP is the two-way beam-pattern factor from the
split-beam target position measurement. E and NE are the
peak and average noise energy, respectively, from Figure 2.
As recommended we use TSu Z E NE but this makes
little difference at the high SNR. TSu and TSc and SNRu
and SNRc are the uncorrected (off axis) and corrected (on
axis) TS and SNR, respectively. The corrected values
include the beam pattern correction shown in Equation (4).
TSc and SNRc are estimates of TS and SNR, respectively.
Similar to TS estimation only well defined, single-target
echoes will be considered for SNR estimation. Echoes may
be rejected when the peak is poorly defined, when
additional echoes are too close, when the variation and
slope in the selected noise windows is excessive or when
the estimates from the two noise windows are too different.
Substantial numbers of STE will have to be examined to
establish acceptable limits for particular situations. Figure 3
shows an echo trace that would not be acceptable for SNR
measurement as the left-hand shoulder on the peak
interferes with the noise measurement.
Estimates of the SNR can be obtained from 20 or 40 log r
data when the corresponding 20 or 40 log r factors are
approximately constant over the range interval that includes
the signal and noise samples. This will be the case when the
interval is much smaller than the target range.
Single-target detection and TS estimation are routinely
done in split-beam echosounders. The EK500, for example,
outputs an echo trace file that includes estimates of echo
126
R. Kieser et al.
100 kHz. Although this paper focuses on the SNR for single
targets we note that for the EI of a target distribution with
constant volume-backscatter coefficient (e.g. a target distribution with constant average density and TS) situation i)
and ii) will yield SNRs that will decrease with range as
20 log r 2ar and 0, respectively.
The effects of low signal to noise:
evidence of TS bias from TS
measurements
Figure 3. An echo trace that is not acceptable for SNR
measurement as the left hand shoulder, which may be from
a nearby second target, interferes with the peak and the noise
measurement.
peak height (TSu) and information on echo quality but does
not provide noise estimates. As before the latter may be
obtained from sample data. However this requires that
the sample data use the same units or are converted to the
same units. This approach is useful when only relatively
low-resolution sample data or high-resolution EI data are
available.
A well-known example of potential TS bias with range, and
hence presumably decreasing SNR, has been described by
Reynisson and Sigurdsson (1996) and Reynisson (1999)
and is shown in Figure 4. Redfish of the same size (mean
length 37 cm and TS 40 dB) are often distributed between
100 and 300-m depth. TS estimates were made with five
different beam acceptance angles, only targets that are
detected within the specified off-axis beam angle being
accepted.
Figure 4 shows that the TS estimate in general increases
with range. It also increases when a larger beam acceptance
Noise and SNR range dependence
Evidence from echograms, plots of echo intensity vs. range,
and oscilloscope observations of the echosounder output
voltage generally show noise levels that increase with
range. More rapid increase with range is observed for
40 log r than for 20 log r data. Two simple situations are:
(i) constant noise level at the transducer face, and
(ii) reverberation or volume backscatter from distributed
targets in the water column.
The former could be from vessel or ambient noise while
reverberation could be from plankton or bubbles and
suspended silt. Given a single target with constant TS and
20 or 40 log r TVG signal, noise and SNR range
dependence are:
TVG: 20 log r TVG: 40 log r
SNR
Signal
20 log r
Constant
e
i) Constant noise 20 log r C 2ar 40 log r C 2ar 40 log r 2ar
ii) Reverberation Constant
20 log r
20 log r
The last column confirms the earlier observation that the
SNR is independent of the type of TVG used. Noise from
the receiver front end will produce the same effect as
a constant noise level at the transducer face. For a wellengineered echosounder internally generated receiver noise
will generally be negligible compared to vessel and
ambient noise, especially at operating frequencies below
Figure 4. Redfish TS vs. depth measured with five different beam
acceptance angles. At 250-m depth and from left to right TS lines
use beam acceptance angles of 1.1, 1.6, 2.6, 3.6, and 4.4(. From
Reynisson and Sigurdsson (1996).
Definition of signal-to-noise ratio and its role in split-beam measurements
angle is used. These effects are particularly evident below
220 m where the SNR presumably is a limiting factor. The
increase in estimated TS with increasing beam acceptance
angle is more traceable than the increase in TS with range
as fish in a narrow depth band are more likely to be
physically similar and have similar TS than fish from
different depths. In addition, the effective SNR (SNRu) will
certainly decrease with increasing beam angle while its
decrease with range is less predictable.
We will not pursue this example as measurements of the
SNR are required to further explain, model, and quantify
the observed TS bias and its dependence on the SNR. Work
is in progress to do so, but is complicated by the fact that
only echo-integration data with 1-m resolution rather than
sample data with 0.1-m resolution are available.
We note that the TS increase above 175-m depth is not
explained by the fishing results that indicate constant fish
size over the entire depth range. This is supported by
trawling results from several acoustic surveys on the
species in question (e.g. Magnusson et al., 1996). The
increase may indicate changes in swimbladder volume or in
tilt-angle distribution of the fish. The effect of these factors
on target strength has been demonstrated by several authors
(e.g. Nakken and Olsen, 1977; Blaxter and Batty, 1990).
Effects of low SNR: target measurements
and simulation of TS bias
A series of split-beam target experiments was conducted in
the Fraser River (Enzenhofer et al., 1998). The prevailing
SNR was below 20 dB which is not uncommon for riverine
measurements. A split-beam angle measurement bias was
observed, which was unexpected at the time and a splitbeam simulation model (Kieser et al., 2000) was developed
that explained the significant bias that was observed under
the prevailing low SNR. The model demonstrated that the
split-beam angle measurement and the well-known TS bias
become significant below similar SNR levels. We have
expanded this model by including the SNR range dependence described above.
The simulation uses the following echosounder parameters: beam width 7(, frequency 38 kHz, a 0.011 dB m1,
sound speed 1500 m s1, TS 30 dB, TS threshold 45 dB
and two-way beam-pattern threshold 12 dB (beam
acceptance angles). Figure 2 yields an estimate of SNR0
29.6 dB at the target range r0 172.0 m. Assuming constant
target size and constant noise level at the transducer, the
SNR range dependence is given by SNR(r) Z
SNR0 40 log r/r0 2a(r r0). With this the SNR drops
from 33 dB at 100-m to 14 dB at 350-m range (Figure 5a).
Pulsewidth is not included as it only enters the simulation
indirectly through the SNR as a shorter pulse will require
wider bandwidth and hence will admit more noise energy.
Model results for the simulated SNR, the bias in the
SNR, and the bias in TS are shown in Figure 5a, b, and c,
127
respectively. Only targets that pass both the TS and twoway beam-pattern threshold are shown and used for the bias
curves. SNR and TS are shown in dB but calculations are
done in physical units. Simulated TS vs. two-way beam
pattern are shown in Figure 6a and b for target depths
between 150 to 200 and 300 to 350 m, respectively. The
results are summarized as:
R
SNR
SNRbias
TSbias
TSbias2
173.6
323.8
29.8
15.4
3.1
4.5
0.2
1.1
0.2
0.3
where R is the mean range of the accepted targets, SNR is
the SNR used by the simulation and SNRbias reflects the
bias in the SNR that is estimated from the accepted targets.
TSbias and TSbias2 give the TS bias that is estimated from
all accepted targets and from those that have a two-way
estimated beam pattern that is less than 2 dB. The bias
columns indicate that measurements will tend to overestimate the SNR and TS. Significant bias is observed at
SNR of less than 15 dB, especially when targets from a far
off-axis position are accepted. The bias in the estimated
SNR is related to the well-known TS bias. It is larger than
the TS bias as the TS calculations do not include the noise
correction recommended earlier.
The simulation model can be used to qualitatively and
quantitatively explore the relation between SNR, TS, range,
beam angle threshold, and other parameters. It may be used
to understand a measurement of interest, to optimize
measurement parameters and to possibly correct for SNR
and TS bias. Good SNR measurements are a prerequisite,
however. Consideration and measurement of the SNR can
play an important role in developing good measurement
practice and parameters and in identifying sources of
measurement variability and bias. The SNR can make
a significant contribution to optimize data quality and
interpretation.
Discussion and recommendations
It is said that one person’s signal is another person’s noise.
Generally noise can be defined as the unwanted part of the
signal. Signal and noise occur at the same time and
following optimal signal processing, remaining noise
cannot be separated from the signal. Traditional fisheriesacoustic work focuses on the signal which may be the echo
amplitude or power or the average volume-backscatter
strength and it uses thresholding to eliminate noise.
However noise and SNR are seldom measured. The SNR
is a key quantity in any measurement and should therefore
be monitored routinely to assure data quality. SNR
measurements are particularly important when split-beam
TS and target-position measurements are made under
difficult conditions, such as at large range or on small
128
R. Kieser et al.
Figure 5. SNR, SNR bias, and TS bias vs. range. a) The line gives the SNR that is used for the simulation and the points are from accepted
targets only. Note the large scatter in the simulated values. b) SNR bias and c) TS-bias curves are from a polynomial fit to the
corresponding values from the accepted targets. All calculations use physical rather than dB values.
targets. They also are required for modelling split-beam and
other acoustic measurement processes (Ehrenberg, 1979;
Kieser et al., 2000; Sawada and Furusawa, 2000; Sawada
et al., 2002).
The present paper stems from our earlier work that taught
us that SNR measurements are required for meaningful
comparison between target-position measurements and
model results (Kieser et al., 2000). Although not discussed
here we note that quantitative analyses require that signal
and noise have well-defined statistical properties. It therefore
will be important to measure signal and noise power and
obtain at least some indication of their statistical properties.
The model results presented here confirm the observed
increase in TS bias with increased range or decreasing SNR
and they highlight a corresponding bias in the measured
SNR. Given good SNR measurements the split-beam model
will provide a tool to optimize data-acquisition parameters
and to predict and confirm data quality. In addition, it has
the potential to provide corrections for SNR, TS, and other
measured quantities when signal and noise are well defined.
A tighter comparison between TS and other measurement
and model results is desirable; however measurements from
the same fish over a wide SNR will be required to conclusively compare measurement and model. This is difficult
to achieve but measurements could be conducted at sea on
an aggregation of single fish with different SNRs that are
obtained by lowering the transducer, using different transducer beam width, changing transmit power (for nonreverberation noise only), or injecting a noise signal into the
front end of the echosounder or into its digital data stream.
Finally target tracking may be a useful tool to follow a fish
through the beam and to relate observations to the SNR.
Note that the SIMRAD EK500 can provide an absolute
measurement of passive-noise power (SIMRAD, 1993;
Takao and Furusawa, 1995). This is helpful in determining
the minimum possible noise level for different sea
conditions, water depths, vessel speeds, engine rpm,
propeller pitch, etc. As it is an absolute measurement it
can be used to monitor noise from a given vessel over long
periods of time or to compare noise between vessels.
However additional steps and a new mindset are required to
readily measure the SNR from an active sonar. These
include: (i) Detailed observation of noise on a standard
echogram and on echograms with different thresholds and
a review of TS vs. depth and TS vs. beam pattern and other
plots. (ii) Quantitative observations begin with signal and
noise measurements which are easily made on a few pings
but routine measurements will require sophisticated
software. (iii) Developers of commercial echosounders
and post-processing software should encourage signal and
noise measurements and their practical use by including
noise measurements in their products. For example, STE
Definition of signal-to-noise ratio and its role in split-beam measurements
Figure 6. A plot of simulated TS vs. two-way beam pattern for
a) 150 to 200 and b) 300 to 350-m range bins.
data that now include TS, target location in the beam and
depth should be complemented by noise estimates and data
from windows on both sides of the echo peak, or just the
latter alone, that can be used to estimate mean noise power
and statistical properties.
Capable and flexible instruments and software for
fisheries-acoustic measurements and data analysis are
available and should be used. Additional diagnostic tools
for the estimation of TS bias, split-beam target detection
probability, effective sampling volume (Foote, 1991), and
other effects are needed. Many of these will require good
SNR estimates to generate informative results and to
provide possible corrections. The SNR will be a regular and
rewarding topic in this context and we hope that this paper
will encourage its routine measurement and use.
Acknowledgements
Seminal discussions and guidance from J. E. Ehrenberg and
comments from R. B. Mitson and M. Furusawa are
gratefully acknowledged.
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