IEC 61280-2-8:2021
(Main)Fibre optic communication subsystem test procedures - Part 2-8: Digital systems - Determination of low BER using Q-factor measurements
Fibre optic communication subsystem test procedures - Part 2-8: Digital systems - Determination of low BER using Q-factor measurements
IEC 61280-2-8:2021 specifies two main methods for the determination of low BER values by making accelerated measurements. These include the variable decision threshold method (Clause 5) and the variable optical threshold method (Clause 6). In addition, a third method, the sinusoidal interference method, is described in Annex B. This second edition cancels and replaces the first edition published in 2003. This edition constitutes a technical revision. This edition includes the following significant technical changes with respect to the previous edition:
- correction of errors in Formula (8) in 5.5.2 and in a related formula in 5.5.3;
- correction of errors in the references to clauses, subclauses, figures, procedures, and in the Bibliography;
- alignment of the terms and definitions in 3.1 with those in IEC 61281-1.
Procédures d'essai des sous-systèmes de télécommunication fibroniques - Partie 2-8: Systèmes numériques - Détermination de faibles valeurs de BER en utilisant des mesures du facteur Q
L'IEC 61280-2-8:2021 spécifie deux méthodes principales permettant de déterminer de faibles valeurs de BER en réalisant des mesures accélérées. Ces méthodes utilisent soit un seuil de décision variable (Article 5), soit un seuil optique variable (Article 6). De plus, une troisième méthode fondée sur le brouillage sinusoïdal est décrite à l’Annexe B. Cette deuxième édition annule et remplace la première édition parue en 2003. Cette édition constitue une révision technique. Cette édition inclut les modifications techniques majeures suivantes par rapport à l’édition précédente:
- correction d’erreurs dans la Formule (8) en 5.5.2 et dans une formule associée en 5.5.3;
- correction d’erreurs dans les références aux articles, paragraphes, figures et procédures, ainsi que dans la bibliographie;
- alignement des termes et définitions en 3.1 sur ceux de l’IEC 61281-1.
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IEC 61280-2-8 ®
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STANDARD
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Fibre optic communication subsystem test procedures – Digital systems –
Part 2-8: Digital systems – Determination of low BER using Q-factor
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IEC 61280-2-8 ®
Edition 2.0 2021-03
REDLINE VERSION
INTERNATIONAL
STANDARD
colour
inside
Fibre optic communication subsystem test procedures – Digital systems –
Part 2-8: Digital systems – Determination of low BER using Q-factor
measurements
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 33.180.10 ISBN 978-2-8322-9530-4
– 2 – IEC 61280-2-8:2021 RLV © IEC 2021
CONTENTS
FOREWORD . 4
1 Scope . 6
2 Normative references . 6
3 Terms, definitions, and abbreviated terms . 6
3.1 Terms and definitions . 6
3.2 Abbreviated terms . 7
4 Measurement of low bit-error ratios . 7
4.1 General considerations . 7
4.2 Background to Q-factor . 9
5 Variable decision threshold method . 11
5.1 Overview. 11
5.2 Apparatus . 14
5.3 Sampling and specimens . 14
5.4 Procedure . 15
5.5 Calculations and interpretation of results . 16
5.5.1 Sets of data . 16
5.5.2 Convert BER using inverse error function . 17
5.5.3 Linear regression . 18
5.5.4 Standard deviation and mean . 19
5.5.5 Optimum decision threshold . 20
5.5.6 BER optimum decision threshold . 20
5.5.7 BER non-optimum decision threshold . 20
5.5.8 Error bound . 20
5.6 Test documentation . 20
5.7 Specification information . 21
6 Variable optical threshold method . 21
6.1 Overview. 21
6.2 Apparatus . 21
6.3 Items under test . 22
6.4 Procedure for basic optical link . 22
6.5 Procedure for self-contained system . 22
6.6 Evaluation of results . 23
Annex A (normative) Calculation of error bound in the value of Q . 25
Annex B (informative) Sinusoidal interference method . 27
B.1 Introduction Overview . 27
B.2 Apparatus . 27
B.3 Sampling and specimens . 27
B.4 Procedure . 28
B.4.1 Optical sinusoidal interference method . 28
B.4.2 Electrical sinusoidal interference method . 29
B.5 Calculations and interpretation of results . 30
B.5.1 Mathematical analysis . 30
B.5.2 Extrapolation . 30
B.5.3 Expected results . 31
B.6 Documentation . 32
B.7 Specification information . 32
Bibliography . 33
Figure 1 – Sample eye diagram showing patterning effects . 10
Figure 2 – More accurate measurement technique using a DSO that samples noise
statistics between eye centres . 10
Figure 3 – Bit error ratio as a function of decision threshold level . 12
Figure 4 – Plot of Q-factor as a function of threshold voltage . 13
Figure 5 – Set-up for the variable decision threshold method . 15
Figure 6 – Set-up of initial threshold level (approximately at the centre of the eye) . 15
Figure 7 – Effect of optical bias . 21
Figure 8 – Set-up for optical link or device test . 22
Figure 9 – Set-up for system test . 23
Figure 10 – Extrapolation of log BER as a function of bias . 24
Figure B.1 – Set-up for the sinusoidal interference method by optical injection . 28
Figure B.2 – Set-up for the sinusoidal interference method by electrical injection . 30
Figure B.3 – BER result from the sinusoidal interference method (data points and
extrapolated line) . 31
Figure B.4 – BER versus optical power for three methods . 32
Table 1 – Mean time for the accumulation of 15 errors as a function of BER and bit rate . 7
Table 2 – BER as a function of threshold voltage . 17
Table 3 – f as a function of D . 18
i i
Table 4 – Values of linear regression constants . 19
Table 5 – Mean and standard deviation . 19
Table 6 – Example of optical bias test . 23
Table B.1 – Results for sinusoidal injection . 29
– 4 – IEC 61280-2-8:2021 RLV © IEC 2021
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
FIBRE OPTIC COMMUNICATION SUBSYSTEM TEST PROCEDURES –
DIGITAL SYSTEMS –
Part 2-8: Digital systems –
Determination of low BER using Q-factor measurements
FOREWORD
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This redline version of the official IEC Standard allows the user to identify the changes made to
the previous edition IEC 61280-2-8:2003. A vertical bar appears in the margin wherever a change
has been made. Additions are in green text, deletions are in strikethrough red text.
IEC 61280-2-8 has been prepared by subcommittee 86C: Fibre optic systems and active
devices, of IEC technical committee 86: Fibre optics. It is an International Standard.
This second edition cancels and replaces the first edition published in 2003. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) correction of errors in Formula (8) in 5.5.2 and in a related formula in 5.5.3;
b) correction of errors in the references to clauses, subclauses, figures, procedures, and in
the Bibliography;
c) alignment of the terms and definitions in 3.1 with those in IEC 61281-1.
The text of this International Standard is based on the following documents:
FDIS Report on voting
86C/1708/FDIS 86C/1711/RVD
Full information on the voting for its approval can be found in the report on voting indicated in
the above table.
The language used for the development of this International Standard is English.
This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in
accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement, available
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the specific document. At this date, the document will be
• reconfirmed,
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• replaced by a revised edition, or
• amended.
IMPORTANT – The "colour inside" logo on the cover page of this document indicates
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of its contents. Users should therefore print this document using a colour printer.
– 6 – IEC 61280-2-8:2021 RLV © IEC 2021
FIBRE OPTIC COMMUNICATION SUBSYSTEM TEST PROCEDURES –
DIGITAL SYSTEMS –
Part 2-8: Digital systems –
Determination of low BER using Q-factor measurements
1 Scope
This part of IEC 61280 specifies two main methods for the determination of low BER values by
making accelerated measurements. These include the variable decision threshold method
(Clause 5) and the variable optical threshold method (Clause 6). In addition, a third method,
the sinusoidal interference method, is described in Annex B.
2 Normative references
There are no normative references in this document.
3 Terms, definitions, and abbreviated terms
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at http://www.iso.org/obp
3.1.1
amplified spontaneous emission
ASE
impairment generated in optical amplifiers
optical power associated to spontaneously emitted photon amplified by an active medium in an
optical amplifier
3.1.2
bit error ratio
BER
P
e
the number bits in error as a ratio of the total number of bits
number of errored bits divided by the total number of bits, over some stipulated period of time
3.1.3
intersymbol interference
ISI
mutual interference between symbols in a data stream, usually caused by non-linear effects
and bandwidth limitations of the transmission path
overlap of adjacent pulses as caused by the limited bandwidth characteristics of the optical
devices in a fibre optic link
3.1.4
Q-factor
Q
ratio of the difference between the mean voltage of the 1 and 0 rails, and to the sum of their
standard deviation values
3.2 Abbreviated terms
AC alternating current
CW continuous wave (normally referring to a sinusoidal wave form)
DC direct current
DSO digital sampling oscilloscope
DUT device under test
PRBS pseudo-random binary sequence
SNR signal-to-noise ratio
4 Measurement of low bit-error ratios
4.1 General considerations
Fibre optic communication systems and subsystems are inherently capable of providing
exceptionally good error performance, even at very high bit rates. The mean bit error ratio (BER)
−12 −20
may typically lie in the region 10 to 10 , depending on the nature of the system. While this
type of performance is well in excess of practical performance requirements for digital signals,
it gives the advantage of concatenating many links over long distances without the need to
employ error correction techniques.
The measurement of such low error ratios presents special problems in terms of the time taken
to measure a sufficiently large number of errors to obtain a statistically significant result. Table 1
presents the mean time required to accumulate 15 errors. This number of errors can be
regarded as statistically significant, offering a confidence level of 75 % with a variability of 50 %.
Table 1 – Mean time for the accumulation of 15 errors
as a function of BER and bit rate
BER
–6 –7 –8 –9 –10 –11 –12 –13 –14 –15
10 10 10 10 10 10 10 10 10 10
Bits/s
1,0M 1,5 s 15 s 2,5 min 25 min 4,2 h 1,7d 17 d 170 d 4,7 years 47 years
2,0M 750 ms 7,5 s 75 s 750 s 2,1 h 21 h 8,8 d 88 d 2,4 years 24 years
10M 150 ms 1,5 s 15 s 2,5 min 25 min 4,2 h 1,7 d 17 d 170 d 4,7 years
50M 30 ms 300 ms 3,0 s 30 s 5,0 min 50 min 8,3 h 3,5 d 35 d 350 d
100M 15 ms 150 ms 1,5 s 15 s 2,5 min 25 min 4,2 h 1,7 d 17 d 170 d
500M 3 ms 30 ms 300 ms 3,0 s 30 s 5,0 min 50 min 8,3 h 3,5 d 35 d
1,0G 1,5 ms 15 ms 150 ms 1,5 s 15 s 2,5 min 25 min 4,2 h 1,7 d 17 d
10G 150 μs 1,5 ms 15 ms 150 ms 1,5 s 15 s 2,5 min 25 min 4,2 h 1,7 d
40G 38 μs 380 μs 3,8 ms 38 ms 380 ms 3,8 s 38 s 6,3 min 63 min 10,4 h
100G 15 μs 150 μs 1,5 ms 15ms 150 ms 1,5 s 15 s 2,5 min 25 min 4,2 h
– 8 – IEC 61280-2-8:2021 RLV © IEC 2021
Mean times for the accumulation of 15 errors
BER
Bit rate
−5 −6 −7 −8 −9 −10 −11 −12 −13 −14 −15
10 10 10 10 10 10 10 10 10 10 10
1,0 Mbit/s 150 ms 1,5 s 15 s 2,5 min 25 min 4,2 h 1,7d 17 d 170 d 4,7 47
years years
2,0 Mbit/s 75 ms 750 ms 7,5 s 75 s 750 s 2,1 h 21 h 8,8 d 88 d 2,4 24
years years
4,7
10 Mbit/s 15 ms 150 ms 1,5 s 15 s 2,5 min 25 min 4,2 h 1,7 d 17 d 170 d
years
50 Mbit/s 3,0 ms 30 ms 300 ms 3,0 s 30 s 5,0 min 50 min 8,3 h 3,5 d 35 d 350 d
100 Mbit/s 1,5 ms 15 ms 150 ms 1,5 s 15 s 2,5 min 25 min 4,2 h 1,7 d 17 d 170 d
500 Mbit/s 300 μs 3 ms 30 ms 300 ms 3,0 s 30 s 5,0 min 50 min 8,3 h 3,5 d 35 d
1,0 Gbit/s 150 μs 1,5 ms 15 ms 150 ms 1,5 s 15 s 2,5 min 25 min 4,2 h 1,7 d 17 d
10 Gbit/s 15 μs 150 μs 1,5 ms 15 ms 150 ms 1,5 s 15 s 2,5 min 25 min 4,2 h 1,7 d
40 Gbit/s 3,8 μs 38 μs 380 μs 3,8 ms 38 ms 380 ms 3,8 s 38 s 6,3 min 63 min 10,4 h
100 Gbit/s 1,5 μs 15 μs 150 μs 1,5 ms 15ms 150 ms 1,5 s 15 s 2,5 min 25 min 4,2 h
The times given in Table 1 show that the direct measurement of the low BER values expected
from fibre optic systems is not practical during installation and maintenance operations. One
way of overcoming this difficulty is to artificially impair the signal-to-noise ratio at the receiver
in a controlled manner, thus significantly increasing the BER and reducing the measurement
time. The error performance is measured for various levels of impairment, and the results are
then extrapolated to a level of zero impairment using computational or graphical methods
according to theoretical or empirical regression algorithms.
The difficulty presented by the use of any regression technique for the determination of the
error performance is that the theoretical BER value is related to the level of impairment via
the inverse complementary error function (erfc). This means that very small changes in the
impairment lead to very large changes in BER; for example, in the region of a BER value of
−15
10 , a change of approximately 1 dB in the level of impairment results in a change of three
orders of magnitude in the BER. A further difficulty is that a method based on extrapolation is
unlikely to reveal a levelling off of the BER at only about 3 orders of magnitude below the lowest
measured value.
It should also be noted that, in the case of digitally regenerated sections, the results obtained
apply only to the regenerated section whose receiver is under test. Errors generated in
upstream regenerated sections may generate an error plateau which may have to be taken into
account in the error performance evaluation of the regenerator section under test.
As noted above, two main methods for the determination of low BER values by making
accelerated measurements are described. These are the variable decision threshold method
(Clause 5) and the variable optical threshold method (Clause 6). In addition, a third method,
the sinusoidal interference method, is described in Annex B.
It should be noted that these methods are applicable to the determination of the error
performance in respect of amplitude-based impairments. Jitter may also affect the error per-
formance of a system, and its effect requires other methods of determination. If the error
performance is dominated by jitter impairments, the amplitude-based methods described in this
document will lead to BER values which are lower than the actual value.
The variable decision threshold method is the procedure which can most accurately measure
the Q-factor and the BER for optical systems with unknown or unpredictable noise statistics. A
key limitation, however, to the use of the variable threshold method to measure Q-factor and
BER is the need to have access to the receiver electronics in order to manipulate the decision
threshold. For systems where such access is not available, it may be useful to utilize the
alternative variable optical threshold method. Both methods are capable of being automated in
respect of measurement and computation of the results
4.2 Background to Q-factor
The Q-factor is the signal-to-noise ratio (SNR) at the decision circuit and is typically expressed
as [1] :
μμ−
1 0
Q = (1)
σσ+
where
µ and µ are the mean voltage levels of the "1" and "0" rails, respectively;
1 0
σ and σ are the standard deviation values of the noise distribution on the "1" and "0" rails,
1 0
respectively.
An accurate estimation of a system’s transmission performance, or Q-factor, must shall take
into consideration the effects of all sources of performance degradation, both fundamental and
those due to real-world imperfections. Two important sources are amplified spontaneous
emission (ASE) noise and intersymbol interference (ISI). Additive noise originates primarily from
ASE of optical amplifiers. ISI arises from many effects, such as chromatic dispersion, fibre non-
linearities, multi-path interference, polarization-mode dispersion and use of electronics with
finite bandwidth. There may be other effects as well; for example, a poor impedance match can
cause impairments such as long fall times or ringing on a waveform.
One possible method to measure Q-factor is the voltage histogram method in which a digital
sampling oscilloscope is used to measure voltage histograms at the centre of a binary eye to
estimate the waveform’s Q-factor [2]. In this method, a pattern generator is used as a stimulus
and the oscilloscope is used to measure the received eye opening and the standard deviation
of the noise present in both voltage rails. As a rough approximation, the edge of visibility of the
noise represents the 3σ points of an assumed Gaussian distribution. The advantage of using
an oscilloscope to measure the eye is that it can be done rapidly on real traffic with a minimum
of equipment.
The oscilloscope method for measuring the Q-factor has several shortcomings. When used to
measure the eye of high-speed data (of the order of several Gbit/s), the oscilloscope’s limited
digital sampling rate (often in the order of a few hundred kilohertz) allows only a small minority
of the high-speed data stream to be used in the Q-factor measurement. Longer observation
times could reduce the impact of the slow sampling. A more fundamental shortcoming is that
the Q estimates derived from the voltage histograms at the eye centre are often inaccurate.
Various patterning effects and added noise from the front-end electronics of the oscilloscope
can often obscure the real variance of the noise.
Figure 1 shows a sample eye diagram made on an operating system. It can be seen in this
figure that the vertical histograms through the centre of the eye show patterning effects (less
obvious is the noise added by the front-end electronics of the oscilloscope). It is difficult to
predict the relationship between the Q measured this way and the actual BER measured with
a test set.
____________
Figures in square brackets refer to the Bibliography.
– 10 – IEC 61280-2-8:2021 RLV © IEC 2021
NOTE The data for measuring the Q-factor are obtained from the tail of the Gaussian distributions.
Figure 1 – Sample eye diagram showing patterning effects
Figure 2 shows another possible way of measuring Q-factor using an oscilloscope. The idea is
to use the centre of the eye to estimate the eye opening and use the area between eye centres
to estimate the noise. Pattern effect contributions to the width of the histogram would then be
reduced. A drawback to this method is that it relies on measurements made on a portion of the
eye that the receiver does not really ever use.
Figure 2 – More accurate measurement technique using a DSO
that samples noise statistics between eye centres
It is tempting to conclude that the estimates for σ and σ would tend to be overestimated and
1 0
that the resulting Q measurements would always form a lower bound to the actual Q for either
of these oscilloscope-based methods. That is not necessarily the case. It is possible that the
histogram distributions can be distorted in other ways, for example, skewed in such a way that
the mean values overestimate the eye opening – and the resulting Q will actually not be a lower
bound. There is, unfortunately, no easily characterized relationship between oscilloscope-
derived Q measurements and BER performance.
5 Variable decision threshold method
5.1 Overview
This method of estimating the Q-factor relies on using a receiver front-end with a variable
decision threshold. Some means of measuring the BER of the system is required. Typically, the
measurement is performed with an error test set using a pseudo-random binary sequence
(PRBS), but there are alternate techniques which allow operation with live traffic. The
measurement relies on the fact that for a data eye with Gaussian statistics, the BER may be
calculated analytically as follows:
| V −μ | | V −μ |
th 1 th 0
BER(V ) = erfc + erfc
(2)
th
2 σ σ
1 0
where
µ , µ and σ , σ are the mean and standard deviation of the “1” and “0” data rails;
1 0 1 0
V is the decision threshold level;
th
erfc(.) is the complementary error function given by
∞
2 2
1 1
−β / 2 − x /2
erfc(x) = e dβ ≅ e
(3)
∫
2π x 2π
x
|V −−μ | |V μ |
th 1 th 0
PV( ) erfc + erfc
(2)
e th
2 σσ
where
P is the BER;
e
V is the decision threshold level;
th
µ , µ and σ , σ are the mean and standard deviation of the "1" and "0" data rails;
1 0 1 0
erfc(.) is the complementary error function given by
∞
−−β / 22x /
(3)
erfc( x) e dβ≅ e
∫
2π x 2π
x
The approximation is nearly exact for x > 3.
The BER, given in Formula (2), is the sum of two terms. The first term is the conditional
probability of deciding that a "0" has been received when a "1" has been sent, and the second
term is the probability of deciding that a "1" has been received when a "0" has been sent.
=
=
– 12 – IEC 61280-2-8:2021 RLV © IEC 2021
In order to implement this technique, the BER is measured as a function of the threshold voltage
(see Figure 3). Formula (2) is then used to convert the data into a plot of the Q-factor versus
threshold, where the Q-factor is the argument of the complementary error function of either term
in Formula (2). To make the conversion, the approximation is made that the BER is dominated
by only one of the terms in Formula (2) according to whether the threshold is closer to the "1's"
or the "0's" rail of the eye diagram.
Figure 3 – Bit error ratio as a function of decision threshold level
Figure 4 shows the results of converting the data in Figure 3 into a plot of Q-factor versus
threshold. The optimum Q-factor value as well as the optimum threshold setting needed to
achieve this Q-factor are obtained from the intersection of the two best-fit lines through the data.
This technique is described in detail in [3].
Figure 4 – Plot of Q-factor as a function of threshold voltage
The optimum threshold as well as the optimal Q can be obtained analytically by making use of
the following approximation [4] for the inverse error function:
−1
1
(4)
log erfc(x) ≈1,192 − 0,6681x − 0,0162x
where x is the log(BER).
–5 –10
NOTE Equation (4) is accurate to ±0,2 % over the range of BER from 10 to 10 .
−1
1
log erfc(x) ≈−1,192 0,6681xx− 0,0162
(4)
where
x is log(P ).
e
−5 −10
NOTE 1 Formula (4) is accurate to ±0,2 % over the range of P from 10 to 10 .
e
After evaluating the inverse error function, the data are plotted against the decision threshold
level, V . As shown in Figure 4, a straight line is fitted to each set of data by linear regression.
th
The equivalent variance and mean for the Q calculation are given by the slope and intercept
respectively.
The minimum BER can be shown to occur at an optimal threshold, V , when the two
th-optimal
terms in the argument in Formula (2) are equal, that is
– 14 – IEC 61280-2-8:2021 RLV © IEC 2021
μV−−V μ
( ) ( )
1 th−−optimal th optimal 0
Q
(5)
opt
σσ
An explicit expression for V in terms of µ and σ can be derived from Formula (5)
th-optimal 1,0 1,0
to be:
σ μ +σμ
0 1 10
V = (6)
th−optimal
σσ+
The value of Q is obtained from Formula (1). The residual BER at the optimal threshold can
opt
be obtained from Formula (2) and is approximately
−Q/ 2
( opt )
e
P ≅ (7)
e-optimal
Q 2π
opt
NOTE 2 This approximation is nearly exact for Q > 3.
opt
It should be noted that even though the variable threshold method makes use of Gaussian
statistics, it provides accurate results for systems that have non-Gaussian noise statistics as
well, for example, the non-Gaussian statistics that occur in a typical optically amplified system
[5] [6]. This can be understood by examining Figure 1. The decision circuit of a receiver operates
only on the interior region of the eye. This means that the only part of the vertical histogram
that it uses is the "tail" that extends into the eye. The variable decision threshold method
amounts to constructing a Gaussian approximation to the tail of the real distribution in the centre
region of the eye where it affects the receiver operation directly. As the example in Figure 1
shows, this Gaussian approximation will not reproduce the actual histogram distribution at all,
but it does not need to, for purposes of Q estimation.
Another way to view the variable decision threshold technique is to imagine replacing the real
data eye with a fictitious eye having Gaussian statistics. The two eye diagrams have the same
BER versus decision threshold voltage behaviour, so it is reasonable to assign them the same
equivalent Q value, even though the details of the full eye diagram may be very different. Of
course, it does need to be kept in mind that However, this analysis will not work for systems
dominated by noise sources whose "tails" are not easily approximated to be Gaussian in shape;
as, for example, would occur in a system dominated by cross-talk or modal noise. In taking
these measurements, an inability to fit the data of Q-factor versus threshold to a straight line
would provide a good indication of the presence of such noise sources.
Experimentally, it has been found that the Q values measured using the variable decision
threshold method have a statistically valid level of correlation with the actual BER
measurements.
5.2 Apparatus
An error performance analyser consisting of a pattern generator and a bit error rate ratio
detector.
5.3 Sampling and specimens
The device under test (DUT) is a fibre optic digital system, consisting of an electro-optical
transmitter at one end and an opto-electronic receiver at the other end. In between the
transmitter and the receiver can be an optical network with links via optical fibres (for example,
a DWDM network).
==
5.4 Procedure
Data for the Q measurement are collected at both the top "1" and bottom "0" regions of the eye
−5 −10
as BER (over the range 10 to 10 ) versus decision threshold. The equivalent mean (μ) and
variance (σ) of the "1's" and "0's" are determined by fitting this data to a Gaussian characteristic.
The Q-factor is then calculated using Formula (1).
a) Connect the pattern generator and error detector to the system under test in accordance
with Figure 5.
Figure 5 – Set-up for the variable decision threshold method
b) Set the clock source to the desired frequency.
c) Set up the pattern generator’s pattern, data and clock amplitude, offset, polarity and
termination as required.
d) Set up the error detector’s pattern, data polarity and termination as required.
e) Set the decision threshold voltage and data input delay to achieve a sampling point that is
approximately in the centre of the data eye as shown in Figure 6. This is the initial
sampling point.
Figure 6 – Set-up of initial threshold level (approximately at the centre of the eye)
f) Enable the error detector's gating function and set it to gate by errors, for a minimum of 10,
100 or 1 000 errors.
g) Adjust the error detector's decision threshold voltage in a positive direction until the
−10
measured BER increases to a value greater than 1 × 10 . Note the decision threshold
voltage (V ) and the BER.
b1
−5
h) Increase the decision threshold voltage until the BER rises above 10 and note the decision
threshold voltage (V ) and the BER.
a1
i) Note the difference between the two threshold values V and V and choose a step size
a1 b1
(V ) that provides a reasonable number (greater than 5) of measurement points between
step1
these two decision threshold extremes. Starting from the threshold value V , decrease the
a1
– 16 – IEC 61280-2-8:2021 RLV © IEC 2021
threshold value by the step size, V . At each step, run a gating measurement on the
step1
error detector. Record the measured BER value and the corresponding decision threshold
voltage.
j) The gating measurement from the error detector accumulates data and error information
until the minimum number of errors – as specified in 5.5 f) – have been recorded. Selecting
a larger minimum number of errors provides a statistically more accurate BER but at the
expense of measurement time, particularly when measuring the low BER values. For a
statistically significant result, the number of errors counted should not be less than 15.
−10
k) Continue until the measured BER falls below 10 . This set of decision threshold voltage
versus BER is the "1" data set.
l) Adjust decision threshold voltage back to the initial sampling point value and then continue
−10
in a negative direction until the BER increases again to greater than 10 . Note down the
threshold value (V ) and the BER.
b0
−5
m) Decrease the decision threshold voltage until the BER rises above 10 and note the
decision threshold voltage (V ) and the BER.
a0
n) Note the difference between the two threshold values V and V and choose a step size
a0 b0
) that provides reasonable number (greater than 5) of measurement points between
(V
step0
these two decision threshold extremes. Starting from the threshold value V , increase the
a0
threshold value by the step size, V . At each step, run a gating measurement on the error
step0
detector. Record the measured BER and the corresponding decision threshold voltage.
−10
o) Continue until the measured BER falls below 1 × 10 . This set of decision threshold
voltage versus BER is the "0" data set.
5.5 Calculations and interpretation of results
5.5.1 Sets of data
The procedure in 4.7 5.4 provides two sets (for the "0" and "1" rails) of data in the form:
D , BER
1 1
D , BER
2 2
.
.
D , BER
n n
where
D is the decision threshold voltage for “i”-th reading (for i =1, 2…,n);
i
BER is the bit error rate for “i”-th reading (for i = 1, 2…,n);
i
n is the total number of data pairs.
D ,P
1 e1
D ,P
2 e 2
.
.
D ,P
nne
where
D is the decision threshold voltage for "i"-th reading (for i = 1, 2…,n);
i
P is the bit error ratio for "i"-th reading (for i = 1, 2…,n);
e i
n is the total number of data pairs.
NOTE The total number of data pairs for the "0" and "1" rails need not be equal.
As an example, the voltage and BER values shown in Table 2 were obtained in a real-life
experiment.
Table 2 – BER as a function of threshold voltage
“1” rail “0” rail
Threshold voltage BER Threshold voltage BER
V V
–1,75 5,18E-05 –4,37 8,76E-05
–1,80 2,09E-05 –4,34 1,90E-05
–1,85 7,33E-06 –4,31 5,18E-06
–1,90 2,77E-06 –4,28 1,06E-06
–1,95 9,61E-07 –4,25 2,12E-07
–2,00 1,96E-07 –4,22 3,45E-08
–2,05 6,30E-08 –4,19 3,52E-09
–2,10 1,95E-08 –4,16 2,77E-10
–2,15 3,45E-09
–2,20 1,39E-09
"1" rail "0" rail
Threshold voltage BER Threshold voltage BER
V V
–5 –5
−1,75 5,18 × 10 −4,37 8,76 × 10
–5 –5
−1,80 −4,34
2,09 × 10 1,90 × 10
–6 –6
−1,85 −4,31
7,33 × 10 5,18 × 10
–6 –6
−1,90 −4,28
2,77 × 10 1,06 × 10
–7 –7
−1,95 9,61 × 10 −4,25 2,12 × 10
–7 –8
−2,00 1,96 × 10 −4,22 3,45 × 10
–8 –9
−2,05 −4,19
6,30 × 10 3,52 × 10
–8 –10
−2,10 −4,16
1,95 × 10 2,77 × 10
–9
−2,15
3,45 × 10
–9
−2,20 1,39 × 10
5.5.2 Convert BER using inverse error function
Each BER value is then converted through an inverse error function, using the following
approximation given in Formula (4).
−1
1
2
(8)
f = log erfc(x ) = 1,192 − 0,6681{x }− 0,0162{x }
i i i i
n
where x = log (BER ).
i 10 i
– 18 – IEC 61280-2-8:2021 RLV © IEC 2021
−1
1
2
f=log erfc(x ) =1,192−−0,668 1 xx0,016 2
{ } { } (8)
i i ii
where
x = log (P ).
i 10 e i
This will produce two sets of data (for the "1" and "0") of the form:
D ,f
D ,f
.
.
D ,f
nn
which should approximately fit a straight line.
Using the values given in Table 2, we get the sets of data shown in Table 4.
Table 3 – f as a function of D
i i
"1" rail "0" rail
D f D f
i i i i
V V
−1,75 3,757 8 −4,37 3,636 0
−1,80 3,963 8 −4,34 3,984 7
−1,85 4,195 6 −4,31 4,270 6
−1,90 4,404 3 −4,28 4,605 2
−1,95 4,625 7 −4,25 4,929 3
−2,00 4,944 9 −4,22 5,275 7
−2,05 5,162 9 −4,19 5,682 3
−2,10 5,379 9 − 4,16 6,097 5
−2,15 5,685 8
−2,20 5,839 0
5.5.3 Linear regression
Using the above data, a linear regression technique is used to fit, in turn, each set of data
to a straight line with an equation of the form:
Y = A + BX
where
Y = erf (BER) (inverse error function of BER),
c
X = D (decision threshold voltage)
Y = A + BX
where
−1
1 −1
Y = (*[F] inverse error function of F);
erfc(P )
e
X = D (decision threshold voltage).
With n points of data per set, then, for both the top ("1") and bottom ("0") data sets, the following
calculations should be performed [67]:
X Y
( )( )
∑∑
X Y
( )( ) XY −
∑∑
∑
XY
− n
∑
n
B =
R = (9)
X
( ) XY
∑ ( ) ( )
2 ∑ ∑
X −
XY− −
∑
∑∑
n
nn
YX
...
IEC 61280-2-8 ®
Edition 2.0 2021-03
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Fibre optic communication subsystem test procedures –
Part 2-8: Digital systems – Determination of low BER using Q-factor
measurements
Procédures d’essai des sous-systèmes de télécommunications fibroniques –
Partie 2-8: Systèmes numériques – Détermination de faibles valeurs de BER en
utilisant des mesures du facteur Q
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IEC 61280-2-8 ®
Edition 2.0 2021-03
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Fibre optic communication subsystem test procedures –
Part 2-8: Digital systems – Determination of low BER using Q-factor
measurements
Procédures d’essai des sous-systèmes de télécommunications fibroniques –
Partie 2-8: Systèmes numériques – Détermination de faibles valeurs de BER en
utilisant des mesures du facteur Q
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 33.180.10 ISBN 978-2-8322-9497-0
– 2 – IEC 61280-2-8:2021 © IEC 2021
CONTENTS
FOREWORD . 4
1 Scope . 6
2 Normative references . 6
3 Terms, definitions, and abbreviated terms . 6
3.1 Terms and definitions . 6
3.2 Abbreviated terms . 7
4 Measurement of low bit-error ratios . 7
4.1 General considerations . 7
4.2 Background to Q-factor . 8
5 Variable decision threshold method . 10
5.1 Overview. 10
5.2 Apparatus . 13
5.3 Sampling and specimens . 13
5.4 Procedure . 13
5.5 Calculations and interpretation of results . 15
5.5.1 Sets of data . 15
5.5.2 Convert BER using inverse error function . 16
5.5.3 Linear regression . 17
5.5.4 Standard deviation and mean . 18
5.5.5 Optimum decision threshold . 18
5.5.6 BER optimum decision threshold . 18
5.5.7 BER non-optimum decision threshold . 19
5.5.8 Error bound . 19
5.6 Test documentation . 19
5.7 Specification information . 19
6 Variable optical threshold method . 19
6.1 Overview. 19
6.2 Apparatus . 20
6.3 Items under test . 20
6.4 Procedure for basic optical link . 20
6.5 Procedure for self-contained system . 21
6.6 Evaluation of results . 22
Annex A (normative) Calculation of error bound in the value of Q . 24
Annex B (informative) Sinusoidal interference method . 26
B.1 Overview. 26
B.2 Apparatus . 26
B.3 Sampling and specimens . 26
B.4 Procedure . 27
B.4.1 Optical sinusoidal interference method . 27
B.4.2 Electrical sinusoidal interference method . 28
B.5 Calculations and interpretation of results . 29
B.5.1 Mathematical analysis . 29
B.5.2 Extrapolation . 29
B.5.3 Expected results . 30
B.6 Documentation . 31
B.7 Specification information . 31
Bibliography . 32
Figure 1 – Sample eye diagram showing patterning effects . 9
Figure 2 – More accurate measurement technique using a DSO that samples noise
statistics between eye centres . 10
Figure 3 – Bit error ratio as a function of decision threshold level . 11
Figure 4 – Plot of Q-factor as a function of threshold voltage . 12
Figure 5 – Set-up for the variable decision threshold method . 14
Figure 6 – Set-up of initial threshold level (approximately at the centre of the eye) . 14
Figure 7 – Effect of optical bias . 20
Figure 8 – Set-up for optical link or device test . 21
Figure 9 – Set-up for system test . 21
Figure 10 – Extrapolation of log BER as a function of bias . 23
Figure B.1 – Set-up for the sinusoidal interference method by optical injection . 27
Figure B.2 – Set-up for the sinusoidal interference method by electrical injection . 29
Figure B.3 – BER result from the sinusoidal interference method (data points and
extrapolated line) . 30
Figure B.4 – BER versus optical power for three methods . 31
Table 1 – Mean time for the accumulation of 15 errors as a function of BER and bit rate . 7
Table 2 – BER as a function of threshold voltage . 16
Table 3 – f as a function of D . 17
i i
Table 4 – Values of linear regression constants . 18
Table 5 – Mean and standard deviation . 18
Table 6 – Example of optical bias test . 22
Table B.1 – Results for sinusoidal injection . 28
– 4 – IEC 61280-2-8:2021 © IEC 2021
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
FIBRE OPTIC COMMUNICATION SUBSYSTEM TEST PROCEDURES –
Part 2-8: Digital systems –
Determination of low BER using Q-factor measurements
FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote international
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2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
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3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
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6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of patent
rights. IEC shall not be held responsible for identifying any or all such patent rights.
IEC 61280-2-8 has been prepared by subcommittee 86C: Fibre optic systems and active
devices, of IEC technical committee 86: Fibre optics. It is an International Standard.
This second edition cancels and replaces the first edition published in 2003. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) correction of errors in Formula (8) in 5.5.2 and in a related formula in 5.5.3;
b) correction of errors in the references to clauses, subclauses, figures, procedures, and in
the Bibliography;
c) alignment of the terms and definitions in 3.1 with those in IEC 61281-1.
The text of this International Standard is based on the following documents:
FDIS Report on voting
86C/1708/FDIS 86C/1711/RVD
Full information on the voting for its approval can be found in the report on voting indicated in
the above table.
The language used for the development of this International Standard is English.
This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in
accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement, available
at www.iec.ch/members_experts/refdocs. The main document types developed by IEC are
described in greater detail at www.iec.ch/standardsdev/publications.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under "http://webstore.iec.ch" in the data related to
the specific document. At this date, the document will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The "colour inside" logo on the cover page of this document indicates
that it contains colours which are considered to be useful for the correct understanding
of its contents. Users should therefore print this document using a colour printer.
– 6 – IEC 61280-2-8:2021 © IEC 2021
FIBRE OPTIC COMMUNICATION SUBSYSTEM TEST PROCEDURES –
Part 2-8: Digital systems –
Determination of low BER using Q-factor measurements
1 Scope
This part of IEC 61280 specifies two main methods for the determination of low BER values by
making accelerated measurements. These include the variable decision threshold method
(Clause 5) and the variable optical threshold method (Clause 6). In addition, a third method,
the sinusoidal interference method, is described in Annex B.
2 Normative references
There are no normative references in this document.
3 Terms, definitions, and abbreviated terms
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at http://www.iso.org/obp
3.1.1
amplified spontaneous emission
ASE
optical power associated to spontaneously emitted photon amplified by an active medium in an
optical amplifier
3.1.2
bit error ratio
BER
P
e
number of errored bits divided by the total number of bits, over some stipulated period of time
3.1.3
intersymbol interference
ISI
overlap of adjacent pulses as caused by the limited bandwidth characteristics of the optical
devices in a fibre optic link
3.1.4
Q-factor
Q
ratio of the difference between the mean voltage of the 1 and 0 rails, to the sum of their standard
deviation values
3.2 Abbreviated terms
AC alternating current
CW continuous wave (normally referring to a sinusoidal wave form)
DC direct current
DSO digital sampling oscilloscope
DUT device under test
PRBS pseudo-random binary sequence
SNR signal-to-noise ratio
4 Measurement of low bit-error ratios
4.1 General considerations
Fibre optic communication systems and subsystems are inherently capable of providing
exceptionally good error performance, even at very high bit rates. The mean bit error ratio (BER)
−12 −20
may typically lie in the region 10 to 10 , depending on the nature of the system. While this
type of performance is well in excess of practical performance requirements for digital signals,
it gives the advantage of concatenating many links over long distances without the need to
employ error correction techniques.
The measurement of such low error ratios presents special problems in terms of the time taken
to measure a sufficiently large number of errors to obtain a statistically significant result. Table 1
presents the mean time required to accumulate 15 errors. This number of errors can be
regarded as statistically significant, offering a confidence level of 75 % with a variability of 50 %.
Table 1 – Mean time for the accumulation of 15 errors
as a function of BER and bit rate
Mean times for the accumulation of 15 errors
Bit rate BER
−5 −6 −7 −8 −9 −10 −11 −12 −13 −14 −15
10 10 10 10 10 10 10 10 10 10 10
1,0 Mbit/s 150 ms 1,5 s 15 s 2,5 min 25 min 4,2 h 1,7d 17 d 170 d 4,7 47
years years
2,0 Mbit/s 75 ms 750 ms 7,5 s 75 s 750 s 2,1 h 21 h 8,8 d 88 d 2,4 24
years years
10 Mbit/s 15 ms 150 ms 1,5 s 15 s 2,5 min 25 min 4,2 h 1,7 d 17 d 170 d 4,7
years
50 Mbit/s 3,0 ms 30 ms 300 ms 3,0 s 30 s 5,0 min 50 min 8,3 h 3,5 d 35 d 350 d
100 Mbit/s 1,5 ms 15 ms 150 ms 1,5 s 15 s 2,5 min 25 min 4,2 h 1,7 d 17 d 170 d
500 Mbit/s 300 μs 3 ms 30 ms 300 ms 3,0 s 30 s 5,0 min 50 min 8,3 h 3,5 d 35 d
1,0 Gbit/s 150 μs 1,5 ms 15 ms 150 ms 1,5 s 15 s 2,5 min 25 min 4,2 h 1,7 d 17 d
10 Gbit/s 15 μs 150 μs 1,5 ms 15 ms 150 ms 1,5 s 15 s 2,5 min 25 min 4,2 h 1,7 d
40 Gbit/s 3,8 μs 38 μs 380 μs 3,8 ms 38 ms 380 ms 3,8 s 38 s 6,3 min 63 min 10,4 h
100 Gbit/s 1,5 μs 15 μs 150 μs 1,5 ms 15ms 150 ms 1,5 s 15 s 2,5 min 25 min 4,2 h
– 8 – IEC 61280-2-8:2021 © IEC 2021
The times given in Table 1 show that the direct measurement of the low BER values expected
from fibre optic systems is not practical during installation and maintenance operations. One
way of overcoming this difficulty is to artificially impair the signal-to-noise ratio at the receiver
in a controlled manner, thus significantly increasing the BER and reducing the measurement
time. The error performance is measured for various levels of impairment, and the results are
then extrapolated to a level of zero impairment using computational or graphical methods
according to theoretical or empirical regression algorithms.
The difficulty presented by the use of any regression technique for the determination of the
error performance is that the theoretical BER value is related to the level of impairment via
the inverse complementary error function (erfc). This means that very small changes in the
impairment lead to very large changes in BER; for example, in the region of a BER value of
−15
10 , a change of approximately 1 dB in the level of impairment results in a change of three
orders of magnitude in the BER. A further difficulty is that a method based on extrapolation is
unlikely to reveal a levelling off of the BER at only about 3 orders of magnitude below the lowest
measured value.
It should also be noted that, in the case of digitally regenerated sections, the results obtained
apply only to the regenerated section whose receiver is under test. Errors generated in
upstream regenerated sections may generate an error plateau which may have to be taken into
account in the error performance evaluation of the regenerator section under test.
As noted above, two main methods for the determination of low BER values by making
accelerated measurements are described. These are the variable decision threshold method
(Clause 5) and the variable optical threshold method (Clause 6). In addition, a third method,
the sinusoidal interference method, is described in Annex B.
It should be noted that these methods are applicable to the determination of the error
performance in respect of amplitude-based impairments. Jitter may also affect the error per-
formance of a system, and its effect requires other methods of determination. If the error
performance is dominated by jitter impairments, the amplitude-based methods described in this
document will lead to BER values which are lower than the actual value.
The variable decision threshold method is the procedure which can most accurately measure
the Q-factor and the BER for optical systems with unknown or unpredictable noise statistics. A
key limitation, however, to the use of the variable threshold method to measure Q-factor and
BER is the need to have access to the receiver electronics in order to manipulate the decision
threshold. For systems where such access is not available, it may be useful to utilize the
alternative variable optical threshold method. Both methods are capable of being automated in
respect of measurement and computation of the results
4.2 Background to Q-factor
The Q-factor is the signal-to-noise ratio (SNR) at the decision circuit and is typically expressed
as [1] :
μμ−
1 0
Q= (1)
σσ+
where
µ and µ are the mean voltage levels of the "1" and "0" rails, respectively;
1 0
____________
Figures in square brackets refer to the Bibliography.
σ and σ are the standard deviation values of the noise distribution on the "1" and "0" rails,
1 0
respectively.
An accurate estimation of a system’s transmission performance, or Q-factor, shall take into
consideration the effects of all sources of performance degradation, both fundamental and
those due to real-world imperfections. Two important sources are amplified spontaneous
emission (ASE) noise and intersymbol interference (ISI). Additive noise originates primarily from
ASE of optical amplifiers. ISI arises from many effects, such as chromatic dispersion, fibre non-
linearities, multi-path interference, polarization-mode dispersion and use of electronics with
finite bandwidth. There may be other effects as well; for example, a poor impedance match can
cause impairments such as long fall times or ringing on a waveform.
One possible method to measure Q-factor is the voltage histogram method in which a digital
sampling oscilloscope is used to measure voltage histograms at the centre of a binary eye to
estimate the waveform’s Q-factor [2]. In this method, a pattern generator is used as a stimulus
and the oscilloscope is used to measure the received eye opening and the standard deviation
of the noise present in both voltage rails. As a rough approximation, the edge of visibility of the
noise represents the 3σ points of an assumed Gaussian distribution. The advantage of using
an oscilloscope to measure the eye is that it can be done rapidly on real traffic with a minimum
of equipment.
The oscilloscope method for measuring the Q-factor has several shortcomings. When used to
measure the eye of high-speed data (of the order of several Gbit/s), the oscilloscope’s limited
digital sampling rate (often in the order of a few hundred kilohertz) allows only a small minority
of the high-speed data stream to be used in the Q-factor measurement. Longer observation
times could reduce the impact of the slow sampling. A more fundamental shortcoming is that
the Q estimates derived from the voltage histograms at the eye centre are often inaccurate.
Various patterning effects and added noise from the front-end electronics of the oscilloscope
can often obscure the real variance of the noise.
Figure 1 shows a sample eye diagram made on an operating system. It can be seen in this
figure that the vertical histograms through the centre of the eye show patterning effects (less
obvious is the noise added by the front-end electronics of the oscilloscope). It is difficult to
predict the relationship between the Q measured this way and the actual BER measured with
a test set.
NOTE The data for measuring the Q-factor are obtained from the tail of the Gaussian distributions.
Figure 1 – Sample eye diagram showing patterning effects
– 10 – IEC 61280-2-8:2021 © IEC 2021
Figure 2 shows another possible way of measuring Q-factor using an oscilloscope. The idea is
to use the centre of the eye to estimate the eye opening and use the area between eye centres
to estimate the noise. Pattern effect contributions to the width of the histogram would then be
reduced. A drawback to this method is that it relies on measurements made on a portion of the
eye that the receiver does not really ever use.
Figure 2 – More accurate measurement technique using a DSO
that samples noise statistics between eye centres
It is tempting to conclude that the estimates for σ and σ would tend to be overestimated and
1 0
that the resulting Q measurements would always form a lower bound to the actual Q for either
of these oscilloscope-based methods. That is not necessarily the case. It is possible that the
histogram distributions can be distorted in other ways, for example, skewed in such a way that
the mean values overestimate the eye opening – and the resulting Q will actually not be a lower
bound. There is, unfortunately, no easily characterized relationship between oscilloscope-
derived Q measurements and BER performance.
5 Variable decision threshold method
5.1 Overview
This method of estimating the Q-factor relies on using a receiver front-end with a variable
decision threshold. Some means of measuring the BER of the system is required. Typically, the
measurement is performed with an error test set using a pseudo-random binary sequence
(PRBS), but there are alternate techniques which allow operation with live traffic. The
measurement relies on the fact that for a data eye with Gaussian statistics, the BER may be
calculated analytically as follows:
|V −−μ | |V μ |
th 1 th 0
PV( ) erfc + erfc
(2)
e th
2 σσ
10
=
where
P is the BER;
e
V is the decision threshold level;
th
µ ,µ and σ , σ are the mean and standard deviation of the "1" and "0" data rails;
1 0 1 0
erfc(.) is the complementary error function given by
∞
−−β / 22x /
(3)
erfc( x) e dβ≅ e
∫
2π x 2π
x
The approximation is nearly exact for x > 3.
The BER, given in Formula (2), is the sum of two terms. The first term is the conditional
probability of deciding that a "0" has been received when a "1" has been sent, and the second
term is the probability of deciding that a "1" has been received when a "0" has been sent.
In order to implement this technique, the BER is measured as a function of the threshold voltage
(see Figure 3). Formula (2) is then used to convert the data into a plot of the Q-factor versus
threshold, where the Q-factor is the argument of the complementary error function of either term
in Formula (2). To make the conversion, the approximation is made that the BER is dominated
by only one of the terms in Formula (2) according to whether the threshold is closer to the "1's"
or the "0's" rail of the eye diagram.
Figure 3 – Bit error ratio as a function of decision threshold level
Figure 4 shows the results of converting the data in Figure 3 into a plot of Q-factor versus
threshold. The optimum Q-factor value as well as the optimum threshold setting needed to
achieve this Q-factor are obtained from the intersection of the two best-fit lines through the data.
This technique is described in detail in [3].
=
– 12 – IEC 61280-2-8:2021 © IEC 2021
Figure 4 – Plot of Q-factor as a function of threshold voltage
The optimum threshold as well as the optimal Q can be obtained analytically by making use of
the following approximation [4] for the inverse error function:
−1
1
log erfc(x) ≈−1,192 0,6681xx− 0,0162 (4)
where
x is log(P ).
e
−5 −10
NOTE 1 Formula (4) is accurate to ±0,2 % over the range of P from 10 to 10 .
e
After evaluating the inverse error function, the data are plotted against the decision threshold
level, V . As shown in Figure 4, a straight line is fitted to each set of data by linear regression.
th
The equivalent variance and mean for the Q calculation are given by the slope and intercept
respectively.
The minimum BER can be shown to occur at an optimal threshold, V , when the two
th-optimal
terms in the argument in Formula (2) are equal, that is
μV−−V μ
( ) ( )
1 th−−optimal th optimal 0
Q (5)
opt
σσ
An explicit expression for V in terms of µ and σ can be derived from Formula (5)
th-optimal 1,0 1,0
to be:
σ μ + σμ
0 1 10
(6)
V =
th−optimal
σσ+
==
The value of Q is obtained from Formula (1). The residual BER at the optimal threshold can
opt
be obtained from Formula (2) and is approximately
− Q/ 2
( opt )
e
(7)
P ≅
e-optimal
Q 2π
opt
NOTE 2 This approximation is nearly exact for Q > 3.
opt
It should be noted that even though the variable threshold method makes use of Gaussian
statistics, it provides accurate results for systems that have non-Gaussian noise statistics as
well, for example, the non-Gaussian statistics that occur in a typical optically amplified system
[5] [6]. This can be understood by examining Figure 1. The decision circuit of a receiver operates
only on the interior region of the eye. This means that the only part of the vertical histogram
that it uses is the "tail" that extends into the eye. The variable decision threshold method
amounts to constructing a Gaussian approximation to the tail of the real distribution in the centre
region of the eye where it affects the receiver operation directly. As the example in Figure 1
shows, this Gaussian approximation will not reproduce the actual histogram distribution at all,
but it does not need to, for purposes of Q estimation.
Another way to view the variable decision threshold technique is to imagine replacing the real
data eye with a fictitious eye having Gaussian statistics. The two eye diagrams have the same
BER versus decision threshold voltage behaviour, so it is reasonable to assign them the same
equivalent Q value, even though the details of the full eye diagram may be very different.
However, this analysis will not work for systems dominated by noise sources whose "tails" are
not easily approximated to be Gaussian in shape; as, for example, would occur in a system
dominated by cross-talk or modal noise. In taking these measurements, an inability to fit the
data of Q-factor versus threshold to a straight line would provide a good indication of the
presence of such noise sources.
Experimentally, it has been found that the Q values measured using the variable decision
threshold method have a statistically valid level of correlation with the actual BER
measurements.
5.2 Apparatus
An error performance analyser consisting of a pattern generator and a bit error ratio detector.
5.3 Sampling and specimens
The device under test (DUT) is a fibre optic digital system, consisting of an electro-optical
transmitter at one end and an opto-electronic receiver at the other end. In between the
transmitter and the receiver can be an optical network with links via optical fibres (for example,
a DWDM network).
5.4 Procedure
Data for the Q measurement are collected at both the top "1" and bottom "0" regions of the eye
−5 −10
as BER (over the range 10 to 10 ) versus decision threshold. The equivalent mean (μ) and
variance (σ) of the "1's" and "0's" are determined by fitting this data to a Gaussian characteristic.
The Q-factor is then calculated using Formula (1).
a) Connect the pattern generator and error detector to the system under test in accordance
with Figure 5.
– 14 – IEC 61280-2-8:2021 © IEC 2021
Figure 5 – Set-up for the variable decision threshold method
b) Set the clock source to the desired frequency.
c) Set up the pattern generator’s pattern, data and clock amplitude, offset, polarity and
termination as required.
d) Set up the error detector’s pattern, data polarity and termination as required.
e) Set the decision threshold voltage and data input delay to achieve a sampling point that is
approximately in the centre of the data eye as shown in Figure 6. This is the initial
sampling point.
Figure 6 – Set-up of initial threshold level (approximately at the centre of the eye)
f) Enable the error detector's gating function and set it to gate by errors, for a minimum of 10,
100 or 1 000 errors.
g) Adjust the error detector's decision threshold voltage in a positive direction until the
−10
. Note the decision threshold
measured BER increases to a value greater than 1 × 10
voltage (V ) and the BER.
b1
−5
h) Increase the decision threshold voltage until the BER rises above 10 and note the decision
threshold voltage (V ) and the BER.
a1
i) Note the difference between the two threshold values V and V and choose a step size
a1 b1
(V ) that provides a reasonable number (greater than 5) of measurement points between
step1
these two decision threshold extremes. Starting from the threshold value V , decrease the
a1
threshold value by the step size, V . At each step, run a gating measurement on the
step1
error detector. Record the measured BER value and the corresponding decision threshold
voltage.
j) The gating measurement from the error detector accumulates data and error information
until the minimum number of errors – as specified in f) – have been recorded. Selecting a
larger minimum number of errors provides a statistically more accurate BER but at the
expense of measurement time, particularly when measuring the low BER values. For a
statistically significant result, the number of errors counted should not be less than 15.
−10
k) Continue until the measured BER falls below 10 . This set of decision threshold voltage
versus BER is the "1" data set.
l) Adjust decision threshold voltage back to the initial sampling point value and then continue
−10
in a negative direction until the BER increases again to greater than 10 . Note down the
threshold value (V ) and the BER.
b0
−5
m) Decrease the decision threshold voltage until the BER rises above 10 and note the
decision threshold voltage (V ) and the BER.
a0
n) Note the difference between the two threshold values V and V and choose a step size
a0 b0
(V ) that provides reasonable number (greater than 5) of measurement points between
step0
these two decision threshold extremes. Starting from the threshold value V , increase the
a0
threshold value by the step size, V . At each step, run a gating measurement on the error
step0
detector. Record the measured BER and the corresponding decision threshold voltage.
−10
o) Continue until the measured BER falls below 1 × 10 . This set of decision threshold
voltage versus BER is the "0" data set.
5.5 Calculations and interpretation of results
5.5.1 Sets of data
The procedure in 5.4 provides two sets (for the "0" and "1" rails) of data in the form:
D ,P
1 e1
D ,P
2 e 2
.
.
D ,P
nne
where
D is the decision threshold voltage for "i"-th reading (for i = 1, 2…,n);
i
P is the bit error ratio for "i"-th reading (for i = 1, 2…,n);
e i
n is the total number of data pairs.
The total number of data pairs for the "0" and "1" rails need not be equal.
As an example, the voltage and BER values shown in Table 2 were obtained in a real-life
experiment.
– 16 – IEC 61280-2-8:2021 © IEC 2021
Table 2 – BER as a function of threshold voltage
"1" rail "0" rail
Threshold voltage BER Threshold voltage BER
V V
–5 –5
−1,75 −4,37
5,18 × 10 8,76 × 10
–5 –5
−1,80 −4,34
2,09 × 10 1,90 × 10
–6 –6
−1,85 7,33 × 10 −4,31 5,18 × 10
–6 –6
−1,90 2,77 × 10 −4,28 1,06 × 10
–7 –7
−1,95 9,61 × 10 −4,25 2,12 × 10
–7 –8
−2,00 −4,22
1,96 × 10 3,45 × 10
–8 –9
−2,05 −4,19
6,30 × 10 3,52 × 10
–8 –10
−2,10 −4,16
1,95 × 10 2,77 × 10
–9
−2,15 3,45 × 10
–9
−2,20 1,39 × 10
5.5.2 Convert BER using inverse error function
Each BER value is then converted through an inverse error function, using the following
approximation given in Formula (4).
−1
1
2
(8)
f=log erfc(x ) =1,192−−0,668 1{xx} 0,016 2{ }
i i ii
where
x = log (P ).
i 10 e i
This will produce two sets of data (for the "1" and "0") of the form:
D ,f
D ,f
.
.
D ,f
nn
which should approximately fit a straight line.
Using the values given in Table 2, we get the sets of data shown in Table 4.
Table 3 – f as a function of D
i i
"1" rail "0" rail
D f D f
i i i i
V V
−1,75 3,757 8 −4,37 3,636 0
−1,80 3,963 8 −4,34 3,984 7
−1,85 4,195 6 −4,31 4,270 6
−1,90 4,404 3 −4,28 4,605 2
−1,95 4,625 7 −4,25 4,929 3
−2,00 4,944 9 −4,22 5,275 7
−2,05 5,162 9 −4,19 5,682 3
−2,10 5,379 9 − 4,16 6,097 5
−2,15 5,685 8
−2,20 5,839 0
5.5.3 Linear regression
Using the above data, a linear regression technique is used to fit, in turn, each set of data
to a straight line with an equation of the form:
Y = A + BX
where
−1
1 −1
Y = (*[F] inverse error function of F);
erfc(P )
e
X = D (decision threshold voltage).
With n points of data per set, then, for both the top ("1") and bottom ("0") data sets, the following
calculations should be performed [7]:
X Y
( )( )
∑∑
X Y
( )( ) XY−
∑∑
∑
XY− n
∑
n
B= (9)
R =
X
XY
( )
∑ ( ) ( )
∑ ∑
2
X −
XY− −
∑
∑∑
n
nn
YX
∑∑
AB−
nn
where
R is the coefficient of determination (a measure of how well the data fits a straight line);
is the sum of values from 1 to n.
∑
Using the values given in Table 3, we get the values shown in Table 4.
=
...
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