Fibre optic communication subsystem test procedures - Digital systems -- Part 2-8: Determination of low BER using Q-factor measurements

Provides two main methods for the determination of low BER values by making accelerated measurements. The two main methods are the variable decision threshold method (clause 4) and the variable optical method (clause 5). In addition a third method, the sinusodial interference method, is described in Annex B.

Prüfverfahren für Lichtwellenleiter-Kommunikationsuntersysteme - Digitale Systeme -- Teil 2-8: Bestimmung von geringen Bitfehlerverhältnissen (BERs) mit Hilfe von Q-Faktormessungen

Procédures d'essai des sous-systèmes de télécommunication à fibres optiques - Systèmes numériques -- Partie 2-8: Détermination du faible Taux d'Erreur Binaire (TEB) en utilisant les mesures du facteur Q

Provides two main methods for the determination of low BER values by making accelerated measurements. The two main methods are the variable decision threshold method (clause 4) and the variable optical method (clause 5). In addition a third method, the sinusodial interference method, is described in Annex B.

Preskusni postopki komunikacijskega podsistema optičnih vlaken – Digitalni sistemi – 2-8. del: Ugotavljanje nizkega razmerja bitne napake (BER) s pomočjo meritev Q-faktorja (IEC 61280-2-8:2003)*

General Information

Status
Published
Publication Date
31-Aug-2004
Technical Committee
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
01-Sep-2004
Due Date
01-Sep-2004
Completion Date
01-Sep-2004

Relations

Buy Standard

Standard
EN 61280-2-8:2004
English language
32 pages
sale 10% off
Preview
sale 10% off
Preview
e-Library read for
1 day

Standards Content (Sample)

SLOVENSKI SIST EN 61280-2-8:2004

STANDARD
september 2004
Preskusni postopki komunikacijskega podsistema optičnih vlaken – Digitalni
sistemi – 2-8. del: Ugotavljanje nizkega razmerja bitne napake (BER) s
pomočjo meritev Q-faktorja (IEC 61280-2-8:2003)*
Fibre optic communication subsystem test procedures - Digital systems - Part 2-8:
Determination of low BER using Q-factor measurements (IEC 61280-2-8:2003)
ICS 33.180.01 Referenčna številka
SIST EN 61280-2-8:2004(en)
©  Standard je založil in izdal Slovenski inštitut za standardizacijo. Razmnoževanje ali kopiranje celote ali delov tega dokumenta ni dovoljeno

---------------------- Page: 1 ----------------------

EUROPEAN STANDARD EN 61280-2-8
NORME EUROPÉENNE
EUROPÄISCHE NORM April 2003

ICS 33.180.10


English version


Fibre optic communication subsystem test procedures -
Digital systems
Part 2-8: Determination of low BER using Q-factor measurements
(IEC 61280-2-8:2003)


Procédures d'essai des sous-systèmes  Prüfverfahren für Lichtwellenleiter-
de télécommunications à fibres optiques - Kommunikationsuntersysteme -
Systèmes numériques Digitale Systeme
Partie 2-8: Détermination du faible Teil 2-8: Bestimmung von geringen
Taux d'Erreur Binaire (TEB) Bitfehlerverhältnissen (BERs)
en utilisant les mesures du facteur Q mit Hilfe von Q-Faktormessungen
(CEI 61280-2-8:2003) (IEC 61280-2-8:2003)






This European Standard was approved by CENELEC on 2003-03-01. CENELEC members are bound to
comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration.

Up-to-date lists and bibliographical references concerning such national standards may be obtained on
application to the Central Secretariat or to any CENELEC member.

This European Standard exists in three official versions (English, French, German). A version in any other
language made by translation under the responsibility of a CENELEC member into its own language and
notified to the Central Secretariat has the same status as the official versions.

CENELEC members are the national electrotechnical committees of Austria, Belgium, Czech Republic,
Denmark, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Luxembourg, Malta,
Netherlands, Norway, Portugal, Slovakia, Spain, Sweden, Switzerland and United Kingdom.

CENELEC
European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung

Central Secretariat: rue de Stassart 35, B - 1050 Brussels


© 2003 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC members.

Ref. No. EN 61280-2-8:2003 E

---------------------- Page: 2 ----------------------

EN 61280-2-8:2003 - 2 -
Foreword

The text of document 86C/485/FDIS, future edition 1 of IEC 61280-2-8, prepared by SC 86C, Fibre optic
systems and active devices, of IEC TC 86, Fibre optics, was submitted to the IEC-CENELEC parallel
vote and was approved by CENELEC as EN 61280-2-8 on 2003-03-01.

The following dates were fixed:

– latest date by which the EN has to be implemented
 at national level by publication of an identical
 national standard or by endorsement (dop) 2003-12-01

– latest date by which the national standards conflicting
 with the EN have to be withdrawn (dow) 2006-03-01

Annexes designated "normative" are part of the body of the standard.
Annexes designated "informative" are given for information only.
In this standard, annex A is normative and annex B is informative.
__________

Endorsement notice

The text of the International Standard IEC 61280-2-8:2003 was approved by CENELEC as a European
Standard without any modification.
__________

---------------------- Page: 3 ----------------------

INTERNATIONAL IEC
STANDARD 61280-2-8
First edition
2003-02
Fibre optic communication subsystem test
procedures – Digital systems
Part 2-8:
Determination of low BER
using Q-factor measurements
© IEC 2003 ⎯ Copyright - all rights reserved
No part of this publication may be reproduced or utilized in any form or by any means, electronic or
mechanical, including photocopying and microfilm, without permission in writing from the publisher.
International Electrotechnical Commission, 3, rue de Varembé, PO Box 131, CH-1211 Geneva 20, Switzerland
Telephone: +41 22 919 02 11 Telefax: +41 22 919 03 00 E-mail: inmail@iec.ch  Web: www.iec.ch
PRICE CODE
Commission Electrotechnique Internationale U
International Electrotechnical Commission
ɆɟɠɞɭɧɚɪɨɞɧɚɹɗɥɟɤɬɪɨɬɟɯɧɢɱɟɫɤɚɹɄɨɦɢɫɫɢɹ
For price, see current catalogue

---------------------- Page: 4 ----------------------

– 2 – 61280-2-8 © IEC:2003(E)
CONTENTS
FOREWORD . 4
1 Scope . 5
2 Definitions and abbreviated terms . 5
2.1 Definitions . 5
2.2 Abbreviations. 5
3 Measurement of low bit-error ratios . 6
3.1 General considerations . 6
3.2 Background to Q-factor . 7
4 Variable decision threshold method . 9
4.1 Overview . 9
4.2 Apparatus .12
4.3 Sampling and specimens .12
4.4 Procedure.12
4.5 Calculations and interpretation of results .13
4.6 Test documentation .17
4.7 Specification information .17
5 Variable optical threshold method.17
5.1 Overview .17
5.2 Apparatus .18
5.3 Items under test.18
5.4 Procedure for basic optical link .18
5.5 Procedure for self-contained system .19
5.6 Evaluation of results.20
Annex A (normative) Calculation of error bound in the value of Q .22
Annex B (informative) Sinusoidal interference method .24
Bibliography .30
Figure 1 – A sample eye diagram showing patterning effects . 8
Figure 2 – A more accurate measurement technique using a DSO that samples the
noise statistics between the eye centres . 8
Figure 3 – Bit error ratio as a function of decision threshold level .10
Figure 4 – Plot of Q-factor as a function of threshold voltage .10
Figure 5 – Set-up for the variable decision threshold method .12
Figure 6 – Set-up of initial threshold level (approximately at the centre of the eye) .12
Figure 7 – Effect of optical bias .17
Figure 8 – Set-up for optical link or device test.19
Figure 9 – Set-up for system test .19
Figure 10 – Extrapolation of log BER as function of bias .21
Figure B.1 – Set-up for the sinusoidal interference method by optical injection .25
Figure B.2 – Set-up for the sinusoidal interference method by electrical injection .27
Figure B.3 – BER Result from the sinusoidal interference method
(data points and extrapolated line) .28
Figure B.4 – BER versus optical power for three methods .29

---------------------- Page: 5 ----------------------

61280-2-8 © IEC:2003(E) – 3 –
Table 1 – Mean time for the accumulation of 15 errors as a function of BER and bit rate . 6
Table 2 – BER as function of threshold voltage .14
Table 3 – f as a function of D .14
i i
Table 4 – Values of linear regression constants .15
Table 5 – Mean and standard deviation.16
Table 6 – Example of optical bias test.20
Table B.1 – Results for sinusoidal injection.26

---------------------- Page: 6 ----------------------

– 4 – 61280-2-8 © IEC:2003(E)
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
FIBRE OPTIC COMMUNICATION SUBSYSTEM TEST PROCEDURES –
DIGITAL SYSTEMS –
Part 2-8: Determination of low BER
using Q-factor measurements
FOREWORD
1) The IEC (International Electrotechnical Commission) is a worldwide organisation for standardisation comprising
all national electrotechnical committees (IEC National Committees). The object of the IEC is to promote
international co-operation on all questions concerning standardisation in the electrical and electronic fields. To
this end and in addition to other activities, the IEC publishes International Standards. Their preparation is
entrusted to technical committees; any IEC National Committee interested in the subject dealt with may
participate in this preparatory work. International, governmental and non-governmental organisations liasing with
the IEC also participate in this preparation. The IEC collaborates closely with the International Organisation for
Standardisation (ISO) in accordance with conditions determined by agreement between the two organisations.
2) The formal decisions or agreements of the IEC on technical matters express, as nearly as possible, an
international consensus of opinion on the relevant subjects since each technical committee has representation
from all interested National Committees.
3) The documents produced have the form of recommendations for international use and are published in the form
of standards, technical specifications, technical reports or guides and they are accepted by the National
Committees in that sense.
4) In order to promote international unification, IEC National Committees undertake to apply IEC International
Standards transparently to the maximum extent possible in their national and regional standards. Any
divergence between the IEC Standard and the corresponding national or regional standard shall be clearly
indicated in the latter.
5) The IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any
equipment declared to be in conformity with one of its standards.
6) Attention is drawn to the possibility that some of the elements of this International Standard may be the subject
of patent rights. The IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 61280-2-8 has been prepared by subcommittee 86C: Fibre optic
systems and active devices, of IEC technical committee 86: Fibre optics.
The text of this standard is based on the following documents:
FDIS Report on voting
86C/485/FDIS 86C/505/RVD
Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
The committee has decided that the contents of this publication will remain unchanged
until 2010. At this date, the publication will be
• reconfirmed;
• withdrawn;
• replaced by a revised edition, or
• amended.

---------------------- Page: 7 ----------------------

61280-2-8 © IEC:2003(E) – 5 –
FIBRE OPTIC COMMUNICATION SUBSYSTEM TEST PROCEDURES –
DIGITAL SYSTEMS –
Part 2-8: 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 4) and the variable optical threshold method (Clause 5). In addition, a third method,
the sinusoidal interference method, is described in Annex B.
2 Definitions and abbreviated terms
2.1 Definitions
For the purposes of this document, the following terms and definitions apply.
2.1.1
amplified spontaneous emission
ASE
impairment generated in optical amplifiers
2.1.2
bit error ratio
BER
the number bits in error as a ratio of the total number of bits
2.1.3
intersymbol interference
ISI
mutual interference between symbols in a data stream, usually caused by non-linear effects
and bandwidth limitations of the transmission path
2.1.4
Q-factor
Q
ratio of the difference between the mean voltage of the 1 and 0 rails, and the sum of their
standard deviation values
2.2 Abbreviations
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

---------------------- Page: 8 ----------------------

– 6 – 61280-2-8 © IEC:2003(E)
3 Measurement of low bit-error ratios
3.1 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
–12 –20
(BER) 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
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 error function (erfc). This means that very small changes in the impairment
–15
lead to very large changes in BER; for example, in the region of a BER value of 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.

---------------------- Page: 9 ----------------------

61280-2-8 © IEC:2003(E) – 7 –
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 4) and the variable optical threshold method (Clause 5). 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
standard 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
3.2 Background to Q-factor
The Q-factor is the signal-to-noise ratio (SNR) at the decision circuit and is typically expressed
1
as [3] :
µ − µ
1 0
(1)
Q =
σ +ı
1 0
where µ and µ are the mean voltage levels of the “1” and “0” rails, respectively, and σ and
1 0 1
σ are the standard deviation values of the noise distribution on the “1” and “0” rails,
0
respectively.
An accurate estimation of a system’s transmission performance, or Q-factor, must 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 [4]. 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.

1
Figures in square brackets refer to the bibliography.

---------------------- Page: 10 ----------------------

– 8 – 61280-2-8 © IEC:2003(E)
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.
Gaussian
approximation
Actual
Decision circuit operates in this region distribution
IEC  042/03
NOTE The data for measuring the Q-factor is obtained from the tail of the Gaussian distributions.
Figure 1 – A 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.
Measure noise here
Measure eye opening here
µ − µ σ − σ
1 0 1 0
Noise estimate here excludes isolated “1’s”
IEC  043/03
Figure 2 – A more accurate measurement technique using a DSO
that samples the noise statistics between the eye centres

---------------------- Page: 11 ----------------------

61280-2-8 © IEC:2003(E) – 9 –
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.
4 Variable decision threshold method
4.1 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:
§ ·
§ · § ·
1 | V − µ | | V − µ |
th 1 th 0
¨ ¸
¨ ¸ ¨ ¸
BER(V ) = erfc + erfc (2)
th
¨ ¸
¨ ¨ ¸
¸
2 ı ı
© 1 ¹ © 0 ¹
© ¹
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)
³
2π x 2π
x
(The approximation is nearly exact for x > 3.)
The BER, given in equation 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). Equation 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 equation 2. To make the conversion, the approximation is made that the BER is
dominated by only one of the terms in equation 2 according to whether the threshold is closer
to the “1's” or the “0's” rail of the eye diagram.

---------------------- Page: 12 ----------------------

– 10 – 61280-2-8 © IEC:2003(E)
−4
10
6

10
8

10
10

10
12

10
14

10
16

10
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8
Threshold voltage
IEC  044/03
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 is obtained from the intersection of the two best-fit lines through the data.
This technique is described in detail in [2].
16
Optimum Q
14
12
|Slope| = 1/σ
1
10
8
6
4
2
0
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8
µ Threshold voltage µ
0
1
Optimum threshold
IEC  045/03
Figure 4 – Plot of Q-factor as a function of threshold voltage
BER
Q from BER

---------------------- Page: 13 ----------------------

61280-2-8 © IEC:2003(E) – 11 –
The optimum threshold as well as the optimal Q can be obtained analytically by making use of
the following approximation [1] for the inverse error function:
−1
ª 1 º
­ ½
2
(4)
log erfc( x) ≈1,192 − 0,6681 x − 0,0162 x
® ¾
« »
2
¯ ¿
¬ ¼
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 .
After evaluating the inverse error function, the data is 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 equation 2 are equal, that is
(µ −V ) (V − µ )
1 th−optimal th−optimal 0
= = Q (5)
opt
ı ı
1 0
An explicit expression for V in terms of µ and σ can be derived from equation (5)
th-optimal 1,0 1,0
to be:
ı µ + σ µ
0 1 1 0
V = (6)
th−optimal
ı +ı
0 1
The value of Q is obtained from equation 1. The residual BER at the optimal threshold can
opt
be obtained from equation 2 and is approximately
2
−()Q / 2
opt
e
BER ≅ (7)
optimal
Q 2π
opt
NOTE This approximation is nearly exact for Q opt >3.
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
[4]. 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,
...

Questions, Comments and Discussion

Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.