IEC TR 61282-10:2013

IEC/TR 61282-10 ®
Edition 1.0 2013-01
TECHNICAL
REPORT
colour
inside
Fibre optic communication system design guides –
Part 10: Characterization of the quality of optical vector-modulated signals
with the error vector magnitude

IEC/TR 61282-10:2013(E)
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IEC/TR 61282-10 ®
Edition 1.0 2013-01
TECHNICAL
REPORT
colour
inside
Fibre optic communication system design guides –

Part 10: Characterization of the quality of optical vector-modulated signals

with the error vector magnitude

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
PRICE CODE
V
ICS 33.180.01 ISBN 978-2-83220-567-9

– 2 – TR 61282-10 © IEC:2013(E)
CONTENTS
FOREWORD . 4
0 Introduction . 6
0.1 Introduction to vector modulated signals . 6
0.2 Digital coding with vector modulation . 6
0.2.1 General . 6
0.2.2 Constellation diagram . 7
0.2.3 IQ diagram . 7
0.3 Polarization multiplexing . 8
0.4 Error vector . 8
1 Scope . 9
2 Normative references . 9
3 Terms and definitions . 9
4 Error vector magnitude calculations and conditions . 10
4.1 Reference vector assignment . 10
4.2 Normalization of the measured data . 10
4.3 Conditions to be specified with EVM . 11
rms
5 Apparatus for measuring vector modulated signals . 11
5.1 Coherent detector. 11
5.2 Local oscillator . 12
5.2.1 Detection based on electrical real-time sampling . 12
5.2.2 Detection based on optical equivalent-time sampling . 13
5.2.3 One-symbol delayed interferometer . 16
5.2.4 Constellations of non-differential and differential phase modulation
formats . 17
5.3 Digital postprocessing . 18
5.3.1 Impairment compensation . 18
5.3.2 Relative timing skew . 19
5.3.3 IQ phase angle distortion . 19
5.3.4 Offset and relative gain distortion . 20
5.3.5 Polarization alignment . 21
5.3.6 Corrected results . 21
5.3.7 Phase tracking (intradyne detection) . 21
5.3.8 Demodulation (optional) . 22
6 Additional measurement parameters to characterize special details of the signal . 23
6.1 Time-resolved EVM . 23
6.2 EVM with reference filter . 25
6.3 Magnitude error . 26
6.4 Phase error . 26
6.5 I-Q gain imbalance . 27
6.6 I-Q offset . 27
6.7 Quadrature error . 27
Annex A (informative) Relationship between EVM and Q factor . 29
Annex B (informative) Details and implementations of vector signal measurement . 30
Bibliography . 31

TR 61282-10 © IEC:2013(E) – 3 –
Figure 1 – Constellation diagram for QPSK coding . 7
Figure 2 – IQ diagram for the same QPSK coding . 8
Figure 3 – Relationship of error vector to reference vector and measured signal vector
in the constellation diagram . 8
Figure 4 – Block diagram of the main functions for vector signal measurement . 11
Figure 5 – Configuration based on coherent detection with a local oscillator . 12
Figure 6 – Configuration for linear optical sampling. 14
Figure 7 – Schematic comparison of real-time sampling and equivalent-time sampling
to observe a repetitive signal pattern . 16
Figure 8 – One-symbol delayed interferometer for detecting differential phase
modulation . 17
Figure 9 – Simulation of an ideal (D)QPSK signal, represented as a constellation
diagram displaying the absolute phase and amplitude of the optical field (left) . 18
Figure 10 – Simulation of a (D)QPSK signal distorted with 10° IQ-quadrature error . 18
Figure 11 – Calculated influence of impairment . 19
Figure 12 – Error in I and Q determination from phase angle deviation . 19
Figure 13 – Calculated influence of impairment . 20
Figure 14 – Calculated influence of impairment . 21
Figure 15 – IQ-diagram with indicated reference constellation and exemplary error
vectors (left) and time domain plot of the EVM values for each measured sample (right). 23
Figure 16 – Measured time-resolved EVM plots of a 28 GBd QPSK signal affected by
8 ps skew . 24
Figure 17 – Noise-averaged IQ-diagrams and time-resolved EVM plots of a 28 GBd
QPSK signal with 0 p skew (top) and 8 ps skew (bottom) . 25
Figure 18 – Eye-diagram of reference with steep transitions; measured signal I-Q
diagram with symbols at decision time; EVM at symbol decision time (red) and EVM for
all sample points (blue) . 26
Figure 19 – Eye-diagram of reference with raised-cosine filtering; measured signal I-Q
diagram with symbols at decision time; EVM at symbol decision time (red) and EVM for
all sample points (blue) . 26

Table B.1 – Methods for measuring vector modulated optical signals . 30

– 4 – TR 61282-10 © IEC:2013(E)
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
FIBRE OPTIC COMMUNICATION SYSTEM DESIGN GUIDES –

Part 10: Characterization of the quality of optical vector-modulated
signals with the error vector magnitude

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
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9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
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The main task of IEC technical committees is to prepare International Standards. However, a
technical committee may propose the publication of a technical report when it has collected
data of a different kind from that which is normally published as an International Standard, for
example "state of the art".
IEC 61282-10, which is a technical report, has been prepared by subcommittee 86C: Fibre
optic systems and active devices, of IEC technical committee 86: Fibre optics.
The text of this technical report is based on the following documents:
Enquiry draft Report on voting
86C/1071/DTR 86C/1087/RVC
Full information on the voting for the approval of this technical report can be found in the
report on voting indicated in the above table.

TR 61282-10 © IEC:2013(E) – 5 –
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
A list of all parts in the IEC 61282 series, published under the general title Fibre optic system
communication system design guides, can be found on the IEC website.
The committee has decided that the contents of this publication will remain unchanged until
the stability date indicated on the IEC web site under "http://webstore.iec.ch" in the data
related to the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
A bilingual version of this publication may be issued at a later date.
The contents of the corrigendum of April 2013 have been included in this copy.

IMPORTANT – The 'colour inside' logo on the cover page of this publication 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 – TR 61282-10 © IEC:2013(E)
0 Introduction
0.1 Introduction to vector modulated signals
Vector or complex modulation is well known since the 1980s in mobile communication and in
CATV transmission. In fibre optic telecommunication, coherent transmission was considered
during the late 1980s to improve sensitivity and therefore the reach of an optic transmission
line. With the introduction of EDFA optical amplification, the need for coherent transmission
was then considered less urgent. Recently the foreseeable shortage of transmission capacity
and the economic need to optimize transmission capacity without deploying new fibres lead
back to the same approach taken for wireless communication in the early 1990s, expanding
transmission capacity over a limited number of channels by working with digital complex
modulation or vector modulation [1 – 3] .
The main difference to on-off keying is that vector modulation, as indicated by the name, is
characterized by an additional dimension in modulation space:
Modulation: on-off vector
Amplitude X X
Phase - X
0.2 Digital coding with vector modulation
0.2.1 General
The additional phase dimension offers new possibilities for coding a binary signal and in
particular for coding more than 1 bit to each digital symbol. That is, a symbol can be assigned
to more than the two states 0 and 1. Consider the following bit stream

This can, for example, be coded to a symbol alphabet consisting of four elements {A,B,C,D},
as shown. As two bits are combined to a new symbol, only half as many symbols need to be
transmitted, reducing the transmission clock by a factor of two. This new reduced clock rate is
called symbol rate. Consequently, the symbol rate is half the transmission rate for this case.
In practice, of course, it is not possible to transmit letters, but instead a coding scheme onto
the transmitted electromagnetic wave can be selected, such as this:
00→ a× sin(ω× t+ 45°)
10→ a× sin(ω× t+135°)
(1)
11→ a× sin(ω× t+ 225°)
01→ a× sin(ω× t+ 315°)
This example uses a pure phase modulation called quadrature phase-shift keying, QPSK,
using four vectors defined by the amplitude of the signal and the four relative phases. If in
addition the amplitude is also modulated, it is possible to code more bits to one alphabet of
vectors. This is especially the case for higher level QAM signals.
______________
Numbers in square brackets refer to the bibliography.

TR 61282-10 © IEC:2013(E) – 7 –
To create these kinds of modulation formats, typically two modulators are needed. These two
modulators typically operate respectively in-phase and quadrature, denoted I and Q. This is
why this kind of modulator is described as an IQ modulator. The vector signal is described by
the two parameters:
(2)
where for the example of QPSK, a signal corresponds to ∅ values of 45°, 135°, 225° or 315°
and the amplitude a is constant.
A common way to display this kind of signal uses IQ or constellation diagrams. In Figure 1,
the constellation diagram is shown for the above-described coding scheme.
0.2.2 Constellation diagram
The constellation diagram indicates the amplitude and phase of the signal at the decision
point. This is the point in time when the signal must have the correct phase and amplitude
value for error-free transmission. This corresponds to the point in on-off modulation where the
receiver decides whether the signal is 1 or 0. At each coding location, a cluster of points is
displayed, corresponding to a point for each detected symbol in a data pattern.
Q (quadrature)
I (in-phase)
IEC  2441/12
Figure 1 – Constellation diagram for QPSK coding
0.2.3 IQ diagram
The IQ diagram displays the complete phase and amplitude transitions between transmitted
vectors as the signal is sampled. It reflects directly the combined I and Q components of the
signal at any sample time of the data acquisition. The traces on the diagram show the path of
the signal vector over the data pattern.

– 8 – TR 61282-10 © IEC:2013(E)
IEC  2442/12
Figure 2 – IQ diagram for the same QPSK coding
0.3 Polarization multiplexing
The phase modulation of a signal is demodulated by optical mixing, as described below. The
mixing depends on the relative polarization of the two optical carriers. Since the incoming
signal generally has an unknown and nonconstant polarization, demodulation then needs to
produce demodulated signals for two orthogonal polarization axes. With this doubling of the
demodulation information, it is then also possible to detect signals based on two carriers with
orthogonal polarization, each carrying independent bit streams, to double the transmission
rate for a given wavelength channel. For such polarization multiplexed signals, two
independent pairs of I and Q traces exist and two separate constellation or IQ diagrams are
used.
0.4 Error vector
Each transmitted symbol is described by a vector with amplitude and phase, which codes a
number of bits. Deviations from ideal modulation and impairments during transmission impact
the received vector with noise and distortions resulting in a different vector location in the IQ
diagram, compared to the reference vector for that symbol, as illustrated in Figure 3.
Q
IQ measured
Error vector
IQ reference
I
I error
IQ phase error
IEC  2443/12
Figure 3 – Relationship of error vector to reference vector and measured
signal vector in the constellation diagram
Q error
TR 61282-10 © IEC:2013(E) – 9 –
FIBRE OPTIC COMMUNICATION SYSTEM DESIGN GUIDES –

Part 10: Characterization of the quality of optical vector-modulated
signals with the error vector magnitude

1 Scope
The purpose of this part of IEC 61282 is to define the error vector magnitude (EVM) as a
metric for quantifying the quality of an optical vector-modulated (modulation of phase and
possibly magnitude) signal from a transmitter or optical transmission link. The considerations
required for reproducible measurement results are detailed. The relationships with other
related parameters from constellation diagram analysis like error vector, phase error,
magnitude error, I-Q offset and time-resolved EVM are described, as well as the relationship
between EVM and Q-factor.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and
are indispensable for its application. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 61280-2-8, Fibre optic communication subsystem test procedures – Digital systems –
Part 2-8: Determination of low BER using Q-factor measurements
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
error vector
difference between a measured IQ vector and the reference vector for the closest symbol D or
alternatively for the correct symbol when a known symbol sequence is measured
Note 1 to entry: If the closest symbol and correct symbol differ at the decision point, then the signal is impaired
sufficiently to produce a bit error.
3.2
error vector magnitude
EVM
length of a given error vector
Note 1 to entry: For a vector modulated signal that has been measured to give the time-dependent I and Q traces
with sampling interval, T , as outlined in Clause 5, the EVM of a particular measurement sample with index k is
s
given by
2 2
EVM(kT)= (kT) + (kT)  (3)
s s Q s
I
err
err
where
r(k)
(kT )= (kT )− I
s s
I αI ref
err meas
r(k)
(kT )= (kT )− Q
Q s αQ s
ref
err meas
– 10 – TR 61282-10 © IEC:2013(E)
and I and Q correspond to the reference symbol r(k) for the sample k, that is r(k) is an index pointing to the
ref ref
symbol with the reference vector for sample k.
In practical measurements the measured vector has arbitrary magnitude scaling within the receiver sensitivity, so
normalization with a factor α of the measured vectors is required to make the error vector independent of the
scaling, as described in 4.2.
3.3
RMS error vector magnitude
EVM
rms
root-mean-square of the error vector magnitudes for the N symbol decision times of a burst of
N symbols, either determined from directly measured samples or interpolated from the
neighbouring samples
1 N
(4)
EVM = EVM()n
rms
∑
n=1
N
Note 1 to entry: The r.m.s. EVM is usually expressed in per cent of the magnitude of the longest reference vector.
In Equation (4), it is assumed that the reference vector and the measured vector are equally scaled with the factor
α, as detailed below.
Note 2 to entry: The r.m.s. error vector magnitude of a burst of N measured symbols can be used as a figure of
merit for complex signals, specifying the quality of the signal in one number [4].
4 Error vector magnitude calculations and conditions
4.1 Reference vector assignment
The reference vectors are defined as a normalized set of vectors representing the ideal
constellation points. Assigning the reference vector for a sample corresponds to determining
r(k) in Equation (3). The reference vectors are scaled so that the longest vector has a
magnitude of 1. For QPSK or DQPSK the reference vectors are defined as follows:
r
⎛ ± ⎞
⎛ ⎞
I
r ⎜ 2 ⎟
ref
⎜ ⎟ (5)
S = = ,    r = 14
ref
⎜ r ⎟ 1
⎜ ⎟
±
Q
⎝ ref ⎠
⎝ ⎠
In this case, the magnitude of all four symbols is 1. For higher level QAM signals, the values
need to be calculated accordingly, such that the outermost symbol has a magnitude of 1.
4.2 Normalization of the measured data
Typically, the measured data have arbitrary scaling; depending on signal strength, link
attenuation and receiver responsivity, so it is necessary to normalize the measured data to
the reference vectors.
The normalization factor α is chosen to match the measured vectors to the reference by first
finding the value of a scaling factor β for the reference vectors that minimizes the
corresponding unnormalized EVM without changing the distribution of the measured vectors.
rms
Then the inverse of β is used as α to scale the measured vectors to the normalized reference.
For this purpose, the unnormalized EVM is expressed as
rms
N
r(n)
U = β × S − S ()n
meas
∑
ref
n =1
N
(6)
⎛ I ()n ⎞
meas
where  S ()n = ⎜ ⎟
meas
⎜ ⎟
Q ()n
⎝ meas ⎠
The value of β that gives minimum U is determined by solving
∂U
(7)
=0
∂β
TR 61282-10 © IEC:2013(E) – 11 –
2 2
N
⎛ ⎞
r(n ) r (n )
⎜ I + Q ⎟
∑ ref ref
n =1
⎝ ⎠
(8)
leading to α = =
N
β r(n ) r (n )
(I × I ()n + Q × Q ()n )
meas meas
∑ ref ref
n =1
Note that the same scaling factor is used for both I and Q, so it does not compensate for
distortion of the constellation diagram. However, the factor is determined independently for
both polarization planes, if the signal is polarization multiplexed. With these values, the
normalized detected vector is calculated with the following equations. Here the scaling is
shown for each symbol with index n, but it can similarly be applied to all IQ sample pairs with
index k.
I ()n ⎛ I ()n ⎞
⎛ ⎞
meas,y
meas,x
⎜ ⎟ ⎜ ⎟ (9)
S ()n = α             S ()n = α
norm,x x norm,y y
⎜ ⎟
⎜ ⎟
Q ()n
Q ()n
meas,x meas,y
⎝ ⎠ ⎝ ⎠
In terms of this normalization, the r.m.s. error vector modulation for the two polarizations is
calculated by these equations.
(10) N
r(n)
EVM = S − S ()n
rms,x norm,x
∑
ref,x
n=1
N
(10)
N
r(n)
EVM = S − S ()n
rms,y ∑ norm,y
ref,y
n=1
N
4.3 Conditions to be specified with EVM
rms
The conditions to be specified are as follows:
measurement bandwidth;
signal filtering (if used);
phase tracking bandwidth (if nonlinear tracking is applied).
5 Apparatus for measuring vector modulated signals
5.1 Coherent detector
A set-up to detect and evaluate optical vector modulated signals can be meaningfully
described in terms of two main functional parts, a coherent detector and the data
postprocessor, as shown in Figure 4.
The coherent detector converts the incoming optical vector modulated signal into an electrical
signal which provides its in-phase and quadrature amplitude. Most commonly, the I and Q
signals are converted for two orthogonal polarization states, labelled in Figure 4 as x and y.
One of the following implementations is usually used: mixing the signal in an optical
interferometer with the carrier from a local oscillator or with a delayed fraction of itself.

I
x
Q
x
Coherent detector
Local oscillator I Data postprocessor
y
One-symbol-delay IF
Q
y
IEC  2444/12
Figure 4 – Block diagram of the main functions for vector signal measurement

– 12 – TR 61282-10 © IEC:2013(E)
5.2 Local oscillator
This implementation uses a coherent light source, i.e. laser, as a local oscillator that is set
close to the same frequency as the signal carrier. The frequency offset must be significantly
less than the detection bandwidth of the measurement system. Depending on the sampling
method, the laser generates either a continuous carrier or short pulses. In each case, the
output of the optical detector is digitized and processed to correct for impairments introduced
by the optical front end and digitizer.
5.2.1 Detection based on electrical real-time sampling
Figure 5 is a schematic showing the configuration of a coherent detector using a local
oscillator for real-time sampling [5].
jΦ (t)
s
Polarization-diverse baseband mixer
A (t)e
Data signal
s
X-pol.
ππ PBS
0 0
PD
Optical
Optical
90-degree
90° hybrid
hybrid
PD
Y-pol.
Raw data Post-data
Raw data Post-data
Digitizer
Digitizer
correction prproocceessssiingng
correction
Optical
PD
X-pol.
Optical
90-degree
90° hybrid
LO
hybrid
PD
PBS
Y-pol.
jΦ (t)
r
Local beam（ (CCWW)）e
IEC  2445/12
Figure 5 – Configuration based on coherent detection with a local oscillator
jΦ (t)
s
For each polarization component, the observed data signal, , and a continuous local
A (t) e
s
jΦ (t)
r
beam, , are mixed together in an optical 90° hybrid. Here the phases of the signal and
A e
r
reference beams are described by:
ˆ
Φ (t )=ω t+φ (t )+φ +φ (t )
(11)
s s s s s
and
ˆ
Φ (t)=ω t+φ +φ (t)
(12)
r r r r
where
and  are the angular frequencies;
ω ω
s r
describes the phase modulation waveform;
φ (t)
s
describes the initial phase of the signal;
φ
s
describes the initial phase of the reference;
φ
r
TR 61282-10 © IEC:2013(E) – 13 –
ˆ ˆ
and  describe the random variables which show the respective phase noise.
φ (t)
φ (t)
s r
The frequency of the local beam is located at or near the centre of the observed signal
bandwidth (homodyne or intradyne detection). The in-phase (I) and quadrature (Q) channels
of the optical hybrid are given by:
j[Φ (t)−Φ (t)]
s r
I(t)= Re{a A A (t)e } (13)
1 r S
and
j[Φ (t)−Φ (t)]
s r
Q(t)= Im{a A A (t)e }, (14)
2 r s
where a and a are the detector gain of the respective detectors.
1 2
These analog signals are sampled and converted to digital with the sampling period, T . The
s
sampled values are described by
j[Φ (kT )−Φ (kT )]
ˆ ˆ
s s r s
(15)
I(kT )= Re{a A A (kT )e }= 4a A A (kT )cos(∆ωkT +φ (kT )+∆φ+φ (kT )−φ (kT ))
s 1 r S s 1 r S s s s s s s r s
and
j[Φ ( kT )−Φ ( kT )]
s s r s ˆ ˆ
(16)
Q( kT )= Im{a A A ( kT )e }= 4a A A ( kT )sin(∆ωkT +φ ( kT )+∆φ+φ ( kT )−φ ( kT ))
s 2 r s s 1 r S s s s s s s r s
where
describes the frequency offset;
∆ω=ω −ω
s r
describes the phase modulation to be measured;
φ (kT )
s s
describes the initial phase offset.
∆φ=φ −φ
s r
The frequency and phase offsets are removed from the I and Q data by the post-processing.
For such an offset removing process to work properly, the phase noise
ˆ ˆ
φ (nT )−φ (nT ),
s symbol r symbol
(17)
included in the extracted packet must be sufficiently small. This requires N T to be
p symbol
smaller than the laser coherence time. At the same time, for a high-order modulation format in
which a large number of constellation elements are used, N must be large enough for most
p
elements to appear in the extracted packet. Therefore, a signal light source (laser) is required
with a linewidth that is sufficiently narrow for the employed modulation format. Accordingly, in
the phase modulation measurement system discussed here, the linewidth of the local
oscillator must be as narrow as that of the signal laser.
5.2.2 Detection based on optical equivalent-time sampling
Optical sampling is a technique that measures the time-dependence of optical waves using a
gate effect whose response is much faster than that of conventional electronic circuits. Here,
we focus on sampling the complex amplitude and exclude techniques that sample only the
intensity.
Figure 6 shows the configuration for linear optical sampling (LOS) [6 – 8]. The set-up is
similar to that for real-time sampling, but the local beam is a sampling pulse rather than a

– 14 – TR 61282-10 © IEC:2013(E)
continuous beam. The interpulse coherence should correspond to a laser linewidth that is
compatible with the used sampling rate and phase tracking algorithms. We denote the
complex amplitude of the sampling pulse as
jΦ (t )
r
(18)
δ(t−τ )e
where
δ(t) is a function representing the pulse shape;
Φ (t) is the phase of the pulse;
r
τ is the time of the centre of the pulse.
j ( )
Φs t
Polarization-diverse baseband mixer
A (t)e
Data signal s
X-pol.
ππ PBS
0 0
PD
Optical
Optical
90-degree
90° hybrid
hybrid
PD
Y-pol.
Raw data Post-data
Raw data Post-data
Digitizer
Digitizer
correction prproocceessssiingng
correction
Optical PD
X-pol.
Optical
90-degree
90° hybrid
Sampling pulse LO
hybrid
PD
PBS
Y-pol.
Sampling trigger
Data signal
Sampling pulse
IEC  2446/12
Figure 6 – Configuration for linear optical sampling
Since the electronic circuit that includes the photodetector only responds to the incoming
frequency of the sampling pulse train, the photocurrents observed in the I- and Q-channels
are integrals during the response time, or the linear correlation of the data and local (pulse)
beams. Consequently, we obtain
 
j[Φ (t )−Φ (t )]
s r (19)
I(τ )= Re a A (t )δ(t−τ )e dt
 
1 s
∫
 
and
 
[ ]
jΦ (t )−Φ (t )
s r
(20)
Q(τ )= Im a A (t )δ(t−τ )e dt
 
2 s
∫
 
If the sampling pulse can be approximated by the δ-function, and the detectors’ sensitivities,
a and a are balanced, we obtain
1 2
jΦ (τ )
s
I(τ )+ jQ(τ )≅ A (τ )e , (21)
s
TR 61282-10 © IEC:2013(E) – 15 –
i.e. the observed signal resembles the instantaneous complex amplitude of the data signal. By
scanning the timing of the sampling pulse, τ, with respect to that of the observed data signal,
it is possible to reconstruct the entire waveform.
To obtain a meaningful interference signal, the spectrum of the sampling pulse must
encompass that of the measured signal. This is shown by using Parseval’s equation to
transform Equation (21) as:
j[Φ (t )−Φ (t−τ )]
s r
I(τ )+ jQ(τ )= A (t )δ(t−τ )e dt
S
∫
(22)
~
~
* jωτ
= A (ω )D (ω )e dω
s
∫
where
~ ~ jΦ (t−τ )
jΦ (t )
s r
and are the Fourier transforms of and , respectively.
A (ω) D(ω) A (t)e δ(t−τ )e
s s
In the spectral domain, we can see that the observed signal is proportional to the product of
the spectral amplitudes of the data signal and sampling pulse, and disappears when their
overlap is small. Therefore, in typical LOS implementations, the sampling laser must have
tunable wavelength to obtain an efficient spectral overlap with the signal. Alternatively, a
configuration that uses short optical pulses for a nonlinear-optics gate before making the
mixing with a tunable CW LO has also been achieved [8].
Since the optical gate is much faster than the following electronics, very high time-resolution
for analyzing temporal waveforms can be achieved, even to the sub-ps level. Hence, an LOS
implementation can be designed to have a measurement bandwidth in excess of the signal
bandwidth, yielding a distortion-free measurement suitable for e.g. EVM-related analysis in
component testing. It should be noted that the equivalent time sampling technique is not
specific to optical sampling. It can be used for electrical sampling just as the optical sampling
can be implemented as real-time sampling.
A straightforward variation of the procedure for real-time sampling also allows construction of
the constellation based on equivalent-time optical sampling [9]. Figure 7 compares the real-
time sampling scheme to the equivalent-time sampling scheme. For simplicity here, in both
cases the sampling is shown synchronized to the symbol rate, so the samples are at the
centre of the symbols. Let T be the under-sampling period, which is set at MT . M is an
os symbol
integer that shows the ratio of the sampling rate to the symbol rate. As seen in Figure 7, the
equivalent-time sampling scheme (b) needs M times the observation time to collect the same
number of samples, compared with real-time sampling Figure 7(a) for one sample per symbol.
This means that equivalent-time sampling requires M times the coherence of both the data
signal and the local (sampling) beam. However, with proper choice of sampling rate it has
been shown that equivalent-time optical sampling schemes are compatible with typical laser
linewidth used for coherent optical transmission, e.g. for DP-QPSK or DP-16QAM.

– 16 – TR 61282-10 © IEC:2013(E)
NT
symbol
T
symbol
π π 0 π π 0
0 0 0 0
・・・ ・・・
IEC  2447/12
Figure 7a – Real-time sampling
Acquired sample
Sampling pulse
NMT
symbol
T = MT
os symbol
T
symbol
π π 0 π π 0 π π 0
0 0 0 0 0
・・・ ・・・
・・・
~ ~
IEC  2448/12
Figure 7b – Equivalent-time sampling
Figure 7 – Schematic comparison of real-time sampling and equivalent-time
sampling to observe a repetitive signal pattern
5.2.3 One-symbol delayed interferometer
Differential phase modulation can be detected by using a one-symbol delayed interferometer,
without coherent detection [10,11]. A typical set-up is shown in Figure 8. The data signal is
divided into two parts, one of which is delayed by the length of one symbol before being
introduced into the optical hybrid. Let
ˆ
j{ω t+φ (t )+φ (t )}
s s s
e
(23)
be the phase-modulated signal, then the output of the I- and Q-channels of the optical hybrid
is given by
ˆ ˆ
j{−ωT +φ (t−T )−φ (t)+φ(t−T )−φ(t)}
symbol s symbol s symbol
I+ jQ= e (24)
These signals are sampled and converted to digital traces. The differential phase is
reconstructed by
Q
ˆ ˆ
(25)
∆φ = arctan( )=φ (t− T )−φ (t)+φ (t− T )−φ (t)−ω T
mes s symbol s s symbol s s symbol
I
where the last term is the offset to be removed by postprocessing. Equation (25) shows the
observed differential modulation, φ (t-T )-φ (t), and the phase noise contribution,
s symbol s
ˆ ˆ
, which are the same as what is seen in receivers for differential phase
φ (t− T )−φ (t)
s symbol s
modulation formats.
For polarization multiplexed optical signals, the one-bit delay technique requires a polarization
tracking device which is set in front of the set-up to separate the X and Y polarization into
individual measurement set-ups.

TR 61282-10 © IEC:2013(E) – 17 –
Baseband mixer
PD
Data signal
Optical
Optical
Raw data Post-data
Raw data Post-data
DDigigititizizeerr
9090°-degr hybried e
processing
correction
processing
jΦ (t) correction
D
A e
s
hybrid
T
symbol
PD
ππ
0 0
IEC  2449/12
Figure 8 – One-symbol delayed interferometer for detecting
differential phase modulation
5.2.4 Constellations of non-differential and differential phase modulation formats
As was described in 5.2.1, the I-Q diagram of (absolute) phase modulation format is described
by Equations (13) and (14). The comparable I-Q diagram for differential phase modulation,
which is observed in the one-symbol delayed receiver, is described by
j{φ (t –T )–φ (t)}
∗
s symbol s
I (t)= Re{a A(t – T )A(t)e } (26)
diff 1 s symbol s
j{φ (t –T )–φ (t)}
∗
s symbol s
Q (t)= Im{a A(t – T )A(t)e } (27)
diff 2 s symbol s
which can be defined as the differential constellation map in DxPSK formats.
Figure 9 shows a simulation of a QPSK signal measured with a local oscillator reference (left)
and with the one-symbol delay interferometer (right). The two IQ diagrams are fundamentally
different since the constellation diagram (left) directly represents the amplitude and phase of
the optical signal, while the differential constellation diagram (right) displays the phase
difference of the optical signal when mixed with itself with a one-symbol relative delay. In
addition, the amplitude shown in the differential constellation diagram represents the mixing of
the two copies of the signal. Some statistical values, such as the EVM, magnitude error, and
phase error, can also be defined for differential phase modulation formats, by using I (t) and
diff
Q (t) as in Equations (26) and (27). However, comparing the statistical measures based on
diff
absolute phase with the measures based on differential phase is not straightforward.
Figure 10 shows an example of a QPSK signal which is distorted by 10° of IQ quadrature
error. The distortion affects the constellation diagram differently compared to the differential
constellation diagram, which clearly illustrates the difference expected in e.g. a calculated
EVM. In the differential phase modulation format, the quality of the signal or the bit error rate
is more concerned with the phase error, rather than EVM.

– 18 – TR 61282-10 © IEC:2013(E)
Q
Q
diff
I
I diff
IEC  2450/12
Figure 9 – Simulation of an ideal (D)QPSK signal, represented as a constellation
diagram displaying the absolute phase and amplitude of the optical field (left)
With the one symbol delay interferometer technique, the corresponding differential
constellation diagram displays the phase difference between two consecutive symbols.
Q
diff
Q
I I
diff
IEC  2451/12
Figure 10 – Simulation of a (D)QPSK signal distorted with 10° IQ-quadrature error
Note that the distortion affects the constellation diagram (left) differently than the differential
constellation diagram (right). This effect will make EVM comparisons between the two
approaches difficult.
5.3 Digital postprocessing
5.3.1 Impairment compensation
The following parameters shall be corrected along the specified wavelength range of a
receiver to define the receiver as reference receiver:
• relative timing skew between the signal input S and the I , Q , I , Q output;
x x y y
• phase angle deviation from 90° between I and Q and between I and Q ;
x x y y
• offset and relative gain;
• alignment between incoming signal polarization and receiver axes.

TR 61282-10 © IEC:2013(E) – 19 –
A recent overview of digital signal processing for receivers is given in [12].
5.3.2 Relative timing skew
Relative timing skew describes the
...