IEC 61280-2-13:2024

IEC 61280-2-13 ®
Edition 1.0 2024-07
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Fibre optic communication subsystem test procedures −
Part 2-13: Digital systems − Measurement of error vector magnitude

Procédures d’essai des sous-systèmes de télécommunication fibroniques –
Partie 2-13: Systèmes numériques – Mesure de l’amplitude du vecteur d’erreur
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IEC 61280-2-13 ®
Edition 1.0 2024-07
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Fibre optic communication subsystem test procedures −

Part 2-13: Digital systems − Measurement of error vector magnitude

Procédures d’essai des sous-systèmes de télécommunication fibroniques –

Partie 2-13: Systèmes numériques – Mesure de l’amplitude du vecteur d’erreur

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 33.180.10  ISBN 978-2-8322-9403-1

– 2 – IEC 61280-2-13:2024 © IEC 2024
CONTENTS
FOREWORD . 3
INTRODUCTION . 5
1 Scope . 6
2 Normative references . 6
3 Terms and definitions . 6
4 Background and terminology . 8
4.1 General . 8
4.2 Vector modulated signals . 9
4.3 Constellation diagram . 10
4.4 Normalization of the reference constellation . 11
4.5 Scaling of the measured vectors . 12
4.6 Error vector magnitude of individual symbols . 12
4.7 Root-mean-square EVM . 13
4.8 Calculation of the scale factor . 14
4.9 Iterative calculation of the scale factor . 15
4.10 EVM for polarization multiplexed signals . 16
5 EVM measurement procedure . 16
5.1 Apparatus . 16
5.2 Preparation of data samples . 17
5.3 Calculation of the RMS EVM . 17
5.3.1 General . 17
5.3.2 Procedure with known reference states . 18
5.3.3 Procedure with unknown reference states . 18
5.4 Reporting . 19
Annex A (informative) Relationship between RMS EVM and Q-factor . 20
Bibliography . 25

Figure 1 – Constellation diagrams of measured QPSK and 16-QAM symbols . 11
Figure 2 – Error vector magnitude D(k) of a single QPSK symbol . 13
Figure A.1 – In-phase and quadrature histograms of a QPSK signal . 22
Figure A.2 – In-phase and quadrature histograms of a 16-QAM signal . 23

Table A.1 – Q-factor parameters for a QPSK signal . 22
Table A.2 – Q-factor parameters for a 16-QAM signal . 24

INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
FIBRE OPTIC COMMUNICATION SUBSYSTEM TEST PROCEDURES –

Part 2-13: Digital systems – Measurement of 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) IEC draws attention to the possibility that the implementation of this document may involve the use of (a)
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the latest information, which may be obtained from the patent database available at https://patents.iec.ch. IEC
shall not be held responsible for identifying any or all such patent rights.
IEC 61280-2-13 has been prepared by subcommittee 86C: Fibre optic systems and active
devices, of IEC technical committee 86: Fibre optics. It is an International Standard.
The text of this International Standard is based on the following documents:
Draft Report on voting
86C/1900/CDV 86C/1924/RVC
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.

– 4 – IEC 61280-2-13:2024 © IEC 2024
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/publications.
A list of all parts of the IEC 61280 series, published under the general title Fibre optic
communication subsystem test procedures, can be found on the IEC website.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under webstore.iec.ch in the data related to the
specific document. At this date, the document will be
• reconfirmed,
• withdrawn, or
• revised.
INTRODUCTION
The error vector magnitude (EVM) is a single, real-valued parameter that characterizes the
signal quality of n-state amplitude phase shift keyed (n-APSK) signals, which are also known
as vector modulated signals. Similar to the Q-factor used for intensity-modulated
directly-detected optical signals, it measures the average deviations of the transmitted signal
states from their ideal values. These deviations can be caused by noise and by linear and
nonlinear waveform distortions. The EVM is therefore a useful quantity to characterize the
quality of transmitted source signals at the input of a transmission system or the quality of
received signals at the output of a transmission system [1] .
Despite the fact that the EVM is often reported by commercial optical modulation analysers,
there are only a few standards that define a procedure for calculating the EVM of optical signals.
ITU-T Recommendation G.698.2 [2], for example, specifies a maximal EVM value for
polarization-multiplexed 100 Gbit/s QPSK signals generated by an optical transmitter at the
input of a DWDM transmission system. These recommendations provide detailed instructions
for numerical signal processing steps that are to be performed on the received signal before
the EVM is calculated. The steps include removal of undesired frequency and phase offsets,
spectral filtering, DC offset removal, and even the addition of artificial noise to the signal.
Similarly, OIF Implementation Agreement OIF-400ZR-01.0 [3] describes a set of signal
processing steps for determining the EVM in polarization-multiplexed 400 Gbit/s 16-QAM
signals, which include the addition of artificial noise, but does not specify a maximal EVM value
for the transmitted signals at the input of the transmission system.
The detailed signal processing steps defined in ITU-T G.698.2 and in OIF-400ZR-01.0 are
specific to the particular modulation formats and to the applications considered in these
documents. They are not applicable to arbitrary n-APSK signals or to other applications.
This document specifies a general procedure for calculating the EVM of optical n-APSK signals
from a set of transmitted and properly received symbols. It does not specify any signal
processing steps necessary to extract the symbols from the raw received signals or optional
processing steps impacting the signal quality. This document rather defines the normalization
of the reference states used in the EVM calculations as well as a procedure for proper scaling
of the measured signal states. It is intended to serve as a reference for instrument vendors,
transmission equipment manufacturers, and users of such instruments and transmission
equipment.
The procedures described in this document apply to single-polarized optical signals as well as
to conventional polarization-multiplexed signals with independently modulated polarization
tributaries, which are often referred to as three-dimensionally (3-D) coded signals. In general,
it is not advisable to apply these procedures without modifications to four-dimensionally (4-D)
coded signals, in which optical amplitude, phase and polarization state are simultaneously
modulated to encode the information data [4]. At the time of writing, procedures for calculating
the EVM of 4-D coded signals were still under study.

___________
Numbers in brackets refer to the Bibliography.

– 6 – IEC 61280-2-13:2024 © IEC 2024
FIBRE OPTIC COMMUNICATION SUBSYSTEM TEST PROCEDURES –

Part 2-13: Digital systems – Measurement of error vector magnitude

1 Scope
This part of the IEC 61280-2 series defines a procedure for calculating the root-mean-square
error vector magnitude of optical n-APSK signals from a set of measured symbols. It specifically
defines the normalization of the reference states and a procedure for optimal scaling of the
measured symbol states.
The procedure described in this document applies to single-polarized optical signals as well as
to conventional polarization-multiplexed signals with independently modulated polarization
tributaries. In general, it is not advisable to apply these procedures without modification to
signals, in which optical amplitude, phase, and polarization state are simultaneously modulated
to encode the information data.
This document does not specify any signal processing steps for extracting the symbols from
the received optical signals, because these steps depend on the optical receiver and can vary
with the type of the transmitted n-APSK signal. These and optional additional signal processing
steps are defined in application-specific documents.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminology databases for use in standardization at the following
addresses:
• IEC Electropedia: available at https://www.electropedia.org/
• ISO Online browsing platform: available at https://www.iso.org/obp
3.1
digital modulation
modulation of an optical sinusoidal carrier by a digital signal
Note 1 to entry: Digital modulation is generally an amplitude shift keying, a frequency shift keying, a phase shift
keying or their combination.
[SOURCE: IEC 60050-713:1998, 713-07-12, modified – addition of "optical".]
3.2
binary (digital) signal
digital signal in which each signal element has one of two permitted discrete values
[SOURCE: IEC 60050-704:1993, 704-16-03]

3.3
n-ary (digital) signal
digital signal in which each signal element has one of n permitted discrete values
[SOURCE: IEC 60050-704:1993, 704-16-05]
3.4
n-state amplitude phase shift keying
n-APSK
digital modulation in which each element of a modulating signal is represented by one of n
specified combinations of phase and amplitude of a sinusoidal oscillation
[SOURCE: IEC 60050-713:1998, 713-07-13, modified – Note 1 to entry deleted.]
3.5
quadrature phase shift keying
QPSK
quadrature phase modulation phase shift keying in which the phase shift takes four values
that are multiples of 90°
[SOURCE: IEC 60050-702:2018, 702-06-43]
3.6
n-state quadrature amplitude modulation
n-QAM
an n-state amplitude phase shift keying which can be obtained by amplitude shift keying of two
carriers in quadrature, the modulated signals being added
2p
Note 1 to entry: In some cases, n is equal to 2 , where p is an integer, and the signal constellation points form a
square (e.g. for square n-QAM).
[SOURCE: IEC 60050-713:1998, 713-07-14, modified – Note 1 to entry added.]
3.7
signal constellation (in digital modulation)
scatter of n points representing in an amplitude-phase diagram the modulated signal in n-state
amplitude phase shift keying
Note 1 to entry: The signal constellation is often plotted in a two-dimensional IQ diagram, in which the two axes
represent the in-phase and quadrature components of the amplitude phase shift keyed signals.
[SOURCE: IEC 60050-713:1998, 713-07-15, modified – Note 1 to entry added.]
3.8
input signal (of a transmission system)
transmitted source signal
signal applied to the input port of the sending terminal equipment of a transmission system
[SOURCE: IEC 60050-704:1993, 704-04-11]
3.9
reference signal (of a transmission system)
ideal undistorted version of the transmitted source signal

– 8 – IEC 61280-2-13:2024 © IEC 2024
3.10
output signal (of a transmission system)
received source signal
signal emitted from an output port of the receiving terminal equipment of a transmission system
Note 1 to entry: Ideally, the output signal of a transmission system should be an undistorted version of the
corresponding input signal.
[SOURCE: IEC 60050-704:1993, 704-04-12]
3.11
polarization multiplex transmission
polarization multiplexed transmission
method of transmission employing multiplexing of two orthogonally polarized signals at the input
terminal of a transmission path and complementary demultiplexing at the output terminal
[SOURCE: IEC 60050-704:1992, 704-08-09, modified – "polarization" added to the term; "of
two orthogonally polarized signals" added to the definition.]
3.12
decision circuit (for a digital signal)
circuit that decides the probable value of a signal element of a received digital signal
[SOURCE: IEC 60050-704:1992, 704-16-12]
3.13
symbol (in digital modulation)
one of the n states of the modulated signal in n-state amplitude phase shift keying
3.14
error vector magnitude
EVM
difference between the measured signal and a reference
Note 1 to entry: A reference is a perfectly modulated signal.
[SOURCE: ISO/IEC 24769-2:2013, 3.1.1]
3.14.1
RMS error vector magnitude
EVM
rms
E
rms
root-mean-square average of the error vector magnitudes of N symbols of an n-APSK signal
Note 1 to entry: The value of the RMS EVM is greater than zero and is usually expressed in percent.
4 Background and terminology
4.1 General
Clause 4 provides background information on the EVM calculations and defines the terminology
used in this document.
The error vector magnitude (EVM) is a single, real-valued parameter that measures the average
deviations of the various signal states in n-state amplitude phase shift keyed (n-APSK) signals
from their ideal values. Its value is zero for an ideal n-APSK signal and larger than zero for real
(i.e. distorted) n-APSK signals. The EVM is frequently expressed in percent.

Frequently, n-APSK signals are also referred to as vector modulated signals (see 4.2), because
they can be represented as vectors in a two-dimensional constellation diagram, as described
in 4.3. The average EVM of a transmitted signal is determined from a fairly large number of
transmitted symbols (e.g. larger than 1 000) by first calculating the deviation of the transmitted
state (i.e. the measured state) from its corresponding ideal state individually for each
transmitted symbol, as described in 4.6, and then averaging these deviations as the root-mean-
square of the individual deviations, as described in 4.7.
The resulting quantity is usually referred to as the root-mean-square EVM and abbreviated as
RMS EVM or EVM . The RMS EVM can be viewed as a generalization of the Q-factor, which
rms
is often used to characterize the quality of binary and n-ary intensity-modulated signals. In fact,
RMS EVM and Q-factor are closely related, as described in Annex A.
Important elements of the EVM calculation are the normalization of the reference states, which
is specified in 4.4, and the scaling of the measured states, which is specified in 4.5 and 4.8.
4.2 Vector modulated signals
In general, vector modulated signals are composed of an in-phase component, characterized
by a time-varying amplitude A (t), and a quadrature component, characterized by a time-varying
I
amplitude A (t). Both components are modulated on the same optical carrier frequency, with
Q
the optical phase of the quadrature component being shifted by 90° relative to the in-phase
component. Hence, the time-varying optical amplitude of vector modulated signals can be
represented by a complex function A (t), as shown in Formula (1).
c
j ωt+φ ()t
[ ]
ss

A t P At+ jeA t
( ) ( ) ( ) (1)
c SI Q

where
P is the average optical power of the signal;
S
A (t) is the in-phase component of the modulated signal;
I
A (t) is the quadrature component of the modulated signal;
Q
ω = 2πf is the angular frequency of the unmodulated optical signal (i.e. optical carrier);
s s
φ (t) represents additional optical phase variations.
s
2 2
NOTE 1 In Formula (1), the amplitudes A (t) and A (t) are normalized so that the time average is
I Q I Q
equal to 1. This normalization is different from the one used for calculating the EVM.
Equivalently, A (t) can be represented by a 2-dimensional vector A (t), as shown in Formula (2),
c v
where A (t) and A (t) define the components of this vector.
I Q

At( )
I
j ωt+φ ()t
[ ]
ss
A tP= e
( )  (2)
vS
At
( )

Q

In quadrature phase shift keying (QPSK), for example, A (t) and A (t) are independent binary
I Q
amplitude modulated signals (whose symbol periods are properly synchronized), whereas in
16-state quadrature amplitude modulation (16-QAM), A (t) and A (t) are both quaternary
I Q
amplitude modulated signals.
=
– 10 – IEC 61280-2-13:2024 © IEC 2024
NOTE 2 Vector modulated signals are often generated by two independent optical amplitude modulators (e.g. Mach-
Zehnder modulators) that are connected in parallel to the same light source and operated in such a way that the
optical phase in one of the modulators is delayed by 90° relative to that in the other modulator. More information on
the generation and detection of vector modulated signals can be found in IEC TR 61282-16 [6].
4.3 Constellation diagram
The time varying signal components A (t) and A (t) of a vector modulated signal can be plotted
I Q
in a two-dimensional graph, according to Formula (2). Typically, the abscissa represents the in-
phase component A (t) and the ordinate the quadrature component A (t). In general, these plots
I Q
display only one pair of amplitude values A t ,A t for each transmitted symbol, which
( ) ( )
I k Q k

corresponds to a two-dimensional state vector S(k), as shown in Formula (3).
A t
( )
I k
S k =
( ) (3)

At
( )
Q k
where
k is an integer, with k = 1, 2, 3, …, N.
The time t at which the amplitudes A (t) and A (t) are sampled shall be chosen to best represent
k I Q
the state of the transmitted n-APSK symbol. However, no decision shall be made on the
probable value of the transmitted symbol (i.e. the samples shall be taken prior to a decision
circuit). Moreover, the signal amplitudes of all analysed symbols shall be sampled at the same
position within each symbol period T , so that all sampling times are spaced by an integer
s
multiple of T , as described by Formula (4).
s
t kT+Δ t
(4)
k s
where
Δt is the time offset in each symbol period;
k is an integer, with k = 1, 2, 3, …, N.
The scatter plot of the state vectors S(k) of a vector modulated signal is called a constellation
diagram. Figure 1 displays the constellation diagrams of two widely used n-APSK signals: a
transmitted QPSK signal and a transmitted square 16-QAM signal.
NOTE The signal amplitudes displayed in Figure 1 are scaled according to the procedures described in 4.5 and 4.8.
=
a) QPSK b) Square 16-QAM
Key
Solid black dots Measured signal states (scaled as described in 4.5 and 4.8)
White crosses Reference states (see 4.4)
Dashed lines Midpoints between the in-phase and quadrature components of the reference states
Figure 1 – Constellation diagrams of measured QPSK and 16-QAM symbols
4.4 Normalization of the reference constellation
The signal constellation of an ideal n-APSK signal is represented by n different points in the
constellation diagram, which correspond to n different reference vectors R(m), m = 1, 2, …, n.
The reference vectors shall be normalized so that the longest vector has unity length, as shown
in Formula (5).
max R m = 1
{ ( ) }
(5)
mn= 1, . ,
The reference states are unitless.
NOTE The reference states are sometimes normalized so that the average power of all possible reference states
n
1 2
is equal to one, i.e. . This normalization is often used in EVM calculations of electrical n-APSK
R i =1
( )
∑
n
i=1
signals [5]. For QPSK signals, it is identical to the normalization specified in 4.4, but for n-APSK signals of higher
cardinality, like 16-QAM signals, the two normalizations lead to substantially different EVM values [1]. The
normalization defined in this document is commonly used for optical signals and is identical to the one used in OIF-
400ZR-01.0 [3].
– 12 – IEC 61280-2-13:2024 © IEC 2024
4.5 Scaling of the measured vectors
The measured state vectors S(k) of the transmitted n-APSK signal in general are scaled
differently than the reference vectors R(m). For a useful comparison between S(k) and R(m),
rescale the measured states S(k), i.e. multiply with a common scale factor α. This scaling is
impeded by the fact that the state vectors S(k) are typically scattered around the ideal
constellation points and can even exhibit significant offsets from these points. Since the EVM
characterizes the deviation of the measured state vectors S(k) from their ideal states R(m), the
optimal scale factor α is the one that minimizes the average deviations of the scaled state
vectors αS(k) from the associated reference vectors R[m(k)], for all k = 1, …, N. The calculation
of the optimal scale factor is specified in 4.8 and 4.9.
The scaled state vectors are represented by S (k) = α S(k), where α denotes the common scale
α
factor.
4.6 Error vector magnitude of individual symbols
To calculate the EVM of the measured signal, each of the measured state vectors S (k) is
α
associated with a reference vector R(m) from the set of n possible states, ideally with the
transmitted reference vector.
If the sequence of the transmitted reference states is known, which is the case when a well-
defined test signal has been transmitted, the reference vectors can be determined from this
sequence by properly correlating the received symbols with the transmitted states. If the
transmitted states are unknown, which is often the case, each S (k) is associated with the
α
reference vector R(m) that is closest to S (k) in the constellation diagram.
α
NOTE For signals with only a few possible states n (e.g. for QPSK signals), it is often straightforward to associate
a measured state with the transmitted reference state. However, this association becomes increasingly more difficult
with increasing number of states n, especially when the measured signal is noisy or otherwise distorted. Improperly
associated states generally lead to an underestimation of the EVM. However, the number of improperly associated
states is usually much smaller than that of properly associated states (e.g. because of the exponential distribution
of noise), so that the impact on the RMS EVM can be disregarded in many cases.
The association of each S (k) with a corresponding R(m) thus establishes a relationship between
α
k and m, which can be described by a function m(k), so that each measured state vector S(k) is
associated with a reference vector R[m(k)].
The EVM of the k-th received symbol is given by the distance D(k) between S (k) and R[m(k)],
α
as described by Formula (6) and illustrated in Figure 2.
D k = SRk − mk
( ) ( ) ( ) (6)
α

Key
Solid gray dots Measured signal states
Solid black dot Selected signal state for which D(k) is calculated
White crosses Reference states
Figure 2 – Error vector magnitude D(k) of a single QPSK symbol
4.7 Root-mean-square EVM
The average error vector magnitude E of all transmitted symbols is given by the root-mean-
rms
square average of all D(k), k = 1, …, N, as shown in Formula (7).
N
E SRkk− m (7)
( ) ( )
∑
rms α 
N
k=1
This parameter is often referred to as the rms error vector magnitude and abbreviated as RMS
EVM or EVM .
rms
For most accurate results, a large number N of symbols should be collected. Each of the
possible states of the n-APSK signal should be represented with the same probability as
expected in normal operation of the transmission system. For signals with equiprobable
distribution of all possible states, at least 100 symbols should be collected for each state. For
signals with probabilistically shaped constellation [8], the states in the analysed set of symbols
should be represented according to the prescribed probability function for the symbols.
Specially designed test signals are sometimes transmitted for the EVM measurement, to ensure
the desired distribution of the transmitted symbols as well as randomization of the order in
which they are transmitted. Once the symbols have been collected, their EVM can be evaluated
in arbitrary order. If necessary, the symbols can be collected in several independent
measurements.
The RMS EVM of the QPSK symbols displayed in the example of Figure 1 a) is 17 %, whereas
the RMS EVM of the 16-QAM symbols in Figure 1 b) is only 8,6 %. In both cases, the EVM
calculation includes 64 000 symbols.
=
– 14 – IEC 61280-2-13:2024 © IEC 2024
4.8 Calculation of the scale factor
As explained in 4.5, the measured state vectors S(k) are scaled so that the deviations of the
scaled state vectors S (k) = α S(k) from their associated reference vectors are minimal. Proper
α
scaling is necessary to avoid undesired offsets in E . The scale factor α shall be calculated
rms
from the measured states and their associated reference states as shown in Formula (8).
N
R mk 
( )
∑
 
k =1
α =
(8)
N
 
SR(k ) ⋅ mk( )
∑
 
k =1
⋅
where " " denotes the scalar vector product.
For signals with equiprobable distribution of all possible n signal states, Formula (8) can be
approximated by Formula (9).
n
1 2
R i
( )
∑
n
i=1
α =
(9)
N
SR(k ) ⋅ mk( )
∑
 
N
k =1
For signals with probabilistically shaped constellation, Formula (8) can be approximated by
Formula (10).
n
pi R i
( ) ( )
∑
i=1
α =
(10)
N
SRk ⋅ mk 
( ) ( )
∑
 
N
k =1
where
n
p(i) is the probability of reference symbol i to be transmitted, with .
pi = 1
( )
∑
i=1
NOTE 1 For signals with equiprobable distribution of all possible states, p(i) = 1/n, for i = 1, …, n, in which case
Formula (10) becomes Formula (9).
The scale factor α in Formula (8) is derived by scaling all reference vectors R(m) with a common
factor β, whose value is selected so that it minimizes the root-mean-square distance D
rms
between S(k) and βR(m), where D is defined in Formula (11).
rms
N
D SRk−β m k (11)
( ) ( )
rms ∑

N
k=1
=
The desired value of β can be calculated analytically from the condition , which
∂D ∂=β 0
rms
yields β = 1/α, where α is given by Formula (8).
NOTE 2 In general, it is not possible to calculate the optimal scale factor α directly from Formula (6) by minimizing
E , because α scales not only the centroid of the measured state vectors but also the added noise and waveform
rms
distortions, which can introduce a significant offset in E .
rms
When the sequence of the transmitted (ideal) states is known and properly correlated with that
of the received symbols, all reference states R[m(k)] can be determined a priori, so that the
desired scale factor α can be directly calculated from Formula (8).
When the received symbols are unknown, α cannot be calculated from Formula (8) until each
measured state S(k) is associated with a corresponding reference state R(m), as described in
4.6. Since S(k) shall be associated with the reference state R(m) that is closest to the scaled
state S (k), the scale factor α generally has to be known before α can be calculated from Formula
α
(8). In this case, α shall be determined using the iterative procedure described in 4.9.
NOTE 3 For signals with very few possible states, like QPSK signals, it is possible to assign the reference states
directly to the measured states without prior scaling. For QPSK signals, for example, all measured states found in a
given quadrant are assigned the one and only reference state in this quadrant. In this case, α can be calculated
directly from Formula (8).
4.9 Iterative calculation of the scale factor
The iterative procedure for calculating alpha, as described in 4.9, is only required if the
transmitted symbols are unknown. The procedure starts with an initial rough estimate of the
desired scale factor, denoted α , which is used as a first approach to scale the measured state
vectors. For signals with equiprobable distribution of all possible signal states, an initial
estimate of α can be obtained from the square root of the ratio of the average power of all
reference states R(m) to the average power of all measured symbols S(k), as shown in Formula
(12).
n
1 2
R (i)
∑
n
i=1
α = (12)
N
1 2
S(k )
∑
N
k=1
For signals with probabilistically shaped constellations, the reference states shall be weighted
by the probability of their occurrence in the transmitted signal, as shown in Formula (13).
n
pi R i
( ) ( )
∑
i=1
α =
(13)
N
1 2
S k
( )
∑
N
k=1
where
n
p(i) is the probability of reference symbol i to be transmitted, with .
pi = 1
( )
∑
i=1
NOTE 1 For signals with equiprobable distribution of all possible states, where p(i) = 1/n, for i = 1, …, n, Formula
(13) is identical to Formula (12). Hence, Formula (13) is a generalized form of Formula (12).The initial estimate of
Formula (13) is most accurate for signals with fairly small waveform distortions and low noise. For noisy signals, a

– 16 – IEC 61280-2-13:2024 © IEC 2024
more accurate estimate of the scale factor can often be obtained by analysing the distribution of the sampled symbols
in the constellation diagram. In the case of square n-QAM signals, for example, the scale factor can be obtained from
histograms of the in-phase and quadrature components of the measured signal states, as shown in Figure A.2 for a
16-QAM signal. If the waveform distortions in the signal are small, α can be obtained from the distance between the
two outermost peaks, , so that . More refined estimates could be used for highly
D = μ -μ αD= 2
out 4 1 1 out
distorted signals. However, the methods are usually specific to a particular modulation format and, therefore, cannot
easily be generalized to arbitrary n-APSK signals.
Once the initial estimate α has been determined, the following procedure shall be performed.
a) Scale the measured state vectors as S (k) = α S(k), using the initial scale factor α ;
α1 1 1
b) For each symbol k, find the reference state R(m) that is closest to S (k) (see 4.6), to obtain
α1
a first relation between m and k, denoted m (k);
c) Calculate α from Formula (8), using m(k) = m (k) from step b), to obtain an improved scale
;
factor α
d) Rescale the measured state vectors as S (k) = α S(k), using α from step c).
α2 2 2
e) For each symbol k, find the reference state R(m) that is closest to S (k) (see 4.6), yielding
α2
a second relation between m and k, denoted m (k);
f) Repeat steps c) through e) until there is no significant difference between α and α ;
l l−1
g) Calculate the EVM D(k) for each symbol k, using m (k) and S (k) from the last iteration of
l αl
steps d) and e) in Formula (5).
NOTE 2 If the transmitted signal is distorted by excessive noise or other waveform distortions, it is possible that
the nearest reference state of a transmitted symbol does not correspond to its ideal state. In this case, the distance
calculated from Formula (5) is smaller than it would be if the corresponding reference state was known, thus resulting
in an underestimation of the RMS EVM. This problem is not encountered when the reference states of the transmitted
signals are known.
4.10 EVM for polarization multiplexed signals
In polarization multiplexed signals, two different n-APSK signals are transmitted, either
simultaneously or alternatingly, in two orthogonal polarization states. The signals corresponding
to these two states are usually referred to as the X-polarized and Y-polarized signals. In this
case, the transmitted symbols shall be measured and processed separately for the X- and Y-
polarized signals, so that two root-mean-square EVM values are obtained. If the X- and Y-
polarized signals have identical reference states R(m), the two EVM values may be averaged
by root-mean-square to a single RMS EVM value.
5 EVM measurement procedure
5.1 Apparatus
A linear optical receiver shall be used to convert the optical signals to be analysed into electrical
signals. The receiver shall have enough optical and electrical bandwidth to capture the entire
spectrum of the transmitted signal. The received analogue electrical signals shall be converted
to digital signals, using analogue-to-digital converters, and recorded as digital data to allow
further signal processing and analysis.
NOTE Suitable optical receivers include optical modulation analyzers and well-calibrated commercial
telecommunication receivers. Optical n-APSK signals are frequently detected with intradyne coherent receivers
having phase and polarization diversity [7]. These receivers typically generate four analogue electrical signals, from
which the transmitted symbols can be retri
...