Method and system for measuring average Q-factor in optical networks
Field of the invention
The invention relates to a technology for determining average value of Quality
factor (Q- factor) for signals transmitted via optical communication links.
Background of the invention
The Q-factor is a parameter that directly reflects the quality of a digital optical
communications signal. The higher the Q-factor, the better the quality of the optical
signal. Q-factor measurement is related to the analogue signal and in this respect
differs from bit error rate (BER) tests. As the Q-factor is related to the analogue
signal, it gives a measure of the propagation impairments caused by optical noise,
non-linear effects, polarization effects and chromatic dispersion. The mathematical
definition of the Q-factor (Q) is the signal-to-noise ratio of the analogue signal; in a
real system, Q can be determined based on Bit Error Rate (BER) using equation (1):

The Q-factor can be measured separately for each transmission channel assigned to a
single transmission signal. Q-factor measurement methods are usually intended for
the purposes of manufacturing, installation, optimization, maintenance and
troubleshooting, and monitoring of an optical transmission network.
US 2004/0218919 describes a system, method and apparatus for monitoring
impairment related parameters such as Q-factor within an all-optical system by using
forward error correction (FEC) to derive a bit error rate (BER), which BER is used to
determine the impairment related parameters. The Q factor determination process is
illustrated in Fig. 3 depicting bit error rate plotted as a function of decision threshold
level in Volts.
US 2005/0152693 proposes a technique for Q-factor measurement for per-
channel power control in an optical transmission network, by injection of a dummy

signal into the optical transmission network in addition to the communications
signals, with the dummy signal being controllable with regard to its power, and
determination of a channel-average Q-factor using BER measurements.
A Committee Draft of the International Electrotechnical Commission
numbered IEC 61280-2-11 Ed 1.0 (dated 23.07.2004) describes averaged Q-fector
determination using amplitude histogram evaluation for optical signal quality
monitoring, and is incorporated herewith by reference. It is pointed out that when a
system's BER is too low to be measured within a reasonable length of time, it is
useful to adopt Q-factor measurements. However, all sampling-based methods require
synchronization and then some analysis, i.e., require complex equipment as in the
BER measurement. Therefore a relatively simple asynchronous histogram method
was developed for Q-factor measurement. Average Q-factor (Qavg) measurement
through asynchronous sampling is a cost effective alternative to BER measurements.
Fig. 1 reproduces the corresponding figure of the Committee Draft which
presents a typical eye-pattern (10) of a high bit rate binary optical signal and its
amplitude histogram 12, built using asynchronous optical sampling of the optical
signal. It is determined, that among the amplitude sampling points that compose the
histogram, those points whose level is higher than a predetermined threshold level,
Hthi, belong to level "Mark"(or "1"), while those points whose level is lower than a
predetermined threshold level, aoj belong to level "Space" (i.e., "0"). The averaged
Q-factor Qavg is defined by the following formula (2):

Where" JXJ, «vg " and "a i, avg" are the mean and standard deviations of the Mark (i=l),
and Space level (i=0) distributions, respectively. The data obtained by asynchronous
sampling includes unwanted cross-point data in the eye-diagram, which decreases the
measured value of the averaged Q factor. The two threshold levels ( thi and tho) are
set in order to remove the cross-point data. They may also serve thresholds of
sensitivity for distinguishing "0" and "1" digital values.
Fig. 2 presents a block diagram shown in Fig. 2 of the above-mentioned
Committee Draft, recommending a system 20 for asynchronous measurement of the

averaged Q-factor, Qavg, of an optical signal transmitted via line 24. Operations of
sampling the optical signal, and the histogram-based processing of the samples are
performed according to clock signals of a clock oscillator 22. The clock signal is not
synchronized to the optical signal in the transmission line 24, and is sent to both a
sampling module 28 via an electrical pulse generator 26, and to a signal processing
circuit 30. The repetition rate of the electrical pulse train is to be consistent with the
sampling rate. The sampling module shall sample the optical signals at a specified
repetition rate with a specified sampling window by using an electrical pulse train
generated with an electrical pulse generator and detect the level of the sampled
signals. The sampled values are sent to the signal processing circuit. The accuracy of
Qavg depend on the sampling window (specified sampling time width).
The method of processing further includes utilizing tables that present
preliminarily obtained correlation of the QaVg with the absolute or theoretical value of
Q or BER.
US 2003/0011837 discloses a monitoring system using the above-mentioned
method of histograms. It includes first and second evaluation sections for obtaining an
averaged Q-factor parameter and a waveform distortion parameter from an optical
signal amplitude histogram collected from optical signals under measurement. The
monitoring system further includes a third evaluation section for determining both the
averaged Q-factor parameter and waveform distortion parameter, and for making a
decision as to whether the main factor of the optical signal quality degradation is
some waveform distortion or not by comparing the averaged Q-factor parameter and
waveform distortion parameter with their initial values or initial characteristics which
are obtained when no optical signal quality degradation is present. Comparison of a
number of the Q factor measurements are proposed for diagnosing appearance of a
quality degradation.
Though'the asynchronous sampling technology is more economic, it definitely
suffers from inaccuracy in comparison with quite expensive techniques of
synchronized measurements of Q-factor. Still it remains quite complex since it
involves a statistical algorithm with further multistage processing.

Summary of the invention
It is therefore the object of the present invention to propose a technology for
average Q-factor measurement, being both relatively simple and rather accurate.
The above object can be achieved using a technique for determining averaged Q-
factor (Qavg) of an optical binary signal transmitted at a bit rate X, based on
amplitude histogram evaluation and on asynchronous sampling. The proposed
technique is inexpensive since it uses sampling pulses, which have bit rate Y lower
than X and are not synchronized with the optical signal. The technique proposes
conducting N sampling sessions and constructing N respective amplitude histograms
for the sessions, wherein an initial session is conducted at a randomly selected initial
phase of the sampling pulses, and N-l sessions are held at different phases shifted in
respect of the initial phase. The technique then compares the obtained N amplitude
histograms to select there-from the amplitude histogram having the minimal
cumulative value of cross-point data. The averaged Q-factor is determined from the
selected histogram, with accuracy comparable with that of synchronous methods.
Formally, there is proposed a method of determining averaged Q-factor (Qavg) for
an optical binary signal transmitted via an optical communication line at a bit rate X,
based on amplitude histogram evaluation and asynchronous sampling, the method
comprising:
a) providing sampling pulses having bit rate Y lower than X and not
synchronized with the optical signal, and applying the sampling pulses to the
optical signal at a randomly selected initial phase, during a pre-selected
sampling session;
b) measuring amplitude values of the optical signal at moments of time
defined by the sampling pulses during the pre-selected sampling session;
c) building an amplitude histogram using the amplitude values obtained at
step (b), said amplitude histogram comprising at least two peaks and among
them two extremely positioned peaks corresponding to two average levels
"1" and "0" of the optical binary signal, the amplitude histogram also
comprising cross-point data between said two extremely positioned peaks;
d) shifting phase of the sampling pulses;

e) repeating steps b), c), d) N-l number of times thereby obtaining N
amplitude histograms for N respective different phases of the sampling pulses;
f) comparing the obtained N amplitude histograms and selecting there-from
such an amplitude histogranawhere a cumulative value of the cross-point data
is minimal;
g) determining a value of Qavg for the histogram selected at step (f).
The value Qavg is determined conventionally, according to equation (2).
The cumulative value of the cross-point data should be understood as a sum
(the integral) of all frequency values under the histogram curve between said two
levels of amplitude. Said two levels may respectively correspond to  and n o avg-
In a slightly differing version of the method, said two levels may respectively
correspond to tho and (tho-
The threshold level definitions are equal to those in the Committee Draft of
the International Electrotechnical Commission numbered IEC 61280-2-11 Ed 1.0
dated 23.07.2004, which is incorporated herein by reference.
Actually, the method proposes considering the value of QaVg determined at
step (g) to be the most accurate one for the asynchronous sampling at the selected bit
rate of the sampling pulses and the selected sampling session's period, since the
determined Qavg value is maximally close to a value of QaVg would it be determined by
synchronous sampling.
Indeed, one of the asynchronous sets of measurements at a particular phase of
the sampling signals will inevitably be applied to the optical signal at such a phase,
which will result in the sampling of the optical signal at positions closer to the center
of its bit pulse period, than it would occur at other sets of measurements. The specific
histogram built on such a set of measurements (obtained at the mentioned particular
phase) will definitely have the cumulative cross-point data lower than other
asynchronously obtained histograms. It is therefore understood why the determined
Qavg value for such a phase of asynchronous sampling pulses is maximally close to a
value of Qavg, would it be determined by a method of synchronous sampling.
In other words, the method proposes real time shifting of the beginning point of
the sample (probe) session, building histograms for each such phase shift, selecting

the most characteristic histogram from the point of minimal cumulative cross-point
data, and further computing the average Q-factor (Qavg) so as to finally find the best
signal to noise ratio which will manifest the measurement maximally close to that
which could be made by a synchronous sampling method.
Preferably, the bit rate Y of the sampling pulses is selected as Y=X/k, where k is
an integer.
Further preferably, in step (d), the phase shift is made for a non-integer number of
bit durations of the optical signal. It would be desired to be made "within the duration
of a bit pulse" of the optical signal, while it is understood that, in practice, the phase
shift of the asynchronous low bit rate sampling pulses will always comprise more
than one bit durations of the optical signal. Therefore the condition is to make a phase
shift for a non-integer number of the bit durations of the optical signal: the new phase
should differ from the previous phase by A = qTb + D, wherein q is an integer, Tb is
the duration of a bit of the optical signal and D is a mathematical fraction of Tb.
The fraction D of the bit duration is preferably not equal and not proportional
to a half of the bit duration, i.e., D=( p*Tb)/m, where p and m are integers, p=0...m-l;
m>2.
Alternatively, the phase shift can be performed by introducing controllable jitter in
the optical system (say, in the optical signal or in the sampling pulses), thereby
obtaining relative phase shift of the sampling pulses.
One preferred embodiment of the method may comprise:
gradually changing the phase of the sampling pulses in a discrete
manner N times,
building N said histograms for each discrete phase of the sampling
pulses;
computing the cumulative value of the cross-point data for each of
the N obtained histograms;
selecting the histogram, having the minimal cumulative value of the
cross-point data, for determining Qavg;
determining the Qavg according to equation (2).
According to a second aspect of the invention, there is also provided a system
for implementing the above-defined method.

The system, for example, can be defined as a system for determining averaged
Q-factor Qavg for an optical binary signal transmitted via an optical communications
line at a bit rate X, based on amplitude histogram evaluation and asynchronous
sampling, and comprising:
a medium for conducting the binary optical signal having bit rate X,
a generator of asynchronous sample pulses having bit rate Y less than X,
a sampling assembly for measuring amplitude values of the binary optical signal at
moments of time manifested by said sample pulses during a pre-selected period of
sampling session (or based on a pre-selected number of sample pulses),
means for controlled phase shifting of the sample pulses upon expiration of the period
of sampling session (or the number of sampling pulses),
a processing means for building and storing amplitude histograms of the binary
optical signal per each specific phase of the sample pulses corresponding to the
predetermined sampling session period (or said number of sample pulses);
said processing means being also capable of
calculating and comparing cumulative values of cross-point data of the amplitude
histograms built for different phases of the sample pulses, and
determining average Q-factor Qavg based on the histogram having the minimal
cumulative value of the cross-point data.
The generator of sampling pulses may have controllable bit rate.
The means for the controlled phase shifting of the sample pulses preferably
comprises a generator of clocks having bit rate Y, and a controllable assembly of one
or more delay lines connectable in various combinations between the output of the
generator of clocks and the input of the generator of sample pulses.
The means for the controlled phase shifting of the sample pulses can be
adapted, for example, to periodically shift the phase of the sample pulses generated by
their generator for a non-integer number of bit durations of the optical binary signal.
Alternatively, the above-mentioned means may comprise the clock generator
modulated by a jitter source, which can be controllable.

Description of the drawings
The invention will further be described with reference to the following non-
limiting drawings in which:
Fig. 1 (prior art) is an illustration of a typical asynchronous eye-pattern and its
amplitude histogram obtained by asynchronous optical sampling.
Fig. 2 (prior art) is a diagram of a system for asynchronous measurement of Qavg
using the histogram shown in Fig. 1.
Fig. 3 a, b, c illustrate three simplified different time diagrams of a binary optical
signal passing via an optical communications line and being sampled by lower bit rate
sampling pulses at three different phases.
Fig. 4 a, b, c, d, e, f illustrate amplitude histograms practically obtained for a binary
signal sampled at different phases of sampling pulses, according to the method
proposed by the invention.
Fig. 5 is an exemplary block diagram of a system capable of performing the sampling
and the processing according to the inventive method.
Detailed description of the preferred embodiments
Figs 3a, b, c can be understood as a general illustration of a method known as
asynchronous sampling.
Fig. 3a shows a binary optical signal 30 which, while being initially a digital
signal with distinctive power levels of "1" and "0", has become an analog-like quasi -
sinusoidal signal upon passing an optical link and suffering from such effects as
chromatic dispersion, non-linearity, etc. Let the bit rate X of the binary signal 30 is
quite high, (say, measured in Gb/s). Asynchronous sampling of such a signal is
proposed to be done by sample pulses having much lower bit rate Y. It should be
noted that equipment for sampling optical signals at low bit rates is significantly
simpler and cheaper than analogous equipment working at modern high bit rates. In
this drawing, the bit rate of the sample pulses is shown only twice as low (see circles
32 indicating the timing of the sample pulses with respect to the diagram 30 of the
binary optical signal). Random asynchronous sampling may give inadequate results,
since the sampled portions of the optical signal may occur to be placed between bits

thereof, and will therefore belong to the transition portions of the signal (i.e., those
between the high level "0" and the low level "1" of the signal). Fig. 3a shows such a
typical non-synchronized case.
Fig. 3b illustrates the progressing optical signal 30 having the same bit rate X
(the drawing shows a different binary succession of the signal). As proposed by the
invention, the signal 30 is sampled by the sampling pulses having the mentioned bit
rate Y; however, the sample pulses (marked by stars 34 on the optical signal 30) are
shifted by phase with reference to the initial phase of sample pulses 32 in Fig. 3a.
Though the sampling pulses 34 also fall on transition portions of the signal, they
occur to be closer to the center of bit durations of the signal 30.
Fig. 3c shows yet another phase of sampling pulses with respect to the optical
signal 30. Now the sampling pulses 36 (marked with vertical strips on the signal 30)
occur to be located quite close to the center of the bit positions of the optical signal,
and thus actually approach to becoming the synchronized sampling pulses.
It should be noted that the above three time diagrams should be understood as
simplified examples only. The bit rate Y of the sample pulses may be much lower
than the bit rate X of the optical signal, the ratio X/Y may constitute any arbitrary
number, the number and value of phase shifts may vary. It is therefore never known in
advance, which of the phase shifts will present the sampling most similar to the
synchronized sampling, and thus the statistical processing is required, using amplitude
histograms arid selecting there-from the one having the minimal cumulative cross-
point data for calculating the most accurate QaVg.
Fig. 4 a, b, c, d, e f are presented to illustrate the inventive idea and show six
amplitude histograms built for a binary optical signal sampled at six sampling
sessions. The six histograms 4a-4f are built for these six sampling sessions which are
performed at respective six different, randomly selected phases of sampling pulses.
Each of these statistic amplitude histograms was conventionally built using data about
values of the optical binary signal at the time of sampling pulses. The horizontal axis
of the histograms presents values of the sampled binary signal, and the vertical axis

presents frequency (or number of times) of appearance of the particular amplitude
value during the sampling session.
One should keep in mind that the sample pulses are not synchronized with the optical
binary signal under investigation, and that phase of the sampling pulses changes each
session.
The six experimental sampling sequences comprised each 50,000 sample pulses, the
measuring (sampling) session therefore comprised 50,000 sample measurements.
Each of the six statistical amplitude histograms shown in Figs. 4a - 4f is built using
50,000 readings of amplitude. The amplitude "1" on the horizontal axis means the
level of the optical signal assigned to the logical "1". The amplitude "0" on the
horizontal axis means the level of the optical signal assigned to the logical "0". These
two levels respectively correspond to o avg and iaVg- Every value of the amplitude
is considered with respect to a corresponding "1" or "0" threshold (tho and tho,
respectively).
Values of the vertical axis reflect the statistical frequency (number of times 1 to
50,000) at which the particular value of amplitude has been registered during one and
the same sampling session.
The theoretical Q factor was preliminarily determined according to equation (1) for
the optical signal under investigation, and it was equal to 6. It should be noted that
BER to be used in the equation (1) was measured by the synchronous method of
sampling.
For each of the histograms obtained by the proposed asynchronous method, QaVg was
then calculated using formula (2).
It has been shown in the experiment that the histograms a - d illustrate cases when the
phase of the asynchronous sampling occurred to be drastically non synchronized with
the bits of the optical signal. The histograms e and f (of sessions 5 and 6) look much
more similar to a reasonable statistical reflection of a binary optical signal, and they
indeed correspond to "lucky" phases of the sampling signals which are maximally
close to the phase of the sampling pulses would they be synchronized. As has been
shown in the experiment, the histogram "f' gives the best calculated value of Qavg,
which is maximally close to the theoretical Q. Among the six presented histograms,

the 6th histogram "f" is characterised by the minimal cumulative cross-point data
between the "0" and "1" binary levels of the amplitude.
The presentedlix histograms serve the proof of the proposed method for determining
Qavg of an optical signal by asynchronous sampling. .
Fig. 5 presents a block diagram of an exemplary system 120 for implementing
the method according to the invention.
For example, the diagram can be similar to that in Fig. 2, wherein the clock oscillator
block 22 of Fig. 2 is replaced with a controlled clock oscillator block 122 comprising
a clock oscillator 123 and a delay block 125. The signal processing circuit 30 is
replaced with a processing block 130.
In the new block 122, the bit rate of the clock 123 can be controllable, and the phase
thereof is definitely controllable - with the aid of the controllable delay block 125.
The controlled phase of the clock will further become the shifted phase of sampling
pulses issued from the electrical pulse generator 26. According to the embodiment
proposed in this drawing, the phase of the clock can be changed by selecting various
delay circuits (say, lines or the like within the controllable block 125), to be connected
to the output of the clock 123. Each specific delay circuit/delay circuit combination
corresponds to a particular phase of the sampling pulses, which is assigned to a
particular asynchronous measuring session for determining Qavg- It is desired that the
smallest delay difference which can be provided by a delay circuit or a combination
thereof be Tb/m, where Tb is the bit duration of the binary optical signal, and m is
integer >2.The sampling module 28 measures amplitude of the optical signal
whenever sampling pulses are sent from the generator 26. Upon obtaining and storing
the readings obtained from the sampling module 28 for each of the sessions, the
processing block 130 constructs an amplitude histogram for each of the sessions, and
determines the histogram with the minimal cumulative cross-point data between two
extremely located peaks of the particular histogram. The block 130 also calculates
Qavg for each of the histograms and then picks the value of Qavg of the histogram with
the minimal cumulative cross-point data as the most accurate value of QaVg for the
optical signal in the communication line 24.

Other implementations can be proposed for the above-described asynchronous
method of determining Qavg , as well as other versions of the method could be
developed. It should be appreciated that such versions and implementations should be
considered partof the invention, which is defined by the claims which follow.

Claims:
1. A method for determining averaged Q-factor, Qavg , for an optical binary
signal transmitted via an optical communications line at a bit rate X, based on
amplitude histogram evaluation and asynchronous sampling, the method comprising:
a) providing sampling pulses having bit rate Y lower than X and not
synchronized with the optical signal, and applying the sampling pulses to the
optical signal at a randomly selected initial phase, during a pre-selected
sampling session;
b) measuring amplitude values of the optical signal at moments of time
defined by the sampling pulses during the pre-selected sampling session;
c) building an amplitude histogram using the amplitude values obtained at
step (b), said amplitude histogram comprising at least two peaks and among
them two extremely positioned peaks corresponding to two average levels "1"
and "0" of the optical binary signal, the amplitude histogram also comprising
cross-point data between said two extremely positioned peaks;
d) shifting phase of the sampling pulses;
e) repeating steps b), c), d) N-l number of times thereby obtaining N
amplitude histograms for N respective different phases of the sampling pulses;
f) comparing the obtained N amplitude histograms and selecting there-from
such an amplitude histogram where a cumulative value of the cross-point data
is minimal;
g) determining a value of Qavg for the histogram selected at step (f).

2. The method according to Claim 1, wherein the cumulative value of the cross-
point data is the integral of frequency values under the histogram curve between said
two levels of amplitude, respectively corresponding to  aVg and  o avg-
3. The method according to Claim 1, wherein the cumulative value of the cross-
point data is tie integral of frequency values under the histogram curve between said
two levels of amplitude, respectively corresponding to  aVg and  aVg

4. The method according to any one of Claims 1 to 3, wherein the bit rate Y of
the sampling pulses is selected as Y=X/k, where k is an integer.
5. The method according to any one of Claims 1 to 4, wherein step (d) is
performed by introducing controllable jitter, thereby obtaining relative phase shift of
the sampling pulses.
6. The method according to any one of Claims 1 to 5, comprising, in step (d),
shifting the phase of sampling pulses for A being a non-integer number of bit
durations of the optical signal, so that A = qTb + D, wherein q is an integer, Tb is the
duration of a bit of the optical signal, and D is a fraction of Tb.
7. The method according to Claim 6, wherein D = (p*Tb)/m, where p and m are
integers, p=0.. .m-1; m>2.
8. The method according to Claim 7, comprising gradually changing the phase of
the sampling pulses in a discrete manner.
-
9. A system capable of implementing the method according to any one of the
preceding claims.
10. A system for determining averaged Q-factor Qavg for an optical binary signal
transmitted via an optical communications line at a bit rate X, based on amplitude
histogram evaluation and asynchronous sampling, the system comprising:
a medium conducting the binary optical signal having bit rate X,
a generator of sample pulses having bit rate Y less than X,
a sampling assembly for measuring amplitude values of the binary optical signal at
moments of time manifested by said sample pulses during a pre-selected period of
sampling session,
means for controlled phase shifting of the sample pulses upon expiration of the period
of sampling session,

a processing means for building and storing amplitude histograms of the binary
optical signal per each specific phase of the sample pulses corresponding to the
predetermined sampling session period;
said processing means being also capable of
calculating and comparing cumulative values of cross-point data of the amplitude
histograms built for different phases of the sample pulses, and
determining average Q-factor Qavg based on the histogram having the minimal
cumulative value of the cross-point data.
11. The system according to Claim 10, wherein the means for the controlled phase
shifting of the sample pulses comprises a generator of clocks having bit rate Y, and a
controllable assembly of one or more delay circuits connectable in various
combinations between the output of the generator of clocks and the input of the
generator of sample pulses.
12. The system according to Claim 10, wherein the means for the controlled phase
shifting of the sample pulses comprises a generator of clocks having bit rate Y, and
modulated by jitter.
13. The system according to any one of Claims 10 to 12, wherein the generator of
sampling pulses has controllable bit rate.

A technique for determining averaged Q-factor, Qavg,
for an optical binary signal transmitted at a bit rate
X, based on amplitute histogram evaluation and on
asynchronous sampling. The technique is inexpensive
since it uses sampling pulses, which have bit rate Y
lower than X and are not synchronized with the optical
signal. The technique proposes conducting N sampling
sessions and constructing N respective amplitute
histograms for the sessions, wherein an initial session
is conducted at a randomly selected initial phase of
the sampling pulses, and N-1 sessions are held at
different phases shifted in respect of the initial
phase. The technique then compares the obtained N
amplitute histograms to select there-from the
amplitude histogram having the minimal cumulative valve
of cross-point data. The averaged Q-factor is
determined from the selected histogram, with accuracy
comparable with that of synchronous methods.