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IMPACT OF THE FREQUENCY RESPONSEFLUCTUATIONS OF THE MULTIMODEFIBER ON THE OFDM TRANSMISSION
Lukasz Maksymiuk and Bartosz WisnickiInstitute of Telecommunications, Warsaw University of Technology,00-665 Nowowiejska 15/19, Warsaw, Poland; Correspondingauthor: [email protected]
Received 6 August 2012
ABSTRACT: Described is an analysis of the frequency responsefluctuations of the multimode fiber impact on the Orthogonal frequency
division multiplexing (OFDM) transmission. There is provided theory,numerical calculations and measurements. We analyze extreme andmoderate frequency response fluctuation cases. Orthogonal frequency
division multiplexing transmission is possible even in pass band whenthe spatial light filtration is moderate. VC 2012 Wiley Periodicals, Inc.
Microwave Opt Technol Lett 55:845–849, 2013; View this article online
at wileyonlinelibrary.com. DOI: 10.1002/mop.27402
Key words: multimode fibers; OFDM; frequency response; pass band
1. INTRODUCTION
The idea of an OFDM (Orthogonal Frequency Division Multi-
plexing) transmission over fiber is not new and has been studied
extensively for singlemode fibers. The transmission of an adap-
tively modulated OFDM signal over multimode fiber has
recently gained very high interest as well [1, 2]. As it comes for
multimode fibers, numbers of concepts vary from baseband
OFDM [1] to subcarrier OFDM generation [3], coherent [4, 5]
and non-coherent detection (Intensity Modulation—Direct
Detection) [1, 2]. Most of the papers focus on some different
modifications of an OFDM itself [3, 6, 7] and/or analysis of the
impact of different impulse/frequency response of different mul-
timode fiber samples on the transmission performance [8]. It is
well known that the frequency response realization depends on
the multimode fiber type, wavelength, launch type, etc. It is also
known that the frequency response of a particular MMF (Multi-
mode Fiber) based optical link may not be stable over time [9].
The fluctuations of the frequency response are more pronounced
when the light source is highly coherent and when within the
optical link there are many points with spatial light filtration
properties, such as connectors. It has to be noted here that little
to no research was conducted to analyze the influence of the
fluctuations of the frequency response of the multimode fiber
over time on the OFDM transmission. Therefore, this article is
devoted to the analysis of the frequency response fluctuation
impact of an electrically generated OFDM signal transmitted in
baseband and pass band of the multimode fiber. We present nu-
merical calculations based on the mathematical model described
in Section 2 and measurements conducted in a test setup. We
will show that the impact of a frequency response fluctuation
may theoretically vary from significant to very small. In many
practical considerations, the impact is moderate, which enables
the OFDM transmission both in baseband and pass band of the
multimode fiber, however some assumptions have to be made
and care taken when designing practical systems. In this work,
we present the case of an electrically generated baseband
OFDM signal IM–DD (Intensity Modulation–Direct Detection)
transmission over multimode fiber. Baseband OFDM ranges
from DC to fmax carrier. The OFDM signal is generated in such
a manner that in the IFFT the coefficients corresponding to the
same subcarrier frequency (fc and �fc) are paired and carry the
same signal; this is shown in Figure 1. The electrical signal
obtained at the output of the IFFT block is a real valued OFDM
baseband signal and directly modulates the laser. The advantage
of such approach is that there is no need of the signal mixing
with the carrier frequency, therefore simplifying the transceiver.
The disadvantage is the double size of the IFFT block, as we
also need coefficients for negative frequencies. The proposed so-
lution is similar to the DMT (Discreet Multitone Modulation)
approach in the ADSL (Asynchronous Digital Subscriber Line).
DC subcarrier was not used, as we did not want the signal to
have any bias. Furthermore, the idea was to insert OFDM sub-
carriers not only in the baseband of the multimode fiber, but
also in pass band; this has been illustrated in Figure 1. The fmax
value of an OFDM signal was chosen in such a way that it
matches the maximal frequency of the first pass band of the
simulated and measured multimode fiber sample. The utilization
of the multimode fiber pass band with the use of an OFDM has
many advantages over any other concept, such as SCM. Orthog-
onal Frequency Division Multiplexing is a technique designed to
be adaptive to the changing frequency response and channel
noise. It is therefore an ideal solution to be utilized in existing
multimode fiber links, where different fiber samples exhibit dif-
ferent frequency response characteristics. An OFDM can adapt
to a particular frequency response and therefore maximize possi-
ble throughput with maintaining desired BER of the link.
2. MULTIMODE FIBER FREQUENCY RESPONSEFLUCTUATIONS—THEORY
The frequency response of the multimode fiber, when neglecting
chromatic dispersion, may be expressed with the following
equation [10, 11]:
H fð Þ ¼XMk¼1
Pk exp �j2pf skLð Þ � 10�c kð ÞL=10; (1)
where f is the frequency, L is the fiber length, Pk is the input
power of the k-th mode group, M is the total number of mode
groups, sk is the group delay of the k-th mode group, and c (k)
is the attenuation in dB/km of the k-th mode group. As a mode
group N, we understand a set of LPpq modes such that the num-
ber of the mode group is given by: N ¼ 2 q þ p � 1. Modes
within a mode group have very similar propagation constants,
and an assumption is made that they have equal powers [11];
DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 55, No. 4, April 2013 845
complete mode mixing within the mode group. Moreover, in
modern silica glass GI (Graded Index) multimode fibers, there is
very low mode coupling between the mode groups [10, 11].
Therefore, we may treat Eq. (1) as a very good approximation
of a real fiber frequency response. Additionally, in the numerical
calculations we assumed DMA (Differential Mode Attenuation).
Thus, the mode group attenuation coefficient is given with the
following expression [12]:
c kð Þ ¼ c0 þ c0 � Iq g k � k0ð Þ2a= aþ2ð Þh i
; (2)
where c0 is the intrinsic fiber attenuation, Iq is the q-th order
modified Bessel function of the first kind, g is the weighting
constant, k is the mode group number, and a is the refracting
profile coefficient of the fiber. For a particular fiber, the varia-
tions of mode group powers result in frequency response
changes. When the powers change in time, the frequency
response of the MMF fluctuates in time as well. As the mode
coupling is negligible, the only source of Pk changes in time is
the spatial light filtration at couplers/splitters and connectors.
Basically, a splitter or an imperfect connector when illuminated
with coherent light causes the fluctuations of the total transmit-
ted power (modal noise [13]) but also variations of the power
coupled to each modal group (variations of power distribution
among mode groups in fiber). The latter effect causes the
changes of the shape of the frequency response of a particular
MMF-based optical link. Time-dependent mode coupling at the
connector may be caused by: laser mode power distribution
changes (VCSEL) or by phases variations of modes due to the
temperature or/and induced mechanical stress variations. This
effect was examined in details in [9]. According to [9], the fre-
quency response variations are higher in pass band than in base-
band, moreover the higher the pass band region (with increasing
frequency), the higher the fluctuation.
Figure 2 Top: block schematic of a numerical procedure; bottom:
block schematic of an experimental setup
Figure 3 Frequency response fluctuations—numerical calculations,
experiment no. 1, random powers of modes (see description in Section
3.1)
Figure 1 Block schematic depicting the principle of baseband OFDM signal generation and reception and an exemplary frequency response of the
fiber with baseband OFDM region marked; S/P and P/S stand for Parallel to Serial and Serial to Parallel conversions
846 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 55, No. 4, April 2013 DOI 10.1002/mop
3. NUMERICAL CALCULATION—BACKGROUND
The transmission of an OFDM signal in the MMF based optical
link exhibiting frequency response fluctuation was modeled in
MatLab. The block schematic of a numerical procedure is
depicted in Figure 2. The numerical calculations steps were as
follows: (1) a baseband OFDM signal was generated for a par-
ticular number of subcarriers, cyclic prefix length, frequency
spacing and number of bits (all carriers modulated with quadri
phase shift keying (QPSK)); (2) an MMF frequency response
realization was calculated [with the use of Eq. (1)] for a particu-
lar fiber type and a particular or random distribution of mode
group powers (calculated for each of the realizations); (3) an
OFDM signal spectrum was multiplied by a complex frequency
response of the fiber; (4) an AWGN was added to the signal
before demodulation; (5) OFDM was demodulated and equalized
(correction of phases and amplitudes of each subcarriers; as
usual for OFDM systems); (6) for each of the subcarriers MER
(Modulation Error Ratio) parameters were calculated. The simu-
lated fiber was OM1, with the 62.5 lm core diameter, the nu-
merical aperture NA ¼ 0.275, the length of 4.4 km and a gradi-
ent profile of refraction with a ¼ 0.2025. The wavelength of
light was assumed to be 1310 nm. The common simulation pa-
rameters were as follows: (1) the number of bits transmitted for
every frequency response realization at one subcarrier frequency
was 567, the total number of bits transmitted at all subcarriers
amounted to 567*62 ¼ 35 154; (2) the number of subcarriers
was 64 (1st DC subcarrier and 64th were not used for transmis-
sion); (3) the cyclic prefix was 5%, (4) frequency spacing
between subcarriers—8 MHz; (5) the number of frequency
response realizations was 150 (iterations of Monte Carlo simula-
tions); (6) the DMA coefficient g ¼ 6. The amount of AWGN
was chosen at particular level to make the results comparable
with measurements (Section 4).
3.1. Numerical Calculation—Experiment no. 1, Extreme CaseTo show how big an impact on the frequency response the
power distribution within the mode groups has, numerical Monte
Carlo simulations were performed. For every iteration, average
powers of modes within mode groups were random numbers
between 0 and 1 (uniform distribution). The procedure was
repeated 150 times resulting in different MMF frequency
response realizations—for every realization an OFDM signal
was transmitted in the simulated optical link (see Fig. 2). As a
result, the plots of MER versus the number of subcarriers for
different realizations of fiber’s frequency responses were
obtained. This case gives a deeper insight in the problem, it pro-
vides every possible result of a frequency response realization,
thus it may be assumed as the worst possible case in terms of
frequency response variations and OFDM transmission. The
obtained results are depicted in Figures 3 and 4. In the first one,
we may observe frequency response realizations, whereas in the
second one MER obtained in the simulated transmission at differ-
ent subcarriers. The observed variations of the fibers frequency
response are extremely high, especially in the pass band (see Fig.
3). The magnitude at frequency 350 MHz varies between �3 and
�25 dB, more than 20 dB. It is obvious that such variations may
have an extreme impact on the OFDM signal. The obtained MER
values in the pass band are between 13 dB (rather good) and
below 0 dB (very poor, noise is higher than signal). If the
changes of the frequency response are frequent, the transmission
in the pass band in such a case will not be possible. It has to be
noted here that taking into account every kind of power distribu-
tion within modegroups for a particular fiber (as it was proceeded
in the described experiment) leads to similar results as consider-
ing different realizations of multimode fiber impulse response,
shown in [8]. Luckily, when we observe frequency response var-
iations of a real MMF based link, they are not so extreme as
shown in Figure 3. They are more likely to be like those provided
in Figure 7 (measurements).
3.2. Numerical calculation—experiment no. 2, Moderate CaseLet us assume a moderate case of the frequency response varia-
tions caused by the spatial light filtration imposed by a single
connector. By analyzing the frequency responses obtained in the
previous experiment (Figure 3), the one was chosen that resem-
bles the frequency response obtained in the measurements pre-
sented in the next section (see Figure 7). Mode group powers
distribution providing this particular realization of frequency
response was set as average values for further numerical calcula-
tions. Before we provide any further description, a comment on
the idea of choosing a particular frequency response has to be
given. In the optical link based on the multimode fiber, it is vir-
tually impossible to know the exact power distribution in the
fiber (by knowing the network parameters), only some rough
assumptions can be made. The distribution depends on the type
of excitation (the type of laser, the patchcord type used, offset,
transversal output field distribution of the laser, which may vary
with the temperature), connector offsets, dust at connectors, the
fiber type, external stress imposed to the fiber, etc. It is obvious
that we cannot know exactly all these parameters, as for exam-
ple a particular offset at the connector due to some misalign-
ments. Moreover, it is very difficult to measure power distribu-
tion in the fiber; the existing methods are complicated and give
only some rough assumptions. Therefore, an indirect method
was used: observation of the frequency response shape. All pa-
rameters in the simulation were chosen as similar to measure-
ment setup as possible: the fiber type and all the parameters
(NA, core diameter etc.), the wavelength, DMA. Once again, as
in experiment no. 1, a Monte-Carlo simulation was performed
(the procedure was according to schematic presented in Fig. 2);
in this case resultant powers of mode groups for each iteration
were given by the following equation:
Pk ¼ N mean; std deviationð Þ ¼ N Parbk ;rk
� �; (2)
Figure 4 MER values versus subcarrier number—numerical calcula-
tions, experiment no. 1, random powers of modes (see description in
Section 3.1)
DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 55, No. 4, April 2013 847
where N() is a normal distribution random number, Parbk is an ar-
bitrary power of a mode group (for a chosen frequency response
realization) and rk is a standard deviation. Assuming that all the
spatial light filtration is imposed by an axially misaligned con-
nector at the front end of the fiber span and that this axial mis-
alignment is relatively small (less than several micro meters),
then [9]:
rk �r0 � Pk; k > 1
0; k ¼ 1,
�(3)
where r0 is equal for all the mode groups except mode group
number 1. In Figures 5 and 6, there are presented numerical
results for r0 ¼ 0.1. In Figure 5, we see the fluctuations of fre-
quency response of the fiber around a particular shape of the fre-
quency response given for an arbitrary Pkarb. Fluctuations in the
pass band are greater than in the baseband, and with increasing
the r0 the behavior of fluctuations does not change, they become
only more pronounced. By analyzing MERs versus the subcar-
rier number in the OFDM signal transmission (Fig. 6), we
clearly see that the characteristic resembles the shape of fre-
quency response of the fiber. Moreover, the fluctuations of the
frequency response impose the fluctuations of MER at a particu-
lar subcarrier. Some small fluctuations are also present even for
the first few subcarriers (lower ones), for which we do not
observe fluctuations of the frequency response of the fiber. This
is basically because each OFDM subcarriers spectrum has some
side lobes that extend over higher subcarriers, which in this case
are affected by frequency response fluctuations.
4. MEASUREMENTS
The schematic of a measurement setup used for the OFDM
transmission over MMF is depicted in Figure 2. It consisted of
the Arbitrary Waveform Generator, a directly modulated DFB
laser operating at 1310 nm, a multimode fiber spool (OM1,
4400 m), an InGaAs photodiode and an oscilloscope. An OFDM
signal generation, demodulation, and MER calculation was con-
ducted in MatLab. The parameters of the OFDM signal used in
the experiment resembled those used in the numerical calcula-
tions provided in the previous section. The number of subcar-
riers was set to 64 (including DC, which was not used in the
transmission), the subcarriers spacing was 8 MHz (similar as in
numerical calculations). The spatial light filtration was due to a
connector between a patchcord connected in front to the laser
and an MM fiber spool at the far end. The patchcord was based
on the same fiber type as the fiber spool. The launch type was
an OFL (Overfilled Launch). It has to be noted that the connec-
tor used in the experiment was a standard FC/PC adapter. In the
connection described here, we have measured additionally the
frequency response characteristic of the optical link (frequency
domain measurement); results are provided in Figure 7. The
measurement shown here is an optical frequency response of the
multimode fiber based link, thus a 3 dB drop in power designa-
tes bandwidth of the fiber baseband. We clearly observe fluctua-
tions of the frequency response characteristic in time due to the
spatial light filtration at the connector. The frequency response
measurement was repeated every 3 s. The frequency response
fluctuations are similar to those obtained with numerical calcula-
tions, compare Figures 7 and 5. In Figure 8, there is shown the
final result of MER versus the subcarrier number of an OFDM
Figure 5 Frequency response fluctuations—numerical calculations,
experiment no. 2, standard deviation of the average mode powers within
mode group �0.1 (see description in Section 3.2)
Figure 6 MER values versus subcarrier number—numerical calcula-
tions, experiment no. 2, standard deviation of the average mode powers
within mode group �0.1 (see description in Section 3.2)
Figure 7 Frequency response measurement of the multimode fiber
sample used in the experiment
848 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 55, No. 4, April 2013 DOI 10.1002/mop
signal transmitted over a multimode fiber based optical link. In
the figure, there are presented eight curves, each gathered in 10-
s intervals. Analyzing the results, we notice that the MER fluc-
tuations obtained in the measurement are similar to those pre-
sented in Figure 6—the numerical calculations. Similarly as in
the numerical simulations, a 4 dB drop in the optical frequency
response of the fiber results in an about 8 dB drop in the MER
value. The speed of fluctuations, how fast the frequency
response changes, depends on the speed of ambient conditions
variations. It means the frequency of vibrations inducing stress
to the fiber, speed of temperature changes, etc. Although in the
controlled conditions in a laboratory, it is possible to slow down
the frequency response variations, they cannot be eliminated al-
together and in the real life we never have so called controlled
environment.
5. CONCLUSION
In this article, we have analyzed the influence of the frequency
response of the multimode fiber on the transmission of an
OFDM over a multimode fiber. We have confirmed, both
numerically and experimentally, that the transmission is possible
in the baseband and in the pass band. We analyzed the MER
versus the subcarriers number, the obtained characteristic reflects
the multimode fiber sample frequency response shape; a 4 dB
drop in the optical frequency response of the fiber leads to an
about 8 dB decrease in the MER value. Additionally, we have
analyzed the influence of frequency response variations due to
the spatial light filtration on the OFDM transmission. In the nu-
merical simulations, we have shown that the impact can vary
from very large to small. In the worst case, the fluctuations in
the pass band are so severe that they completely disable the
transmission in the pass band. However, in the baseband the
transmission is still possible. When we consider moderate spatial
light filtration, one connector, the MER fluctuations imposed by
fluctuations of frequency response can be tolerable, and lead to
about 1 dB changes in MER. The latter numerical results were
confirmed with the measurements. Finally, it has to be con-
cluded that the OFDM transmission ranging to the pass band of
the multimode fiber is a very promising method of extending
the throughput of existing multimode fiber links. It has the
advantage over different methods of the pass band transmission
in that it can easily adapt to changes of the frequency response
characteristic of the multimode fiber, both in the baseband and
pass band, as it is an imminent feature of an OFDM technique.
Although if one wants to maximize the overall throughput of
the multimode fiber based link employing OFDM, the spatial
light filtration leading to the frequency fluctuation has to be
reduced. The latter leads to the need of connectors and coupler/
splitters number reduction within a particular optical link. In
this article, we have also shown a method of numerical model-
ing of the impact of frequency response fluctuations on the
OFDM transmission that is universal and can be used in differ-
ent scenarios of multimode fiber link.
ACKNOWLEDGMENT
This work has been supported by the European Union in the frame-
work of European Social Fund through the Warsaw University of
Technology Development Programme, realized by Center for
Advanced Studies.
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Figure 8 MER values versus subcarrier number—OFDM transmission
experiment over multimode fiber sample (OM1, 4.4 km)
DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 55, No. 4, April 2013 849
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