Dispersion Analysis within a Measured 1,4 km MIMO Multimode
Channel
Andreas Ahrens, Steffen Schr¨oder and Steffen Lochmann
Hochschule Wismar, University of Technology, Business and Design, Philipp-M¨uller-Straße 14, 23966 Wismar, Germany
Keywords:
Multiple-Input Multiple-Output System, Optical Fibre Transmission, Multimode Fiber (MMF), Modal
Dispersion, Chromatic Dispersion.
Abstract:
In this contribution a signal theoretic Multiple Input Multiple Output (MIMO) system model for estimat-
ing modal and chromatic dispersion is developed. Based on channel measurements within a 1,4 km MIMO
multimode channel parameters for modal and chromatic dispersion are estimated. Furthermore, taking given
parameters of the dispersion into account, the introduced signal theoretic MIMO system model enables a
reconstruction of the MIMO specific impulse responses.
1 INTRODUCTION
The increasing desire for communication and infor-
mation interchange has attracted a lot of research
since Shannon’s pioneering work in 1948.
A possible solution was presented by Teletar and
Foschini in the mid 90’s, which revived the MIMO
(multiple-input multiple-output) transmission philos-
ophy introduced by van Etten in the mid 70’s (Telatar,
1999; Foschini, 1996; van Etten, 1975; van Etten,
1976).
Since the capacity of wireless multiple-input
multiple-output (MIMO) systems increases linearly
with the minimum number of antennas at both,
the transmitter as well as the receiver side, MIMO
schemes have attracted substantial attention (Zhou
et al., 2005; Mueller-Weinfurtner, 2002) and can be
considered as an essential part of increasing both
the achievable capacity and integrity of future gen-
erations of wireless systems (K¨uhn, 2006; Zheng
and Tse, 2003). MIMO transmission has influenced
nearly any standard of wireless communication.
However, the MIMO principle is not limited to
wireless communication channel and a lot of scenar-
ios can be described by the MIMO technology (K¨uhn,
2006; B¨ulow et al., 2011; Singer et al., 2008).
Within the last years, the concept of MIMO (mul-
tiple input multiple output) transmission over mul-
timode and multicore fibers has attracted increasing
interest in the optical fiber transmission community,
e. g. (B¨ulow et al., 2010; B¨ulow et al., 2011; Singer
et al., 2008), targeting at increased fiber capacity.
Usually, the fibre capacity is limited by the dis-
persion. In multimode fibres the modal dispersion
dominates the chromatic dispersion by orders. Only
systems with Restricted Mode Launching (RML),
e.g. the 10 Gbit Ethernet system standard 10GBASE-
SR, focus on the description of both dispersion ef-
fects(Pimpinella et al., 2011; Castro et al., 2012).
Since the modal and the chromatic dispersion are
considered to be independent, the system impulse re-
sponse is given by the convolution of these individual
impulse responses.
Against this background, the novel contribution of
this paper is that based on channel measurement with
a 1,4 km multimode fibre, a signal theoretic MIMO
system model for estimating modal and chromatic
dispersion is developed.
By taking given parameters of the dispersion into
account, the introduced system model enables a re-
construction of the MIMO specific impulse responses.
Thus, a fundamental algorithm for further studies on
the impact of dispersion and for a comparison of dif-
ferent MIMO systems utilizing different wavelengths
is presented.
The remaining part of this contribution is orga-
nized as follows: Section 2 introduces our system
model. The measurement setup for estimating the
channel impulse responses is presented in section 3.
In section 4 our signal theoretic system model is in-
troduced and discussed. The associated performance
results are presented and interpreted in section 5. Fi-
nally, section 6 provides our concluding remarks.
391
Ahrens A., Schröder S. and Lochmann S..
Dispersion Analysis within a Measured 1,4 km MIMO Multimode Channel.
DOI: 10.5220/0004495203910397
In Proceedings of the 4th International Conference on Data Communication Networking, 10th International Conference on e-Business and 4th
International Conference on Optical Communication Systems (OPTICS-2013), pages 391-397
ISBN: 978-989-8565-72-3
Copyright
c
2013 SCITEPRESS (Science and Technology Publications, Lda.)
2 MULTIMODE MIMO
CHANNEL
In order to form the optical MIMO channel, different
sources of light have to be launched into the multi-
mode fibre. In this work a (2×2) optical multimode
MIMO channel is studied. The corresponding elec-
trical MIMO system model is highlighted in Fig. 1.
u
s 1
(t)
u
s 2
(t)
u
k 1
(t)
u
k 2
(t)
g
11
(t)
g
21
(t)
g
12
(t)
g
22
(t)
Figure 1: Electrical MIMO system model (example: n = 2).
In Fig. 2 the optical MIMO setup is shown
schematically. On the left side the transmitter side
is represented for launching different sources of light
into the fibre. By coupling light in the center of the
multimode core, described by TX
1
, low-order mode
groups are activated (e.g. fundamental mode). For
activating high order mode groups, described by TX
2
,
light has to be launched into the fibre with an given
eccentricity.
At the receiver side, different spatial filters are
used to separate the different mode groups. For low-
order mode groups the spot filter (described by RX
1
)
and for higher order mode groupsthe ring filter is used
(described by RX
2
). Together with the mode group
coupling along the 1,4 km long fibre, the MIMO sys-
tem model according to Fig. 1 can be formed (Pankow
et al., 2011).
3 MEASUREMENT SETUP
In order to evaluate the potential of MIMO in the
field of optical multimode communication channels,
a good knowledge of the MIMO specific impulse re-
sponses and their corresponding dispersion parameter
is needed. For analyzing the MIMO specific impulse
responses, the measurement setup depicted in Fig. 3
is used. For measuring the impulse responses, the in-
put impulse was generated by using the Picosecond
Diode Laser System (PiLas). For the measurement
10µm
10µm
TX
2
TX
1
δ
RX
2
RX
2
RX
1
r
Figure 2: Forming the optical MIMO channel (left: light
launch positions at the transmitter side with a given eccen-
tricity δ, right: spatial configuration at the receiver side as a
function of the mask diameter r).
campaign two different laser diodes are used: The
spectral properties of each laser diode are determined
by measurement. The first laser diode has a center
wave length (CWL) of 1326 nm and a spectral half
width of approximately 8 nm. The second laser diode
has a CWL of 1576 nm and a spectral half width of
approximately 10 nm. Fig. 4 shows exemplarily the
Pulse
Generator
SM 10/125
Positioner (Alignment Unit)
X
Y
GI 50/125
Fixed
GI-Fiber
Moveable
SM-Fiber
GI
50/125
GI
50/125
GI
50/125
GI
50/125
ring
center
Spatial Filter Characteristic
Oscilloscope
&
Analysis
Figure 3: Measurement setup for measuring the MIMO spe-
cific impulse responses.
measured spectrum of the 1576 nm Fabry-Perot laser
with the typical modal structure.
1565 1570 1575 1580 1585
0
10
20
30
40
Operating Wavelength (innm)
Power (innW)
Figure 4: Spectrum of used Fabry-Perot Laser (resolution
bandwidth (RBW) of optical spectrum analyzer 0,07 nm).
For generating a MIMO system, different sources
of light have to be launched into the multimode fi-
bre. For the measurement campaign the laser light
will be launched through a single mode waveguide
OPTICS2013-InternationalConferenceonOpticalCommunicationSystems
392
into the core of a multimode waveguide. For the
(2×2) MIMO System two different sources of light
are needed. This part is realized by the first coupler
component using a splicer. In a splicer the end of
the transmitter waveguide and the beginning of the
transmission path are clamped together where they
are aligned exactly to each other (Fig. 5). By using the
center launch condition only the fundamental mode is
stimulated, represented by the signal u
s1
(t) in Fig. 1.
The signal u
s2
(t) in Fig. 1 represents the offset launch
condition for activating higher order mode groups.
For the measurements an eccentricity of 10µ m was
chosen. As a transmission channel a graded-index fi-
bre of 1,4 km length was chosen. At the receiver side,
Figure 5: Transmitter side configuration with center and
offset light launch condition.
for separating the different optical channels, different
spatial filters (i. e, the spot filter with a diameter of
r = 15µm for low order mode groups and the cor-
responding ring filter for higher order mode groups)
are used (Fig. 6). These spatial filters have been pro-
duced by depositing a metal layer at fibre end-faces
and subsequent ion milling (Pankow et al., 2011; Aust
et al., 2012). To determine the appropriate impulse re-
sponse for the respective channel, the particular trans-
mitter/receiver combination has to be chosen.
Figure 6: Receiver side filter configuration for separating
the different channels.
Fig. 7 highlights the electrical impulse for measur-
ing the MIMO-specific impulse responses. The pulses
are chosen in a way that the same optical power is
coupled into the multimode fibre core. Theoretically,
an impulse like a dirac delta pulse has to be chosen in
order to measure the channel impulse response unaf-
fectedly from the input impulse. However, in this case
the optical power is no longer sufficient to make the
modal structure measurable. Thus, the input impulses
shown in Fig. 7 are a good compromise to an impulse
like a dirac delta impulse at a reasonable amount of
coupled transmit power. The MIMO-specific impulse
responses are obtained after deconvolution with the
measured impulse responses.
0 0.1 0.2 0.3 0.4 0.5
0
5
10
15
20
25
30
t (inns)
u
s
(t) (inmV)
λ = 1326 nm
λ = 1576 nm
Figure 7: Input impulse for calculating the MIMO-specific
impulse responses at different operating wavelength.
4 SIGNAL THEORETIC SYSTEM
MODEL
The limiting factor in transmitting high speed data
over single input single output (SISO) multimode
fibers is modal and chromatic dispersion. In order to
be able to study the effect of modal and chromatic dis-
persion especially in MIMO communication, a sim-
plified SISO system model is developed, which takes
the modal as well as the chromatic dispersion of a
multimode fibre into account. Thereby the individual
mode groups, which propagate along the fibre with
different speed, are modeled as a Gaussian impulse
sequence as highlighted in Fig. 8. This sequence is
described mathematically as
g(t) =
q1
=0
a
δ(t τ
) (1)
by taking q dominant mode groups into account
which propagate along the fibre. The delay time of
each mode group is described τ
and the mode group
dependent weighting factor by a
.
Since the modal as well as the chromatic disper-
sion are independent from each other, the gaussian
impulse sequence can be decomposed into two parts:
a weighted dirac delta impulse response g
m
(t) for the
DispersionAnalysiswithinaMeasured1,4kmMIMOMultimodeChannel
393
t
g(t)
τ
0
τ
1
τ
2
τ
3
a
0
a
3
a
2
a
1
Figure 8: Approximated impulse responses.
description of the modal dispersion (Fig. 9) and a
common gaussian part g
c
(t) for the description of the
chromatic dispersion (Fig. 10). The resulting SISO
specific impulse response can be obtained by convo-
lution of g
m
(t) and g
c
(t) and results in:
g(t) = g
m
(t) g
c
(t) . (2)
Fig. 8 shows an exemplarily impulse response de-
t
g
m
(t)
τ
0
τ
1
τ
2
τ
3
g
m 0
g
m 3
g
m 2
g
m 1
Figure 9: Weighted Dirac delta impulse pulse response for
the description of the SISO specific mode dispersion.
composed into individual gaussian impulses. In this
work it is assumed that all mode groups are de-
scribed by Gaussian impulses with individual delay
and spread parameters. This sequence of weighted
Gaussian pulses can now be decomposed into a se-
quence weighted dirac impulses (Fig. 9), for the de-
scription of the modal dispersion, and into a Gaussian
pulse (Fig. 10), for the description of the chromatic
dispersion.
t
g
c
(t)
σ
c
b
b
e
Figure 10: Gaussian pulse to describe chromatic dispersion.
Fig. 9 and 10 also highlights the parameters of the
presented SISO system model. The parameter τ
de-
scribes the average delay time for the mode group ,
g
m
is the amplitude of th mode group and σ
c
de-
scribes the spread of each mode group, which is as-
sumed to be the same for all mode groups.
4.1 Modal Dispersion
When launching light into the fibre, different mode
groups will be activated which propagate along the
fibre with different speed and different attenuation.
This effect can be described by a sum of weighted
dirac delta impulses as shown in Fig. 9. Taking the q
dominant mode groups into account, the mode disper-
sion is described by the following impulse response
g
m
(t) =
q1
=0
g
m
δ(t τ
) (3)
with the parameter τ
as the delay time and the param-
eter g
m
as the weighting coefficient of the -th mode
group.
The amount of modal dispersion included in the
measured impulse response can now be described ac-
cording to wireless transmission channels by a delay
spread parameter σ
m
(P¨atzold, 2002). The parame-
ter σ
m
describes the spread of the whole impulse re-
sponse and can be used as a reference value for the
modal dispersion. The delay spread is given by:
σ
m
=
v
u
u
t
1
A
q1
=0
(τ
g
m
)
2
(
t
m
)
2
. (4)
Therein, the average delay of all modal groups
(i.e.t
m
) results in
t
m
=
1
A
q1
=0
τ
(g
m
)
2
(5)
with normalization parameter A =
q1
=0
(g
m
)
2
. With
this normalization parameter, the mode-group depen-
dent weighting coefficients fulfil the boundary condi-
tion
1
A
q1
=0
(g
m
)
2
= 1 . (6)
4.2 Chromatic Dispersion
Theoretically, in the absent of chromatic disper-
sion, each mode group can be described by a sin-
gle dirac delta impulse with a mode dependent de-
lay and weighting factor. However, as the operat-
ing wavelength increased, the modes within a mode
group travel with different speed and therefore the de-
lay time between the different modes within a mode
group become visible. This results in a broadening of
the beforehand analyzed individual mode group dirac
delta impulses. The parameter for this widening is the
spread parameter σ
c
. However, through the widening
of the mode group dependent dirac delta impulses, the
amplitude of impulse response is also weighted, i.e.,
OPTICS2013-InternationalConferenceonOpticalCommunicationSystems
394
the amplitude of impulse response a
and the modal
dependent weighting factors g
m
depend on the pa-
rameter σ
c
.
The chromatic dispersion of each mode group is
described by a normalized Gaussian impulse (Fig. 10)
and is given as
g
c
(t) =
1
σ
c
2π
e
t
2
2σ
2
c
(7)
The parameter b in Fig. 10 represents the normaliza-
tion factor of the Gaussian impulse and results in
b =
1
σ
c
2π
. (8)
4.3 Spread Parameters
For the SISO system model, modal and chromatic dis-
persion are described by their corresponding spread
parameters. Assuming that the individual mode
groups are described as Gaussian pulses
g(t) =
q1
=0
a
δ(t τ
) , (9)
the parameter a
is obtained by combining (3) and (7)
and results in
a
= g
m
1
σ
c
2π
. (10)
Taking this equation into account, the mode group de-
pendent weighting factor g
m
can be obtained as
g
m
= a
σ
c
2π (11)
by taking into account that the measured amplitude
a
contains the information about the width of the
gaussian pulse (i.e. chromatic dispersion) as well
as the mode-dependent weighting factor. Therefore,
the weighting factor g
m
can be determined with the
predetermined spread parameter σ
c
and the measured
amplitude a
, i.e.
g
m
= a
σ
c
2π . (12)
Since the weighting of each mode group is described
by the modal dispersion completely, the chromatic
dispersion corresponding spread parameter σ
c
can be
calculated by taking the measured amplitudes a
into
account.
4.4 MIMO System Model
In this work a (2 × 2 MIMO system model is inves-
tigated and the beforehand introduced signal theo-
retic SISO system model has now to be extended to
the MIMO system model. The corresponding elec-
trical MIMO system model is highlighted in Fig- 1
with the four existing transmission paths g
νµ
(t) (with
ν = 1, 2,... ,n
R
and µ = 1,2,.. .,n
T
), which will be
measured and analyzed separately. The number of
transmitters is given by the n
T
and the number of re-
ceivers by n
R
, respectively. Therefore, the impulse
response is given by
g
νµ
(t) = g
(νµ)
m
(t) g
(νµ)
c
(t) . (13)
According to equation (14) the modal dispersion can
be described by
g
(νµ)
m
(t) =
q1
=0
g
(νµ)
m
δ(t τ
(νµ)
) (14)
with the delay of th mode group τ
(νµ)
and the corre-
sponding weighting factors g
(νµ)
m
. The average delay
of the mode groups can be calculated by
t
(νµ)
m
=
1
A
(νµ)
q1
=0
τ
(νµ)
g
(νµ)
m
2
(15)
with the normalization factor A =
q1
=0
g
(νµ)
m
2
(P¨atzold, 2002). Finally, the modal dispersion results
in:
σ
(νµ)
m
=
v
u
u
t
1
A
(νµ)
q1
=0
τ
(νµ)
·g
(νµ)
m
2
t
(νµ)
m
2
.
(16)
Assuming that the same laser is used for measuring all
four impulse responses, the chromatic dispersion can
be considered to be same within all four transmission
path. Taking (7) into account, the following equation
holds
g
(νµ)
c
(t) = g
c
(t) . (17)
5 RESULTS
Within this paper, channel measurements within a 1,4
km (2 ×2) MIMO system are carried out. For the
investigated optical MIMO channel an eccentricity δ
of 10µm and a mask diameter r of 15µm were chosen
(Fig. 2). Fig. 11 shows the four impulse responses
for an operating wavelength of 1326 nm according to
Fig. 1. Compared to 1576 nm depicted in Fig. 12 the
influence of the chromatic dispersion is highly visible.
The impulse responses are obtained after deconvo-
lution with the input impulse depicted in Fig. 7. Fur-
thermore it is assumed that each optical input within
DispersionAnalysiswithinaMeasured1,4kmMIMOMultimodeChannel
395
0 1 2
0
1
2
0 1 2
0
1
2
0 1 2
0
0.2
0.4
0.6
0 1 2
0
0.2
0.4
0.6
t (inns)
t (inns)
t (inns)
t (inns)
T
s
g
1 1
(t)
T
s
g
1 2
(t)
T
s
g
2 1
(t)
T
s
g
2 2
(t)
Figure 11: Measured electrical MIMO impulse responses
with respect to the pulse frequency f
T
= 1/T
s
= 5,00 GHz
at 1326 nm operating wavelength.
0 1 2 3
0
0.1
0.2
0 1 2 3
0
0.1
0.2
0 1 2 3
0
0.05
0.1
0 1 2 3
0
0.05
0.1
t (inns)
t (inns)
t (inns)
t (inns)
T
s
g
1 1
(t)
T
s
g
1 2
(t)
T
s
g
2 1
(t)
T
s
g
2 2
(t)
Figure 12: Measured electrical MIMO impulse responses
with respect to the pulse frequency f
T
= 1/T
s
= 5,00 GHz
at 1576 nm operating wavelength.
the multimode fiber will be fed by a system with iden-
tical mean properties with respect to transmit filtering
and pulse frequency f
T
= 1/T
s
. For numerical assess-
ment within this paper, the pulse frequency is chosen
to be f
T
= 5,00 GHz Taking the measured impulse
Table 1: Parameters of the calculated chromatic dispersion.
λ (in nm) σ
c
in (ps)
1326 15
1576 129
responses, depicted in Fig. 11 and 12, into account,
the obtained parameters for the chromatic dispersion
are presented in Tab. 1. For the same operating wave-
length, the chromatic dispersion is assumed to be the
same for all propagation paths and all individualmode
groups. For comparison reason, the chromatic disper-
sion can be approximated by the following equation
τ
c
= D
c
δ
λ
ℓ . (18)
The impulse spread τ
c
can be described as the width
of each impulse or mode group, measured at a 50%
decay of the maximum amplitude and to be assumed
to be approximately twice as large as the calculated
spread parameter σ
c
. The dispersion parameter D
c
at the operating wavelength of 1576 nm can be as-
sumed to be 20 ps/(nmkm) (Senior, 2008). Together
with the length of the measured multimode fibre of
= 1,4 km and the spectral width δ
λ
(FWHW, Full
Width Half Maximum) of the laser diode of 10 nm,
an impulse spread τ
c
of approximately 280 ps is ob-
tained. With τ
c
2σ
c
the measured values of σ
c
can
be justified. At a operating wavelength of 1326 nm
the chromatic dispersion tends to be zero. At this par-
ticular operating wavelength no chromatic dispersion
appears. Therefore, at the operating wavelength of
1326 nm, the chromatic dispersion is not exactly zero,
but much lower compared with an operating wave-
length of 1576 nm.
The estimated parameters of the modal dispersion
are highlighted in Tab. 2.
Table 2: Parameters of the calculated modal dispersion.
λ (in nm) σ
c
(in ps)
- g
11
(t) g
12
(t) g
21
(t) g
22
(t)
1326 38 215 62 199
1576 159 424 185 353
Next to analyzed parameters of modal and chro-
matic dispersion, the introduced system model en-
ables a reconstruction of the MIMO specific impulses
responses by taking the estimated dispersion parame-
ters into account. In Fig. 13 and 14 the approximated
impulse response g
22
(t) is shown exemplarily at dif-
ferent operating wavelength by using the beforehand
introduced system model and the estimated parame-
ters of modal and chromatic dispersion. As shown by
Fig. 13 and 14 the approximated impulse responses
show a good correlation with the measured impulse
responses.
6 CONCLUSIONS
Based on channel measurements, in this work a signal
theoretic MIMO system model for estimating modal
and chromatic dispersion is introduced and parame-
ters for modal and chromatic dispersion for an 1,4 km
multimode MIMO channel are estimated.
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396
−0.5 0 0.5 1 1.5 2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
t (inns)
T
s
g
2 2
(t)
Measured
Calculated
Figure 13: Calculated and measured impulse response
g
22
(t) at 1326 nm operating wavelength.
−0.5 0 0.5 1 1.5 2 2.5 3
0
0.02
0.04
0.06
0.08
0.1
t (inns)
T
s
g
2 2
(t)
Measured
Calculated
Figure 14: Calculated and measured impulse response
g
22
(t) at 1326 nm operating wavelength.
ACKNOWLEDGEMENTS
The authors wish to thank their co-worker, Mr. Ralph
Bornitz, for supporting the measurement campaign.
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