Opt Quant Electron
DOI 10.1007/s11082-015-0164-8
Optical filter analyses for demultiplexing all-optical
OFDM transmission systems
J. Y. Sung1 • C. W. Hsu1 • H. Q. Su1
C. W. Chow1 • C. H. Yeh2
•
Received: 31 May 2014 / Accepted: 30 March 2015
Springer Science+Business Media New York 2015
Abstract Using a single optical filter to demultiplex the all-optical orthogonal frequencydivision multiplexing (OFDM) system was regarded as cost-effective and simple. Here, an
all-optical OFDM signal demultiplexer using sinc transfer function was analyzed. The
performance difference for using optical demultiplexers with different transfer functions
was also compared and discussed. Within 20 km transmission, the sinc optical filter providing orthogonality between neighbor optical subcarriers can improve the signal performance by reducing the inter-carrier interference. After 20 km transmission, the signal
performance degradation may mainly be dominated by dispersion for 10 Gb/s channel
capacity; hence the advantage of sinc filter becomes negligible. These analyses provide the
idea for how to choose the optical demultiplexer to integrate the whole optical fast Fourier
transform circuit and optical sampling circuit into a single filter. This can effectively
reduce the system cost and complexity.
Keywords All-opitcal Orthogonal frequency division multiplexing (OFDM) Optical
demultiplexer Optical filter
1 Introduction
Increasing demand of network capacity has made high spectral-efficiency (SE) transmission an important issue. Besides, expanding the transmission distance to reduce the system
cost is also desirable. Orthogonal frequency-division multiplexing (OFDM) technology can
provide both high SE and long transmission distance in fiber-optic communication (by
& C. H. Yeh
yeh1974@gmail.com; yehch@fcu.edu.tw
1
Department of Photonics and Institute of Electro-Optical Engineering, National Chiao Tung
University, Hsinchu 30010, Taiwan
2
Department of Photonics, Feng Chia University, Taichung 40724, Taiwan
123
J. Y. Sung et al.
reducing the chromatic dispersion (CD). Hence it could be a promising candidate for the
future optical communication networks (Armstrong 2009; Chen et al. 2013; Yeh et al.
2011). Recently, all-optical OFDM systems have been proposed (Yeh et al. 2011; Ellis and
Gunning 2005) as an approach to increase the carrier data rate much higher than the typical
optical OFDM system, which generates the OFDM signal through electronic devices. In
these all-optical OFDM systems, we can multiplex different optical orthogonal subcarriers
by specific setup of optical couplers, with each path set by proper time delay among the
subcarriers. Besides, several techniques have been proposed to demultiplex these alloptical OFDM signals at the receiver (Rx). Demultiplexing each optical orthogonal subcarrier with an optical Gaussian filter was proposed in Ref. Ellis and Gunning (2005). The
combination of an arrayed-waveguide-grating (AWG) and some optical samplers to demultiplex the all-optical OFDM signal was used in Takiguchi et al. (2010), Wang et al.
(2011), Rhee et al. (2011). The realization of fast Fourier transform (FFT)/inverse fast
Fourier transform (IFFT) circuit using optical couplers was also introduced in (Takiguchi
et al. 2010). All-optical OFDM FFT can also be achieved through a tree-topology of
Mach–Zehnder delay interferometers (MZDI) (Hillerkuss et al. 2011). Among these
schemes, the demultiplexing approach used in Ref. Ellis and Gunning (2005) is simple;
hence the cost and complexity of the system can be reduced. However, the selection of the
optical filter for all-optical OFDM demultiplexing is critical and it can highly affect the
signal quality of the demultiplexed signal. Typical optical filter with Gaussian or rectangular shape may cause serious inter-carrier interference (ICI). On the other hand, the
approaches used in Chow and Lin (2012), Takiguchi et al. (2010), Wang et al. (2011), Rhee
et al. (2011) seem to have better performance in expense of higher cost and system
complexity.
In this investigation, performance of all-optical OFDM demultiplexers having different
transfer functions is analyzed. Within 20 km transmission, the sinc optical filter providing
orthogonality between neighbor optical subcarriers can improve the signal performance by
reducing the ICI. After 20 km transmission, the signal performance degradation may
mainly be dominated by dispersion for 10 Gb/s channel capacity; hence the advantage of
sinc filter becomes negligible. These analyses provide the idea for how to choose the
optical demultiplexer to integrate the whole optical FFT circuit and optical sampling
circuit into a single filter. This can effectively reduce the system cost and complexity.
2 Theory and principles
An OFDM symbol is the summation of sampling the orthogonal frequency components,
which is
sðnÞ ¼
N 1
1X
nk
uk ej2p N ¼ IFFT fuk g;
N k¼0
ð1Þ
where N is the IFFT size. An all-optical OFDM signal is generated from the IFFT operation using the optical circuit. Assume all the deterministic orthogonal components of the
optical comb source originally have the same amplitude and phase; and the comb source is
modulated by the electrical signal with perfect rectangular shape. Then, a single all-optical
OFDM signal can be written as:
123
Optical filter analyses for demultiplexing all-optical OFDM…
EðtÞ ¼
N1 pffiffiffiffiffi
X
k
Pk ejuk ej2pðT þfc Þt ; t 2 ½0; T Þ;
ð2Þ
k¼0
where E is the electrical field of the optical signal, and T is the time interval of an OFDM
symbol. The number of combs of the optical comb source equals to N.
At the Rx, single optical filters are used to demultiplexing signal from different channels
to reduce the cost. The following filter response is taken into consideration for demultiplexing with ideally no ICI:
t
m
ej2pðT þfc Þt ; m 2 Z:
ð3Þ
hðtÞ ¼ rect
T
The output optical signal from the above filter is:
Z T=2 X
N 1 pffiffiffiffiffi
k
m
Eout ðtÞ ¼ EðtÞ hðtÞ ¼
Pk ejuk ej2pðT þfc Þs ej2pðT þfc ÞðtsÞ ds:
T=2 k¼0
ð4Þ
From the orthogonality, we have,
Z T=2 X
N1 pffiffiffiffiffi
pffiffiffiffiffi
k
m
Eout ð0Þ ¼
Pk ejuk ej2pðT þfc Þs ej2pðT þfc Þs ds ¼ Pk ejuk dmk T: ð5Þ
T=2 k¼0
Hence, it can be observed that the data on each optical orthogonal component are wellseparated from the all-optical OFDM signal without ICI. The filter transfer function is the
Fourier transform of h(t). Hence, we get the filters to be a set of sinc functions centered at
the frequencies of the optical OFDM subcarriers:
n
o
m
t
m
þ fc
:
ð6Þ
ej2pðT þfc Þt ¼ T sin c T f H ð f Þ ¼ FT rect
T
T
Other types of transfer functions may cause little interference but degrades the signal
performance mainly by distortion. This will be discussed in Sect. 3.3. Figure 1 shows one
typical all-optical OFDM Rx scheme using optical sampling and FFT circuit (Wang et al.
2011). At the Rx, the signal is first split into N paths. The optical signal is sampled in each
path. The time delay component is taken after the sampling circuit to shift the sampling
signal from each path into the same time point. The above process can be regarded as the
Fig. 1 One typical all-optical OFDM Rx scheme with optical FFT circuit
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J. Y. Sung et al.
optical serial-to-parallel circuit. The resultant signals are further launched into the optical
FFT circuit. Each output port of the optical FFT circuit is the specific signal modulating the
specific OFDM subcarrier. Each modulating signal is detected after an optical band-pass
filter (OBF) and photo-diode (PD). The optical circuits can also be arranged moderately in
different order. As seen in Fig. 1, this demultiplexing architecture needs a lot of optical
components to achieve the FFT operation, and it could be highly affected by environment
fluctuation.
Figure 2 shows the all-optical OFDM Rx with single OBF. At the Rx, the signal is split
into N paths similar to that in Fig. 1. However, the complex sampling circuit, optical FFT
circuit, and optical band-pass filter at each path are replaced by a single optical filter.
Hence, this system could be much simpler and cost-effective.
3 Simulations and discussions
Here, we numerically analyze filters with different transfer functions to demultiplexing alloptical OFDM signal. VPI Transmission Maker 7.5 and MATLAB 2008a are used for the
simulation.
3.1 Comparing the performance between filters with different transfer
functions
The signal performance using filters with different transfer functions was compared. sinc
filter is an ideal filter providing no ICI and distortion. Figure 3 shows the simulation setup.
A laser source with linewidth of 10 MHz was used. The laser was first modulated by a
10 GHz clock via a phase modulator (PM). More than 13 optical combs with signal-tonoise ratio (SNR) higher than 20 dB were obtained. Hence, 130 Gb/s data rate could be
achieved in this all-optical OFDM system when the data rate of each channel was 10 Gb/s.
For simplicity, only the interference between neighbor channels was considered in the
simulation. A Mach–Zehnder interferometer (MZI) with free spectral range (FSR) of
20 GHz was used to separate the odd and even channel subcarriers into different paths. The
optical subcarriers on each path were modulated by a 10 Gb/s on–off keying (OOK) signal.
The even and odd channels were then combined through an optical coupler (OC) and
were launched into a standard single mode fiber (SSMF), with dispersion parameter of
fc=f1
Fig. 2 Proposed all-optical
OFDM Rx scheme with optical
sinc filter
Sinc
Filter
PD
fc=f3
Sinc
Filter
PD
……
Splitter
PD
……
Tx
All-optical OFDM
Sinc
Filter
fc=f2
fc=fN
Sinc
Filter
123
PD
Optical filter analyses for demultiplexing all-optical OFDM…
10 Gb/s, OOK
MZM
Laser
PM
MZI
MZM
10 GHz
Optical
Filter
PD
Bessel
Filter
Scope/
BERT
10 Gb/s, OOK
Fig. 3 Simulation setup for comparing performance differences among different types of optical filters
16 ps/nm km. The length of the SSMF was swept from 0 to 100 km. At the Rx, different
types of all-optical demultiplexing filters were analyzed. Their shapes were: Gaussian,
Bessel, rectangular, and sinc. The best bandwidth of each filter shape was chosen depending on the lowest bit error rate (BER) achieved. The bandwidth was swept from 5 to
20 GHz with sweeping resolution 0.5 GHz for different SSMF lengths. The best bandwidth
was 8.5, 9, 11.5 GHz for the Gaussian, Bessel and rectangular filters, respectively. Here,
the bandwidth for Gaussian and Bessel filters were defined as the 3 dB bandwidth, while
the bandwidth of the rectangular filter was the whole pass-band. Before the PD, an optical
amplifier was used to maintain the input power in the comparison. After the PD, a 4-th
order electrical Bessel filter was used.
Figure 4a shows the BER for each type of all-optical OFDM demultiplexing filter at
different SSMF lengths. Figure 4b–e show the back-to-back (B2B) eye diagrams after
different demultiplexing filters set at the best bandwidths (8.5, 9, 11.5 GHz for the
Gaussian, Bessel and rectangular filters, respectively). As shown in Fig. 4a, the sinc filter
works much better than the other types of demultiplexing filters at transmission distances
within 20 km. This can be explained by the theory described in Sect. 2, which indicates
that the sinc filter ideally demultiplex an all-optical OFDM signal with no ICI (the interference among neighbor channels). It is also worth mentioning that the signal BER for
using sinc filter is still observably high, this may be attributed to mainly three factors.
Firstly, the model described in Sect. 2 assumed the optical field to be totally deterministic,
which is impossible for practical communication systems. In our simulation, laser linewidth of 10 MHz was used as practical cases. Secondly, the electronic modulating signal
was not perfectly rectangular-shaped owing to the limited speed of the electronic devices.
Hence, the orthogonality between each subcarrier was destroyed. Thirdly, the electric
beating noise cannot be completely filtered using a 4-th order Bessel electrical filter.
After 20 km SSMF transmission, the merit of using a sinc demultiplexing filter became
insignificant. This may come from other degradation mechanisms after fiber transmission,
which will be discussed in the Sect. 3.2. Moreover, Because Gaussian and Bessel filters
have more similar shape in their transfer function to the sinc function, they work better for
demultiplexing all-optical OFDM signal than that rectangular filters. This will be further
discussed in Sect. 3.3.
Here, we want to emphasize the fact more than one phase response can be found for a
specific power response. This means that even if we fix the power response to be sinc,
Gaussian, or Bessel, we may find more than one phase response for the filter depending on
the design process. Hence, while we want to include the phase response into the filter
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J. Y. Sung et al.
(a)
0
0
-10
-2
log(BER)
log(BER)
Fig. 4 a The BER-distance plot
of using different optical
demultiplexing filters. The B2B
all-optical OFDM demultiplexed
eye diagrams using, b Gaussian
filter, c Bessel filter,
d rectangular filter, and e sinc
filter
-20
-4
-6
Sinc
Bessel
Gaussian
Rectangular
-8
-10
0
20
[km]
60
80
100
Sinc
Bessel
Gaussian
Rectangular
-30
-40
40
0
20
40
60
80
100
[km]
(b)
(c)
Bessel
Gaussian
(d)
(e)
Rectangular
Sinc
performance, it is difficult to find a justifiable reference for the phase response. Under this
consideration, the phase part of the de-multiplexer is not considered here for providing a
more fair comparison and analyses.
3.2 Characterization of the all-optical OFDM transmission mechanisms
We observe from Fig. 4a that the sinc demultiplexing filter did not outperform other types
of filters as expected when the transmission distance[20 km. Besides, we can observe that
the BER did not strictly degrade with the increase of transmission distance. At the
transmission around 50–60 km, there is merely slight decrease in BER. To explain why the
sinc filter did not work better after 20 km transmission, we may first analyze the relations
123
Optical filter analyses for demultiplexing all-optical OFDM…
between signal performance degradation and its dominating mechanisms. Here, we
categorized four mechanisms for degrading signal performance of an all-optical OFDM
system: the interference among neighbor channels, signal dispersion of each channel,
signal SNR, and the beating noise coming from non-band-limited signal. In Sect. 2 and 3.1,
we have explained and demonstrated how the sinc filter can eliminate the interference
among channels; hence, we will exclude this reason for the following analyses. Single
optical channel is therefore considered for the following simulation and analyses. Figure 5
shows the simulation setup of a single optical baseband transmission system. We emulated
this system as one perfect channel of the all-optical OFDM system with no ICI. In the
analysis, the SSMF attenuation coefficient and the chromatic dispersion would be switched-off in turn. Two different electrical filters were introduced in the system. One electrical filter (rectangular-shaped) was added prior to the MZM, making the modulating
electric signal to be band-limited or not. Another electrical filter was a 4-th order Bessel
filter added after the PD. If the modulating electric signal was pre-filtered to be bandlimited; then the beating noise only generated in the baseband, and could not be filtered.
The 4-th order Bessel filter at the Rx could decrease the noise generating from shot noise,
out-of-band beating noise (if the modulating electric signal was not band-limited), and
thermal noise. As shown in Fig. 5, a CW signal was modulated via the MZM by a 10 Gb/s
electrical signal and was launched into the SSMF. After the fiber transmission, an optical
rectangular filter was used to reduce the beating noise as well as avoiding changing the
signal spectrum and shape. It was also used to emulate the reduction of noise other than the
beating noise of the all-optical OFDM signal. Different bandwidths of the optical filter
were used to see how the noise can be reduced by the optical filter.
Figure 6a–d show the relationship between the BER and the transmission distances at
different bandwidths of the optical rectangular filter with and without the two electrical
filters at the Tx and Rx respectively. First, the attenuation of the SSMF was set zero, and
we only analyzed the chromatic dispersion effect. As shown in Fig. 6a–d, high signal
distortion occurred when the bandwidth of the optical filter was smaller than the optical
signal bandwidth (\30 GHz). Hence, we can conclude that the noise reduction by using an
optical filter is negligible, and the optical filter is mainly contributed for the channel
demultiplexing. The influence of the optical filter will thus be neglected for the following
analyses, where we will focus on only the curves with optical filter bandwidth[30 GHz. In
Fig. 6a, b, by using an electrical filter to band-limit the generated optical signal, the BER
degraded strictly with increasing transmission distance. These BER curves behaved similar
as typical dispersion dominated distortion. It can be concluded that the dispersion is less
significant for the local minimum phenomenon of Fig. 4a. When the electrical filter was
removed from the Tx, the optical signal was not band-limited. From Fig. 6c, d, we can see
that the BER was not strictly increased with the transmission distance. In Fig. 6c, there is a
slight decrease in BER at the transmission around 60–70 km, which is similar to the curve
in Fig. 4a. The 10 km offset of the local minimum of Fig. 4a may be aroused from the
Laser
MZM
Optical
Filter
PD
Bessel
Filter
Scope/
BERT
Rectangular
Filter
10 Gb/s, OOK
Fig. 5 The simulation setup of a single optical baseband transmission system
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J. Y. Sung et al.
(a)
0
-20
log(BER)
Fig. 6 Electrical filter (a) used
at both Tx and Rx, b used only at
Tx, c used only at Rx, d not used
at Tx and Rx
-40
5 GHz
10 GHz
15 GHz
20 GHz
>=25 GHz
-60
-80
-100
0
(b)
20
40
[km]
60
80
100
0
log(BER)
-20
-40
5 GHz
10 GHz
15 GHz
20 GHz
25 GHz
>=30 GHz
-60
-80
-100
0
(c)
20
40
[km]
60
80
100
60
5 GHz
10 GHz
15 GHz
20 GHz
25 GHz
30 GHz
>=35 GHz
80
100
0
log(BER)
-20
-40
-60
-80
-100
0
(d)
20
40
[km]
0
log(BER)
-20
5 GHz
10 GHz
15 GHz
20 GHz
25 GHz
30 GHz
>=35 GHz
-40
-60
-80
-100
0
20
40
[km]
60
80
100
imperfection of orthogonality and more serious dispersion and beating condition. From
Fig. 6a–c, it was also concluded that the sharp increase in BER at short distance was
mainly caused by dispersion. If no filters were used for Tx and Rx as in Fig. 6d, the beating
noise, shot noise, and the thermal were detected and made the BER poor at shorter
transmission distance.
123
Optical filter analyses for demultiplexing all-optical OFDM…
0
Fig. 7 The electrical filter was
used only at the Rx end with no
dispersion in the fiber
log(BER)
-20
-40
-60
5 GHz
10 GHz
>15 GHz
-80
-100
0
20
40
[km]
60
80
100
Figure 7 shows the relationship between the BER and the transmission distance at
different optical rectangular filter bandwidths. Here, the dispersion of the SSMF was set
zero, and we only analyzed the attenuation effect. The BER curves were nearly unaffected
by the fiber attenuation. Hence, we can observe that the SNR decreasing owing to the
SSMF attenuation was not important if enough power was given. By comparing Figs. 6
and 7, we can conclude that the BER curve of the sinc demultiplexing filter shown in
Fig. 4a was mainly aroused from both the ICI and beating noise induced by band-unlimited
electrical signal. The decrease in BER at long transmission was mainly resulted from the
dispersion.
3.3 Practical embodiment of sinc filter for all-optical OFDM system
Waveshaper from Finisar is a liquid crystal on silicon (LCoS) based device which can
embody an optical filter with nearly arbitrary shape. Within the operation range of
wavelengths, an input light is first separate into different components of different wavelengths; then each wavelength is process by the liquid crystal. By using waveshaper, any
frequency response with finite bandwidth can be approximately realized. sinc filter is not
physically obtainable in practical condition since infinitely wide bandwidth should be
accurately controlled to guarantee its rectangular-shaped impulse response. To realize a
quasi-sinc optical filter, we can consider clipping the sinc response with a rectangular
window. Hence, the quasi-sinc filter can be realized by waveshaper. Since the side-lobe
away from the central peak of the sinc response will gradually degrade; and hence will
cause little contribution for the final output signal, it is believed that the windowing
technique will work well for generating the quasi-sinc filter. Figure 8a shows the signal
performance under using different quasi-sinc filters. Each quasi-sinc filter is generated by
further filtering the sinc filter with rectangular windows. ‘‘Win-k’’ symbolized different
bandwidth of the window. While k = 1, the window bandwidth includes the first null of
the sinc response, and while k = 2, the window bandwidth includes the second null of the
sinc response. It can be seen that, while the window bandwidth is larger than the bandwidth
occupied within the second null of the sinc filter, the signal performance will degrade little.
Hence, we may use some techniques similar to waveshaper for building the quasi-sinc
filter.
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J. Y. Sung et al.
(a)
24
sinc
sinc (Win1)
sinc (Win2)
sinc (Win3)
22
20
18
Q [dB]
Fig. 8 a Signal performance for
sinc transfer function using
different window sizes. b The
difference in transfer functions of
different filters. c The B2B BERpower relation
16
14
12
10
8
6
0
20
40
60
80
100
Distance [km]
(b)
0.8
Power [a.u.]
sinc (Win2)
sinc (Win1)
Gaussian
Bessel
1
0.6
(b)
0.4
0.2
0
-0.2
-20
-15
-10
-5
0
5
10
15
20
Offset Frequency [GHz]
(c) -3
sinc
Gaussian
Bessel
-4
-5
log(BER)
-6
-7
-8
-9
-10
-11
-12
-32
-30
-28
-26
-24
-22
-20
-18
-16
Received Power [dBm]
It is also worth mentioning that the Gaussian and Bessel filters will provide similar
ability for demultiplexing the all-optical OFDM signal because of their similarity in response shape. Both Gaussian and Bessel filter can be viewed as a two-stage filter, which an
adequately shaped filter is cascaded after the sinc filter to realize the Gaussian or Bessel
shaped filter response. Hence, the performance degradation may mainly come from the
123
Optical filter analyses for demultiplexing all-optical OFDM…
signal distortion of the signal rather than interference among neighbor channels. Figure 8c
shows the relation between the BER and the receiving power for different demultiplexing
using different filters. It can be seen that the distortion and low channel interference caused
by using Gaussian and Bessel filters will result in more than 3 dB power penalty. The
Bessel has worse performance may mainly come from more noise for its wider bandwidth.
The main contribution of this paper is now the analyses of signal performance demultiplexed by different filters under different scenarios. The sinc-shaped filter is seen to
have the most ideal transfer function to de-multiplex signals suffered from merely ICI;
hence, it is used as a reference for the comparison, which provides the upper bound of the
signal performance. Moreover, The ICI is not the most critical issue while the transmission
distance is long since the dispersion will be the dominant factor affecting the signal
performance. For dispersion dominant signal degradation, we can use typical Gaussian and
Bessel filters as a replacement of the sinc-shaped filter since the can provide similar
performance. Hence, the cost can be further reduced.
Here, we also want to clarify that it is believed that even lower bandwidth can be
achieved by the similar techniques use by Waveshaper. By analyzing the technique used by
Waveshaper, we can deduce that if we can get beam with narrower width and well control
of the liquid crystal, the minimum bandwidth supported by the device can be further
reduced. But indeed this will result in much more money and is temporarily not commercial. This did not contradict with what we have done in the manuscript since it is more
on the analyses as explained above.
4 Conclusion
Signal performance after demultiplexer with different transfer functions was analyzed. We
have theoretically verified that ideally the sinc demultiplexing filter can effectively demultiplex the all-optical OFDM signal without ICI. Different choices of the optical filters
to demultiplex the all-optical OFDM channel were compared. From the analysis results,
the sinc demultiplexing filter worked well in dispersion non-dominated system. After
20 km SSMF transmission, the merit of using a sinc demultiplexing filter was becoming
less.
Acknowledgments This work was supported by Ministry of Science and Technology, Taiwan ROC,
MOST-103-2218-E-035-011-MY3 and MOST-103-2221-E-009-030-MY3.
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