200G System with PDM-16QAM :
Performance Evaluation and Trade-offs
Siddharth J. Varughese, Varughese Mathew, Smaranika Swain, Deepa Venkitesh∗ and R. David Koilpillai
Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai 60036 India.
∗ email: [email protected]
Abstract—Realization of increased spectral efficiency with polarization multiplexing and advanced modulation formats require
performance optimization at the transmitter and the receiver,
considering the laser linewidth, chromatic dispersion, polarization
mode dispersion and nonlinear effects. This paper addresses the
performance optimization of a 200G system using PDM-16QAM.
DSP algorithms for the mitigation of the phase noise of the
laser, drifts in modulator bias, frequency drifts of the transmitter
and receiver lasers are discussed in detail. Frequency domain
and a time domain approach is discussed to compensate for
the impairments introduced due to chromatic dispersion and
polarisation mode dispersion. The performance of a complete
200G system in the presence of different impairments and the
associated trade-offs are discussed in detail.
I.
I NTRODUCTION
With the increased number of devices connected to the
Internet around the globe and the use of high bandwidth
applications, there has been an increase in the demand for large
capacity optical transmission systems and networks. Owing
to its ability to operate at the limits of receiver sensitivity,
coherent systems have been proposed as the way forward
to achieve large capacity. Through coherent detection and
polarization diversity schemes, it is possible to extract the
optical parameters namely amplitude, phase, frequency and polarization in the electrical domain. Using all these parameters,
it is possible to achieve high spectral efficiencies in optical
communication systems. The advances of high speed Analog to
Digital Converters (ADC) and Digital Signal Processors (DSP)
have also made it possible to use powerful DSP techniques to
mitigate channel impairments and achieve high baud rates.
Leveraging the above-mentioned advantages, the current
50 GHz ITU-T grids are being upgraded to 100 G services
[1]. A bit rate of 100 Gbps is achieved through polarization
multiplexing data at 25 Gbaud, modulated in the QPSK format.
In order to further increase the data rates, many techniques
have been proposed, studied and demonstrated [2]–[5] with a
potential to scale to transmission at Tbps. With the existing
50 GHz grid, higher baud rates can have significant filtering
penalty because of the corresponding expanded signal spectrum. The use of Quadrature Amplitude Modulation(QAM)
with a restricted baud rate is an alternate option that is
being explored. Polarization Division Multiplexing of 16 QAM
(PDM-16QAM) is a suitable choice to achieve 200 Gbps with
a baud rate of 25 Gbaud owing to its relatively low OSNR and
spectral requirements [6], [7].
When such advanced modulation formats are implemented,
the impairments posed by the various components, the fiber
channel and their corresponding penalties are more severe and
need to be mitigated. The phase noise of the laser is a fundamental impairment, whose effects become more critical when
the number of phase levels in signaling increases. The chromatic dispersion (CD), polarization mode dispersion (PMD)
and the different nonlinearities in the fiber pose additional
impairments. Thus the performance of a 200 G system needs to
be evaluated, considering the effects of all these impairments.
In this paper, we discuss the challenges in implementing a
PDM-16QAM optical communication system in real time. We
consider the different mechanisms that deteriorate the system
performance and analyze the corresponding trade-offs. The
structure of the paper is as follows. In Section II we discuss the
impact of the non-idealities in the different components at the
transmitter and receiver ends. We evaluate the impact of the
laser linewidth, followed by the influence of drift in modulator
bias and further discuss the effects of detuning between the
transmitting and receiving laser. In Section III we discuss the
effects of the fiber channel focusing primarily on Chromatic
Dispersion (CD) and Polarisation Mode Dispersion (PMD).
In Section IV, we study the performance of a PDM-16QAM
system for distances upto 1000 km under the impairments
mentioned above.
II.
T RADE - OFFS AT T RANSMITTER AND R ECEIVER
A. Impact of Laser Linewidth
Ideally, in any communication system, the transmitting
carrier should operate at a single frequency. However any
practical laser source will have a finite linewidth and this
introduces undesired phase perturbations in the signal caused
by the fluctuations in the frequency of operation. The laser
phase noise (θ(k)) is usually modeled as a random-walk
process which can be expressed as [8]
θ(k) =
k
X
φi ,
(1)
i=0
where φi ’s are independent, identically distributed Gaussian
random variables with zero mean and variance (σ 2 ) given by
σ 2 = 2π∆f Ts ,
(2)
where ∆f is the laser linewidth and Ts is the symbol period.
Phase noise can prove to be very detrimental to the BER
performance of the system when implementing higher order
modulation (HOM) formats, such as QAM that are very
sensitive to the phase of the received symbol. In this paper,
we present the performance of a PDM-16QAM system under
the influence of different laser linewidths.
Fig. 1.
Block Diagram representing a PDM-16QAM system
Fig. 1 shows the block diagram of a typical coherent optical
communication system used for our simulations. The laser
has a center wavelength of 1550 nm, at 2 mW power and
has an Optical Signal to Noise Ratio (OSNR) of 60 dB. The
linewidth of this laser is varied to study its impact on the
system performance. A Polarization Beam Splitter (PBS), with
an extinction of 18 dB, is used to generate the two orthogonal
polarizations for polarization multiplexing. All QAM optical
systems convert the electrical signals to optical signals using
an IQ modulator that consists of two Mach-Zender Modulators
(MZM) and 90◦ phase- shifter. Each of these MZMs needs to
be appropriately biased so that the optical output corresponds
exactly to the electrical input. The output field (Eout ) of a
MZM in push-pull configuration is given by [9]
π(v(t) − Vnull )
Eout = Ein sin
,
(3)
2Vπ
where Ein is the optical input field to the MZM, v(t) is
the modulating signal, Vnull is the voltage required to obtain
Eout = 0 and Vπ is the additional voltage required to get the
maximum optical output.
For QAM signaling, the modulating signal is of the form
[10]
v(t) = Vbias + vs (t),
(4)
with Vbias = Vnull to ensure that the various levels of the
electrical signal vs (t) are converted to the corresponding levels
in the optical signal. The modulator is modeled to have a
finite extinction of 30 dB. Two unique deBruijn sequences
are generated for transmission along each polarization. The
amplitude of each level has been adjusted to compensate for
the non-linear response of the IQ modulator.
The fiber has an attenuation of 0.2 dB/km and a length of
80 km. The fiber is followed by an EDFA to compensate for
the attenuation introduced by the fiber. The effects of CD and
PMD of the fiber are not considered for the simulation results
presented in this section. The signal is then passed through
a optical bandpass filter of bandwidth 62.5 GHz (2.5 times
symbol rate) and fed into the polarization diversity hybrid
receiver. The electrical output signal, which is passed through
a fifth-order Bessel function with a 3-dB bandwidth of 17.5
GHz (0.7 times symbol rate), is captured by an ADC, whose
sampling rate is ten times the symbol rate, and passed to the
DSP block.
Within the DSP block, the signal is down-sampled and
passed to the phase- recovery block, to mitigate the distortions
caused by the finite linewidth of the laser. There are many techniques to compensate for laser phase noise in a received signal
[11]–[13]. In our simulations, we use a Decision DirectedLeast Mean Square (DD-LMS) technique to compensate for
the phase noise [14]. The length of training sequence used is
15 symbols for all the simulations presented in this paper.
Fig. 2. Performance of a PDM-16QAM system for different laser linewidths
Fig. 2 shows BER as a function of OSNR for different
laser linewidths. The figure also shows the threshold for
Forward Error Correction (FEC) Codes for reference [15]. As
expected, increasing linewidth severely degrades the system
performance. Even with a fine linewidth of 500 KHz, the
OSNR penalty is almost 2 dB. Note that the linewidth of
the transmitter and the local oscillator are identical for our
simulations, as is the case for a real-time implementation.
As HOM formats such as 64QAM are used, the maximum
tolerable linewidth will decrease and fine linewidth lasers will
be needed for optimum performance. As can be seen from eqn.
(2), the effect of phase noise can be reduced by increasing the
symbol rate as they are directly proportional to each other. The
symbol rate is finally decided by the available bandwidth and
the available electronics.
B. Influence of drifts in Modulator Bias
As discussed in Section II A, for QAM signalling, the IQ
modulator is biased at the null in order to achieve maximum
depth of modulation. However, in a practical implementation
it is very difficult to maintain Vbias at Vnull because Vnull is
dependent on temperature and hence keeps drifting; albeit at
a slow rate (hundreds of µs) [16]. Fluctuations in Vnull will
cause non-uniform positioning of the constellation points, and
a consequent error.
In our simulation, we evaluate how the drifts in Vnull can
degrade the system performance for a PDM-16QAM system.
We use the same simulation set-up shown in Fig. 1. All
parameters of the simulation are identical to the previous
section except for the linewidth of the laser, which is fixed at 50
KHz. Drift in null voltage leads to a change in bias conditions;
hence the effect of these drifts is studied by changing the bias
voltage of the modulator.
C. Impact of drift between the wavelengths of the Transmitting
Laser and the Local Oscillator
In a coherent receiver, the received signal is allowed to
mix with a local oscillator. In a homodyne system, the local
oscillator should have the same operating wavelength as that of
the transmitting laser. In practice, no two lasers will oscillate
at identical frequencies, unless they are frequency locked.
There will always be a finite difference between the operating
wavelength of the transmitter and the local oscillator, which
inturn drifts with time. The timescales of these drifts are
however much larger when compared to the symbol duration.
Such an offset adds a phase to the received symbol, given by
φn = 2πfd nTs ,
(5)
th
where φn is the phase added to the n symbol, fd is the detuning (offset) between the local oscillator and the transmitting
laser and Ts is the symbol period.
(a) No drift
Fig. 3.
(b) 0.15Vπ drift
Received constellation for various drifts in Vnull .
Fig. 3 shows the received constellation corresponding to
the case where (a) there is no drift and (b) a drift of 0.15Vπ in
Vnull . These constellations were obtained after correcting for
phase noise. From this figure it is seen that the constellation
points get skewed when there is a drift in Vnull . Since the
standard 16QAM decision boundaries are used at the receiver,
there will be increased probability of error in the demodulated
symbols leading to a BER performance degradation in the
system.
Fig. 4.
OSNR penalty for drifts in Vnull voltage
Fig. 4 shows the OSNR penalty in order to maintain a
BER of 10−3 . These results show that drifts in Vnull can
prove to be detrimental to the system. Even a drift of 0.1Vπ
can give rise to an OSNR penalty as large as 3 dB. The
effect of such drifts turn out to be more severe for HOM
formats for which the decision boundaries are more stringent.
A robust feedback control of bias voltage, is therefore, a prerequisite for a practical implementation in order to minimize
the performance penalty.
Fig. 5. BER performance as a function of frequency detuning between the
transmitter and local oscillator for different linewidths of the laser
In our simulation, we evaluate the effect of detuning on
the system performance. We use the setup given in Fig. 1
with Vbias set to Vnull . The DSP block in this simulation
uses a fourth power-periodogram technique to compensate for
frequency detuning [17].
Fig. 6. OSNR penalty as function of frequency detuning for a BER of 10−3
Fig. 5 shows the BER performance for different values
of frequency detuning estimated for different laser linewidths.
The OSNR is kept fixed at 19 dB. We see that the periodogram
technique is effective and can accurately predict the detuning
and compensate for it. Fig. 6 shows the OSNR penalty to
maintain the BER at 10−3 . The OSNR penalty for 5 GHz
of detuning is less than 0.5 dB for 50 KHz laser linewidth.
However this technique is limited by the sampling rate as
it involves a Fourier transform and aliasing can affect the
compensation algorithm. Thus, this technique can accurately
be used to predict and compensate a detuning |fd | < F8s , where
Fs is the sampling rate [18].
III.
T RADE - OFFS IN FIBER CHANNEL
A. Chromatic Dispersion and Polarization Mode Dispersion
Chromatic Dispersion (CD) is the phenomenon in which
the different spectral components of the pulse travel at different
group velocities [19]. This results in broadening in time
domain and a consequent inter-symbol interference. The extent
of broadening is decided by the accumulated dispersion in
the fiber and the baud-rate. In a polarization- multiplexed
system, data modulated in two orthogonal polarizations are
propagated through the fiber. The absence of perfect cylindrical
symmetry leads to different effective refractive indices for
the two orthogonal polarizations in the fiber - referred to
as Principal States of Polarization (PSP). This leads to a
Differential Group Delay (DGD) between the two PSPs. In
addition, due to the environmental fluctuations, there is a
random rotation of the PSPs in a fiber leading to a statistically
varying DGD between the two polarizations. The RMS time
average of DGD is referred to as Polarization Mode Dispersion
(PMD). A rotation of the PSP by an angle of π/4 from
the launched polarization is considered to be the worst case
scenario [20].
CD and PMD are the two major linear channel impairments
that limit the performance of a high speed optical fiber communication system. Traditionally, Dispersion Compensating
Fibers (DCF) were used to compensate for CD in the optical
domain. However DCFs introduce additional losses, therefore
requiring additional optical amplifiers that increase noise and
the cost of the system. The use of coherent optical receiver
enables us to compensate for CD and PMD in the electrical
domain by using suitable DSP algorithms.
The effect of CD on a pulse with envelope A(z, t) can be
written as [21]
∂A(z, t)
Dλ2 ∂ 2 A(z, t)
=j
,
(6)
∂z
4πc
∂t2
where D is the dispersion coefficient of the fiber measured in
ps/km-nm, λ is the carrier wavelength of the pulse, and c is
the speed of light in vacuum. Solving eqn. (6) in the frequency
domain, we get [21]
A(z, w) = A(0, w)e−
jDλ2 w2 z
4πc
.
where hij (t) represents the impulse response of the j th input
polarization on the ith output polarization. In particular the
frequency response H(ω) = F {h(t)} for first order PMD is
given by [20]
!
jωτ
cos θ − sin θ
e 2
0
cos θ
sin θ
H(ω) =
jωτ
sin θ
cos θ
− sin θ cos θ
0
e− 2
(11)
where τ is the DGD parameter and θ is the angle between the
launched polarization and the PSP of the fiber. In eqn. (11), θ
is considered as a constant to the first order. Random changes
in θ leads to higher order PMD. The above impairments can
be digitally equalized in the time domain or in the frequency
domain, as discussed in the next sub-sections.
The data impaired with CD and PMD is generated using
open source code Optilux [22]. It simulates the pulse propagation through the fiber by numerically solving the non-linear
Schrodinger equation (NLSE) by using the Split Step Fourier
method. Since the effects of CD and PMD are being analyzed,
the effect of linewidth of the laser is not considered for these
simulations. Dispersion
√ coefficient of 17 ps/km-nm and a DGD
coefficient of 0.1 ps/ km are assumed for the fiber.
B. Frequency Domain Equalization
We can compensate for CD and first order PMD in the
Frequency Domain Equalization (FDE) technique by assuming
the frequency response of the fiber to be [23]
T (ω) = H(ω)G(ω),
(12)
where H(ω) is given by eqn. (11) and G(ω) is given by eqn.
(8). The received signal in the time domain is transformed into
frequency domain through an FFT operation. The resulting
frequency domain signal is multiplied with the inverse of
T (ω) to equalize for the impairments. IFFT operation is then
performed to bring the signal back to time domain.
(7)
Thus, frequency domain transfer function G(z, w) can be
obtained from eqn. (7) as
G(z, w) = e−
jDλ2 w2 z
4πc
(8)
By taking an IFFT of eqn. (8), we can obtain the time domain
response of the fiber as
r
jπct2
c
g(z, t) =
e Dλ2 z .
(9)
2
jDλ z
The above transfer function describes the effect of CD in each
polarisation. The effects of PMD can be modeled through the
matrix [20] given as
hxx (t) hxy (t)
h(t) =
,
(10)
hyx (t) hyy (t)
Fig. 7. BER vs OSNR for different fiber lengths; the rotation between the
PSP and the launched polarisation is assumed to be π8
Fig. 7 shows the BER vs OSNR curve for a system with
θ = π8 and varying fiber lengths. We see that this method
is suitable for compensating any amount of CD without any
OSNR penalty for higher lengths. Fig. 8 shows the BER
vs OSNR curve for different angles of rotation between the
launched polarisation and the principal states of polarisation
of the fiber for a length of 1000 km. From Fig. 8, we see
that the performance of the system degrades with increase
in angle between the PSP and reference polarization. This
compensation technique assumes a prior knowledge of θ of
the system, which can possibly be characterized for a given
link. As indicated in Fig. 8, for θ = π4 , which is the worst
case scenario, the errors introduced due to PMD cannot be
compensated by this algorithm. It is also important to note
that the statistical nature of PMD cannot be compensated by
FDE method discussed here. However, this method is fast,
computationally efficient and comparatively more tolerant to
phase noise, for systems where the PMD impairments are not
severe.
Fig. 9 shows the system performance for various fiber lengths.
We can see that the algorithm is able to compensate for CD and
higher order PMD. The performance improves with increasing
lengths because the number of filter taps as given in eqn.
(13), also increases. However, this technique cannot be adapted
directly for the case where the phase noise of the laser is
significant. In the case where the laser linewidth is large, a
joint estimation of phase noise introduced by the laser and
that due to PMD needs to be implemented.
Fig. 9.
BER vs OSNR for various lengths using time domain equalization
IV.
Fig. 8. BER vs OSNR for different angles between launched polarization
and the PSP; Length of fiber = 1000 km
C. Time Domain Equalization
Filters for dispersion compensation in the time domain
can be obtained by inverting the sign of CD in eqn. (8). To
compensate for CD, we use an impulse invariance method [21].
Since the length is finite, we can implement this digitally using
a finite impulse response (FIR) filter where the number of the
taps and the amplitude can be calculated using
r
jcT 2 − jπcT22 k2
e Dλ z ,
(13)
ak =
Dλ2 z
with
N
N
|D|λ2 z
c≤k ≤b c , N =2×b
c + 1,
2
2
2cT 2
where N is the number of taps and T is the sampling period.
b
Since higher order PMD is a statistical phenomenon, filters
for compensating PMD can be obtained by using adaptive
algorithms. An adaptive algorithm incorporates an iterative
procedure that makes successive corrections to the weight of
the filter in order to minimize the mean error between the
output and the desired symbol. In our simulation, we use an
LMS algorithm to estimate the filter taps of eqn. (10). Data
impaired with CD and PMD is generated such that the higher
order PMD effects are also included, in the worst case scenario
corresponding to θ = π4 . CD compensation is performed using
an FIR filter described in eqn. (13). Subsequently, PMD compensation is implemented using the adaptive LMS algorithm.
The effects of laser linewidth are ignored for these simulations.
200 G COMMUNICATION SYSTEM WITH
PDM-16QAM
We now study the performance of a 200 G PDM-16QAM
communication system with all the impairments mentioned
above. The set up of the simulation is given in Fig. 1. We
vary the length of the fiber and the linewidth to estimate the
OSNR penalty. The modulator is biased at its null point and
the frequency detuning between the transmitter laser and local
oscillator is fixed at 1 GHz. In the simulation the effects of
CD and first order PMD are considered while solving the
NLSE numerically. This assumption of ignoring the higher
order PMD is valid for fibers with low DGD coefficients
and relatively smaller length scales. At the receiver, the DSP
modules are implemented in the following sequence. FDE
is performed for the joint compensation for CD and PMD.
This is followed by frequency offset correction using the
4th power-periodogram technique and clock recovery using
cross-correlation with the trainer sequence. Phase recovery
is subsequently implemented with the DD-LMS filter with a
single tap. The output of this filter is further processed for
BER estimation.
Fig. 10 shows the OSNR penalty to achieve a BER of 10−3
for different laser linewidths and different fiber lengths. From
the figure we can conclude that laser linewidth is the major
source of error in a PDM-16QAM optical communication
system and it is very critical that we use low linewidth
laser for such systems. FDE for joint equalisation of CD
and PMD in the presence of laser phase noise is useful only
for those fiber lengths for which (a) the statistical nature of
PMD can be ignored and (b) θ can be estimated apriori.
The use of an adaptive butterfly filter jointly with the phase
error compensation needs to be implemented for an effective
and complete compensation of CD and PMD. Alternately, a
judicious combination of the frequency domain technique and
the time domain adaptive filters can be implemented achieve
a complete compensation of the various impairments. Nyquist
shaping is expected to further reduce the impairment due to
CD; but that requires DSP at transmitter as well. Non-linear
effects need to be further addressed in case of WDM systems.
[7]
[8]
[9]
[10]
[11]
Fig. 10.
OSNR penalty for different lengths of fiber, corresponding to
different linewidths of laser
[12]
[13]
V.
C ONCLUSION
We studied the different mechanisms that deteriorate the
performance of a PDM 16-QAM system and the extent to
which each one impacts the system performance. We conclude
that laser linewidth plays a crucial role in ensuring errorfree communication when advanced modulation formats are
utilized. Drift in modulator bias voltage has significant impact
on the performance of the system, thus requiring a robust
feedback system for bias control. Frequency detuning between
the transmitter and receiver lasers, CD and PMD can be
effectively mitigated with the advanced DSP techniques.
[14]
[15]
[16]
ACKNOWLEDGMENT
The authors acknowledge Dr. Aravind Kumar Mishra, Aravind P. Anthur and Aneesh S for suggestions and discussions.
This work is a part of the project ’High Capacity Optical
Networks’ funded by Sterlite Technologies Limited.
[17]
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