Download Practical design model of DnPSK systems using direct BER

Journal of Optical Communications
29 (2008) 3
1
J. Opt. Commun. 29 (2008) 3, 001-005
© by Fachverlag Schiele & Schön 2006
Practical design model of DnPSK systems using direct BER counting and rigorous BER modeling
G. Jacobsen, E. Vanin, M. Forzati and L. Wang*
Summary
We present a design model for practical 100 Gb/s transmission DnPSK systems which accounts for imperfections in system components i.e. fiber attenuation, dispersion and non-linear effects, electrical drive circuitry
for optical modulators, optical amplifiers including
amplified spontaneous emission ASE noise and a realistic Rx description with non-ideal Low Pass Filtering
(LPF). The model uses direct error-counting combined
with an analytical rigorous BER model. An example 50
Gs/s DQPSK transmission system with 240 km transmission is considered for a specified 2 6 PRBS symbolsequence as well as for a 2 14 PRBS symbol-sequence
where a selected 2 6 symbol-sequence is used in the
theoretical results. We demonstrate excellent agreement
between the two methods over two orders of magnitude
for the Bit-Error-Rate (BER) in a system regime where
the signal interaction with ASE noise during fiber
transmission is not significant. The analytical BERresults are extended over ten orders of magnitude.
1
Background and Introduction
Ultra high bit-rate transmission (e.g. 100 Gb/s per wavelength in ultra dense WDM configurations with 50 –
100 GHz channel separation) is approaching commercial reality. It is likely that DnPSK (i.e. multilevel PSK
systems where the optical signal phase is encoded in an
integer number of π/n shifts) combined with interferometrical differential detection in the receiver will be of
significant practical interest because such systems are
simple from an optical design perspective (no optical
local oscillator required, no Digital Signal Processing
(DSP) in the receiver).
The practical design of such transmission systems requires detailed knowledge of all imperfections of the
ingoing opto-electrical subsystems. To exemplify, the
performance of the optical modulator that is used to
generate phase modulation in DnPSK systems must
include drive electronics as well as parasitic effects in
the modulator and the description of transmission fibers
and dispersion compensating fibers must include dispersion at least to second order as well as non-linear fiber
effects. The use of such detailed system descriptions
means that simple analytical results for pulse shapes etc
are no longer possible and one need to move to simulation software for obtaining the pulse shapes numerically. As long as the noise influence in the optical domain (from optical amplifiers) are additive and Gaussian (no influence of signal-noise interaction – see [1])
it may still be possible to use an analytical Rx formulation included in the simulation software to specify BitError-Rates over many (10 or more) orders of magnitude. For ASK systems such models are standard at the
moment [1-3] but for DnPSK systems they are currently
being fine tuned and included into the simulation software. The use of simulation tools (e.g. tools from
VPIphotonics™ [3]) sets the standard for software and
services supporting end-to-end photonic design automation and optical equipment configuration. Such products
are used by forward-looking groups, product design and
marketing teams, numerous commercial corporations
and educators university programs across the world. The
tools are characterized by their ability to include practical system parameters into the description of optoelectrical systems and subsystems of interest for description of transmission performance.
Within the context of design of practical DnPSK systems it is of significant interest to account for long symbol-sequences in the BER evaluation. This paper shows
a comparison of direct error counting to the general
DnPSK BER model as derived in [4-6]. The two methods are shown to agree in detail for low error-rates but a
careful description of system imperfections and of the
transmitted signal (symbol-sequence) is required for this
to be valid.
Address of authors:
Acreo AB, Electrum 236, S-164 40 Kista, Sweden
Received 20 February 2008
Journal of Optical Communications
27 (2006) 2
2
2
System under consideration
A 100 Gb/s DQPSK signal is generated by the standard
implementation with two nested MZMs (see e.g. [4]).
The signal is then passed through a multiplexer ArrayWaveguide-Grating (AWG). Finally the signal is transmitted over a 240 km link consisting of three spans,
each of them containing an erbium-doped fiber amplifier (EDFA), 80 km standard single-mode fiber (SSMF),
another EDFA, and dispersion-compensating (DCF)
fiber to fully compensate for the dispersion in the
SSMF. The EDFAs are noise-free. In each span, the
EDFAs provide a power level PL = 0 dBm into the
SSMF (the launch power), and (PL – 5) = –1dBm into
the DCF.
At the receiver side, noise contribution from all six inline amplifiers is added to the signal at the input to the
demultiplexer AWG optical filter. Additional noise is
added at the receiver in order to find the required optical
signal-to-noise ratio (OSNR) need to obtain a bit-error
rate (BER) of 10-3. All optical ASE noise is considered
white and Gaussian distributed. The receiver has two
interferometers of delay time equal to the symbol time
(twice the bit-time) and phase shifts of π/4 and - π/4
respectively and perfect polarization matching between
the interferometer arms is assumed [6]. The electrical
Rx has 4 identical photo-diodes coupled in push-pull at
the outputs of each interferometer. It has an electrical
LPF filter describer as a 3’rd order Bessel filter with 3
dB bandwidth of 37.5 GHz [6]. Thermal noise is not
considered but it can be included as an added Gaussian
noise contribution at the electrical stage of the Rx – see
[6,7].
3
Results and discussions
The signals generated at the transmitter are data modulated by random symbol sequences of length 2 6 (64
symbols) in the case of BER modeling, and 2 14 (16384
symbols) in the case of BER counting. Both symbol
sequences are such that all possible symbols are represented an equal number of times. For the 2 6 symbol
sequence also all two- and three-symbol combinations
are represented an equal number of times, while for the
2 14 symbol sequence this holds also all n-symbol combinations are resented an equal number of times, for n <
7. The optical signal is propagated through the transmission link and at the entrance to the AWG a random
noise is added. After detection by the interferometer Rx
it is determined whether the resulting signal current at
the LPF output is in error. The added ASE is considered
the dominant noise source and electrical thermal noise is
not included.
When using the semi analytical BER model [2] the BER
is evaluated by considering the added noise as white
with a specified optical power. Then the BER is evaluated by averaging over the BER contribution from each
symbol in the 64 symbol-time sequence. In this case it is
not feasible to consider very long symbol-sequences of
e.g. 2 14 symbols.
First an RZ-DQPSK 100 Gb/s (50Gs/s) signal is
launched on the transmission system, and the AWG
(both at the transmitter and receiver side) has a Gaussian transfer function in the frequency domain with a 3
dB bandwidth of 55 GHz. Fig. 1 shows the deterministical signal field at the input to the AWG for a 2 6 PRBS
symbol-sequence. It is apparent that the combined influence of dispersion and fiber non-linear effects during
transmission are not significant in this case. Using a
deterministic signal at higher input power levels for the
64 symbol sequence (up to 7 dBm) a significant nonlinear distortion of the signal is seen. The conclusions
reached in the following in the discussion of Fig. 2 are
not changed by the non-linear distortion. The influence
of non-linearities on the system performance – including signal-ASE interaction – will be the subject of a
subsequent publication.
Fig. 2 shows the BER obtained from direct counting
indicated by crosses and triangles compared to results
using the DQPSK BER model in the range of BER
between 10 −1 and 10 −4 (indicated by curves for three
different 64 symbol-sequences). The crosses and the top
curve consider the symbol-sequence in Fig. 1. The BER
model gives results that fall nicely within the specified
range from the direct counting. A very convincing
agreement is seen. The BER results for the direct error
counting using the 2 14 symbol-sequence (triangles) is
presented as a comparison and as an important practical
design case. It is seen to be noisy below 10 −3 and to
deviate from the short symbol-sequence results. By
choosing 64 symbol-sequences number 2 and 3 - that
are parts of the 2 14 symbol-sequence - for the theoretical model it is possible to specify the lower two curves.
The curve for sequence 2 is seen to fit rather well with
the direct error counting results and apparently the selected 64 symbols accounts for the major contribution to
the errors in the systems. Thus, by matching the theory
BER results to direct error counting BER results - in the
BER range where direct counting results are not noisy it is possible to obtain good agreement between the two
methods. This emphasizes that practical system design
using the analytical BER with a relatively short symbol
sequence should use a properly specified symbolsequence to specify the BER in accordance with direct
error counting results for much longer symbol sequences.
Journal of Optical Communications
27 (2006) 2
In Fig. 3 the semi analytical BER evaluation is extended
down to 10 −13 in the 64 symbol-sequence #1 case. It
appears that the system design below the BER order of
10 −3 is only possible by using semi-analytical Rx modeling (for a realistic computing time). It is obvious from
Figs. 2 and 3 that the excellent agreement between direct error counting and the analytical BER evaluation
over 2 orders of magnitude makes it reasonable to use
the semi analytical design method to predict system
performance over 10 (or more) orders of magnitude.
Fig. 1: The 64 signal symbols in a 2 6 PRBS sequence for a 100 Gb/s
DQPSK modulated signal. Inserted is the DQPSK constellation diagram.
3
Fig. 3: Same as Fig. 2 in the 64 symbol case with analytical BER
results (curve) extended over 10 orders of magnitude. Crosses are
direct error counting results repeated from Fig. 2.
4
Conclusion
In the design of practical 100 Gb/s transmission systems
it is imperative to have design models available which
accounts for practical imperfections in system components i.e. fiber attenuation, dispersion and non-linear
effects, drive circuitry for optical modulators, optical
amplifiers including amplified spontaneous emission
ASE noise and realistic Rx description with non-ideal
Low Pass Filtering (LPF). The present paper combines
the use of direct error-counting and an analytical rigorous BER model for a 50 Gs/s DQPSK transmission
system implementation over 240 km of fiber transmission and for a specified 2 6 PRBS symbol-sequence and
a 2 14 PRBS symbol-sequence.
We demonstrate excellent agreement between the two
methods over two orders of magnitude for the Bit-ErrorRate (BER) in a system regime where the signal interaction with ASE noise during fiber transmission is not
significant. It is also shown that the analytical BER
model gives agreement with direct error counting for
long symbol sequences by identifying a dominating
symbol-pattern (in our case a 64 symbol-sequence) thus
allowing the use of the analytical results for low BER
values also in this case. The analytical results are extended over ten more orders of magnitude and our results give high credibility in using the analytical BER
for system design in low BER cases where the direct
error counting is unfeasible.
In ultra-long (with transmission distances exceeding the
order of 1000 km) 100 Gb/s DQPSK transmission systems the signal-ASE interaction is expected to influence
the BER performance. In that case the analytical modeling in [4-6] is not valid and DnPSK system models need
further development.
References
Fig. 2: Bit-Error-Rate (BER) as a function of Optical Signal to Noise
Ratio (OSNR) at AWG input. Results are obtained using direct error
counting (64 ( 2 6 ) and 18634 ( 2 14 ) symbol sequences) and semianalytical BER model [6] (64 symbol sequences #1-3).
[1] E. Vanin, G. Jacobsen, A. Berntson, Opt. Lett. 32 (2007) 12,
1740 -1742
[2] G. Jacobsen, A. Aurelius, A. Berntson, J. Opt. Commun. 28
(2007) 1, 52-57
[3] VPItransmissionMakerTM &
VPIcomponentMakerTM Version
7.6 - see www.vpiphotonics.com
[4] P.J. Winzer, R.J. Essiambre, IEEE/OSA J. Lightwave Technol.,
24 (2006) 12, 4711-4728.
[5] G. Jacobsen, E. Vanin, J. Op.l Commun. 29 (2008) 1, 49-51
[6] G. Jacobsen, E. Vanin, “BER Model for High Capacity Optical
DnPSK Systems with DQPSK as an Example Case”, to appear in
J. Opt. Commun. 29 (2008)
[7] G. Jacobsen, K. Bertilsson, Z. Xiaopin, IEEE/OSA J. Lightwave
Technol. 16 (1998) 10, 1804 - 1812