Download On the Use of Gaussian Approximation for Reliable Performance

International Journal of Performability Engineering, Vol. 3, No. 4, October 2007, pp. 501-503.
©RAMS Consultants
Printed in India
On the Use of Gaussian Approximation for Reliable
Performance Evaluation in Optical DPSK Systems
Qun Zhang* and Han-Way Huang
Electrical and Computer Engineering Department
Minnesota State University, Mankato, MN 56001, USA
(Received on August 7, 2007)
Abstract – In this paper, we propose to extend the Guassian approximation (GA) method for
reliable system performance evaluation from the traditional optical on-off keying (OOK)
systems to the emerging optical differential phase shift keying (DPSK) systems. The proposed
method can be used to guide efficient numerical estimate as well as experimental measurement
of the noise-loading back-to-back DPSK system performance where the inter-symbolinterference (ISI) is not significant.
Keywords: Bit-error-rate (BER) evaluation, optical fiber communication systems, differential
phase-shift keying (DPSK)
1. Introduction
Reliable back-to-back performance evaluation/measurement is crucial in optical transceiver
design. Also, it is the starting point in the link budget design for optical communication
systems [1]. In the traditional optical on-off keying (OOK) systems, a simple and yet reliable
method, i.e. the Gaussian approximation (GA) method was extensively used for simulation
based performance evaluation and experimental bit error rate (BER) measurement [2-3].
However, it has been shown that this method cannot be used directly for the next generation
optical differential phase shift keying (DPSK) systems [4]. The reason is simple. For OOK
systems, the pdf’s of spaces and marks have respectively, central and non-central χ 2 shapes.
With GA and a decision threshold at which the two types of probability of error are equal, i.e.,
Pr(1|0)=Pr(0|1), the approximated BER could be within one order of magnitude compared to
the exact BER, although the detection threshold may deviate significantly from the its true
values. For DPSK systems, the pdf’s of spaces and marks have similar non-central χ 2 shapes.
As a result, the decision threshold derived from the GA method could be highly accurate,
while the approximated BER values could deviate significantly from the true values. In this
paper, we propose to modify the GA method so that it can be used for the optical DPSK
systems. The proposed method can guide efficient numerical performance estimate as well as
experimental performance measurement for the noise-loading back-to-back DPSK system
where the inter-symbol-interference (ISI) is not significant.
2. Proposed Method
For a back-to-back DPSK system, we employ a recently developed Karhunen-Loéve series
______________________________________________________________________
*
Corresponding author’s email: [email protected]
501
Q. Zhang and H-W Huang
502
expansion (KLSE) method [5] to accurately calculate the exact probability density function
(pdf) of the detected photo voltage for the single shot case. The exact bit error rate (BER) and
thus the exact Q-factor obtained by simply inverting the BER, can be obtained. We then
approximate the exact pdf’s by the Gaussian pdf’s to calculate the approximate Q-factor. The
difference between the exact and the approximate Q-factor values, i.e., the ∆Q can be obtained
next and recorded. Now we investigate the pulse train case. For typical back-to-back systems
that usually have weak ISI, we can apply the GA approximation to obtain the approximated Qfactor values. We then use the recorded ∆Q to correct the approximated Q-factor. We expect
that at high optical signal-to-noise (OSNR) levels, the Q-factor values obtained by using the
proposed method may exaggerate the noise effect due to the existence of ISI. However, for
practical systems that usually can tolerate a higher noise power level, the proposed method
should be able to give good estimate of system performance. We validate our proposed
method using the following example.
3. Example
The analyzed system model is illustrated in Fig. 1. The electrical 40 Gb/s information data
passes through a differential encoder and a driving circuit, and drives the Mach-Zehnder
modulator (MZM) to generate 50% RZ optical signals. The rise time of the trapezoidal NRZ
shaped electrical driving signal is assumed to be ¼ of the bit interval. The low pass response
of the driving circuits is assumed to be 5th order Bessel filter with a 32 GHz 3-dB bandwidth.
The modulator model is based on a Fujitsu EO modulator, and the 3-dBO bandwidth is 33
GHz. The DPSK receiver consists of a 2nd order super-Gaussian shaped optical BPF with a 3dB passband bandwidth of 75 GHz, a delay line interferometer (DI), a balanced photodetector,
a LPF the same as the one for the driving circuits, a sampler, and the decision circuit. To take
into account the bit pattern effects, we use a 8 bit De Bruijn sequence that contains all 3-bit
patterns each with exactly one occurrence. No receiver imperfection is considered.
Fig. 1: System Setup - RZ-DPSK Transmitter and Optically Pre-amplified Receiver
Using the proposed method, we first obtained the exact pdf’s (denoted as pdfexact) at OSNR
= 10 dB for the transmitted 00 and 01 single shot signals, as shown in Fig. 2. Also shown is
the approximated Gaussian pdf’s, denoted as pdfGA . We can clearly see that by using GA, the
BER will be overestimated. Fig. 3 shows the single shot Q values calculated from respectively
pdfexact and pdfGA, vs. OSNR. As expected, we have Qexact > Qexact. Fig. 3 also shows that ∆Q =
Qexact − QGA is not a constant, but rather OSNR-dependent. Next we study the system
performance using the 8-bit pulse train generated. Fig. 4 shows the system performance from
the exact pdf and BER calculation, as well as that from the GA. Apparently BERGA is
dramatically different from the BERexact, and thus is not reliable in indicating the system
performance. However, BERGA-cor, which is obtained by correcting BERGA with the help of
single shot ∆Q, matches BERexact very well at all studied OSNR levels.
pdf
Detected voltage (a.u.)
Fig. 2: Single Shot pdf’s
OSNR (dB)
Fig. 3: Single Shot Q’s and ∆Q
BER
∆Q (dB)
On the Use of Gaussian Approximation for Reliable Performance Evaluation in Optical DPSK Systems
Q (dB)
503
OSNR (dB)
Fig. 4: System BER
4. Conclusions and Future Work
We demonstrate a novel GA method for reliable performance estimation/measurement in
back-to-back Optical DPSK Systems where the ISI may not be significant. For systems with
strong ISI, we could refer the method in [6] and calculate ∆Q for all possible patterns that is
long enough to account for system memory. This is left as a future work.
References
[1] Golovchenko, E. A., A. N., Pilipetskii, N. S. Bergano, C. R. Davidson, F. I. Khatri, R.
M. Kimball, and V. J. Mazurczyk, Modeling of Transoceanic Fiber-Optic WDM
Communication, IEEE Journal of Selected Topics in Quantum Electronics, Vol. 6, No.
2, pp. 337–347, 2000.
[2] Humblet, P. A. and M. Azizoglu, On the bit error rate of lightwave systems with optical
amplifiers, IEEE Journal of Lightwave Technology, vol. 9, no. 11, pp. 1576–1582,
1991.
[3] Bergano, N. S., F. W. Kerfoot, and C. R. Davidson, Margin measurement in optical
amplifier systems, IEEE Photonics Technology Letters, vol. 5, no. 3, pp. 304–306, 1993.
[4] Kim, H. and P. J. Winzer, Nonlinear Phase Noise in Phase-Coded Transmission,
Technical Digest OFC 2005, Vol. 4, paper OThO3, Anaheim, CA, USA.
[5] Zhang, Q. and C. R. Menyuk, A Rigorous Optical DPSK Transceiver Model and BER
Calculation Using the KLSE Method, Proceedings of 41st Conference on Information
Sciences and Systems, paper TP4, Baltimore, MD, 2007.
[6] Anderson, C. J. and J. A. Lyle, Technique for Evaluating System Performance using Q
in Numerical Simulations Exhibiting Intersymbol Interference, IEE Electronics Letters,
Vol. 30, pp. 71-72, 1994.
Qun Zhang is currently an assistant professor at the ECE department of the Minnesota State
University (MSU), Mankato, MN, USA. Prior to joining the MSU, he worked in research
laboratories in PhotonEx Corporation, Corvis Corporation (now part of L-3 Communications),
and Tyco Telecommunications. Dr. Zhang received his Ph. D. degree in electrical engineering
from the University of Virginia, Charlottesville, VA, USA in 2001.
Han-Way Huang is a professor at the ECE department of the Minnesota State University,
Mankato, MN, USA. He received his Ph. D. degree in computer engineering from the Iowa
State University, Ames, IA, USA in 1988.