Pulse formats are a critical ingredient in the design and development of long-haul optical networking equipment. In order to transmit data, these systems require a modulator to convert electrical data signals to optical pulses. Specifically, in the modulator, a "1" is transmitted as a pulse of light while a "0" has no light output. The number of "1's" and "0's" transmitted per second determines the speed of the link (bit rate).
To improve transport system designs, engineers need to pay close attention to the modulation schemes used in network designs. While there are a few modulation choices, this article will focus in on two, non-return-to-zero (NRZ), where the pulse (the 1) is on for an entire period, and return-to-zero (RZ), where the pulse is only on for a short period of time. These schemes impact a number of system design parameters such as transmission at a higher bit-rate, closer channel spacing, dispersion management, and polarization mode dispersion (PMD). This article will explore all of these issues.
Receiver considerations
The duty cycle of a pulse is ρ = Ton/( Ton+ Toff). The eye diagram and frequency spectrum of a 10 Gbps NRZ pulse and an RZ pulse with a 50% duty cycle are shown in Figure 1. It can be seen that the RZ spectrum has a wider bandwidth than the NRZ spectrum. The spectrum of an NRZ signal at 20 Gbps is the same as that of an RZ signal except for the tones at 10 and 30 GHz.
Click here for Figure 1.
Figure 1: Eye diagram and frequency spectrum of a 10-Gbps NRZ pulse and an RZ pulse with 50% duty cycle.
To compare the RZ and NRZ signals, designers must appropriately set the electrical bandwidth of the receiver since the optimum bandwidth depends on the pulse width. It has been documented that the optimum electrical bandwidth for a system with an optically pre-amplified receiver is approximately 0.7 times the data rate and is independent; of the duty cycle.1
Receiver sensitivity is defined as the received optical power required to achieve a certain bit error rate (BER). In Figure 2, the back-to-back sensitivity of a typical optical system is plotted as a function of duty cycle. A matched filter was used in the receiver, and shot noise (detection noise due to the discrete nature of photons) was included.
Click here for Figure 2.
Figure 2: Bit error rate vs. received optical power at different duty cycles for a "back-to-back" system (no optical fiber).
In Figure 2, it's important to note the improvement in receiver sensitivity as the duty cycle is reduced. Here's why. If the average optical power launched into the fiber is kept constant, an optical RZ pulse with a 50% duty cycle will have twice the peak power of an NRZ pulse. This increase in power occurs because optical amplifiers are run in saturation mode, resulting in a gain that scales with average input power. The photodiode is a square-law detector, i.e., the photocurrent is proportional to optical power. Hence the received electrical power (proportional to the square of the photocurrent) is proportional to the square of the optical power.
Therefore, the electrical power of an RZ pulse with a 50% duty cycle will be twice that of an NRZ pulse. There will thus be a 3-dB improvement in receiver sensitivity for a 50% duty cycle pulse due to the higher electrical energy per bit.
In reality, however, RZ systems don't achieve a full 3-dB improvement in receiver sensitivity. Shot noise is higher for a pulse with larger amplitude. Thus, an RZ pulse will be more affected by shot noise, reducing its advantage to approximately 2.5 dB.
Handling Impairments
As mentioned above, the optical fiber itself distorts the signal. Let's look at how these impairments influence both formats and examine whether the sensitivity advantage of the RZ format is maintained in the presence of dispersion and non-linear effects. Let's start with dispersion.
The refractive index of glass is a function of wavelength, which results in the spectral components of a pulse traveling at different group velocities along the fiber. Hence, chromatic (material) dispersion broadens optical pulses beyond their time slot, leading to inter-symbol interference (ISI).
A second component of dispersion in optical fibers is known as waveguide dispersion. This component arises because the proportion of light traveling in the fiber core versus cladding is a function of wavelength. The dispersion coefficient of a fiber is defined as:
D = d(1/Vg)/dλ
The typical dispersion coefficient of single mode fiber (SMF) is 16 ps/nm/km. Non-zero dispersion-shifted fibers (NZDSF) offer lower dispersion coefficients than SMF. Note: the dispersion coefficient of a fiber is also a function of wavelength, otherwise known as dispersion slope.
Chromatic dispersion in a fiber can be compensated for by specially designed fiber with a refractive index profile (core composition) that leads to negative waveguide dispersion characteristics. Another approach is to use zero dispersion-shifted fibers (ZDSFs), which are designed in such a way that the dispersion coefficient at the loss minimum (1550 nm) is 0.
Dispersion compensation schemes must compensate not only for dispersion but also for dispersion slope. In dense wave division multiplexing (DWDM) systems, it is a challenge to compensate for the dispersion and its slope for each channel over the entire optical spectrum.
Since an RZ pulse has a wider optical bandwidth than an NRZ pulse, it is more affected by dispersion, as can be seen from the eye diagrams in Figure 3. For the same reason, slope compensation for an RZ signal is also more difficult. Thus, RZ transmission through dispersion-shifted fiber would require the appropriate slope compensation.
Click here for Figure 3
Figure 3: (a) RZ eye of signal through 80km of SMF with a dispersion of 16 ps/nm.km. (b) NRZ eye of signal through the same fiber.
Non-linearities
High optical densities in the fiber core lead to two types of non-linear effects based on scattering and on the non-linear refractive index. Scattering processes such as stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) manifest themselves as intensity-dependent gain or loss.
Figure 4 shows the input and output spectra of a 100-channel system. The total input power is +16 dBm, traveling through 100 km of single mode fiber. Note the Raman tilt due to SRS in the output spectrum. Energy from the shorter wavelength channels is transferred to the longer wavelength channels.
Click here for Figure 4
Figure 4: Optical spectrum of 100channels before (a) and after (b) transmission through 100 km of optical fiber with a Raman coefficient of 0.4.
The refractive index n of glass is a weak function of optical intensity, i.e., n = n0 + n2*P/Ae , where n0 is the linear term, P is the optical power, and Ae is the effective area of the core. The coefficient n2 for silica fibers is 2.6 x 10-20 m2/W. The non-linear contribution to the refractive index results in an intensity-dependent phase change for light propagating in a fiber of Φnl = g*P*Le, where g = 2*π*n2/(π *Ae) and Le is the effective interaction length.
The intensity-dependent refractive index gives rise to three effects: fluctuations in the phase of the signal on the channel, known as self-phase modulation (SPM); fluctuations in the phase of signals in other channels, known as cross-phase modulation (XPM); and four-wave mixing (FWM), where the beating between two channels leads to tones and sidebands.
Both SRS and SBS depend only on average power and are therefore independent of the modulation format in a dispersion-limited system. However, because of the improved receiver sensitivity of an RZ system, lower average power can be launched into the fiber.
SPM, XPM, and FWM depend on peak power and the interaction time between channels. NRZ pulses have lower peak power but longer interaction times. RZ pulses, on the other hand, have larger peak power and as such are more susceptible to FWM, SPM, and XPM. In the presence of SPM, however, RZ pulses can undergo compression (solitons) and perform better than NRZ pulses.
Overall, the best modulation format in the presence of non-linearities depends on the dispersion management scheme in effect since dispersion causes the energy of a pulse to be dispersed in time. Dispersion management schemes are the subject of much discussion in literature.2,3
Span, link length
The modulation format impacts the design of a given link; each stage of optical amplification introduces noise due to the amplified spontaneous emission of optical amplifiers. As a result, the optical signal-to-noise ratio (OSNR) degrades along the link. An empirical expression for OSNR is given by the following equation:
OSNR (dB) = 58-10*log(N) - NF - 10log(L) + Pout -10*log(M) - κ
where M = number of channels, N = number of amplifiers, L = loss/span,
NF = noise figure of amplifier, Pout = amplifier output power, and κ = other factors.
Since the RZ scheme has a better baseline receiver sensitivity than the NRZ scheme, the span length may be increased (received optical power decreased) for a given launch power and receiver sensitivity. Several authors have shown experimentally that longer link lengths can be achieved with the RZ format.4
Bit rate
As stated above, higher bit-rate systems are limited by dispersion. The RZ format would be beneficial for systems with few channels but would require NRZ as the number of channels increase.5
Dispersion compensation based on chirped Fiber-Bragg gratings (FBG) to compensate for the residual dispersion of dispersion compensation fibers (DCFs) is under development. The effectiveness of FBG modules in mitigating residual dispersion effects at 40 Gbps over the multiple channels of the transmission spectrum is being explored.
Channel spacing
For 10-Gbps systems with 100 GHz spacing between the channels, either the RZ or NRZ formats can be used without interchannel crosstalk. Because of its higher optical bandwidth, however, the RZ format would require greater spacing for 40-Gbps systems unless special filtering techniques are employed in the multiplexer (mux) and demultiplexer (demux).
Polarization mode dispersion (PMD)
Polarization mode dispersion (PMD) is caused by the two polarizations traveling at different speeds along the fiber. PMD is a statistical phenomenon and results in pulse broadening.
The RZ format is more resilient to PMD than the NRZ format because the energy is confined to the center of the bit period. Therefore, a higher differential group-delay is required before the energy leaks out of the bit period to result in ISI.6
Summary
Overall, the RZ format has better baseline receiver sensitivity when the average power into the fiber is kept constant. RZ is more affected by dispersion and dispersion slope. For 10- to 20-Gbps systems, where dispersion and its slope are well compensated, RZ will perform better than NRZ in most cases. On the contrary, since 40-Gbps optical transport systems are currently limited by dispersion and dispersion slope, NRZ may be a better choice for a system with a large number of channels.
It's also important to note that implementing the RZ modulation scheme requires a higher bandwidth driver on the transmit end. Designers may implement this scheme using two optical modulators.7 The problem with this approach, however, is that implementing multiple modulators could lead to higher system design costs.
Acknowledgments
The author would like to acknowledge helpful discussions on receiver sensitivity with Dr. Hari Shankar of Inphi Corporation.
About the Author
Anjali Singh is a senior optical engineer at Inphi Corporation. Prior to joining Inphi, Anjali was at JDS Uniphase, where she developed EDFA and Raman amplifiers for long-haul communications systems. She holds a B.Tech in electrical engineering from the College of Engineering in Guindy, India, an M.S. in electrical engineering from the Inidan Institue of Technology in Madras, and a doctorate in electrical engineering from the University of Rhode Island. Anjali can be reached at asingh@inphi-corp.com.
References
- "Comparison between NRZ and RZ signal formats for In-line Amplifier Transmission in the zero-dispersion regime," T. Matsuda, A. Naka and S. Saito, Journal of Lightwave Technology, Vol. 16, No. 3, March 1998.
- "RZ Versus NRZ in Nonlinear WDM systems," F. Forggieri, P.R. Prucnal, R. W. Tkach and A. R. Chraplyvy, IEEE Photonics Technology Letter, Vol. 9, No.7, July 1997.
- "Four-photon mixing and high-speed WDM systems," R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck and R. M Derosier, Journal of Lightwave Technology, Vol.13, pp.841-849, May 1995.
- "RZ Versus NRZ Modulation Format for Dispersion Compensated SMF-Based 10Gb/s Transmission with more than 100-km Amplifier spacing," C. Caspar, H. M. Foisel, A. Gladisch, N. Hanik, F. Kuppers, R, Ludwig, A. Mattheus, W. Pieper, B. Strebel, and H. G. Weber, IEEE Photonics Technology Letters, Vol. 11, No. 4, April 1999.
- "NRZ Versus RZ in 10-40-Gb/s Dispersion-Managed WDM Transmission Systems," M. I Hayee, and A. E. Willner, IEEE Photonics Tech. Lett, Vol.11, No. 8, August 1999.
- "A Comparison between NRZ and RZ Data Formats with respect to PMD-Induced System Degradation," H. Sunnerud, M. Karlsson and P.A. Andrekson, IEEE Photonics Technology Letters, Vol. 13, No.5, May 2001.
- "Enabling Technologies for 40 Gb/s Long Haul DWDM Transport", B. Mikkelsen, P. Mamyshev, C. Rasmussen, C. Ketchian, NFOEC, 2000.
