Fabrizio Forghieri

On the Performance of Nyquist-WDM Terabit Superchannels Based on PM-BPSK, PM-QPSK, PM-8QAM or PM-16QAM Subcarriers

We investigated through simulations the performance of Nyquist-WDM Terabit superchannels implemented using polarization-multiplexed phase shift-keying based on 2 (PM-BPSK) and 4 (PM-QPSK) signal points or polarization-multiplexed quadrature amplitude modulation based on 8 (PM-8QAM) and 16 (PM-16QAM) signal points. Terabit superchannels are obtained through the aggregation of multiple subcarriers using the Nyquist-WDM technique, based on a tight spectral shaping of each subcarrier which allows very narrow spacing. We first studied the optimum transmitter/receiver filtering in a back-to-back configuration. Then we investigated the maximum reach for different spectral efficiencies, after nonlinear propagation over uncompensated links with lumped amplification. Performance for systems based on both standard single-mode fiber (SSMF) and large effective area non-zero dispersion-shifted fiber (NZDSF) has been analyzed. Assuming SSMF with 25-dB span loss, we found that PM-BPSK can reach 6480 km at a net capacity of 4 Tb/s across the C band. Conversely, PM-16QAM can deliver 27 Tb/s, but over 270 km only. Note that a lower span length, the use of Raman amplification and/or pure silica-core fibers (PSCFs) can significantly increase the maximum reach, but without changing the hierarchy among the performance of modulation formats. We also show that the maximum reachable distance is approximately 2/3 of the one achievable in linear propagation at the optimum launch power, regardless of the modulation format, spacing and fiber type. As additional results, we also verified that the optimum launch power per subcarrier linearly depends on the span loss, varies with the fiber type, but it is independent of the modulation format, and that the relationship between the maximum reachable distance and the span loss is almost linear.

Performance Limits of Nyquist-WDM and CO-OFDM in High-Speed PM-QPSK Systems

We compare by simulation the performance of two techniques for generating polarization-multiplexed quadrature phase-shift keying with a high spectral efficiency (SE). The first is based on coherent optical orthogonal frequency-division multiplexing (CO-OFDM). The second, which we call Nyquist wavelength-division multiplexing (N-WDM), is based on the use of optical pulses having an “almost” rectangular spectrum, with bandwidth ideally equal to the Baud-rate. We show that the two techniques have the same sensitivity and SE under idealized assumptions. However, we found that CO-OFDM requires a much larger receiver bandwidth and proportionally faster speed of the analog-to-digital converters. We also tested CO-OFDM and N-WDM over long-haul nonlinear links and found N-WDM to outperform CO-OFDM in this case, too.

Modeling of the Impact of Nonlinear Propagation Effects in Uncompensated Optical Coherent Transmission Links

We address perturbative models for the impact of nonlinear propagation in uncompensated links. We concentrate on a recently-proposed model which splits up the signal into spectral components and then resorts to a four-wave-mixing-like approach to assess the generation of nonlinear interference due to the beating of the signal spectral components. We put its founding assumptions on firmer ground and we provide a detailed derivation for its main analytical results. We then carry out an extensive simulative validation by addressing an ample and significant set of formats encompassing PM-BPSK, PM-QPSK, PM-8QAM, and PM-16QAM, all operating at 32 GBaud. We compare the model prediction of maximum system reach and optimum launch power versus simulation results, for all four formats, three different kinds of fibers (PSCF, SMF, and NZDSF) and for several values of WDM channel spacing, ranging from 50 GHz down to the symbol-rate. We found that, throughout all tests, the model delivers accurate predictions, potentially making it an effective general-purpose system design tool for coherent uncompensated transmission systems.

Analytical Modeling of Nonlinear Propagation in Uncompensated Optical Transmission Links

We present analytical results on the impact of nonlinear propagation in uncompensated links. We test the accuracy of our model in the context of ultradense wavelength-division-multiplexing polarization-multiplexed quadrature phase-shift keying (PM-QPSK) systems, at the Nyquist spectral efficiency limit. We show that the predicted system performance matches simulation results very accurately over a broad range of system scenarios. A simple closed-form analytical formula provides an effective tool for the quick and accurate prediction of system performance.

The GN-Model of Fiber Non-Linear Propagation and its Applications

Several approximate non-linear fiber propagation models have been proposed over the years. Recent re-consideration and extension of earlier modeling efforts has led to the formalization of the so-called Gaussian-noise (GN) model. The evidence collected so far hints at the GN-model as being a relatively simple and, at the same time, sufficiently reliable tool for performance prediction of uncompensated coherent systems, characterized by a favorable accuracy versus complexity trade-off. This paper tries to gather the recent results regarding the GN-model definition, understanding, relations versus other models, validation, limitations, closed form solutions, approximations and, in general, its applications and implications in link analysis and optimization, also within a network environment.

EGN model of non-linear fiber propagation

The GN-model has been proposed as an approximate but sufficiently accurate tool for predicting uncompensated optical coherent transmission system performance, in realistic scenarios. For this specific use, the GN-model has enjoyed substantial validation, both simulative and experimental. Recently, however, it has been pointed out that its predictions, when used to obtain a detailed picture of non-linear interference (NLI) noise accumulation along a link, may be affected by a substantial NLI overestimation error, especially in the first spans of the link. In this paper we analyze in detail the GN-model errors. We discuss recently proposed formulas for correcting such errors and show that they neglect several contributions to NLI, so that they may substantially underestimate NLI in specific situations, especially over low-dispersion fibers. We derive a complete set of formulas accounting for all single, cross, and multi-channel effects, This set constitutes what we have called the enhanced GN-model (EGN-model). We extensively validate the EGN model by comparison with accurate simulations in several different system scenarios. The overall EGN model accuracy is found to be very good when assessing detailed span-by-span NLI accumulation and excellent when estimating realistic system maximum reach. The computational complexity vs. accuracy trade-offs of the various versions of the GN and EGN models are extensively discussed.

Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links

We show by simulation that PM-QPSK signal components, after propagating in uncompen-sated fiber links, assume Gaussian distribution, both in linear and non-linear regime, even in absence of ASE noise. After DSP equalization, the statistics of decision variables is also Gaussian.

Performance evaluation of coherent WDM PS-QPSK (HEXA) accounting for non-linear fiber propagation effects

Coherent-detection (CoD) permits to fully exploit the four-dimensional (4D) signal space consisting of the in-phase and quadrature components of the two fiber polarizations. A well-known and successful format exploiting such 4D space is Polarization-multiplexed QPSK (PM-QPSK). Recently, new signal constellations specifically designed and optimized in 4D space have been proposed, among which polarization-switched QPSK (PS-QPSK), consisting of a 8-point constellation at the vertices of a 4D polychoron called hexadecachoron. We call it HEXA because of its geometrical features and to avoid acronym mix-up with PM-QPSK, as well as with other similar acronyms. In this paper we investigate the performance of HEXA in direct comparison with PM-QPSK, addressing non-linear propagation over realistic links made up of 20 spans of either standard single mode fiber (SSMF) or non-zero dispersion-shifted fiber (NZDSF). We show that HEXA not only confirms its theoretical sensitivity advantage over PM-QPSK in back-to-back, but also shows a greater resilience to non-linear effects, allowing for substantially increased span loss margins. As a consequence, HEXA appears as an interesting option for dual-format transceivers capable to switch on-the-fly between PM-QPSK and HEXA when channel propagation degrades. It also appears as a possible direct competitor of PM-QPSK, especially over NZDSF fiber and uncompensated links.

Dispersion Compensation and Mitigation of Nonlinear Effects in 111-Gb/s WDM Coherent PM-QPSK Systems

We carried out an extensive simulative analysis to investigate in depth the potential of electronic dispersion compensation (EDC) in amplified multispan 111-Gb/s wavelength- division-multiplexed systems based on polarization-multiplexed quadrature phase-shift keying modulation with coherent detection, also in the presence of substantial fiber nonlinearity. For typical single-mode and nonzero dispersion-shifted fibers, our results show that the use of inline optical dispersion management is always suboptimal versus using EDC at the receiver.

Ultra-Narrow-Spacing 10-Channel 1.12 Tb/s D-WDM Long-Haul Transmission Over Uncompensated SMF and NZDSF

We experimentally investigate the transmission of a 1.12-Tb/s Dense-WDM (D-WDM) system comprising 10 × 112 Gb/s polarization-multiplexed quadrature phase-shift-keying channels with ultra-narrow spacing (1.1 times the Baud rate). The D-WDM signal is generated by means of a recirculating frequency shifter. We used narrow optical filtering of channels at the transmitter to reduce interchannel crosstalk. With 100-km uncompensated spans and EDFA amplification, we reached 800 km over nonzero dispersion-shifted fiber (NZDSF) and 2300 km over standard single-mode fiber, at BER=3·10-3. By simulation, we also investigated transmission over large-effective area NZDSF fiber (LEAF) and pure silica-core fiber (PSCF). We found that the D-WDM channel should achieve a 40% longer reach with LEAF than with NZDSF and a 45% longer reach with PSCF than with standard single-mode fiber.