Tommaso Foggi

Robust Multilevel Coherent Optical Systems With Linear Processing at the Receiver

This paper investigates optical coherent systems based on polarization multiplexing and high-order modulations such as phase-shift keying (PSK) signals and quadrature amplitude modulations (QAM). It is shown that a simple linear receiver processing is sufficient to perfectly demultiplex the two transmitted streams and to perfectly compensate for group velocity dispersion (GVD) and polarization mode dispersion (PMD). In addition, in the presence of a strong phase noise of the lasers at the transmitter and receiver, a symbol-by-symbol detector with decision feedback is able to considerably improve the receiver robustness with a limited complexity increase. We will also discuss the channel estimation and the receiver adaptivity to time-varying channel conditions as well as the problem of the frequency acquisition and tracking. Finally, a new two-dimensional (polarization/time) differential encoding rule is proposed to overcome a polarization-ambiguity problem. In the numerical results, the receiver performance will be assessed versus the receiver complexity.

Maximum-likelihood sequence detection with closed-form metrics in OOK optical systems impaired by GVD and PMD

This paper thoroughly investigates the maximum-likelihood sequence detection (MLSD) receiver for the optical ON-OFF keying (OOK) channel in the presence of both polarization mode dispersion and group velocity dispersion (GVD). A reliable method is provided for computing the relevant performance for any possible value of the system parameters, with no constraint on the sampling rate. With one sample per bit time, a practically exact expression of the statistics of the received samples is found, and therefore the performance of a synchronous MLSD receiver is evaluated and compared with that of other electronic techniques such as combined feedforward and decision-feedback equalizers (FFE and DFE). It is also shown that the ultimate performance of electronic processing can be obtained by sampling the received signal at twice the bit rate. An approximate accurate closed-form expression of the receiver metrics is also identified, allowing for the implementation of a practically optimal MLSD receiver

OFDM versus Single-Carrier Transmission for 100 Gbps Optical Communication

We analyze the orthogonal frequency division multiplexing (OFDM) technique in long-haul next generation optical communication links and compare it with the well-established single-carrier (SC) data transmission using high-level modulation formats and coherent detection. The analysis of the two alternative solutions is carried out in the 100 Gbps scenario, which is commonly considered to be the next upgrade of existing optical links, with special emphasis on quaternary phase-shift keying (QPSK) modulations. The comparison between OFDM and SC takes into account the main linear and nonlinear impairments of the optical channel, e.g., group velocity dispersion (GVD), polarization mode dispersion (PMD), self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM), as well as the phase noise due to transmit and receive lasers, their relative frequency offset, other synchronization aspects, the overall complexity, the power and spectral efficiency, and the technological constraints.

Faster-than-Nyquist and beyond: how to improve spectral efficiency by accepting interference.

We investigate the application of time and frequency packing techniques, an extension of the classical faster-than-Nyquist signaling, to long-haul optical links. These techniques provide a significant spectral efficiency increase and represent a viable alternative to overcome the theoretical and technological issues related to the use of high-order modulation formats. Adopting these techniques, we successfully demonstrate through simulations the transmission of 1 Tbps over 200 GHz bandwidth in a realistic (nonlinear) long-haul optical link.

Impact of Phase Noise and Compensation Techniques in Coherent Optical Systems

One of the most severe impairments that affect coherent optical systems employing high-order modulation formats is phase noise due to transmit and receive lasers. This is especially detrimental in uncompensated links, where an ideal compensator for channel distortions and laser phase noise should first eliminate receive phase noise, then equalize channel distortions, and only later compensate for transmit phase noise. Unfortunately, the simultaneous presence of transmit and receive phase noise makes very difficult to discriminate between them, even in the presence of a pilot tone. Moreover, the picture is different for optical systems using single-carrier or orthogonal frequency division multiplexing, where transmit and receive phase noise components may have a different impact. All these aspects are analyzed and discussed in this paper. A novel digital coherence enhancement (DCE) technique, able to significantly reduce the phase noise of transmit or receive lasers by using an interferometric device plus a very simple electronic processing, is also described. The performance of this technique and the statistical properties of the residual phase noise are analytically derived and verified by simulations, showing a high increase of the maximum bit-rate-distance product. The practical implementation of DCE is finally discussed and some alternative implementation schemes are presented.

Casting 1 Tb/s DP-QPSK communication into 200 GHz bandwidth

We demonstrate the feasibility of a novel time-frequency packing technique to implement DP-QPSK communication with a record spectral efficiency ranging from 5.14 to 4.3 bit/s/Hz over a distance ranging from 3000 km to 5200 km of uncompensated standard fiber, respectively.

Optical Time–Frequency Packing: Principles, Design, Implementation, and Experimental Demonstration

Time-frequency packing (TFP) transmission provides the highest achievable spectral efficiency with a constrained symbol alphabet and detector complexity. In this paper, the application of the TFP technique to fiber-optic systems is investigated and experimentally demonstrated. The main theoretical aspects, design guidelines, and implementation issues are discussed, focusing on those aspects which are peculiar to TFP systems. In particular, adaptive compensation of propagation impairments, matched filtering, and maximum a posteriori probability detection are obtained by a combination of a two-dimensional equalizer and four eight-state parallel Bahl-Cocke-Jelinek-Raviv (BCJR) detectors. A novel algorithm that ensures adaptive equalization, channel estimation, and a proper distribution of tasks between the equalizer and BCJR detectors is proposed. A set of irregular low-density parity-check codes with different rates is designed to operate at low error rates and approach the spectral efficiency limit achievable by TFP at different signal-to-noise ratios. An experimental demonstration of the designed system is finally provided with five dual-polarization QPSK-modulated optical carriers, densely packed in a 100-GHz bandwidth, employing a recirculating loop to test the performance of the system at different transmission distances.

Time-Frequency Packing for High-Capacity Coherent Optical Links

We consider realistic long-haul optical links, with linear and nonlinear impairments, and investigate the application of time-frequency packing with low-order constellations as a possible solution to increase the spectral efficiency. A detailed comparison with available techniques from the literature will be also performed. We will see that this technique represents a feasible solution to overcome the relevant theoretical and technological issues related to this spectral efficiency increase and could be more effective than the simple adoption of high-order modulation formats.

Channel Estimation Algorithms for MLSD in Optical Communication Systems

Maximum likelihood sequence detection represents the most efficient technique in the electrical domain to combat fiber impairments such as polarization-mode dispersion and group-velocity dispersion. In order to successfully apply this technique, it is mandatory to estimate some key channel parameters needed by the Viterbi processor. We propose a simple and effective solution based on the least-mean-square algorithm to perform such an estimation

Blind Adaptive Chromatic Dispersion Compensation and Estimation for DSP-Based Coherent Optical Systems

We propose an accurate and low-complexity blind adaptive algorithm for chromatic dispersion (CD) compensation and estimation in coherent optical systems. The method is based on a Frequency Domain Equalizer (FDE), a low complexity Time Domain Equalizer arranged in a butterfly structure (B-TDE) and an Optical Performance Monitoring (OPM) block in a loop configuration. The loop is such that, at each iteration, the CD value compensated by the B-TDE and estimated by the OPM is given to the FDE; according to this estimation, in the subsequent iteration, the FDE compensates also this quantity. The procedure is repeated until the majority of CD is compensated by the FDE and a small residual quantity is compensated by a low complexity B-TDE with a small number of taps. The method is extended to long haul uncompensated links exploiting the information on the mean square error (MSE) provided by the B-TDE. The proposed algorithm is then experimentally validated for a polarization multiplexed quadrature phase shift keying (PM-QPSK) signal at 112 Gbit/s propagating along 1000 km of uncompensated Z PLUS® optical fiber. A statistical analysis of the performance of the proposed solution, in terms of mean value and standard deviation of the CD estimation error, is carried out, running a set of simulations including different impairments, such as noise, polarization dependent loss, polarization mode dispersion and self-phase modulation in a line of 1000 km of uncompensated G.652 optical fiber. Our method could be used to compensate and estimate any CD quantity without increasing the number of taps in the B-TDE and exploiting devices already included in the system (TDE, FDE and OPM) arranged in a loop.