Giancarlo Prati

Achievable Information Rate in Nonlinear WDM Fiber-Optic Systems With Arbitrary Modulation Formats and Dispersion Maps

The problem of analytical evaluation of the maximum rate at which information can be reliably transmitted on a nonlinear wavelength division multiplexing fiber-optic channel with a given modulation format and detection strategy is addressed. An approximate solution of the nonlinear Schrödinger equation is adopted to obtain an accurate analytical discrete-time channel model, valid for arbitrary link configurations and modulation formats. By exploiting the concept of mismatched decoding, considering a sub-optimum detection strategy that accounts for intra-channel nonlinearities, the proposed model is employed to derive closed-form expressions of the achievable information rate with various modulation formats. All the analytical results are verified through comparison with numerical simulations in different scenarios.

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.

Novel optical line codes tolerant to fiber chromatic dispersion

A novel family of optical line codes to counteract the effects of a dispersive fiber is presented. The performance of the first code in the family, referred to as order-1 code, is analytically evaluated and compared to that of the duobinary and phased amplitude-shift signaling (PASS) codes, which are a modified form of duobinary proposed by Stark et al. (1999). The order-1 line code turns out to be very robust to chromatic dispersion and, for a given penalty, allows the bridging of a distance 1.5 times (or more) greater than duobinary. The novel family of codes was conceived by exploiting the finding that, approximately, a very dispersive fiber turns an input pulse into the form of its Fourier transform seen in the time domain. Higher-order codes allow the bridging of larger distances if combined with appropriate chirping.

Exact analytical evaluation of second-order PMD impact on the outage probability for a compensated system

An exact analytical method for evaluating the outage probability due to second-order polarization mode dispersion in a system with first-order compensation is presented. In an uncompensated system the outage is mainly due to the mean differential group delay, whereas higher order effects have low impact. It is shown that in a compensated system all orders contribute to the outage probability, whereas accounting for exact second-order only gives a slight overestimate. Approximate second-order models leaving residual higher order effects may lead to very different outage probabilities.

Narrow filtered DPSK implements order-1 CAPS optical line coding

A novel family of optical line codes has been presented elsewhere, here referred to as combined amplitude-phase shift (CAPS) codes. We show here that narrow filtering of a differential phase shift keying signal with bandwidth equal to about 2/3 of the bit rate turns out to closely implement the order-1 CAPS line coding. Performance of the two systems is compared for various types of optical filters.

Self-Orthogonalizing Adaptive Equalization in the Discrete Frequency Domain

A self-orthogonalizing discrete adaptive equalizer for synchronous data transmission is presented, based on the overlapsave filtering technique. Self-orthogonalization in the discrete frequency domain is adaptively performed by premultiplying by a diagonal matrix the MSE gradient estimates before projecting by means of Rosens gradient projection method. The diagonal of the matrix is the inverse of the power spectrum of the received sequence taken at equally spaced frequencies, and estimates are obtained by using Bartletts procedure of periodograms averaging for spectrum estimation. Projection is accomplished by means of an off-line derived projection matrix. Confidence of gradient estimates is improved by means of a block correlated estimation technique using available DFTs of blocks of data. This equalizer is compared to time-domain self-orthogonalizing algorithms as regards speed of convergence and ease of implementation. During the short startup phase, convergence is competitive with that of Godards algorithm, which is the fastest algorithm known, and in the decision-directed mode, fast convolution performed by blocks results in a considerable reduction of the number of multiplications with respect to the time domain algorithms. A computationally simpler, unconstrained startup algorithm is also examined, obtained by removing the projection while retaining gradient block estimates in the DFD.

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.

Adaptive minimum MSE controlled PLC optical equalizer for chromatic dispersion compensation

With the advent of very high-bit-rate optical communication systems (40 Gb/s and beyond) and the progressive transformation of the optical layer in a real networking layer, a channel-by-channel adaptive optical equalization will be needed. An adaptive optical equalizer for chromatic dispersion compensation, based on planar lightwave circuit (PLC) technology and controlled by a minimum mean square error (MSE) strategy, is proposed here. It is shown in a rigorous manner how the PLC parameters are to be adjusted and that the control algorithm is effective even with a few stages PLC equalizer, performing better than other nonadaptive control techniques. An analysis of the dynamic behavior of the equalizer shows that, in a realistic time-varying scenario, it can easily adapt to slow channel variations and is able to quickly restore a minimum MSE condition after an abrupt chromatic dispersion variation.