A Multi-Rate Approach for Nonlinear Pre-Distortion Using End-to-End Deep Learning in IM-DD Systems

Modern intra-data center (IDC) interconnects leverage robust and low-cost intensity modulation (IM) and direct detection (DD) optical links, based on multimode fibers (MMFs) and vertical-cavity surface-emitting lasers (VCSELs). Current solutions, based on on-off keying (OOK) modulations, reach up to 25-50 Gbps per lane over nearly 100 meters. The actual target for IDCs is to increase VCSEL-MMF links capacity up to 100 Gbps, using PAM-4 on the same devices. To counteract the consequent linear and nonlinear distortions affecting the transmitted signals, an effective solution is to exploit digital signal processing (DSP). In this manuscript, we propose a novel method to optimize a nonlinear artificial neural network (ANN) digital pre-distorter (DPD), based on End-to-end (E2E) learning, that, trained jointly with a Feed-Forward Equalizer (FFE), fulfills physical amplitude constraints and handles different ratio between the sampling rates incurring along with an optical IM-DD system. We indeed propose an E2E ANN system operating simultaneously at different sampling frequencies. We moreover propose in our training method a substitution to the time-domain injection of the receiver noise in the system with an additive regularization term in the FFE gradient loss. We experimentally show the advantages of our proposed DPD comparing the bit error rate (BER) performance against the same scenario without DPD. We assess the gain in terms of Gross Bit Rate and Optical Path Loss (OPL), at given BER targets, for different fiber lengths

Design rules for reach maximization in uncompensated Nyquist-WDM links

We propose analytical design rules to predict relative maximum reach variations in NyWDM uncompensated links. Tradeoffs among system parameters are shown. Validation is demonstrated using experimental data. The method can be used also for comparison of different modulation format

Efficient Time-Domain DBP using Random Step-Size and Multi-Band Quantization

Employing step-size randomization and multi-band quantization, we propose a reduced complexity time-domain (TD) digital backpropagation (DBP) and experimentally demonstrate penalty-free operation at an average number of ~4 bits per FIR coefficient

Joint Carrier-Phase Estimation for Digital Subcarrier Multiplexing Systems With Symbol-Rate Optimization

Digital subcarrier multiplexing (SCM) has recently emerged as a promising solution for next-generation ultra-high-baudrate coherent optical communication systems. Among its distinctive advantages over traditional single-carrier modulation, SCM enables the exploitation of symbol-rate optimization (SRO), which has been shown to enable the passive mitigation of the nonlinear interference noise (NLIN) that is generated during propagation over dispersion-unmanaged optical fiber systems. However, the full exploitation of SRO-based NLIN mitigation is severely hindered by the uncompensated distortion caused by laser phase noise (LPN) and non-linear phase noise (NLPN), whose impact is magnified by the use of low-baudrate subcarriers. Resorting to low-complexity carrier phase estimation (CPE) algorithms, in this paper we experimentally demonstrate that it is possible to overcome the hurdles posed by LPN and NLPN in SCM systems, provided that adequate joint-subcarrier CPE processing is employed. A dual-stage joint-processing approach composed of a pilot-based CPE optionally followed by a blind phase search (BPS)-based estimator is implemented and experimentally assessed, enabling to effectively optimize the symbol-rate per subcarrier down to 3 GBaud, in accordance with the theoretical SRO predictions for the system under test. In addition, we demonstrate that signal-to-noise ratio (SNR) gains of more than 1 dB can be achieved through joint-subcarrier CPE processing in shorter-reach links, while this gain tends to progressively reduce with increasing propagation distance, down to about 0.5 dB gain after 3000 km propagation

Nonlinear mitigation on subcarrier-multiplexed PM-16QAM optical systems

We report a comprehensive set of experimental, simulation and analytical results on the benefit of nonlinear mitigation strategies for multi-subcarrier (MSC) PM-16QAM transmission systems. First, we demonstrate 9% maximum reach gain enabled by symbol-rate optimization (SRO) of MSC-PM-16QAM in a 31 channels WDM transmission experiment. Then, we demonstrate that, in the considered experimental scenario, the gain provided by digital backpropagation (DBP) over single-carrier (SC) transmission is similar to that achieved by SRO over MSC transmission. Furthermore, we show that the SRO phenomenon can be weakened after self-channel interference (SCI) removal through DBP. As a result, and due to DBP performance limitations in the experiment, the combined eect of SRO and DBP was found to enable only an additional 4% gain in maximum reach. Finally, we address the impact and symbol-rate dependence of nonlinear phase noise (NLPN) in MSC-PM-16QAM transmission, discussing on the NLPN mitigation capability of standard carrier phase estimation (CPE) and on respective gains that could be achieved through its enhanced mitigation

ML-Based Spectral Power Profiles Prediction in Presence of ISRS for Ultra-Wideband Transmission

A generalized method based on machine learning (ML) and artificial neural networks (ANNs) is proposed for a fast and accurate prediction of spectral and spatial evolution of power profiles in support of performance and quality-of-transmission (QoT) real-time assessment of ultra-wideband links. These systems, operating on bandwidths larger than the standard C–band, are affected by inter-channel stimulated Raman scattering (ISRS), whose impact on power profiles evolution along the fiber is generally estimated by solving numerically a set of nonlinear ordinary differential equations (ODEs). However, the computational effort, in terms of complexity and convergence time to the solution, increases with the bandwidth and the number of transmitted wavelength division multiplexing (WDM) channels, which makes the usual approach no longer particularly suitable to operate in real time. To meet the speed requirements, three different ANNs are introduced to make fast predictions of power profiles over frequency and distance considering a wide range of scenarios: different power per channel values, different fiber types and different span lengths. Two ANNs are used on synthetic data to estimate the impact of linear and nonlinear fiber impairments in support of system modeling. Specifically, one to directly predict the evolution of spectral power profiles along the fiber and the other to estimate the coefficients to insert in a closed-form version of the EGN model. A third ANN operates on experimental data and it is used to predict power profiles at the end of the fiber for fast estimations of system performance. The obtained results show highly accurate predictions with values of maximum absolute error, computed between predicted and actual power profiles, not exceeding 0.2 dB for ∼97% of cases for synthetic data and always below 0.5 dB for experimental data. Such results prove the potential of the proposed approach making it suitable for real time application of QoT estimation