Low-complexity Nonlinear Equalization Research Articles

C-band 120-Gb/s PAM-4 transmissions over a 100-km dispersion-uncompensated SSMF using joint combined pulse shaping and low-complexity nonlinear equalization.

In C-band intensity modulation and direct detection (IM/DD) systems, the frequency-dependent power fading induced by chromatic dispersion (CD) and square-law detection limits the transmission capacity and distance, especially for beyond 100-Gb/s transmissions over a 100-km dispersion-uncompensated link. To reach this goal, we propose a scheme of nonlinear pre-distortion, novel, to the best of our knowledge, combined pulse shaping, and post nonlinear equalization for four-level pulse amplitude modulation (PAM-4)-based IM/DD systems. At the transmitter, the nonlinear pre-distortion is used to generate unequally spaced PAM-4 symbols for pre-compensating the nonlinearities. While the novel pulse shaping, simply shaped by the linear combination of two inter-symbol interference (ISI)-free pulses, alters the frequency-domain power distribution of the PAM-4 signal and results in performance improvement. At the receiver, low-complexity post nonlinear equalization using an absolute-term based nonlinear equalizer with weight sharing (AT-NLE-WS) is performed to eliminate CD-induced power fading and residual nonlinear impairments. With the cooperation of these techniques, record 120-Gb/s PAM-4 signals are successfully transmitted over a 100-km standard single-mode fiber (SSMF) with the measured bit error ratio (BER) below 3.8 × 10-3, achieving >9% improvement of system capacity in comparison with the conventional pulse shaping schemes.

Single-Lane 54-Gbit/s PAM-4/8 Signal Transmissions Using 10G-Class Directly Modulated Lasers Enabled by Low-Complexity Nonlinear Digital Equalization

This work presents the use of a directly modulated laser (DML) in time- and wavelength division multiplexed passive optical networks (TWDM-PONs), in which an EDFA-based booster amplification and an SOA-based pre-amplification are utilized to improve the optical power budget. We experimentally demonstrate the C-band optically amplified data transmissions and compare the performance of the non-return-to-zero on-off keying (NRZ-OOK), four and eight-level pulse amplitude modulation (PAM-4/PAM-8) using a 10-G class DML. With optical amplification, the uplink and downlink power budgets of about 28 dB and 35 dB, respectively, are achieved for the PAM-4 54-Gbit/s signals at the hard-decision forward error correction (HD-FEC) limit of 3.8x10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> after transmissions over a 25-km single-mode fiber link. To mitigate waveform distortions caused by the limited bandwidth, nonlinear dynamics, memory effects, and strong laser frequency chirp of the DML, especially during multi-level signal modulations, artificial neural network-based machine learning equalizers and low-complexity Volterra nonlinear equalizers are applied, which operate at the signal baud rate. The bit error ratio performance in conjunction with an enhanced power budget through the use of a low-complexity nonlinear equalizer can justify the validity of using a DML in the next-generation PONs.

Low-complexity nonlinear equalizer based on artificial neural network for 112 Gbit/s PAM-4 transmission using DML

Artificial neural network (ANN) can easily approximate a nonlinear function and has strong nonlinear representation ability. Nonlinear equalizer based on artificial neural network (ANN-NLE) has been proved to be effective in dealing with linear and nonlinear impairments in different types of short reach intensity modulation with direct detection (IM/DD) systems. However, the complexity of ANN-NLE is very high, which limits the application in low-cost direct detection systems. We propose a novel weight pruning method named dynamic pruning to reduce the complexity of ANN-NLE. We demonstrate a C-band 112 Gbit/s four-level pulse-amplitude modulation (PAM-4) system over 4 km standard single mode fiber (SSMF) transmission. The simulation results show that the dynamic pruning method and weight pruning method have similar computational complexity after pruning, and the dynamic pruning method has better performance and lower bit error rate (BER).

56-Gbit/s PAM-4 Optical Signal Transmission Over 100-km SMF Enabled by TCNN Regression Model

Due to the interaction between chromatic dispersion (CD) and direct detection, the CD induced power-fading effect has been considered as the key point to limit transmission rate and distance in intensity modulation direct-detection (IM/DD) systems. Besides, the performance of the IM/DD systems will be further affected by the bandwidth limitation and nonlinearity effect. In this paper, we propose a low complexity nonlinear equalizer (NLE) based on temporal convolutional neural network (TCNN) regression model which combines dilated convolutions with residual connections. Then, the performance of our proposed equalizer is experimentally demonstrated in 56-Gbit/s 4-level pulse amplitude modulation (PAM4) intensity modulation direct-detection system. The results show that the receiver sensitivity with the help of our TCNN equalizer can be improved about 1.5 dB and 3.5 dB compared to 2D-CNN and 1D-CNN equalizer under 70-km single mode fiber (SMF) transmission. Furthermore, the proposed equalizer can extend maximum transmission distance to 100 km at bit error rate threshold of 3.8 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> .

Physics-Based Deep Learning for Fiber-Optic Communication Systems

We propose a new machine-learning approach for fiber-optic communication systems whose signal propagation is governed by the nonlinear Schrodinger equation (NLSE). Our main observation is that the popular split-step method (SSM) for numerically solving the NLSE has essentially the same functional form as a deep multi-layer neural network; in both cases, one alternates linear steps and pointwise nonlinearities. We exploit this connection by parameterizing the SSM and viewing the linear steps as general linear functions, similar to the weight matrices in a neural network. The resulting physics-based machine-learning model has several advantages over “black-box” function approximators. For example, it allows us to examine and interpret the learned solutions in order to understand why they perform well. As an application, low-complexity nonlinear equalization is considered, where the task is to efficiently invert the NLSE. This is commonly referred to as digital backpropagation (DBP). Rather than employing neural networks, the proposed algorithm, dubbed learned DBP (LDBP), uses the physics-based model with trainable filters in each step and its complexity is reduced by progressively pruning filter taps during gradient descent. Our main finding is that the filters can be pruned to remarkably short lengths—as few as 3 taps/step—without sacrificing performance. As a result, the complexity can be reduced by orders of magnitude in comparison to prior work. By inspecting the filter responses, an additional theoretical justification for the learned parameter configurations is provided. Our work illustrates that combining data-driven optimization with existing domain knowledge can generate new insights into old communications problems.

Low-complexity nonlinear equalizer based on absolute operation for C-band IM/DD systems

The intensity-modulation/direct-detection transmission system operating in the C-band suffers from nonlinear waveform distortions induced by fiber chromatic dispersion due to the square-law detection. The Volterra nonlinear equalizers (VNLEs) can be used at the receiver to compensate for such distortions. However, the major concern about the equalizers is their huge implementation complexity. In this paper, we propose and demonstrate a low-complexity nonlinear equalizer based on the absolute operation for a cost-sensitive IM/DD system. In this equalizer, the cross-beating product terms (required in VNLE) are replaced with the absolute operation of the sum of two input samples. We evaluate the performance of the proposed equalizer over a 56-Gb/s 4-ary pulse amplitude modulation transmission system implemented by using 1.5-µm directly modulated laser or electro-absorption modulated laser. The results show that the proposed equalizer performs similar to the 2nd-order diagonally-pruned VNLE, but lowers the implementation complexity by >20%. We also show that the proposed equalizer outperforms the VNLE when the implementation complexities of the two nonlinear equalizers are similar.

Nonlinear Equalizer Based on Neural Networks for PAM-4 Signal Transmission Using DML

Nonlinear distortion from a directly modulated laser (DML) is one of the major limiting factors to enhance the transmission capacity beyond 10 Gb/s for an intensity modulation direct-detection optical access network. In this letter, we propose and demonstrate a low-complexity nonlinear equalizer (NLE) based on a machine-learning algorithm called artificial neural network (ANN). Experimental results for a DML-based 20-Gb/s signal transmission over an 18-km SMF-28e fiber at 1310-nm employing pulse amplitude modulation (PAM)-4 confirm that the proposed ANN-NLE equalizer can increase the channel capacity and significantly reduce the impact of nonlinear penalties.