Gradient-descent noise whitening techniques for short-reach IM-DD optical interconnects with severe bandwidth limitation.

Bandwidth limitation in optoelectrical components and the chromatic dispersion-induced power fading phenomenon cause severe inter-symbol interference (ISI) in high-speed intensity modulation and direct detection (IM-DD) optical interconnects. While the equalizer implemented in the receiver's digital signal processing procedure can mitigate ISI, it also inevitably enhances the noise located in the decayed frequency region, known as equalization-enhanced colored noise (EECN). Additionally, the nonlinear impairments of the modulator and photodetector also deteriorate the performance of the IM-DD system, especially for high-order modulation formats. In this work, we propose a gradient-descent noise whitening (GD-NW) algorithm to address EECN and extend it by introducing nonlinear kernels to simultaneously mitigate EECN and nonlinear impairments. The proposed algorithms are compared with conventional counterparts in terms of the achievable baud rate and the receiver optical power sensitivity. As a proof-of-concept experiment, we validate the principles of the proposed algorithms by successfully transmitting 360-GBd on-off-keying (OOK) and 180-GBd 4-level pulse-amplitude-modulation (PAM-4) signals in the back-to-back case under a 62-GHz brick-wall bandwidth limitation. 280-GBd OOK and 150-GBd PAM-4 transmissions are also demonstrated over 1-km standard single-mode fiber with a bit error rate below 7% hard-decision forward error correction aided by the proposed approach.

Two-level coding for efficient digital radio-over-fiber transmission with unequal bit protection.

The digital radio-over-fiber (D-RoF) transmission with two-level coding (TLC) is proposed and demonstrated in this Letter. A joint design considering the importance of quantization bits, the protection ability of forward error correction (FEC), and the bit error ratio of quadrature amplitude modulation (QAM) symbols is realized. In TLC-based D-RoF systems, the more significant bits among quantization bits are protected by a FEC and are assigned to the least reliable bits of modulated QAM symbols. Conversely, the less significant bits, without FEC protection, are allocated to the more reliable bits of QAM symbols. Experiments on an 11-km standard single-mode fiber transmission are conducted to evaluate the performance. The results indicate that, with a maximum iteration number of 2, compared to the conventional bit-interleaved coded modulation (BICM) with all bits encoded, the D-RoF based on TLC attains nearly identical performance under the 0.34% error vector magnitude threshold of 65536QAM wireless signals, specifically achieving complexity reductions of 54.55% and 67.66% for 16QAM and 64QAM optical transmissions, respectively.

Computationally efficient composite triple beat cancellation for DML-based DA-RoF fronthaul.

The digital-analog radio-over-fiber (DA-RoF) scheme offers a high-fidelity and spectrally efficient solution for future mobile fronthaul. However, to be implemented in the low-cost directly modulated laser with direct detection (DML-DD) link, both the digital and analog parts in DA-RoF modulation would suffer from the composite second-order (CSO) and composite triple beat (CTB) caused by the chirp-dispersion interaction. In this Letter, we propose and experimentally demonstrate a computationally efficient composite triple beat cancellation (CTB-C) algorithm for DA-RoF fronthaul in the dispersion-uncompensated C-band DML-DD link. The CSO and CTB are suppressed at the receiver-side DSP based on the theoretical model of these nonlinear distortions. In the proof-of-concept experiment, a 1.2-dB improvement in the recovered signal-to-noise ratio (SNR) is obtained with 5.5-GHz 1024-QAM orthogonal frequency division multiplexing (OFDM) signal after 10-km standard single-mode fiber (SSMF) transmission. The proposed CTB-C technique does not require the training process and performs close to the Volterra-based feed-forward equalizer (VFE) under the complexity constraint.

Fast polarization state tracking for dual-polarization direct detection with Jones-space field recovery.

Direct detection system is expected to possess the phase and polarization diversity in order to achieve high spectral efficiency and fiber impairment compensation such as chromatic dispersion and polarization rotation. In this Letter, we theoretically extend the concept of the proposed Jones-space field recovery (JSFR) to include a dynamic polarization rotation matrix and experimentally demonstrate the rapid polarization state tracking ability of the JSFR receiver based on a 3 × 3 optical coupler. Under a rotation of the state of polarization at a rate of 1 Mrad/s, we successfully transmit 59-GBd dual-polarization 16-ary quadrature-amplitude-modulation signals over an 80-km standard single-mode fiber based on a decision-directed least mean square (DD-LMS) or a recursive least square (DD-RLS), with a bit-error rate below the 14% hard-decision forward error correction threshold of 1 × 10-2. The experimental results indicate that the legacy polarization tracking algorithms designed for coherent optical communication are also applicable for this direct detection scheme. To our best knowledge, this work demonstrates the first polarization rotation-tolerant direct detection system with phase and polarization diversity, providing a low-cost and high-speed solution for short-reach communications.

Low-complexity amplitude-division irregular QAM formats for short-reach unamplified coherent optical systems.

A low-complexity scheme is proposed to realize irregular uniform quadrature amplitude modulation (QAM) formats with Gray mapping, which are named amplitude-division irregular QAM (AD-Ir-QAM) formats. Compared to conventional probabilistic shaping (PS) with the Maxwell-Boltzmann (MB) distribution (PS-MB), irregular QAM formats show a smaller peak-to-average power (PAPR) and achieve a better performance in systems with the peak-power constraint. Compared with irregular QAM formats realized by PS (PS-Ir-QAM), AD-Ir-QAM formats realize a more flexible rate adaptation and have a lower implementation complexity. Experimental results obtained in an unamplified coherent optical system show that, at a generalized mutual information (GMI) of 4.5 bits/2D-symbol, AD-Ir-100QAM achieves gains of 2.1 and 0.5 dB in the power budget over PS-MB-100QAM and PS-Ir-100QAM, respectively.

Digital pre-distortion using a Gauss-Newton-based direct learning architecture for coherent optical transmitters.

Digital pre-distortion (DPD) is a powerful technique to mitigate transmitter nonlinear distortion in optical transmissions. In this Letter, the identification of DPD coefficients based on the direct learning architecture (DLA) using the Gauss-Newton (GN) method is applied in optical communications for the first time. To the best of our knowledge, this is the first time that the DLA has been realized without training an auxiliary neural network to mitigate optical transmitter nonlinear distortion. We describe the principle of the DLA using the GN method and compare the DLA with the indirect learning architecture (ILA) that uses the least-square (LS) method. Extensive numerical and experimental results indicate that the GN-based DLA is superior to the LS-based ILA, especially in a low signal-to-noise ratio scenario.

Optical filtering impairment monitoring based on model fusion for optical networks.

Reconfigurable optical add-and-drop multiplexer (ROADM) is a key element in optical networks. As several ROADMs are cascaded over long paths, the penalty induced by ROADM has become non-negligible due to the tight optical filtering. In this case, for efficient and reliable network planning and operation, accurate monitoring of optical filtering penalty is very important. In this paper, we propose a real-time optical filtering monitoring scheme based on model fusion. We combine an analytical model based on the digital communications theory of band-limited channels with linear equalization and a data-driven model implemented using artificial neural network (ANN). The scheme can achieve high accuracy and interpretability. Moreover, since the input features are extracted from configuration parameters and receiver digital signal processing (DSP), no additional devices are needed, which is attractive for practical deployment. Extensive simulations and experiments are conducted to investigate the performance of the scheme, and the results show the superior performance.

Asymmetric point-to-multipoint coherent architecture with a frequency aliasing recovery algorithm for cost-constraint short-reach access networks.

An asymmetric point-to-multipoint (PTMP) coherent architecture combined with a frequency aliasing recovery (FAR) algorithm is proposed for cost-constraint short-reach access networks. In this architecture, the uplink transmitters are simplified significantly with the uplink dual-polarization four-level pulse amplitude modulation (DP-PAM4) and downlink DP quadrature phase shift keying (DP-QPSK) asymmetric transmission design. Digital to analog converters (DACs) and radio frequency (RF) drivers are reduced by half, and in-phase and quadrature modulators (IQMs) are replaced by Mach-Zehnder modulators (MZMs), saving four MZ interferometers (MZIs). Furthermore, based on the asymmetric architecture, the FAR algorithm can recover signals from frequency aliasing caused by frequency offset (FO), even when half of the signal spectrum is aliased. This algorithm enables the asymmetric architecture to narrow down guard bands between subcarriers or even overlap the subcarriers, saving the receiver bandwidth at the aggregation/hub side. The performance of the asymmetric uplink DP-PAM4 transmission with the FAR algorithm is evaluated in both simualations and experiments. The effects of laser linewidths and IQ skew on the performance of the FAR algorithm are also analyzed. Simulation results show the algorithm can recover 16 Gbaud and 32 Gbaud signal from 8 GHz and 16 GHz aliasing, respectively. In the experiments with 10 km fiber transmissions, the FAR algorithm can recover 10 Gbaud signals from 5 GHz frequency aliasing, saving about 20.83% of the total receiver bandwidth in a 2-subcarrier system.

Coherent digital-analog radio-over-fiber (DA-RoF) system with a CPRI-equivalent data rate beyond 1 Tb/s for fronthaul.

We propose and experimentally demonstrate a coherent digital-analog radio-over-fiber (DA-RoF) system and achieve the transmission of Tb/s common public radio interface (CPRI)-equivalent data rate for fronthaul. The proposed coherent DA-RoF system includes DA-RoF modulation, demodulation and DA-RoF compatible coherent digital signal processing (DSP) blocks. A theoretical analysis of the DA-RoF scheme together with parameter optimization is accomplished as well. In the experiment, a 25 Gbaud DA-RoF signal with 1 Tb/s CPRI-equivalent data rate is transmitted in the system, satisfying the error vector magnitude (EVM) requirement for 256-quadrature amplitude modulation (QAM) signal transmission. With the symbol rate reduced to 10 Gbaud, an EVM below 2.5% is achieved, which meets the requirement for 1024-QAM transmission. The experimental results show that the coherent DA-RoF system is a promising solution for future fronthaul.

Cascaded digital-analog radio-over-fiber for efficient SNR scaling at >10†dB per extra bandwidth.

Efficient signal-to-noise ratio (SNR) and spectral efficiency (SE) trade-off can offer fundamental guiding law for future large-capacity and high-fidelity mobile fronthaul. In this Letter, we propose and experimentally demonstrate a cascaded digital-analog radio-over-fiber (CDA-RoF) scheme, which transmits digitized and analog segments using time-division-multiplexing aggregation. Specifically, multiple digital parts generated by a rounding function describe the main features of the original waveform, while the residual error is magnified and delivered as analog RoF with SE advantage. Based on a 20-GHz O-band directly modulated laser (DML), an SNR enhancement of >10 dB is observed for each extra bandwidth. Up to 70.4-dB SNR is also achieved for a 3.5-GHz 1048576-ary quadrature amplitude modulation (1048576-QAM) signal after 20-km standard single-mode fiber (SSMF) transmission.

Coherent chaotic optical communication of 30 Gb/s over 340-km fiber transmission via deep learning.

Chaotic optical communication has attracted much attention as a hardware encryption method in the physical layer. Limited by the requirements of chaotic hardware synchronization, fiber transmission impairments are restrictedly compensated in the optical domain. There has been little experimental demonstration of high-speed and long-distance chaotic optical communication systems. Here, we propose a method to overcome such limitations. Using a deep-learning model to realize chaotic synchronization in the digital domain, fiber transmission impairments can be compensated by digital-signal processing (DSP) algorithms with coherent detection. A successful transmission of 30 Gb/s quadrature phase-shift keying messages hidden in a 15 GHz wideband chaotic optical carrier was experimentally demonstrated over a 340-km fiber link. Meanwhile, the chaotic receiver can be significantly simplified without compromising security. The proposed method is a possible way to promote the practical application of chaotic optical communications.

Feature issue introduction: ultra-wideband optical communications.

This Feature Issue covers the important aspects to develop ultra-wideband optical communication systems including optoelectronics, impairment modeling and compensation, optical amplification, superchannel and multi-band transmission and control, and so forth. This Introduction provides a summary of the articles on these topics in this Feature Issue.

Subcarrier-pairing entropy loading for digital subcarrier-multiplexing systems with colored-SNR distributions.

A subcarrier-pairing entropy loading (SubP-EL) scheme with fairly low complexity is proposed for digital subcarrier-multiplexing (SCM) systems with colored signal-to-noise ratio (SNR) distributions. With the constraint of the target entropy, SubP-EL iteratively optimizes the entropy of subcarriers in pair. After convergence, SubP-EL can approach the optimal performance which is evaluated in simulations and experiments by comparison with the brute-force search method. Meanwhile the complexity of SubP-EL is significantly reduced compared with the brute-force search. In particular, in an 8-subcarrier system with five different SNRs, the complexity of SubP-EL is reduced by approximately a factor of 764, 95 and 13 with the entropy granularities of 0.05 bits/2D-symbol, 0.1 bits/2D-symbol and 0.2 bits/2D-symbol, respectively. The performance of SubP-EL is evaluated in simulations and experiments. In the experiments with 345 km fiber transmissions, the average NGMI gain of SubP-EL over the system without entropy loading is 0.0286 for different optical filtering cases.

Frequency-offset-tolerant optical frequency comb-based coherent transmission for intra-datacenter interconnections.

In recent years, in order to increase the capacity and scalability of intra-datacenter (DC) transmission, the optical frequency comb (OFC) source has been considered promising to replace discrete lasers, aiming to reduce the cost of wavelength division multiplexing (WDM) transmission within DC. In this paper, an OFC based coherent architecture is proposed. An OFC, in the receiver side, is split by a splitter with a uniform power ratio and separately used as local oscillators (LOs) to detect the demultiplexed signals. The signal spectrum is copied onto every tone of the LO-OFC, and a large frequency offset (FO) tolerance is achieved. In addition, the required ADC sampling rate is the same as a system without FO. Extensive simulations are conducted. In the simulated coherent WDM transmission system, a 3-tone-OFC is used to provide 3 carriers, and an 11-tone-OFC is split and used to provide LO-OFCs. For a 64GBd polarization multiplexing 16 quadrature amplitude modulation (PM-16QAM) WDM transmission, the tolerances of FO are up to about ±0.3THz and ±0.374THz for the 1st/3rd signal, and the 2nd signal, respectively, below the pre-forward error correction (FEC) bit error rate (BER) level of 1.25×10-2. Moreover, the maximum tolerance of FO linearly increases with the number of effective tones in LO-OFC. Further, extensive experiments with back-to-back connection are conducted to verify the performance. The tolerance of FO is up to >36 GHz for 36GBd PM-16QAM transmission with a 3-tone-LO-OFC below the BER level of 1.25×10-2. The proposed OFC based coherent architecture is a promising solution for intra-DC interconnections with a large FO.

Ultra-fast RSOP tracking via 3 pilot tones for short-distance coherent SCM systems.

We propose an algorithm to track the rotation of state of polarization (RSOP) for short-distance coherent subcarrier-multiplexing systems. 3 pilot tones are used to estimate RSOP matrices on a block-by-block basis and recover phase noise as well. An ultra-fast RSOP tracking ability using the proposed algorithm is demonstrated by experiment. Specifically, the bit error rate increases from 2.3×10-3 to 5.6×10-3 when the RSOP speed increases from 0 rad/s to 50 Mrad/s. We also demonstrate the robustness of the algorithm against polarization mode dispersion and polarization dependent loss.

Degenerated look-up table-based perturbative fiber nonlinearity compensation algorithm for probabilistically shaped signals.

A degenerated look-up table-based perturbative nonlinearity compensation (DLUT-PNC) algorithm is proposed to compensate for intra-channel fiber nonlinearity. It can flexibly optimize the implementation complexity for probabilistically shaped (PS) signals with different shaping rates. In addition, we propose a homomorphic DLUT-PNC (HDLUT-PNC) scheme to further reduce the complexity. In simulations with a transmission distance of 1200-km for 70-GBaud PS-16QAM signals, both the performances of the DLUT-PNC and HDLUT-PNC are investigated and compared. The HDLUT-PNC scheme significantly reduces the table's input size, number of look-up operations and number of complex multipliers compared to the DLUT-PNC. Moreover, we also numerically investigate 56-Gbaud PS-32QAM signals with a transmission distance of 800-km, and the results are similar. Finally, the performance is verified in experiments for PS-16QAM signals with a transmission distance of 432-km.

Single-step digital backpropagation for subcarrier-multiplexing transmissions.

We propose and demonstrate a single-step digital back propagation (DBP) algorithm for metro and regional transmissions with high order modulation formats. Based on subcarrier-multiplexing (SCM)-DBP, two modifications are made to improve performance and reduce complexity for the targeted link scenarios. First, an infinite impulse response (IIR) filter is adopted in self-subcarrier nonlinear compensation. Second, the second stage chromatic dispersion (CD) compensation is incorporated into an existing adaptive filter. Through experiment, we demonstrate the performance of the proposed scheme, denoted as M-SCM-DBP, for single channel 34.94-GBd SCM PDM-32QAM transmission. With 86.3% complexity reduction compared with the low-pass filter assisted DBP, the proposed M-SCM-DBP achieves 0.6-dB Q2 improvement for SCM-PDM-32QAM transmission over 960-km standard single mode fiber (SSMF). The reach extension of 36% to 1220-km is achieved with only 30.5 complex multiplications per sample, in comparison with the linear compensation scheme. Since the adaptive filter is used to simultaneously compensate 50% CD and other linear impairments, we also investigate the required number of filter taps and its polarization tracking ability.

Reservoir computing system with double optoelectronic feedback loops.

Reservoir computing (RC) by supervised training, a bio-inspired paradigm, is gaining popularity for processing time-dependent data. Compared to conventional recurrent neural networks, RC is facilely implemented by available hardware and overcomes some obstacles in training period, such as slow convergence and local optimum. In this paper, we propose and characterize a novel reservoir computing system based on a semiconductor laser with double optoelectronic feedback loops. This system shows obvious improvement on prediction, speech recognition and nonlinear channel equalization compared to the traditional reservoir computing systems with single feedback loop. Then some influencing factors to optimize the performance of the new RC are numerically studied, and its great potential of addressing more complex and troubling problems in information processing is expected to be exploited.

32 Gb/s chaotic optical communications by deep-learning-based chaos synchronization.

Chaotic optical communications were originally proposed to provide high-level physical layer security for optical communications. Limited by the difficulty of chaos synchronization, there has been little experimental demonstration of high-speed chaotic optical communications, and point to multipoint chaotic optical networking is hard to implement. Here, we propose a method to overcome the current limitations. By using a deep-learning-based scheme to learn the complex nonlinear model of the chaotic transmitter, wideband chaos synchronization can be realized in the digital domain. Therefore, the chaotic receiver can be significantly simplified while still guaranteeing security. A successful transmission of 32 Gb/s messages hidden in a wideband chaotic optical carrier was experimentally demonstrated over a 20 km fiber link. We believe the proposed deep-learning-based chaos synchronization method will enable a new direction for further development of high-speed chaotic optical communication systems and networks.

Nonlinear Tomlinson-Harashima precoding for direct-detected double sideband PAM-4 transmission without dispersion compensation.

In this paper, we propose a nonlinear Tomlinson-Harashima pre-coding (THP) scheme for nonlinear distortion suppression in direct-detected double sideband (DSB) PAM-4 transmission systems. Based on the traditional THP, the feedback term is modified by introducing nonlinear components. In this way, more accurate feedback can be obtained to mitigate the signal distortions, especially the nonlinear distortions including the signal-to-signal beating interference and nonlinear power series caused by chromatic dispersion and square-law detection. Meanwhile, we also propose to only reserve the nonlinear kernels with adjacent tap products in nonlinear THP, for the purpose of computation complexity reduction. To verify the effectiveness, transmissions of double sideband (DSB) PAM-4 signal in 1550nm window are experimentally demonstrated. Volterra FFE is adopted on the receiver side to suppress linear and nonlinear pre-cursors. We optimize various parameters of hardware and apply appropriate simplification to the nonlinear THP kernels. The results indicate that, the proposed nonlinear THP can lead to up to three folds BER reduction, compared to the conventional linear THP. Finally, with the combination of proposed nonlinear THP and conventional Volterra FFE, we successfully transmit 84-Gbps PAM-4 and 107-Gbps PAM-4 respectively over 80 km and 40 km under the hard decision forward error correction (HD-FEC) threshold of 3.8 × 10-3.