Receiver DSP Research Articles

800G/$\lambda $ Self-Homodyne Coherent Links With Simplified DSP for Next-Generation Intra-Data Centers

Assuming a low-latency forward error correction (FEC)-based bit-error-rate (BER) threshold, we demonstrate and provide a detailed analysis of a 120 Gbaud/DP-16QAM single-carrier self-homodyne coherent link in the C-band. Through theoretical and simulation analysis as well as experimental investigation, we find that a minimum receiver DSP based on a simple I-Q correction scheme is needed to compensate for the combined effect of fiber dispersion, I-Q phase rotation, transmitter I-Q impairment, and receiver skew in combination with a finite analog to digital converter (ADC) resolution. Based on the simplified DSP, we demonstrate link budgets of 4.5 dB (for 16 amplified dense wavelength division multiplexing (DWDM) channels) and 5.2 dB (unamplified single-channel case). The amplified DWDM self-homodyne coherent system provides a 12.8 Tb/s capacity per fiber pair and is useful for bandwidth-demanding intra-data center applications.

Deep Neural Network-Based Digital Pre-Distortion for High Baudrate Optical Coherent Transmission

High-symbol-rate coherentoptical transceivers suffer more from the critical responses of transceiver components at high frequency, especially when applying a higher order modulation format. We recently proposed a neural network (NN)-based digital pre-distortion (DPD) technique trained to mitigate the transceiver response of a 128 GBaud optical coherent transmission system. In this paper, we further detail this work and assess the NN-based DPD by training it using either a direct learning architecture (DLA) or an indirect learning architecture (ILA), and compare performance against a Volterra series-based ILA DPD and a linear DPD. Furthermore, we deliberately increase the transmitter nonlinearity and compare the performance of the three DPDs schemes. The proposed NN-based DPD trained using DLA performs the best among the three contenders. In comparison to a linear DPD, it provides more than 1 dB signal-to-noise ratio (SNR) gains at the output of a conventional coherent receiver DSP for uniform 64-quadrature amplitude modulation (QAM) and PCS-256-QAM signals. Finally, the NN-based DPD enables achieving a record 1.61 Tb/s net rate transmission on a single channel after 80 km of standard single mode fiber (SSMF).

Experimental Demonstrations of Matching Filter-Free Digital Filter Multiplexed SSB OFDM IMDD Transmission Systems

Matching filter (MF)-free digital filter multiplexed (DFM) single sideband (SSB) OFDM intensity modulation and direct detection (IMDD) dual-channel transmissions of 51.25Gbit/s over 25km SSMFs are experimentally demonstrated. It is shown that both transmission system impairments and digital filter characteristic variations can only lead to <1dB transmission performance degradations. Compared with the MF-free DFM-based double sideband (DSB) OFDM technique, the SSB technique has a similar receiver DSP complexity and provides almost twice the maximum signal transmission capacity. When compared with a conventional DFM technique incorporating a dedicated shaping and matching filter pair for each channel, the present SSB technique achieves a 10-fold reduction of receiver DSP complexity and 7.82Gbit/s of additional signal transmission throughput. We demonstrate these throughput and complexity advantages by modelling and measurement.

ROADM-Induced Anomaly Localization and Evaluation for Optical Links Based on Receiver DSP and ML

With the advance of elastic optical networks, optical communication systems are becoming more flexible and dynamic. In this scenario, soft failures are more likely to occur due to various link impairments, of which the filter impairment caused by WSS is a major one. If these soft failures are not handled properly and timely, the quality-of-transmission (QoT) will degenerate, even leading to service disruption. During this process, it is important to know the accurate location and the magnitude of soft failure. However, it is difficult for traditional methods to accomplish this target. Fortunately, with the fast progress of the powerful machine learning (ML) algorithms, a new promising way is provided to address this problem. In this article, we propose to use artificial neural network (ANN) and Gaussian process regression (GPR) to localize the soft failure location and estimate anomaly value. The input of the ANN and GPR is extracted from the power spectrum density (PSD) and the equalizer taps, which can be easily obtained from a coherent receiver. We explore two types of soft failure caused by the WSS, including the offset of WSS's center frequency, i.e., frequency shift (FS), and the tightening of WSS's 3-dB bandwidth, i.e., frequency tightening (FT). To validate the proposed method, we perform extensive simulations. The localization accuracy of the ANN can reach 95%, and the mean-absolute-error (MAE) of the GPR can reach 0.1-GHz, demonstrating the effectiveness of the proposed method. Besides, we validate the generalization of the proposed method under different link conditions. Finally, the importance of each input feature is explored, showing the effectiveness of the selected features.

Reduced sampling rate Kalman filters for carrier phase and frequency offset tracking in 200\xa0Gbps 16 QAM coherent communication system

We propose 1 state and 2 state multi-step Kalman filters (MKFs) to estimate and compensate CFO, LPN and NLPN in long-haul coherent fiber-optic communication systems. The proposed filters generate state estimates once every m symbols and therefore operate at a reduced sampling rate compared to conventional KFs that perform symbol by symbol processing. No computations are performed to obtain phase estimates of the intermediate m-1 samples; instead, the present and previous estimates are averaged and used to derotate the intermediate m-1 samples which are then demodulated to recover the transmitted symbols. This reduces the computational load on the receiver DSP. Further, in order to improve estimation accuracy, we adaptively vary the process noise covariance Q. Simulation results of 200 Gbps PDM 16 QAM system over 12 spans shows that the proposed 1 state MKF can reduce the sampling rate requirement by a factor of m = 20 with Q-factor degradation of 1.32 dB compared to single-step KF at linewidth of 100 kHz. The 2 state MKF tracks PN and CFO with a maximum step size of m=10 for a CFO of 100 MHz at linewidth of 100 kHz. We also study the dynamic performance of the proposed algorithms by applying step change to CFO. The 2 state MKF with adaptive Q is able to track a step change of 400 MHz of CFO with m = 1 and 3 with high estimation accuracy but slower convergence time compared to the non-adaptive 2 state MKF. Finally, we study the computational requirements of the proposed MKFs and show that they offer significant reduction in computations compared to single-step KF thus making the proposed filters suitable for hardware implementation.

Revisiting Efficient Multi-Step Nonlinearity Compensation With Machine Learning: An Experimental Demonstration

Efficient nonlinearity compensation in fiber-optic communication systems is considered a key element to go beyond the "capacity crunch''. One guiding principle for previous work on the design of practical nonlinearity compensation schemes is that fewer steps lead to better systems. In this paper, we challenge this assumption and show how to carefully design multi-step approaches that provide better performance--complexity trade-offs than their few-step counterparts. We consider the recently proposed learned digital backpropagation (LDBP) approach, where the linear steps in the split-step method are re-interpreted as general linear functions, similar to the weight matrices in a deep neural network. Our main contribution lies in an experimental demonstration of this approach for a 25 Gbaud single-channel optical transmission system. It is shown how LDBP can be integrated into a coherent receiver DSP chain and successfully trained in the presence of various hardware impairments. Our results show that LDBP with limited complexity can achieve better performance than standard DBP by using very short, but jointly optimized, finite-impulse response filters in each step. This paper also provides an overview of recently proposed extensions of LDBP and we comment on potentially interesting avenues for future work.

Soft Failure Identification for Long-haul Optical Communication Systems Based on One-dimensional Convolutional Neural Network

With the advance of elastic optical networks, optical communication systems are becoming more flexible and dynamic. In this scenario, soft failures are more likely to occur due to various link impairments. If these soft failures are not handled properly and timely, service disruption may occur. Identifying the cause of soft failure is a key step to restore the degraded links. However, it is difficult for traditional methods to accomplish this task. Fortunately, powerful machine learning (ML) algorithms provide a promising path to address this problem. In this article, a novel two-stage soft failure identification scheme based on a convolutional neural network (CNN) and receiver DSP is proposed. The input of the CNN is the power spectrum density (PSD) extracted from a coherent receiver, and the output contains the identified cause of soft failures together with their probabilities. Extensive simulations are performed to validate the proposed method. Four types of soft failure causes are explored including the offset of optical filter's center frequency (FS), the tightening of optical filter's 3-dB bandwidth (FT), SNR degradation due to the increased amplified spontaneous emission (ASE) noise, and the Kerr nonlinear effect. When only one soft failure cause exists, excellent accuracy is achieved. When multiple soft failure causes exist, the probabilities of these causes provided by the CNN are used to gain insight into their influences on the system. Finally, we investigate the interpretation of the CNN and a reasonable interpretation is given and discussed.

100 GBd IM/DD transmission over 14 km SMF in the C-band enabled by a plasmonic SSB MZM.

100 Gb/s NRZ-OOK transmission over 14 km standard single mode fiber in the C-band is demonstrated with a simple intensity modulation and direct detection scheme. The transmission concept utilizes single sideband modulation and comprises a single differential digital-to-analog converter with adjustable phase offset, a new dual electrode plasmonic Mach-Zehnder modulator, a laser at 1537.5 nm, standard single mode fibers, a photodiode, an analog-to-digital converter, and linear offline digital signal processing. The presented SSB concept requires no DSP and complex signaling at the transmitter. The demonstrated SSB transmitter increased the possible transmission distance by a factor of 4.6 compared to a DSB transmitter. We also investigated the equalization requirements. A T/2-spaced feedforward equalizer requires 27 taps to achieve transmission over 10 km with a BER below the HD-FEC limit. In comparison to a DSB transmitter, the SSB transmitter reduced the receiver DSP complexity by a factor of 13.7.

A SiGe HBT BiCMOS 1-to-4 ADC Frontend Enabling Low Bandwidth Digitization of 100 GBaud PAM4 Data

Market forecasts for intra and inter data center interconnects predict high growth rates in the upcoming years. This is associated with increasing requirements in terms of costs, power consumption, and bit rate per wavelength. Today, PAM4 systems are frequently used at up to 100 Gb/s per wavelength. The next logical step is to double the symbol rate to allow bit rates of 200 Gb/s at the same modulation format and at the same direct detection scheme. Such systems require three-digit gigasample analog-to-digital converters with bandwidths larger than 50 GHz, which are not available today as CMOS components. To extend the bandwidth of CMOS converters, we suggest the use of ADC frontends, which sample and demultiplex the analog input signals simultaneously. At the outputs of such ADC frontends, the signals can then be digitized by parallel converters with lower bandwidth and at a lower conversion rate. In this article, we present the circuit implementation of a 1-to-4 ADC frontend in IHP 130 nm SiGe HBT BiCMOS and demonstrate its integration into a 100 GBaud PAM4 transmission system with only 14 GHz of digitizer bandwidth. For optimum performance, the mitigation of intersymbol and interchannel interferences is mandatory in the transmission system. We describe and compare two different receiver DSP architectures for reduction of these interferences and evaluate their performances in electrical and optical back-to-back experiments. Furthermore, we report on transmission experiments over 500 m, 10 km, and 40 km SMF at 1550 nm wavelength. With linear equalization, we obtained a BER below the HD-FEC threshold of 3.8 × 10−3 and with 3 rd order Volterra equalization, we even achieved a BER below the KP4 threshold of 2.3 × 10 −4 .

The Impact of Local Oscillator Frequency Jitter and Laser Linewidth to Ultra High Baud Rate Coherent Systems

Through theoretical analysis and simulation, we investigate the system impact due to a sinusoidal jitter tone and the resultant local oscillator (LO) laser linewidth requirement in ultra-high baud rate and long distance coherent optical systems. We also carried out experiments in 64 Gbaud, dual-polarization (DP)-16 QAM systems to verify the theoretical analysis and simulation. We have also obtained a jitter interference tolerance mask to qualify LO lasers. A jitter tone with a frequency lower than ∼1 MHz has a higher tolerance since it generally causes constant frequency or phase shift, which can be tracked by a receiver DSP. For a jitter tone with a frequency higher than ∼1 MHz, the tolerance becomes much tighter since the tone will affect laser lineshape and induce equalizer-enhanced phase noise (EEPN). Consequently, a jitter tone in the higher frequency region could severely affect the system performance. Theoretical analysis and numerical result illustrate that EVM2 due to the effect of laser linewidth and a sinusoidal jitter tone is proportional to the weighted sum of $[ \Delta \nu \times B_{s}\times \text{L}] $ and $[ \Delta f_{pp}\times B_{s}\times \text{L}] ^{2}$ , where Δν is the laser linewidth, $B_{s}$ is the baud rate, $\Delta f_{pp}$ is the laser peak-to-peak frequency deviation due to a sinusoidal jitter tone, and L is the fiber transmission length. This result is applicable for all orders of QAM constellations. The implication to future 100 Gbaud and beyond systems is delineated.

Simplified Carrier Recovery for Intradyne Optical PSK Receivers in udWDM-PON

We present an optimized carrier recovery architecture based on differential detection for coherent optical receivers that substantially reduces the required DSP hardware resources, aimed at cost-effective transceivers for access networks applications. The proposed architecture shares the 1-symbol complex correlation required for differential phase detection within both the frequency estimation and the phase recovery blocks of the receiver DSP, thus lowering the energy consumption of the digital coherent receiver and increasing the tolerance against fast wavelength drifts of the lasers. We prototyped the proposed carrier recovery in a commercial field-programmable gate array (FPGA) for real-time evaluation with differential phase shift keying (DPSK) data at 1.25 Gb/s. The optical transmission system implemented direct-phase modulation of commercial DFB lasers, 25 km of single-mode fiber, and a coherent intradyne receiver with low-cost optical front-end based on 3×3 coupler and three photodiodes providing phase-diversity operation. Results show high performance in real time for DPSK, achieving –55 dBm sensitivity at BER = 10−3 in a 6.25 GHz spaced ultra-dense wavelength-division multiplexing grid, high tolerance to optical phase noise, and enhanced mitigation of the fast wavelength drifts from lasers enabled by feedforward DSP correction and feed-back local oscillator automatic tuning.

70.46 Tb/s Over 7,600 km and 71.65 Tb/s Over 6,970 km Transmission in C+L Band Using Coded Modulation With Hybrid Constellation Shaping and Nonlinearity Compensation

We demonstrate 70.46 Tb/s transmission over 7,600 km and 71.65 Tb/s transmission over 6,970 km with C+L band EDFAs using a multidimensional coded modulation format with hybrid probabilistic and geometric constellation shaping. The proposed format (4D-PS-9/12-56APSK) is designed to approach Shannon limit and to improve the performance of nonlinearity compensation over conventional and probabilistically shaped 2-D formats. The receiver DSP uses multistage nonlinearity compensation that includes fast least-mean-square equalizer and generalized filter in addition to digital back propagation. The adaptive linear filters are aided by coded modulation decisions. We study the contribution of each algorithm and show an average total nonlinearity compensation benefit of 1.4 dBQ at the designed amplifier power.

Generation and Coherent Reception of 107-GBd Optical Nyquist BPSK, QPSK, and 16QAM

We present a 107-GBd coherent optical system for the generation and reception of m-ary phase-shift keyed (PSK) and quadrature-amplitude modulated (QAM) signals, including Nyquist pulse shaping. It is based on phase-stable optical time-division multiplex (OTDM) of two tributaries, which are modulated at half the target symbol rate, optical Nyquist filtering, and a broadband digital coherent receiver. The system is analyzed in back-to-back experiments with binary PSK (BPSK) modulation, quadrature-PSK (QPSK) modulation, as well as with 16-ary QAM. Compared to all-ETDM implementations, the transmitter is based on independent electro-optical modulation of two time-division multiplex tributaries and subsequent optical interleaving after modulation. Although this scheme implies increased hardware complexity, it enables lower penalties with respect to theory compared to all-ETDM experiments presented so far. This is due to the reduced hardware speed requirements. The measured penalties at bit-error ratios of 1 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> are 0.5, 1.5, and 6 dB for single-polarization BPSK, QPSK, and 16QAM, respectively. Furthermore, the employed phase-stable optical multiplexer allows use of standard receiver DSP at the broadband digital coherent receiver without need for special treatment of the individual OTDM tributaries.

Performance Assessment of Noise-Suppressed Nyquist-WDM for Terabit Superchannel Transmission

This paper focuses on terabit superchannel transmission with enhanced network reach by using an emerging noise-suppressed Nyquist wavelength division multiplexing (NS-N-WDM) technique for polarization multiplexing quadrature phase shift keying subchannels at different symbol rate to subchannel spacing ratios up to 1.28, and for the first time, it was compared experimentally with the transmission capability of no-guard-interval coherent optical orthogonal frequency division multiplexing (NGI-CO-OFDM) on the same testbed. At 2 × 10-3 bit error ratio, the maximum reachable distance is 3200 and 2800 km SMF-28 with erbium-doped-fiber-amplifier-only amplification for NGI-CO-OFDM and NS-N-WDM terabit superchannels, respectively, at 100 Gb/s/ch. For 11 ntn112 and 11 × 128 Gb/s/ch NS-N-WDM transmission under assumption of different coding gain with hard-decision and soft-decision forward error correction, their maximum achievable distance was found to be equivalent, which are 2100 and 2170 km, respectively, both were achieved by using digital noise filtering and 1-bit maximum likelihood sequence estimation at the receiver DSP. In addition, the back-to-back characteristics of NS-N-WDM superchannel such as analog-to-digital converter bandwidth requirement and its tolerance to unequal subchannel power were experimentally evaluated and studied.

Field Transmission of 100 G and Beyond: Multiple Baud Rates and Mixed Line Rates Using Nyquist-WDM Technology

Successful joint experiments with Deutsche Telecom (DT) on long-haul transmission of 100 G and beyond are demonstrated over standard single-mode fiber (SSMF) and inline erbium-doped fiber amplifier-only amplification. The transmission link consists of eight nodes and 950-km installed SSMF in DT's optical infrastructure with the addition of lab SSMF for extended optical reach. The first field transmission of 8 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\,\times\,$</tex></formula> 216.8-Gb/s Nyquist-WDM signals is reported over 1750-km distance with 21.6-dB average loss per span. Each channel modulated by a 54.2-Gbaud PDM-CSRZ-QPSK signal is on 50-GHz grid, achieving a net spectral efficiency (SE) of 4 bit/s/Hz. We also demonstrate mixed data-rate transmission coexisting with 1 T, 400 G, and 100 G channels. The 400 G uses four independent subcarriers modulated by 28-Gbaud PDM-QPSK signals, yielding the net SE of 4 bit/s/Hz while 13 optically generated subcarriers from single optical source are employed in 1 T channel with 25-Gbaud PDM-QPSK modulation. The 100 G signal uses real-time coherent PDM-QPSK transponder with 15% overhead of soft-decision forward-error correction. The digital postfilter and 1-bit maximum likelihood sequence estimation are introduced at the receiver DSP to suppress noise, linear crosstalk, and filtering effects. Our results show the future 400 G and 1 T channels utilizing the Nyquist wavelength division multiplexing technique can transmit long-haul distance with higher SE using the same QPSK format.

Simple Fiber Model for Determination of XPM Effects

Previous investigations have revealed that the impairments of the cross-phase modulation (XPM) in dense wavelength-division multiplexing (DWDM) systems include two aspects: the XPM-induced phase noise and the XPM-induced polarization scattering. Such XPM phenomena are strongly dependent on the transmission system configurations and are nonintuitive. In this paper, a simple fiber model is proposed to facilitate the determination of XPM effects. By employing this model, the phase noise and polarization scattering are calculated based on the system configurations and the time-consuming computation by the split step Fourier method is avoided. The proposed model is verified by the dual polarization quadrature phase-shift keying coherent DWDM experiments and simulations in terms of the variance and autocorrelations of phase noise and polarization crosstalk as well as their dependence on relative polarization states and the overall Q-impairment. The proposed model helps deeper analysis of XPM phenomena, and eventually, leads to development of various XPM mitigation methods through transmission system design and coherent receiver DSP.