PAM-4 System Research Articles

Simplified THP and M-Log-MAP Decoder Based Faster Than Nyquist Signaling for Intra-Datacenter Interconnect

In this paper, a joint application of simplified Tomlinson-Harashima precoding (THP) and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -log-maximum a posteriori probability ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -log-MAP) decoder at transceivers is proposed for low complexity faster than Nyquist (FTN) 4-ary pulse amplitude modulation (PAM4) signaling. A THP with only two taps is applied at the transmitter for FTN-induced inter-symbol interference elimination and equalization-induced noise amplification issue mitigation, which effectively relieves the burden of the receiver. At the receiver, a low complexity M-log-MAP decoder is equipped for residual impairments cancellation, thus a feedback channel is not required to accurately obtain the channel state information for the transmitter. Taking advantage of this collaborative approach, the proposed scheme performs much better than applying the two schemes separately. We experimentally demonstrate the proposed scheme in 70, 75, and 80GBaud PAM4 systems with a 32-GHz brick-wall filter, corresponding to 0.914, 0.853, and 0.8 FTN compression factor, respectively. The results show that the 80GBaud PAM4 signal is successfully transmitted over 2-km single mode fiber with the bit-error-rate (BER) under the 7% hard-decision forward error correction (HD-FEC) 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> . It is also observed that the proposed scheme shows about 0.7dB receiver sensitivity improvement compared to the error propagation-free decision feedback equalizer, namely the performance upper bound of the THP, at BER of 7% HD-FEC threshold in a 75GBaud FTN PAM4 system. According to the experimental results, the proposed scheme is a promising solution for bandwidth-starved low-cost intra-datacenter interconnect.

Partial response THP for high-speed PAM-4 transmission

Intensity-modulation direct-detection (IM/DD) pulse-amplitude modulation (PAM-4) signals are promising for high-speed data center networks. However, high-speed PAM-4 signals always are subject to critical impairments due to the bandwidth constraint. In the conventional PAM-4 system, a direct detection-faster than Nyquist (DD-FTN) with high complexity is usually appended to the feed-forward equalizer (FFE) for colored noise suppression to maximize transmission performance. In order to yield a simple PAM-4 scheme with similar performance as that of the DD-FTN, we proposed a nonlinear differential coding-generalized Tomlinson-Harashima Precoding (NLDC-GTHP) PAM-4 system. The proposed system consists of a NLDC-GTHP at the transmitter and a simplified two-dimensional constellation distortion (S2DCD) module at the receiver. We experimentally demonstrated the proposed NLDC-GTHP PAM-4 system for 62.5-Gb/s PAM-4 signal transmission over 2-km standard single mode fiber (SSMF) with the 10-dB bandwidth of about 12 GHz. By introducing the NLDC-GTHP and S2DCD, we achieved the similar receiver sensitivity as that of the DD-FTN at the hard-decision forward-error-correction (HD-FEC) bit error rate (BER) threshold, with the decrease of 86% computational complexity.

High Dynamic Range 100G PON Enabled by SOA Preamplifier and Recurrent Neural Networks

In recent years the PON research community has focused on future systems targeting 100 Gb/s/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lambda$</tex-math></inline-formula> and beyond, with digital signal processing seen as a key enabling technology. Spectrally efficient 4-level pulse amplitude modulation (PAM4) is seen as a cost-effective solution that exploits the ready availability of cheaper, low-bandwidth devices, and Semiconductor Optical Amplifiers (SOA) are being investigated as receiver preamplifiers to compensate PAM4's high signal-to-noise ratio requirements and meet the demanding 29 dB PON loss budget. However, SOA gain saturation-induced patterning distortion is a concern in the context of PON burst-mode signalling, and the 19.5 dB loud-soft packet dynamic range expected by the most recent ITU-T 50G standards. In this paper we propose a recurrent neural network equalisation technique based on gated recurrent units (GRU-RNN) to not only mitigate SOA patterning affecting loud packet bursts, but to also exploit their remarkable effectiveness at compensating non-linear impairments to unlock the SOA gain saturated regime. Using such an equaliser we demonstrate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ &gt; 28$</tex-math></inline-formula> dB system dynamic range in 100 Gb/s PAM4 system by using SOA gain compression in conjunction with GRU-RNN equalisation. We find that our proposed GRU-RNN has similar equalisation capabilities as non-linear Volterra, fully connected neural network, and long short-term memory based equalisers, but observe that feedback-based RNN equalisers are more suited to the varying levels of impairment inherent to PON burst-mode signalling due to their low input tap requirements. Recognising issues surrounding hardware implementation of RNNs, we investigate a multi-symbol equalisation scheme to lower the feedback latency requirements of our proposed GRU-RNN. Finally, we compare equaliser complexities and performances according to trainable parameters and real valued multiplication operations, finding that the proposed GRU-RNN equaliser is more efficient than those based on Volterra, fully connected neural networks or long short-term memory units proposed elsewhere.

High Speed DMT for 224 Gb/s and Faster Wireline Transmission

This paper presents a high data rate wireline Discrete Multitone (DMT) transceiver capable of operating at 252 Gbps and higher for short range chip-to-chip and chip-to-module applications. The use of DMT allows for higher spectral efficiency than PAM SERDES systems, using similar bandwidth as proposed 224 Gb/s PAM-4 systems but achieves higher data rates. Data rates have improved over other published wireline DMT designs with the use of narrow sub-channels with both adaptive bit- and power-loading along with a combined transmit and receive side equalization. Simulation and measured results show that the transmit side pre-compensation has improved the BER by a factor of 104 at 250 Gb/s. The system is measured over a channel with a loss of 18 dB at 50 GHz, showing a data rate of 252 Gb/s with a BER of 10-6, and a data rate of 400 Gb/s with a BER of 10-2.

Symbol Diversity as a Means to Make PAM-4 Modulation More Resilient in Harsh Electromagnetic Environments

In this article, symbol diversity is presented for the pulse amplitude modulation PAM-4 encoding scheme. This technique is implemented in order to incorporate electromagnetic resilience in a triple modular redundant communication channel that is subjected to electromagnetic disturbances in reverberant environments. An in-depth numerical study is carried out in light of new electromagnetic disturbance condition monitoring definitions that provide a better insight into the actual state of the system. An explanation of the different fault mechanisms based on the new definitions is provided for the proposed PAM-4 symbol diversity setup and is compared with an undiverse PAM-4 system with a two-out-of-three majority voter. The results show that the proposed symbol diversity technique is quite an effective measure for incorporating fault tolerance in the system design.

Decision region partition aided MLSE for O-band 65-Gbaud PAM-4 system over 40-km transmission with a severe bandwidth constraint.

Maximum likelihood sequence estimation (MLSE) is an optimal solution to realize sequence detection in the digital signal processing (DSP) of short reach O-band intensity modulation/direct detection (IM/DD) systems with bandwidth limitation. However, traditional MLSE requires relatively high computational complexity for short reach optical interconnect. Although the computational complexity of single-symbol sequence detection is quite low, the capability of combating with the inter symbol interference (ISI) is inadequate. To combine the low computational complexity of single-symbol sequence detection with the high reliability of multi-symbol sequence detection in MLSE, decision region partition aided MLSE (DRP-MLSE) is proposed and verified with 60-Gbaud and 65-Gbaud PAM-4 IM/DD systems over 40-km single-mode fiber (SMF) transmission. The experimental results show that the DRP-MLSE can realize similar performance of conventional MLSE with negligible penalty and significantly lower computational complexity.

1600 Gbps PAM-4 FSO link enabled using OFCL-based WDM and OAM-multiplexing techniques

The twisted light beams carry orbital angular momentum (OAM), which acts as additional degrees of freedom. In this work, we have proposed a free space optics (FSO) communication system employing wavelength division multiplexing (WDM), OAM multiplexing, and four-level pulse amplitude modulation (PAM-4) techniques. A 1600 Gbps data has been successfully transmitted over free space in different environmental scenarios such as clear weather, weak turbulence, moderate turbulence, and strong turbulence. The effects of atmospheric turbulence on the PAM-4 signals carrying OAM modes are examined theoretically and simulated for the first time. Optical frequency comb lines are generated by employing a single laser source and used as a broadband laser source. A sufficient low power penalty of 1.489 dB at a BER value ∼ 10-9 along with clear eye diagrams has been achieved for the proposed system. Thus, the proposed 1600 Gbps PAM-4, OAM, and WDM-based system can be a promising solution for the next generation of long-reach and high-data-rate free-space communication.

Performance Investigation of Error-Feedback Noise Shaping in Low-Resolution High-Speed IM/DD and Coherent Transmission Systems

In this paper, we comprehensively investigate the performance of error-feedback noise shaping (EFNS) in low-resolution high-speed intensity-modulation direct-detection (IM/DD) PAM4 and coherent DP-mQAM transmission systems by simulation and experiments. The influence of EFNS parameters and digital to analog converter (DAC) parameters on EFNS performance is first numerically investigated in a low-resolution 56-GBaud 2-km IM/DD PAM4 transmission system. The combination of clipping and EFNS is also numerically evaluated and the impact of overloading is deeply analyzed. For coherent transmission, the EFNS performance is investigated for different modulation formats including QPSK, 16QAM and 64QAM. The optical signal to noise ratio (OSNR) penalties for different modulation formats are evaluated numerically in a low-resolution 56-GBaud 80-km coherent transmission system. Finally, we experimentally demonstrate the EFNS performance in low-resolution 32-GBaud 10-km IM/DD PAM4 and 28-GBaud 80-km coherent DP-64QAM transmission experiments. Extensive numerical and experimental results show that EFNS can effectively mitigate the quantization noise of low-resolution DAC and thus reduce received optical power or OSNR penalty significantly. Although EFNS is a little inferior to DRE at the PNoB of 3, both of them have very similar performance when PNoB <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\geq$</tex-math></inline-formula> 4. Compared with DRE, EFNS has lower computational complexity and no processing latency. In addition, no channel response is required for EFNS.

Chaotic optical communications at 56 Gbit/s over 100-km fiber transmission based on a chaos generation model driven by long short-term memory networks.

Chaotic optical communication technology is considered as an effective secure communication technology, which can protect information from a physical layer and is compatible with the existing optical networks. At present, to realize long-distance chaos synchronization is still a very difficult problem, mainly because well-matched hardware cannot always be guaranteed between the transmitter and receiver. In this Letter, we introduce long short-term memory (LSTM) networks to learn a nonlinear dynamics model of an opto-electronic feedback loop, and then apply the trained deep learning model to generate a chaotic waveform for encryption and decryption at the transmitter and receiver. Furthermore, to improve the security, we establish a deep learning model pool which consists of different gain trained models and different delay trained models, and use a digital signal to drive chaos synchronization between the receiver and transmitter. The proposed scheme is experimentally verified in chaotic-encrypted 56-Gbit/s PAM-4 systems, and a decrypted performance below 7%FEC threshold (BER = 3.8×10-3) can be achieved over a 100-km fiber transmission.

Modified Gerchberg-Saxton Algorithm Based Electrical Dispersion Pre-Compensation for Intensity-modulation and Direct-detection Systems

In intensity-modulation and direct-detection (IM-DD) communication systems, electrical chromatic dispersion (CD) compensation cannot be directly applied in the transceivers due to the absence of phase information. Gerchberg-Saxton (GS) algorithm has been utilized to iteratively solve for real-valued CD pre-compensated signal in an IM-DD system. In this scheme, the amplitude information at the transmitter and phase information before the direct detection receiver are treated as the degree of freedoms (DoFs) and jointly optimized. In this paper, a modified GS algorithm is proposed and experimentally demonstrated for CD pre-compensation in a 28-GBaud PAM-4 system over 80-km single mode fiber (SMF) transmission. Compared with the basic GS electrical dispersion pre-compensation (pre-EDC) scheme, the amplitude information of received samples at the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T/2</i> position is regarded as DoFs as well, in order to reduce the error. Besides, to accelerate the convergence speed, two error reversing factors associated with the phase error at the transmitter and amplitude error at the receiver are introduced. The experimental results show that the bit error rate (BERs) of 56-Gbps PAM-4 signal over 80-km SMF transmission without CD compensation and with 10 iterations of basic GS pre-EDC scheme are 2.35×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> and 5.13×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−2</sup> , respectively, when a 21-taps feedforward equalizer (FFE) is equipped at the receiver side. While the BER can be reduced to below the hard-decision forward error correction (HD-FEC) 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> by the proposed scheme with the iterative number of 10. The results reveal that the proposed scheme is a promising solution for 50-Gbps class 80-km metro optical communication links based on the IM-DD structure.

Low-latency and efficient retiming and equalizing scheme for a 112-Gbps bandwidth-limited optical PAM-4 system.

The bandwidth limitation of optoelectronic devices is a key constraint for realizing higher capacity short-reach optical communication systems. In this work, we show that the performance of the timing recovery algorithm will significantly impact the performance of bandwidth-limited optical PAM-4 signals. To address this problem, we introduce a moving average filter (MAF) into the Gardner retiming loop to realize ultra-stable retiming without any pilot symbols. It enables a significantly reduced timing jitter, especially for bandwidth-limited conditions. Based on simulations, we show that the proposed retiming scheme will give a stable sampling phase, which is beneficial to the performance of the decision feedback equalizer. Compared to the system based on the traditional Gardner timing synchronization algorithm, the 2-dB power budget gain is realized. The proposed method improves the equalization performance of short-reach optical communication systems where complexity and processing latency are important concerns.

Design of a low cost and power efficient 200/400 Gbps optical interconnect using DAC-less simplified PAM4 architecture

Abstract Incoherent addition of three monochromatic laser sources is used to create four distinctive power levels to match the profile of standard quaternary pulse amplitude modulation (PAM4). The proposed PAM4 signal generation results in a lower symbol error rate as compared to standard PAM4 systems. This design improves the signal-to-noise ratio as compared to existing PAM4 schemes and can reduce the cost and power consumption of existing 200 G or higher optical transceivers.

Enhanced hard decision based on multi-dimensional basis expansion in PAM4 transmission

Most of the PAM4 receivers eliminate the linear and nonlinear distortion by equalization and use independent symbols for decision. In this work, to remove the residual correlation between adjacent symbols after equalization, the enhanced hard decision (HD) based on multi-dimensional basis expansion is theoretically investigated and experimentally demonstrated for a 10-GHz directly modulated laser (DML) based 50-Gb/s PAM4 system. After 30-km standard single-mode fiber (SSMF) transmission, compared to the traditional HD, HD with 2-dimensional basis expansion (2D-HD) can achieve reliable transmission below the HD forward error correction (FEC) threshold with a linear feed-forward equalizer (FFE). Sensitivity gain of 1 dB and 2.2 dB can be further obtained by HD with 3-dimensional basis expansion (3D-HD) and 5-dimensional basis expansion (5D-HD), respectively. Moreover, even after the optimal Volterra nonlinear equalizer (VNLE), 5D-HD can still reduce the received optical power (ROP) by 0.6 dB.

Effect of four-wave mixing on the loss budget of four-channel multiplexing NG-PON systems

In this study, the loss budget for adopting non-return-to-zero (NRZ) and four-level pulse amplitude modulation (PAM4) in next-generation passive optical networks (NG-PONs) was investigated by simulation and experiment. Through simulation, the signals are distorted by four-wave mixing (FWM) when the zero-dispersion wavelength locates in the middle of the channels. For 25-Gb/s NRZ, a maximal loss budget of approximately 32.5 dB is obtained. For 50-Gb/s PAM4, the bit error rate cannot reach 1 × 10−3. While, the impact becomes negligible whens the zero-dispersion wavelength stays away from the middle of the channels, and the loss budget is 36 and 25.7 dB for NRZ and PAM4 systems. Therefore, at least a 32.5-dB loss budget ise obtained in a 4 × 25G NRZ system. While, the loss budget cannot reach the basic requirement of 29 dB in the 4×50G PAM4 system. The experimental resultso verify this conclusion.

Multi-distributed probabilistically shaped PAM-4 system for intra-data-center networks

Probabilistically shaped (PS) pulse amplitude modulation (PAM) is a promising technique for intra-data-center networks due to its superior performance, for which a low-complexity and cost-effective distributed matching method is critical. In this work, we propose an energy-level-assigned method to yield PS-PAM-4 signals with various bit rates based on variable probabilistic distributions. We experimentally demonstrate the proposed method in a 25 Gbaud PS-PAM-4 transmission over a bandwidth of approximately 10 GHz. Compared to a uniform PAM-4 system, the proposed multi-distributed PS-PAM-4 system approaches the hard decision threshold at a wide range of received optical power for different applications.

Improved polar decoding for optical PAM transmission via non-identical Gaussian distribution based LLR estimation.

In this paper, an improved polar decoder based on non-identical Gaussian distributions is proposed and experimentally demonstrated for optical pulse amplitude modulation (PAM) interconnection. The principle of the polar coded PAM system is illustrated theoretically and the non-identical Gaussian distributions based log-likelihood ratio (LLR) estimation is introduced in the polar decoder to mitigate nonlinearity. Transmission systems of 28-Gbaud 4-level pulse amplitude modulation (PAM-4) and 8-level pulse amplitude modulation (PAM-8) based on commercial 10-GHz directly modulated laser (DML) are both demonstrated over 10-km standard single-mode fiber (SSMF) in C-band without dispersion compensation. Experimental results show that, aided by the improved polar decoder, the channel nonlinearity can be taken into consideration and additional sensitivity gains of 0.7 dB and 1 dB are respectively achieved compared with traditional polar decoder for PAM-4 and PAM-8 systems.

Mitigation of optical multipath interference impact for directly detected PAMn system.

This paper investigates solutions for mitigating multipath interference (MPI) impact for intensity modulation direct detection systems, particularly for PAM4 systems. We propose a scheme that uses a high pass filter (HPF) at the receiver to remove the MPI induced carrier-carrier beat noise and therefore improve the MPI tolerance. The scheme has been verified via theoretical analysis, numerical simulation, and experiment. For a typical optical transmitter based on Mach-Zehnder modulator (MZM) without frequency chirp, over 5dB MPI tolerance can be improved for 106.4Gb/s PAM4 by using the proposed scheme. Investigation was also extended to electro-absorption modulated laser (EML) and directly modulated laser (DML) based optical transmitters. Results show that transient chirping in EML reduces the effectiveness of proposed MPI mitigation scheme. For EML with chirp factor smaller than 1.5, MPI tolerance gain of 2dB is still achievable. However, the scheme is ineffective for typical DML where the adiabatic chirp significantly broadened the laser linewidth.

Digital Mobile Fronthaul Based on Performance Enhanced Multi-Stage Noise-Shaping Delta-Sigma Modulator

A novel topology multi-stage noise-shaping (MASH) delta-sigma modulator is proposed for 20-km digital mobile fronthaul (MFH) in this article. In the proposed MASH structure, a newly designed feedback unit is combined with a traditional fourth-order sturdy MASH structure to enhance the noise-shaping capacity. The detailed comparison between the conventional fourth-order single delta-sigma modulator (SDSM) and the proposed new topology MASH is presented in a 512/1024 quadrature amplitude modulation (QAM) orthogonal frequency division multiplexing (OFDM) transmission system with the bandwidth of 1.125 GHz. The OFDM signal is quantized to two bits by SDSM/MASH analog-to-digital conversion (ADC), and this digitized signal is transmitted over 20-km single mode fiber (SMF) in 20-Gbaud 4-level pulse amplitude modulation (PAM4) intensity modulation direct detection (IM/DD) system. The signal to noise ratios (SNRs) of the retrieved OFDM signal utilizing the proposed new topology MASH and the fourth-order SDSM ADCs are 38.7dB and 34.5dB, respectively. In the case of 1024-QAM PAM4 system, the error vector magnitude (EVM) floors of the proposed new topology MASH and the conventional fourth-order SDSM schemes are 1.64% and 1.96% over 20-km SMF transmission at off-line digital signal processing (DSP) reception, and 1.2 dB receiver sensitivity improvement is achieved.

Applying the skew-normal distribution to model coherent MPI and to evaluate its impact on PAM signals

Abstract We statistically model the coherent multipath interference (MPI) using an extended skew-normal distribution, with the results showing a good agreement with published experimental data. This distribution is very flexible and permits to model data with large skewness values, which is a typical feature in coherent MPI histograms. Furthermore, the developed model was applied to estimate the impact of coherent MPI on PAM-4 systems, with the results showing a 1-dB Q-penalty for an MPI level of −24 dB and a bit error ratio of 10−3.

High-Capacity Coherent DCIs Using Pol-Muxed Carrier and LO-Less Receiver

A PAM4 based direct detection system has been standardized for short-distance data center interconnects because of its simple architecture. Performance of the PAM4 systems is limited for high dispersion values or demands complicated signal processing for further increase in data rates. A polarization multiplexed carrier based self-homodyne (PMC-SH) link with adaptive polarization control is a practical approach with an laser oscillator (LO)-less and carrier phase recovery (CPR)-free coherent receiver that can replace PAM4 links for achieving high data rates. We analytically find that PMC-SH scheme results in a significantly better BER for a given transmission rate or can achieve doubling of the data rate for given bandwidth of electronics and laser power (when compared with PAM4). Practical implementation of the proposed system with adaptive polarization control is also discussed. Presented theoretical frame work highlights the advantages of such self-homodyne systems over PAM4 based systems in terms of SNR requirements and capacity.