On the Complexity Reduction of the Second-Order Volterra Nonlinear Equalizer for IM/DD Systems

Diamantopoulos, Nikolaos-Panteleimon; Nishi, Hidetaka; Kobayashi, Wataru; Takeda, Koji; Kakitsuka, Takaaki; Matsuo, Shinji

doi:10.1109/jlt.2018.2890118

Cited by 95 publications

(42 citation statements)

References 21 publications

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“…Then, match filtering was performed by a similar 22% roll-off RRC filter, followed by least-means square adaptive equalization. The digital equalizer was a low-complexity nonlinear filter [23], with 71 linear taps and 51 nonlinear taps, composed of a second and third-order polynomial filter with the addition of only 10 second-order cross-beating terms. The equalized PAM-4 eye diagrams obtained after the 2-km SSMF transmissions, are shown in Figure 5c for 25 • C operation and Figure 5d for 50 • C operation.…”

Section: Evaluation Of 60 Gbaud Pam-4 Transmissionmentioning

confidence: 99%

47.5 GHz Membrane-III-V-on-Si Directly Modulated Laser for Sub-pJ/bit 100-Gbps Transmission

et al. 2021

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Near-future upgrades of intra data center networks and high-performance computing systems would require optical interconnects capable of operating at beyond 100 Gbps/lane. In order for this evolution to be achieved in a sustainable way, high-speed yet energy-efficient transceivers are in need. Towards this direction we have previously demonstrated directly-modulated lasers (DMLs) capable of operating at 50 Gbps/lane with sub-pJ/bit efficiencies based on our novel membrane-III-V-on-Si technology. However, there exists an inherent tradeoff between modulation speed and power consumption due to the carrier-photon dynamics in DMLs. In this work, we alleviate this tradeoff by introducing photon–photon resonance dynamics in our energy-efficient membrane DMLs-on-Si design and demonstrate a device with a maximum 3-dB bandwidth of 47.5 GHz. This denotes a bandwidth increase of more than 2x times compared to our previous membrane DMLs-on-Si. Moreover, the DML is capable of delivering 60-GBaud PAM-4 signals under Ethernet’s KP4-FEC threshold (net data rate of 113.42 Gbps) over 2-km of standard single-mode fiber transmission. DC energy-efficiencies of 0.17 pJ/bit at 25 °C and 0.34 pJ/bit at 50 °C have been achieved for the > 100-Gbps signals. Deploying such DMLs in an integrated multichannel transceiver should ensure a smooth evolution towards Terabit-class Ethernet links and on-board optics subsystems.

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Section: Evaluation Of 60 Gbaud Pam-4 Transmissionmentioning

confidence: 99%

47.5 GHz Membrane-III-V-on-Si Directly Modulated Laser for Sub-pJ/bit 100-Gbps Transmission

et al. 2021

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“…As shown in Fig. 2, 56 Gb/s and 84 Gb/s baseband electrical PAM-4 signals with a 15 21 − bits and a 11 21 − bits pseudo-random bit sequence (PRBS) using Nyquist pulse shaping generator (AWG) with a roll-off factor of 0.01 are generated by an arbitrary waveform generator (AWG) (Keysight M8195A). The AWG has a sampling rate of 65 GSa/s, a bandwidth of 25 GHz, a resolution of 8 bits, and up to 16 GSa of waveform memory.…”

Section: Methodsmentioning

confidence: 99%

“…When working with 84 Gb/s PAM-4 signal, 15 21 − bits PRBS can't be selected on the AWG in the experiment due to practical limitations. Therefore, we use 11 21 − bits PRBS for 84 Gb/s PAM-4. The peak-to-peak voltage (Vpp) of electrical PAM-4 signal in AWG is adjusted to 0.35 V, 0.45 V, 0.55 V, 0.65 V, 0.75 V, 0.85 V and 0.95 V for both 56 Gb/s and 84 Gb/s PAM-4 signal, then a 6-dB RF attenuator is placed before the 26 dB RF amplifier (SHF806A) to enable the RF amplifier to work in linear region.…”

Section: Methodsmentioning

confidence: 99%

“…However, VSB modulation has stringent requirements on the bandwidth and central wavelength of the optical filter. The third solution is using either Volterra series nonlinear equalizers or neural network algorithm based equalizers [11]- [14]. However, the nonlinear equalizer usually suffers from high computational complexity, and the neural network algorithm relies on a large amount of training data and computing resources.…”

Section: Introductionmentioning

confidence: 99%

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Piecewise Linear Equalizer for DML Based PAM-4 Signal Transmission Over a Dispersion Uncompensated Link

Kong

Xin

et al. 2020

J. Lightwave Technol.

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Directly modulated laser (DML) and direct detection (DD) based pulse-amplitude modulation (PAM) for short reach optical communications has attracted lots of research interests due to its low cost and simple configuration. However, the directly modulated PAM signal usually suffers from distortions after the transmission over a dispersion uncompensated link. Due to the adiabatic chirp of the DML working in a high output power region, different intensity levels of the PAM signal correspond to different frequency offsets, thus resulting in amplitude-dependent skew after the transmission over a dispersion uncompensated link. It will degrade signal quality and limit transmission distance. In this paper, we, for the first time, propose a computational efficient piecewise linear (PWL) equalizer to correct the amplitude-dependent skew due to the interaction between the DML chirp and chromatic dispersion in the fiber. By using the PWL equalizer, the amplitude-dependent skew is corrected, and we successfully transmit 56 Gb/s PAM-4 signal over 40 km and 84 Gb/s PAM-4 signal over 20 km dispersion uncompensated link in the C band, with a bit error ratio (BER) below the HD-FEC threshold (3.8×10 -3 ). To demonstrate the low computational complexity of the PWL, we compare its complexity with 2 nd order Volterra equalizer for a similar BER performance. The results show that the computational complexity can be reduced by 61.4% and 40.4% for the 56 Gb/s and 84 Gb/s PAM-4 signal transmission, respectively.

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“…In PAM-based optical interconnects, some simplified Volterra nonlinear equalizers (VNLEs) have been widely applied to compensate nonlinear distortions, mainly including the polynomial nonlinear equalizer (PNLE) and sparse VNLE [9,10]. Least-mean square (LMS) adaptive algorithm is one of the most popular algorithms to converge the tap coefficients of VNLE.…”

Section: Introductionmentioning

confidence: 99%

Adaptive moment estimation for polynomial nonlinear equalizer in PAM8-based optical interconnects

Zhou¹,

Wang²,

Wei³

et al. 2019

Opt. Express

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Adaptive moment estimation (Adam) is a popular optimization method to estimate large-scale parameters in neural networks. This paper proposes the first use of Adam algorithm to fast and stably converge large-scale tap coefficients of polynomial nonlinear equalizer (PNLE) for 129-Gbit/s PAM8-based optical interconnects. PNLE is one of simplified Volterra nonlinear equalizer for making a trade-off between complexity and performance. Different from serial least-mean square (LMS) adaptive algorithm, Adam algorithm is a parallel processing algorithm, which can obtain globally optimal tap coefficients without being trapped in locally optimal tap coefficients. Timing error is one of the main obstacles to the PAM systems with high baud rate and high modulation order. Owing to parallel processing and global optimization, Adam algorithm has much better performance on resisting the timing error, which can achieve faster, more-stable and lower-MSE convergence compared to LMS adaptive algorithm. In conclusion, Adam algorithm shows great potential for converging the tap coefficients of PNLE in PAM8-based optical interconnects.

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On the Complexity Reduction of the Second-Order Volterra Nonlinear Equalizer for IM/DD Systems

Cited by 95 publications

References 21 publications

47.5 GHz Membrane-III-V-on-Si Directly Modulated Laser for Sub-pJ/bit 100-Gbps Transmission

47.5 GHz Membrane-III-V-on-Si Directly Modulated Laser for Sub-pJ/bit 100-Gbps Transmission

Piecewise Linear Equalizer for DML Based PAM-4 Signal Transmission Over a Dispersion Uncompensated Link

Adaptive moment estimation for polynomial nonlinear equalizer in PAM8-based optical interconnects

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