Direct-detection Transmission Research Articles

End-to-end learning strategy based on a frequency domain feature decoupling network emulator with joint probabilistic shaping and equalization for a 300-Gbit/s OAM mode division multiplexing transmission

Mode coupling and device nonlinear impairment appear to be a long-standing challenge in the orbital angular momentum (OAM) mode division multiplexing (MDM) of intensity modulation direct detection (IM/DD) transmission systems. In this paper, we propose an end-to-end (E2E) learning strategy based on a frequency domain feature decoupling network (FDFDnet) emulator with joint probabilistic shaping (PS) and equalization for an OAM-MDM IM/DD transmission with three modes. Our FDFDnet emulator can accurately build a complex nonlinear model of an OAM-MDM system by separating the signal into features from different frequency domains. Furthermore, a FDFDnet-based E2E strategy for joint PS and equalization is presented with the aim of compensating the signal impairment for the OAM-MDM IM/DD system. An experiment is carried out on a 300 Gbit/s carrierless amplitude phase-32 (CAP-32) signal with three OAM modes over a 10 km ring-core fiber transmission, and the results show that the proposed FDFDnet emulator outperforms the traditional CGAN emulator, with improvements in the modelling accuracy of 30.8%, 26.3% and 31% for the three OAM modes. Moreover, the receiver sensitivity of the proposed E2E learning strategy is higher than for the CGAN emulator by 3, 2.5, 2.2 dBm and the real channel by 5.5, 5.1, and 5.3 dBm for the three OAM modes, respectively. Our experimental results demonstrate that the proposed FDFDnet emulator-based E2E learning strategy is a promising contender for achieving ultra-high-capacity interconnectivity between data centers.

All-Fiber Low-Modal-Crosstalk Demultiplexers for DSP-Free IM/DD LP-Mode MDM Transmission

Weakly coupled mode-division multiplexing (MDM) techniques supporting intensity modulation and direct detection (IM/DD) transmission are promising methods of enhancing the capacity of short-reach scenarios in which low-modal-crosstalk-mode demultiplexers for degenerate linear polarized (LP) modes are highly desired. In this paper, we review two degenerate-mode reception schemes. Firstly, a low-modal-crosstalk orthogonal combined reception method for degenerate modes is proposed based on all-fiber mode-selective couplers, in which signals in both degenerate modes are demultiplexed into the LP01 mode of single-mode fibers and then are multiplexed into the mutually orthogonal LP01 and LP11 modes of a two-mode fiber (TMF) for simultaneous detection. Secondly, a novel degenerate-mode-selective coupler consisting of an input few-mode fiber and an output TMF is proposed, which could demultiplex degenerate LP modes without any digital signal processing (DSP). Both demultiplexers are achieved based on the taper and polish process. The fabricated devices are characterized and compared. The results show that the proposed schemes can pave the way to the practical implementation of DSP-free IM/DD LP-mode MDM transmission systems.

Modified DDFTN Algorithm for Band-Limited Short-Reach Optical Interconnects

Inter symbol interference (ISI) degrades the performance of intensity modulation and direct detection (IM/DD) transmission systems due to various transceiver and channel impairments. To overcome the ISI of IM/DD transmission systems, the direct detection faster than Nyquist (DDFTN) algorithm has been widely used. However, when a system is subjected to severe ISI, the performance of the conventional DDFTN algorithm is suboptimal. To further improve the performance of IM/DD transmission systems, a modified DDFTN algorithm is proposed. We add least squares (LS) channel estimation after the postfilter. The coefficients of maximum likelihood sequence estimation (MLSE) are close to the initial channel response with LS channel estimation. The performance of the conventional and modified DDFTN algorithms is compared for 112, 140, and 160 Gbit/s PAM4 signals over 2 km, 1 km, and 500 m standard single-mode fibers (SSMFs) in a 3 dB bandwidth, 19 GHz IM/DD system in the C band. For 140 Gbit/s signal transmission over 1 km, the modified DDFTN algorithm achieves the optimal receiver sensitivity of -1.5 dBm at a 7% forward error correction (FEC) threshold of 3.8E-3, which is better than the receiver sensitivity of -0.5 dBm achieved with the conventional DDFTN algorithm. Furthermore, for 160 Gbit/s signal transmission over 500 m, the modified DDFTN algorithm achieves the optimal receiver sensitivity of 1 dBm at 3.8E-3, which is also a superior result compared to the conventional DDFTN algorithm.

Pairwise Tomlinson-Harashima precoding for multiple-lane IM-DD transmissions.

As for the photonic interconnection based on the multiple-lane intensity modulation direct detection (IM-DD) transmission, both intra-channel inter-symbol-interference (ISI) originating from bandwidth constraint, and inter-channel performance discrepancy emerging from inter-channel component differences are the major bottleneck for the throughput enhancement. Here, we propose a pairwise Tomlinson-Harshima precoding (P-THP) scheme, in order to simultaneously deal with both intra-channel ISI and inter-channel performance discrepancy. The effective function of the proposed P-THP scheme is experimentally evaluated by transmitting 4-channel 81-GBaud PAM4 signals over 2 km standard single-mode fiber (SSMF). Compared with the conventional scheme with only applying THP on individual wavelength channel, the required optical received power (ROP) under the back-to-back (B2B) transmission can be reduced by 0.75∼1 dB with the help of proposed P-THP in different experimental component configurations, at the 7% hard decision forward error correction (HD-FEC) threshold of BER = 3.8 × 10-3. After the 2 km SSMF transmission, only the use of proposed P-THP can guarantee to reach the designated HD-FEC threshold, leading to a net rate of >600 Gbit/s.

OAM mode-division multiplexing IM/DD transmission at 4.32 Tbit/s with a low-complexity adaptive-network-based fuzzy inference system nonlinear equalizer.

Stochastic nonlinear impairment is the primary factor that limits the transmission performance of high-speed orbital angular momentum (OAM) mode-division multiplexing (MDM) optical fiber communication systems. This Letter presents a low-complexity adaptive-network-based fuzzy inference system (LANFIS) nonlinear equalizer for OAM-MDM intensity-modulation direct-detection (IM/DD) transmission with three OAM modes and 15 wavelength division multiplex (WDM) channels. The LANFIS equalizer could adjust the probability distribution functions (PDFs) of the distorted pulse amplitude modulation (PAM) symbols to fit the statistical characteristics of the WDM-OAM-MDM transmission channel. Therefore, although the transmission symbols in the WDM-OAM-MDM system are subjected to a stochastic nonlinear impairment, the proposed LANFIS equalizer can effectively compensate the distorted signals. The proposed equalizer outperforms the Volterra equalizer with improvements in receiver sensitivity of 2, 1.5, and 1.3 dB for three OAM modes at a wavelength of 1550.12 nm, respectively. It also outperforms a CNN equalizer, with improvements in receiver sensitivity of 1, 0.5, and 0.3 dB, respectively. Moreover, complexity reductions of 67%, 74%, and 99.9% are achieved for the LANFIS equalizer compared with the Volterra, CNN, and ANFIS equalizers, respectively. The proposed equalizer has high performance and low complexity, making it a promising candidate for a high-speed WDM-OAM-MDM system.

Analyzing Peak-to-Average Power Ratio Characteristics in Multi-Channel Intensity Modulation and Direct Detection Flexible Transceivers Deploying Inverse Fast Fourier Transform/Fast Fourier Transform-Based Processing.

Cascaded inverse fast Fourier transform/fast Fourier transform (IFFT/FFT)-based multi-channel aggregation/de-aggregation offers a promising solution in constructing highly desirable flexible optical transceivers for considerably improving optical networks' elasticity, flexibility, and adaptability. However, the multi-channel aggregation operation unavoidably results in generated signals having high peak-to-average power ratios (PAPRs). To solve this technical challenge, this paper first explores the PAPR characteristics of the corresponding flexible transceivers in optical back-to-back (B2B) and 20 km intensity modulation and direct detection (IMDD) transmission systems, and then numerically investigates the feasibility and effectiveness of utilizing the conventional clipping techniques in reducing their PAPR reductions. The results show that the last IFFT operation size is the primary factor determining the PAPRs rather than the channel count and modulation format. For a given last IFFT operation size, the optimal clipping ratio can be identified, which is independent of channel count. With the identified optimal clipping ratio, when the channel count is >4, every two-channel increase in the channel count can only lead to <1.2 Gb/s decreases in the maximum aggregated signal transmission capacity.

A Simplified Volterra Equalizer Based on System Characteristics for Direct Modulation Laser (DML)-Based Intensity Modulation and Direct Detection (IM/DD) Transmission Systems

The nonlinear Volterra equalizer has been proved to be able to solve the problem of nonlinear distortion, but it has high computational complexity and is difficult to implement. In this paper, a simplified second-order Volterra nonlinear equalizer designed for intensity modulation/direct detection systems based on direct modulated laser is proposed and demonstrated, taking into account the characteristics of the system. It has been proved that the received signal of direct modulation laser/direct detection system can be expressed in Volterra series form, but its form is too complex, and the device parameters should also be considered. We re-derived it and obtained a more concise form. At the same time, we proposed a method to simplify the second-order Volterra nonlinear equalizer without relying on device parameters. The performance of the proposed Volterra nonlinear equalizer is evaluated experimentally on a 56 Gb/s 4-ary pulse amplitude modulation link implemented by using a 1.55 µm direct modulation laser. The results show that, compared with the traditional Volterra nonlinear equalizer, the receiver sensitivity of the equalizer is only reduced by 0.2 dB at most, but the complexity can be reduced by 50%; compared with diagonally pruned Volterra nonlinear equalizers, the complexity of the equalizer is the same, but the reception sensitivity can be improved by 0.5 dB.

Adaptive Hybrid Iterative Linearization Algorithms for IM/DD Optical Transmission Systems

For optical field recovery and linear dispersion compensation, we propose a performance-enhanced linearization algorithm, termed adaptive hybrid multi-constraint iteration algorithm (MCIA), which does not require any physical modifications to standard configurations of intensity-modulation and direct-detection (IM/DD) transmission systems. To improve the sensitivity to the residual inter-symbol interference (ISI) effect, we introduce, after fiber backward-propagation, a linear feed-forward equalizer (FFE) pair into the proposed algorithm. To improve the sensitivity to fiber dispersion estimation errors, we utilize a two-stage dispersion estimator coupled with the G-S iteration. After 100-Gb/s PAM-4 signal transmissions over 400-km fibers, the simulation results show that the MCIA offers a 1.5-dB optical signal-to-noise ratio (OSNR) gain and a 1-dB optical power budget improvement compared with the decision-directed data-aided iterative algorithm (DD-DIA), for highly dispersive IM/DD transmissions. By performing adaptive dispersion estimation, the MCIA has higher tolerance to estimation errors in fiber length. Moreover, for cases subject to large dispersion, the usage of the embedded FFE pair not only desensitizes the MCIA on the limited bandwidth effect, but also accelerates the convergence performance for reaching lower BERs. We experimentally demonstrate that the proposed algorithm can support 150-Gb/s PAM-4 transmissions over 25-km standard single mode fibers (SSMF), where just a 7-tap FFE-pair is required. For 150 Gb/s transmissions, the tolerance to fiber length estimation error is increased from 0.9 km to 20 km.

400 Gbit/s 4 mode transmission for IM/DD OAM mode division multiplexing optical fiber communication with a few-shot learning-based AffinityNet nonlinear equalizer.

Nonlinear impairment in a high-speed orbital angular momentum (OAM) mode-division multiplexing (MDM) optical fiber communication system presents high complexity and strong stochasticity due to the massive optoelectronic devices. In this paper, we propose an Affinity Network (AffinityNet) nonlinear equalizer for an OAM-MDM intensity-modulation direct-detection (IM/DD) transmission with four OAM modes. The labeled training and testing signals from the OAM-MDM system can be regarded as "small sample" and "large target", respectively. AffinityNet can be used to build an accurate nonlinear model using "small sample" based on few-shot learning and can predict the stochastic characteristic nonlinearity of OAM-MDM with a high level of generalization. As a result, the AffinityNet nonlinear equalizer can effectively compensate the stochastic nonlinearity in the OAM-MDM system, despite the large difference between the training and testing signals due to the stochastic nonlinear impairment. An experiment was conducted on a 400 Gbit/s transmission with four OAM modes using a pulse amplitude modulation-8 (PAM-8) signal over a 2 km ring-core fiber (RCF). Our experimental results show that the proposed nonlinear equalizer outperformed the conventional Volterra equalizer with improvements in receiver sensitivity of 1.7, 1.8, 3, and 3.3 dB for the four OAM modes at the 15% forward error correction (FEC) threshold, respectively. In addition, the proposed equalizer outperformed a convolutional neural network (CNN) equalizer with improvements in receiver sensitivity of 0.8, 0.5, 0.9, and 1.4 dB for the four OAM modes at the 15% FEC threshold. In the experiment, a complexity reduction of 37% and 83% of the AffinityNet equalizer is taken compared to the conventional Volterra equalizer and CNN equalizer, respectively. The proposed equalizer is a promising candidate for a high-speed OAM-MDM optical fiber communication system.

Dynamic analysis of PAM-4 IM/DD OAM-based MGDM transmission enabled by mode-group filter approach.

Mode-group-division multiplexing (MGDM)-based intensity modulation direct detection (IM/DD) transmission is an attractive approach to increase the capacity for short-reach optical communication. In this Letter, a simple but versatile scheme of mode group (MG) filtering for MGDM IM/DD transmission is proposed. The scheme is applicable to any mode basis in the fiber, and it satisfies the needs of low complexity, low power consumption, and high system performance. By employing the proposed MG filter scheme, a total raw bit rate of a 152-Gb/s multiple-input-multiple-output (MIMO)-free IM/DD co-channel simultaneous transmit and receive system based on two orbital angular momentum (OAM) MGs, each carrying a 38-GBaud four-level pulse amplitude modulation (PAM-4) signal, is experimentally demonstrated over a 5-km few-mode fiber (FMF). The bit error ratios (BERs) of the two MGs are below the 7% hard-decision forward error correction (HD-FEC) BER threshold at 3.8×10-3, using simple feedforward equalization (FFE). Furthermore, the dependability and robustness of such MGDM links are of great significance. Thus, the dynamic evaluation of BER and signal-to-noise ratio (SNR) for each MG is tested over 210 minutes under different conditions. In the dynamic cases, all the BER results using the proposed scheme can be below 1×10-3, which further confirms the stability and feasibility of our proposed MGDM transmission scheme.

200 Gb/s Optical-Amplifier-Free IM/DD Transmissions Using a Directly Modulated O-Band DFB+R Laser Targeting LR Applications

We experimentally demonstrate an O-band single-lane 200 Gb/s intensity modulation direct detection (IM/DD) transmission system using a low-chirp, broadband, and high-power directly modulated laser (DML). The employed laser is an isolator-free packaged module with over 65-GHz modulation bandwidth enabled by a distributed feedback plus passive waveguide reflection (DFB+R) design. We transmit high baud rate signals over 20-km standard single-mode fiber (SSMF) without using any optical amplifiers and demodulate them with reasonably low-complexity digital equalizers. We generate and detect up to 170 Gbaud non-return-to-zero on-off-keying (NRZ-OOK), 112 Gbaud 4-level pulse amplitude modulation (PAM4), and 100 Gbaud PAM6 in the optical back-to-back configuration. After transmission over the 20-km optical-amplifier-free SSMF link, up to 150 Gbaud NRZ-OOK, 106 Gbaud PAM4, and 80 Gbaud PAM6 signals are successfully received and demodulated, achieving bit error rate (BER) performance below the 6.25%-overhead hard-decision (HD) forward-error-correction code (FEC) limit. The demonstrated results show the possibility of meeting the strict requirements towards the development of 200Gb/s/lane IM/DD technologies, targeting 800Gb/s and 1.6Tb/s LR applications.

High-Capacity IM-DD Transmission in O-Band Using Advanced Maximum Likelihood Sequence Estimation Methods

We propose advanced maximum likelihood sequence estimation (MLSE) methods for increasing the capacity of short-reach intensity-modulated direct detection (IM-DD) transmissions for economically realizing next generation Ethernet such as 800GbE or 1.6TbE. It is particularly important to conquer the traffic growth in data center networks, which has become a major issue. In this article, we introduce a method for reducing the complexity of the Viterbi algorithm, which is a problem in the actual implementation of MLSE, by using a penalty-less truncated trellis diagram with temporal decision results. Next, we introduce a method for improving the demodulation performance by precisely emulating the nonlinear response of the transmission system with low-cost devices using a nonlinear filter. Finally, we introduce a method for reducing the computational complexity with a decision feedback function. Transmission experiments in the O-band with transmission rates of 200 Gbps/lane or higher using each of the proposed methods are also presented. Finally, we present a 200Gbps/lane 4-LAN-WDM 800G 2km transmission experiment using a 4-channel LAN-WDM TOSA designed for 400G transmission.

Comparison of post-equalizers for beyond 100-Gb/s/[formula omitted] C-band signal transmission over a 100-km dispersion-uncompensated SSMF

A comprehensive comparison among different post-equalizers with relatively low complexity is studied for C-band 100-km dispersion-uncompensated standard single-mode fiber (SSMF) intensity modulation and direct detection (IM/DD) transmission systems with data rate beyond 100 Gb/s/λ. These representative post-equalizers include feed-forward equalizer (FFE), polynomial-based nonlinear FFE (P-NFFE), absolute-term based nonlinear FFE (AT-NFFE), FFE combined with decision-feedback equalizer (FFE-DFE), polynomial based nonlinear FFE-DFE (P-NLE), absolute-term based nonlinear FFE-DFE (AT-NLE), and their lower-complexity versions of FFE-DFE-WS, P-NLE-WS, and AT-NLE-WS which use weight sharing (WS) to eliminate weight redundancy. We demonstrate 100-Gb/s/λ and 112-Gb/s/λ on-off keying (OOK) transmissions over a 100-km SSMF. For 112-Gb/s transmission, BERs of FFE-DFE(-WS), P-NLE(-WS), and AT-NLE(-WS) can reach 7% hard-decision forward error correction (HD-FEC) limit at 3.8 × 10−3. Under 7% HD-FEC limit, AT-NLE-WS with 32 real-valued multiplications shows similar BER performance as P-NLE and AT-NLE with a small power penalty of < 0.4 dB, but outperforms P-NLE-WS, AT-NLE, and P-NLE in huge complexity reduction of approximately 83.2%, 92.4%, and 92.7%, respectively. Therefore, taking both the BER performance and the operation complexity into account, AT-NLE-WS is the optimal equalizer and is a strong candidate to be applied in low-cost C-band IM/DD interconnections with data rates beyond 100 Gb/s/λ and transmission distance up to 100 km.

C-band 100-GBaud PS-PAM-4 transmission over 50-km SSMF enabled by FIR-filter-based pre-electronic dispersion compensation.

Chromatic dispersion (CD) is always an obstacle to C-band high-speed intensity modulation and direct detection (IM/DD) transmissions, especially with a fiber reach of > 20 km. To reach beyond net-100-Gb/s IM/DD transmission over 50-km standard single mode fiber (SSMF), we for the first time present a CD-aware probabilistically shaped four-ary pulse amplitude modulation (PS-PAM-4) signal transmission scheme with a FIR-filter-based pre-electronic dispersion compensation (FIR-EDC) for C-band IM/DD transmission system. With the help of the FIR-EDC at the transmitter, 100-GBaud PS-PAM-4 signal transmission at 150-Gb/s line rate and 115.2-Gb/s net rate over 50-km SSMF is realized with only feed-forward equalization (FFE) at the receiver side. The superiority of the CD-aware PS-PAM-4 signal transmission scheme over other benchmark schemes has been successfully verified by experiments. Experimental results show that 24.5% improvement of system capacity is obtained by the FIR-EDC-based PS-PAM-4 signal transmission scheme in comparison to the FIR-EDC-based on-off keying (OOK) signal transmission scheme. Compared with the FIR-EDC-based uniform PAM-4 signal transmission scheme or the PS-PAM-4 signal transmission scheme without EDC, the capacity improvement obtained by the FIR-EDC-based PS-PAM-4 signal transmission scheme becomes more profound. The results show the potential and feasibility of such CD-aware PS-PAM-4 signal transmission scheme applied in CD-constrained IM/DD datacenter interconnects.

Experimental investigation of BDFA-based O-band direct-detection transmission using an optical recirculating loop.

We implemented a bismuth-doped fiber amplifier (BDFA) based optical recirculating loop to investigate the performance of amplified O-band transmission over appreciable distances. Both single-wavelength and wavelength-division multiplexed (WDM) transmission were studied, with a variety of direct-detection modulation formats. We report on (a) transmission over lengths of up to 550 km in a single-channel 50-Gb/s system operating at wavelengths ranging from 1325 nm to 1350 nm, and (b) rate-reach products up to 57.6 Tb/s-km (after accounting for the forward error correction redundancy) in a 3-channel system.

Gerchberg-Saxton Based FIR Filter for Electronic Dispersion Compensation in IM/DD Transmission Part I: Theory and Simulation

Intensity-modulation and direct-detection (IM/DD) transmission over short-reach optical fiber links, require electronic dispersion compensation (EDC) at the transmitter and/or electronic equalization at the receiver. Recently, the iterative Gerchberg-Saxton (GS) algorithm was demonstrated for EDC in IM/DD systems, through treating the amplitude at the transmitter and the phase prior-to the direct detection receiver as a degree of freedom. In Part I of this work, three GS approaches using finite impulse response (FIR) filters for EDC in IM/DD systems are demonstrated. The first two are closely related and rely on a cascaded FIR structure, while the third offers a novel non-iterative EDC solution using a single GS optimized static FIR filter. This is achieved through decoupling pattern dependent aspects of transmission from the GS iterations by targeting a single impulse at the DD receiver. With every successive iteration an impulse response for the GS filter emerges and sets the FIR tap weights. It is also demonstrated that closed-form analytical expressions for the GS filter impulse response can be obtained through small-signal frequency-domain analysis. The FIR filter is simulated using 8-bit finite-precision arithmetic. An adaptive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T$</tex-math></inline-formula> -spaced post feed-forward equalizer (FFE) is utilized for mitigating residual chromatic dispersion. It is shown, that a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T/2$</tex-math></inline-formula> -spaced pre-EDC FIR filter with 417 taps can support 56 Gb/s non-return-to-zero (NRZ) on-off keying (OOK) transmission over 80 km of single mode fiber (SMF) with a chirp-free Mach-Zehnder modulator (MZM). Part II, presents experimental demonstration of the non-iterative GS FIR filter proposed and simulated in this article.

Low-modal-crosstalk orthogonal combine reception for degenerate modes in IM/DD MDM transmission.

Weakly-coupled mode division multiplexing (MDM) techniques supporting intensity modulation and direct detection (IM/DD) transmission is a promising candidate to enhance the capacity of short-reach applications such as optical interconnections, in which low-modal-crosstalk mode multiplexers/demultiplexers (MMUX/MDEMUX) are highly desired. In this paper, we firstly propose an all-fiber low-modal-crosstalk orthogonal combine reception scheme for degenerate linearly-polarized (LP) modes, in which signals in both degenerate modes are firstly demultiplexed into the LP01 mode of single-mode fibers, and then are multiplexed into mutually orthogonal LP01 and LP11 modes of a two-mode fiber for simultaneous detection. Then a pair of 4-LP-mode MMUX/MDEMUX consisting of cascaded mode-selective couplers and orthogonal combiners are fabricated with side-polishing processing, which achieve low back-to-back modal crosstalk of lower than -18.51 dB and insertion loss of lower than 3.81 dB for all the 4 modes. Finally, a stable real-time 4 modes × 4λ × 10 Gb/s MDM-wavelength division multiplexing (WDM) transmission over 20-km few-mode fiber is experimentally demonstrated. The proposed scheme is scalable to support more modes and can pave the way to practical implementation of IM/DD MDM transmission applications.

Improved Weighted Volterra DFE for C-Band 100-Gbit/s PAM-4 Transmission Over 60-km SSMF

To cope with the nonlinear distortions and the chromatic dispersion (CD) induced power fading in double-side band (DSB) intensity modulation and direct detection (IM/DD) transmission systems, high-performance Volterra decision-feedback equalizers (VDFEs) are widely applied. However, similar as linear DFE, the VDFEs suffer from error propagation in the case of wrong decisions. In this letter, to reduce the error propagation probability of VDFEs, we propose and experimentally demonstrate a diagonally-pruned improved weighted VDFE (DP-IWVDFE) in a C-band 4-level pulse amplitude modulation (PAM-4) transmission system. By replacing the hard-decision output by the soft-decision feedback symbol based on a compressed sigmoid nonlinear function in DP-IWVDFE, the error propagation probability can be significantly reduced, which lowers the bit error ratio (BER) by a factor of around two as compared to the DP-VDFE. Besides, 100-Gbit/s PAM-4 transmission over 60-km standard single-mode fiber (SSMF) using DP-IWVDFE is realized with the achieved BER below 3.8 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times 10^{-3}$ </tex-math></inline-formula> , achieving around 3.8-dB, 1.5-dB, and 1-dB improvements of the receiver sensitivity over the polynomial DFE (PDFE), improved weighted PDFE (IWPDFE), and DP-VDFE, respectively.

Ultrahigh-Speed Optical Interconnects With Thin Film Lithium Niobate Modulator

The exponential growth in data-driven applications like artificial intelligence and metaverse poses an increasing demand for integrated optical interconnects with efficient and cost-effective high-capacity solutions. For short-reach optical interconnects dominated by intensity-modulated direct detection (IM-DD), high-speed and large-capacity transmission enabled by high-bandwidth electro-optic devices is always highly desired. In this article, based on a thin film lithium niobate (TFLN) modulator with a 3-dB bandwidth larger than 110 GHz fabricated by ourselves, we experimentally demonstrate ultrahigh-speed optical interconnects with probabilistic shaping pulse amplitude modulation (PS-PAM) signals. With linear pre-equalization and Volterra nonlinear equalizer (VNLE), a 120 Gbaud PS-PAM16 signal with a bit rate up to 408 Gb/s is generated. Compared to the regular-PAM8 signal with the same bit rate of 360Gb/s, the PS-PAM signal demonstrates a receiver sensitivity gain of 2.2 dB. With the help of VNLE, 384.5 Gb/s PS-PAM16 signal can be transmitted over 500 m standard single-mode fiber (SSMF) at the C band. The ultra-broadband TFLN enabled transmission provides a promising solution for future 400G per wavelength data-center interconnects.

Adaptive Bayesian neural networks nonlinear equalizer in a 300-Gbit/s PAM8 transmission for IM/DD OAM mode division multiplexing.

The strong stochastic nonlinear impairment induced by random mode coupling appears to be a long-standing performance-limiting problem in the orbital angular momentum (OAM) mode division multiplexing (MDM) of intensity modulation direct detection (IM/DD) transmission systems. In this Letter, we propose a Bayesian neural network (BNN) nonlinear equalizer for an OAM-MDM IM/DD transmission with three modes. Unlike conventional Volterra and convolutional neural network (CNN) equalizers with fixed weight coefficients, the weights and biases of the BNN nonlinear equalizer are regarded as probability distributions, which can accurately match the stochastic nonlinear model of the OAM-MDM. The BNN nonlinear equalizer is capable of adaptively updating its weights and biases sample-by-sample, according to the probability distribution. An experiment was conducted on a 300-Gbit/s PAM8 signal with three modes over a 2.6-km OAM-MDM RCF transmission. The experimental results demonstrate that the proposed BNN nonlinear equalizer exhibits promising solutions to effectively mitigate nonlinear distortions, which outperforms conventional Volterra and CNN equalizers with receiver sensitivity improvements of 1.0 dBm and 2.5 dBm, respectively, under hard-decision forward error correction (HD-FEC) thresholds. Moreover, compared with the Volterra and CNN equalizers, the complexity of the OAM-MDM is significantly improved through the BNN nonlinear equalizer. The proposed BNN nonlinear equalizer is a promising candidate for the high capacity inter-data center interconnects.