PAM-4 Signal Research Articles

LUT enabled low-complexity electrical dispersion pre-compensation scheme for IM-DD systems.

Frequency selective fading caused by chromatic dispersion (CD) and direct detection is the primary impediment for IM-DD systems in achieving a large capacity-distance product. Gerchberg-Saxton (GS) based electrical dispersion pre-compensation (pre-EDC) schemes enhance IM-DD systems' robustness against chromatic dispersion (CD), but their high computational complexity limits practical implementation. In this Letter, a novel, to the best of our knowledge, low-complexity pre-EDC scheme enabled by the cluster-assisting look-up table (CLUT) technique is proposed to further reduce the computation complexity of the non-iterative FIR-based pre-EDC scheme, in which convolution operation is replaced by tables look-up and accumulation processing. And a key strategy is proposed to balance the number and the total size of the LUTs by establishing LUTs for each cluster center after clustering the tap weights. To validate the effectiveness of the proposed scheme, we experimentally demonstrate the transmission of 80 Gbit/s PAM-4 signals and 100 Gbit/s PAM-6 signals over 20 km standard single-mode fiber (SSMF). The experimental results show that the proposed scheme can eliminate the multiplication in convolution operations and reduce the addition times of 58.54% for PAM-4 and 51.22% for PAM-6 signals at the BER of 7% HD-FEC threshold without any penalty.

A Hybrid Network Integrating MHSA and 1D CNN–Bi-LSTM for Interference Mitigation in Faster-than-Nyquist MIMO Optical Wireless Communications

To mitigate inter-symbol interference (ISI) caused by Faster-than-Nyquist (FTN) technology in a multiple input multiple output (MIMO) optical wireless communication (OWC) system, we propose an ISI cancellation algorithm that combines multi-head self-attention (MHSA), a one-dimensional convolutional neural network (1D CNN), and bi-directional long short-term memory (Bi-LSTM). This hybrid network extracts data features using 1D CNN and captures sequential information with Bi-LSTM, while incorporating MHSA to comprehensively reduce ISI. We analyze the impact of antenna numbers, acceleration factors, wavelength, and turbulence intensity on the system’s bit error rate (BER) performance. Additionally, we compare the waveform graphs and amplitude–frequency characteristics of FTN signals before and after processing, specifically comparing sampled values of four-pulse-amplitude modulation (4PAM) signals with those obtained after ISI cancellation. The simulation results demonstrate that within the Mazo limit for selecting acceleration factors, our proposal achieves a 7 dB improvement in BER compared to the conventional systems without deep learning (DL)-based ISI cancellation algorithms. Furthermore, compared to systems employing a point-by-point elimination adaptive pre-equalization algorithm, our proposal exhibits comparable BER performance to orthogonal transmission systems while reducing computational complexity by 31.15%.

Real-Time Deployment of Pruned Volterra Algorithm for PAM4 Signals in a W-Band Wireless System

Real-Time Deployment of Pruned Volterra Algorithm for PAM4 Signals in a W-Band Wireless System

SkipNet: an adaptive neural network equalization algorithm for future passive optical networking

In this paper, we propose an original adaptive neural network equalizer (NNE) algorithm named SkipNet, which is suitable for rapid training on a packet-by-packet basis for burst-mode non-linear equalization in upstream PON transmission. SkipNet uses the simple LMS algorithm and avoids complex neural network training algorithms such as backpropagation and mini-batch training. We demonstrate SkipNet on captured continuous mode 100 Gbit/s PAM4 signals using an SOA preamplifier to achieve the challenging 29 dB PON optical loss budget. The adaptive SkipNet equalizer is shown to overcome combinations of severe SOA patterning effects and fiber dispersion impairments to achieve >29dB dynamic range back-to-back and >22.9dB dynamic range for up to 81.6 ps/nm accumulated dispersion. It can adapt in as little as 250 training symbols to each impairment scenario, which is equivalent to existing FFE/DFE solutions, while matching the non-linear performance of previously proposed static NNE solutions. To the best of our knowledge, SkipNet is the first ever adaptive NNE framework that can realistically be trained and adapted on a packet-by-packet basis and within strict PON packet preamble lengths.

Bias-aided DD-LMS equalizer for optical multipath-interference-impaired high-speed PAM4 transmission systems

Multipath interference (MPI) noise induces drastic fluctuations in high-speed 4-level pulse amplitude modulation (PAM4) intensity modulation direct detection (IMDD) systems, severely degrading the transmission performance. Here, we propose a bias-aided decision-directed least mean square (DD-LMS) equalizer to eliminate the MPI noise. In the simulation, the proposed bias-aided DD-LMS equalizer could adeptly track and compensate the MPI-impaired PAM4 signal, markedly improving the bit error rate (BER) performance under different MPI levels and laser linewidths. Within a 112 Gbps PAM4 transmission system, the proposed equalizer achieves a MPI tolerance over 4 dB at the KP4-forward error correction (FEC) threshold (2.4 × 10−4), outperforming existing MPI suppression techniques.

Large‐Scale High‐Density Multimode Optical Switch Matrix

AbstractOptical switching technology is emerging as a solution to the limitations of traditional electronic switching. Combining optical switching with mode‐division multiplexing effectively overcomes the limitations of expanding switching capacity solely by increasing the number of ports. This paper introduces a compact four‐mode 2 × 2 optical switch and a four‐mode reconfigurable non‐blocking 4 × 4 optical switch matrix based on the Beneš architecture. The multimode 2 × 2 switch achieves an extinction ratio larger than 15 dB for all modes in the wavelength range of 1530–1590 nm. The multimode 4 × 4 switch matrix has an extinction ratio exceeding 9 dB for all modes and states in the C‐band, with a compact size (1.46 × 0.23 mm2) and low power consumption (0–154 mW). It supports high‐integrity 50 Gbaud PAM4 signal transmission with a bit error rate below the forward error correction limit. These devices pave the way for enhanced integration density and capacity in optical switching systems.

Complex-valued recurrent neural network equalizer with low complexity for a 120-Gbps 50-km optical PAM-4 IM/DD system.

This paper introduces a novel complex-valued recurrent neural networks equalizer (RNNE) designed for a 120-Gbps, 50-km optical 4-level pulse-amplitude modulation (PAM-4) intensity modulation and direct detection (IM/DD) system. By mapping adjacent symbols of PAM-4 signals onto the complex domain, the correlation between two adjacent symbols of PAM-4 signals can be preserved. Based on experimental results, the proposed complex-valued RNNE outperforms the traditional real-valued RNNE with a 1.38-dB system power budget gain at the 7% overhead forward error correction BER threshold of 3.8 × 10-3. We believe that complex-valued RNNE has an advantage over real-valued RNNE in processing real-valued signals in IM/DD systems.

16 × 112 Gbps directly modulated membrane laser array for co-packaged interconnects.

A low-cost and low-power-consumption optical transmitter with a narrow shoreline is crucial for short-reach optical communication. To increase the shoreline bandwidth density (Gbps/mm) at low cost, multiple optical components, including lasers, should be integrated on a single chip. In this study, we develop a sixteen-channel membrane laser array integrated with silica-based spot-size convertors on a SiO2/Si substrate, with a footprint of 1.11 × 2.75 mm2. A thin (340 nm) membrane buried-heterostructure sandwiched between low-index silica-based materials provides high carrier and optical confinement, which contributes to reducing power consumption. We demonstrated direct modulation with 28- and 56-GBaud PAM4 signals and verified that 2-km data transmission is feasible for all sixteen channels.

Fractionally spaced nonlinear Tomlinson-Harashima precoding with weight clustering for C-band 100 Gbaud/λ PAM-4 transmission.

A nonlinear Tomlinson-Harashima precoding (NTHP) scheme has been verified for its capability to effectively address both the linear and nonlinear inter-symbol interferences (ISIs) arising in the intensity-modulation direct-detection (IM-DD) fiber optics transmission. Nevertheless, the application of the NTHP scheme may significantly increase the number of levels for the intensity modulated signals, resulting in the reduction of both eye width and receiver sensitivity. Here, we propose a fractionally spaced NTHP with a weight clustering (FS-NTHP-WC) scheme. Consequently, an accurate ISI feedback can be obtained to enlarge the eye width; meanwhile a hardware-efficient implementation without the equalization penalty can be achieved by weight clustering and pruning. When the C-band 100 Gbaud/λ PAM-4 signals are transmitted, our proposed FS-NTHP-WC scheme not only can achieve 0.25 dB and 0.5 dB gains of receiver sensitivity under back-to-back (B2B) and 2-km standard single-mode fiber (SSMF) transmission conditions, respectively, but can also cut down the computational complexity by 90% and 76% in terms of the number of multiplications and additions, respectively, in comparison with the NTHP scheme.

A PAM-4 signal enabled 400 Gbps hybrid PDM-OAM multiplexing-based FSO transmission system

A PAM-4 signal enabled 400 Gbps hybrid PDM-OAM multiplexing-based FSO transmission system

On the multipath interference mitigation for high-speed IM-DD transmissions with Nyquist subcarrier modulation.

The performance of high-speed intensity modulation direct detection (IM-DD) transmissions is severely degraded due to the occurrence of multipath interference (MPI), especially when a higher-order modulation format is utilized. Here, we propose and demonstrate, for the first time to the best of our knowledge, that a Nyquist subcarrier modulation (Nyquist-SCM) format inherently exhibits resistance to the MPI. We experimentally evaluate the MPI tolerance by transmitting 56 Gbit/s PAM-4 signals and Nyquist-SCM 16QAM signals over the 2 km standard single-mode fiber (SSMF) when the C-band semiconductor laser with a linewidth of 1.7 MHz is utilized. In comparison with the PAM-4 format, the Nyquist-SCM 16QAM format can lead to an enhanced MPI tolerance of 4 dB at the KP4-FEC threshold of BER = 2 × 10-4. In addition, even with the help of MPI mitigation for the PAM-4 signals based on two newly reported methods, the utilization of Nyquist-SCM 16QAM signal can still guarantee an improved MPI tolerance of 1 dB.

Bias-drift insensitive full-field frequency response characterization of a thin-film lithium niobate-based intensity modulator.

We propose a rapid and precise scheme for characterizing the full-field frequency response of a thin-film lithium niobate-based intensity modulator (TFLN-IM) via a specially designed multi-tone microwave signal. Our proposed scheme remains insensitive to the bias-drift of IM. Experimental verification is implemented with a self-packaged TFLN-IM with a 3 dB bandwidth of 30 GHz. In comparison with the vector network analyzer (VNA) characterization results, the deviation values of the amplitude-frequency response (AFR) and phase-frequency response (PFR) within the 50 GHz bandwidth are below 0.3 dB and 0.15 rad, respectively. When the bias is drifted within 90% of the Vπ range, the deviation fluctuation values of AFR and PFR are less than 0.3 dB and 0.05 rad, respectively. With the help of the full-field response results, we can pre-compensate the TFLN-IM for the 64 Gbaud PAM-4 signals under the back-to-back (B2B) transmission, achieving a received optical power (ROP) gain of 2.3 dB. The versatility of our proposed full-field response characterization scheme can extend to various optical transceivers, offering the advantage of low cost, robust operation, and flexible implementation.

Local oscillators-free chip-enabled W-band wireless IM-DD PAM-4 data transmission with simultaneous dual-laser modulation and envelope detection.

Wireless data traffic is expected to exponentially increase in the future, and meeting this demand will require high data rate photonic-wireless links operating in the W-band (75-110 GHz). For this purpose, pulse-amplitude-modulation with four levels (PAM-4)-based intensity modulation and direct detection (IM-DD) photonic-wireless systems are preferred due to their simplified configuration. In this Letter, we present an experimental demonstration of an IM-DD PAM-4 photonic-wireless link in the W-band, leveraging a monolithic dual-laser photonic chip to enhance integration. Through injection-locking by an optical comb, the chip generates a W-band wireless signal via photo-mixing with a photodiode. This comb injection approach facilitates the phase correlation of the chip's two modes, resulting in a stabilized beat note. Additionally, the on-chip integration of the dual lasers enables the modulation of the two modes with a single modulator, improving the signal-to-noise ratio (SNR) while eliminating the need for extra splitters or combiners. Meanwhile, the envelope detector (ED) plays a crucial role in the simplified configuration, contributing to the overall decrease in size, weight, power, and complexity of the system. The integration of the chip-based phase-locked light source and the utilization of the ED thus signify noteworthy features of our experimental setup, which functions without the necessity of both optical and electrical local oscillators. PAM-4 signal modulation is simultaneously applied to the two coherent optical carriers. Our experiments have effectively transmitted 5 and 10 Gbaud PAM-4 W-band wireless signals in a cost-effective, lightweight, and straightforward configuration, achieving a line data rate of up to 20 Gbit/s economically. These experimental results demonstrate the practical potential of implementing fully integrated photonic-wireless transmitters.

Regeneration of 200 Gbit/s PAM4 Signal Produced by Silicon Microring Modulator (SiMRM) Using Mach–Zehnder Interferometer (MZI)-Based Optical Neural Network (ONN)

We propose and demonstrate a Mach–Zehnder Interferometer (MZI)-based optical neural network (ONN) to classify and regenerate a four-level pulse-amplitude modulation (PAM4) signal with high inter-symbol interference (ISI) generated experimentally by a silicon microing modulator (SiMRM). The proposed ONN has a multiple MZI configuration achieving a transmission matrix that resembles a fully connected (FC) layer in a neural network. The PAM4 signals at data rates from 160 Gbit/s to 240 Gbit/s (i.e., 80 GBaud to 120 GBaud) were experimentally generated by a SiMRM. As the SiMRM has a limited 3-dB modulation bandwidth of ~67 GHz, the generated PAM4 optical signal suffers from severe ISI. The results show that soft-decision (SD) forward-error-correction (FEC) requirement (i.e., bit error rate, BER < 2.4 × 10−2) can be achieved at 200 Gbit/s transmission, and the proposed ONN has nearly the same performance as an artificial neural network (ANN) implemented using traditional computer simulation.

DAC-less PAM4 signal generation using a silicon dual-drive push-pull MZI modulator.

In this study, we demonstrate DAC-less PAM-4 signal generation by driving a silicon MZI modulator based on a series push-pull configuration with two independent binary signals of varying amplitudes. Such configuration boosts transfer speed between PAM4 levels, leading to enhanced performance metrics compared to the differential driving scheme. Experimentally, our scheme demonstrated a lower bit-error rate compared to the differential scheme, proving its cost-efficiency and feasibility for PAM4 generation.

Fiber-optic parametric amplifier-based all-optical format conversion enabling optical networks interconnection with different modulation formats

A fiber-optic parametric amplifier (FOPA)-based all-optical format conversion (AOFC) scheme is proposed and numerically simulated to achieve optical networks interconnection with different modulation formats. In this scheme, the power transfer function (PTF) and the relative phase shift (RPS) functions between the input and output optical signals for the single-pump FOPA are derived and numerically analyzed. For the input 20 Gbps bipolar 4-ary pulse amplitude modulation (PAM4) signal, it can be converted into a BPSK signal (BPSK1) based on the power saturation characteristic of the PTF. By adjusting the input power of the input PAM4 signal, it can also be converted into a level-swapping PAM4 signal based on the single-pump FOPA. When the level-swapping PAM4 signal is sent into the single-pump FOPA with suitable power again, another BPSK signal (BPSK2) could also be generated. When the PAM4-to-BPSK format converter based on the single-pump FOPA is combined with the dual-pump FOPA (namely phase-sensitive amplifier, PSA), the 16-ary quadrature amplitude modulation (16QAM) signal can also be de-aggregated into four BPSK signals or two quadrature phase shift keying (QPSK) signals. The constellation diagrams, the power waveforms, the error vector magnitude (EVM) and the bit error rate (BER) of the relevant optical signals are measured to evaluate the scheme performance. The scheme can be deployed at the optical gateway to realize optical networks interconnection using different modulation formats.

Optical PAM-4/PAM-8 generation via dual-Raman process in Rydberg atoms

Abstract A scheme of optical four-level pulse amplitude modulation (PAM-4) is proposed based on dual-Raman process in Rydberg atoms. A probe field counter-propagates with a dual-Raman field which drive the ground and the excited states transition, respectively, and the Rydberg transition is driven by a microwave (MW) field. A gain peak appears in the probe transmission and is sensitive to the MW field strength. Optical PAM-4 could be achieved by encoding a MW signal and decoding the magnitude of a probe signal. Simulation results show that the differential nonlinearity and the integral nonlinearity of the proposed scheme could be reduced by 5 times and 6 times, respectively, compared with the previous scheme, and the ratio of level separation mismatch is close to the ideal value 1. Moreover, the scheme is extended to optical PAM-8 signal, which may further improve the spectral efficiency.

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.

All-Optical format conversion from PAM4 to QPSK based on non-degenerate Phase-Sensitive amplification and pump assisted nonlinear optical loop mirror

An all-optical format conversion (AOFC) scheme from 4-ary pulse amplitude modulation (PAM4) to quadrature phase shift keying (QPSK) based on the non-degenerate phase-sensitive amplification (PSA) and the pump assisted nonlinear optical loop mirror (PA-NOLM) is proposed and numerically simulated for the first time. The input unipolar PAM4 signal with equal amplitude distance (UPAM4-A) is coupled with two input pump lights and injected into the symmetric interferometric fiber optic parameter amplifier (FOPA) to achieve the separation of the UPAM4-A and the new pump light generated at the signal frequency based on the non-degenerate PSA. When the filtered out UPAM4-A is coherent added with the new generated pump, the UPAM4-A signal to the biplolar PAM4 (BPAM4) signal. When the converted BPAM4 is sent into the PA-NOLM after adjusting its power, the BPAM4 signal could be converted into the QPSK signal. The error vector magnitude (EVM) and bit error ratio (BER) performance of the system are measured before and after AOFC with different input and receiver optical signal to noise ratio (OSNR). For the input UPAM4-A signal with an input OSNR of 27 dB, there is about 8.2 dB BER performance improvement in receiver OSNR for the final converted QPSK signal. Additionally, the proposed non-degenerate PSA configuration can be extended to realize the AOFC from one QPSK to two on–off keying (OOK) signals. The scheme can be applied in the optical gateway connecting the long-haul and the short-reach optical networks with suitable modulation formats.