Phase noise-induced interference for coherently detected OTDR systems.

The phase noise-induced interference (PNII) in coherently detected OTDR systems is investigated. A close-form relationship between signal to (interference) noise ratio (SNR) and laser linewidth is derived for the first time, to the best of our knowledge, and numerical simulations are conducted to verify the theoretical results. Additionally, the proportion of noise composition of PNII is studied. It is shown that the amplitude noise accounts for one-third of the total interference. This analytical form of PNII will assist in understanding the COTDR system that utilizes the full field of information (rather than intensity alone) at the receiver and, more importantly, provides a crucial guideline for designing high-performance and cost-effective COTDR systems in various applications.

Modified SiP single-polarization CADD receiver.

In cost-sensitive application scenarios, increasing the data rate per channel under a limited receiver bandwidth is critical, and thus, the transceivers with low costs and high electrical spectral efficiencies (ESEs) are highly desirable. In this Letter, we demonstrate a modified silicon photonic (SiP) carrier-assisted differential detection (CADD) receiver with a record ESE for single polarization. The ESE of the conventional CADD is mainly limited by the transfer function that originated from the optical delay and hybrid. We modify the transfer function of the CADD by placing an additional delay in parallel to the original delay path. Consequently, the modified transfer function exhibits a sharper slope around the zero frequency, leading to a higher ESE. Here we employ complementary metal-oxide-semiconductor-compatible SiP integration to further reduce the cost and footprint of the modified CADD receiver. In the experiment, 280-Gb/s raw rate (net 226-Gb/s) 16-QAM OFDM signal after 80-km SMF transmission was detected using a 36.5-GHz SiP modified CADD receiver, with a bit error ratio below the 24% SD-FEC threshold. To our best knowledge, we achieve a record net 6.2-b/s/Hz ESE for an integrated single-polarization DD receiver with a 16-QAM format.

Impact of non-Gaussian noise on GMI and LDPC performance in neural network equalized systems.

In this Letter, the impact of non-Gaussian noise caused by a nonlinear equalizer on low-density parity-check code (LDPC) performance is investigated in a 25-km 50-Gb/s pulse amplitude modulation4 (PAM4) direct detection system. The lookup table (LUT)-based log-likelihood ratio (LLR) calculation method is proposed to enhance the LDPC performance for the non-Gaussian noise case. Compared to the conventional LLR calculation method based on Gaussian distribution, the proposed method can improve 0.6-dB sensitivity in artificial neural network (ANN) equalizer systems. In addition, the conventional generalized mutual information (GMI) is proven to be an imperfect predictor of LDPC performance after nonlinear equalizers, such as decision feedback equalization (DFE) and ANN equalizer.

Weight-adaptive joint mixed-precision quantization and pruning for neural network-based equalization in short-reach direct detection links.

Neural network (NN)-based equalizers have been widely applied for dealing with nonlinear impairments in intensity-modulated direct detection (IM/DD) systems due to their excellent performance. However, the computational complexity (CC) is a major concern that limits the real-time application of NN-based receivers. In this Letter, we propose, to our knowledge, a novel weight-adaptive joint mixed-precision quantization and pruning approach to reduce the CC of NN-based equalizers, where only integer arithmetic is taken into account instead of floating-point operations. The NN connections are either directly cutoff or represented by a proper number of quantization bits by weight partitioning, leading to a hybrid compressed sparse network that computes much faster and consumes less hardware resources. The proposed approach is verified in a 50-Gb/s 25-km pulse amplitude modulation (PAM)-4 IM/DD link using a directly modulated laser (DML) in the C-band. Compared with the traditional fully connected NN-based equalizer operated with standard floating-point arithmetic, about 80% memory can be saved at a minimum network size without degrading the system performance. Quantization is also shown to be more suitable to over-parameterized NN-based equalizers compared with NNs selected at a minimum size.

Feature issue introduction: ultra-wideband optical communications.

This Feature Issue covers the important aspects to develop ultra-wideband optical communication systems including optoelectronics, impairment modeling and compensation, optical amplification, superchannel and multi-band transmission and control, and so forth. This Introduction provides a summary of the articles on these topics in this Feature Issue.

Deep-learning-enabled high-performance full-field direct detection with dispersion diversity.

Data center interconnects require cost-effective photonic integrated optical transceivers to meet the ever-increasing capacity demands. Compared with a coherent transmission system, a complex-valued double-sideband (CV-DSB) direct detection (DD) system can minimize the cost of the photonic circuit, since it replaces two stable narrow-linewidth lasers with only a low-cost un-cooled laser in the transmitter while maintaining a similar spectral efficiency. In the carrier-assisted DD system, the carrier power accounts for a large proportion of the total optical signal power. Reducing the carrier to signal power ratio (CSPR) can improve the information-bearing signal power and thus the achievable system performance. To date, the minimum required CSPR is ∼7 dB for all the reported CV-DSB DD systems having electrical bandwidths of approximately half of baud rates. In this paper, we propose a deep-learning-enabled DD (DLEDD) scheme to recover the full optical field of the transmitted signal at a low CSPR of 2 dB in experiment. Our proposal is based on a dispersion-diversity receiver with an electrical bandwidth of ∼61.0% baud rate and a high tolerance to laser wavelength drift. A deep convolutional neural network enables accurate signal recovery in the presence of a strong signal-signal beat interference. Compared with the conventional method, the proposed DLEDD scheme can reduce the optimum CSPR by ∼8 dB, leading to a significant signal-to-noise ratio improvement of ∼5.8 dB according to simulation results. We experimentally demonstrate the optical field reconstruction for a 28-GBaud 16-ary quadrature amplitude modulation signal after 80-km single-mode fiber transmission based on the proposed DLEDD scheme with a 2-dB optimum CSPR. The results show that the proposed DLEDD scheme could offer a high-performance solution for cost-sensitive applications such as data center interconnects, metro networks, and mobile fronthaul systems.

Carrier-assisted differential detection with reduced guard band and high electrical spectral efficiency.

For high-capacity and short-reach applications, carrier-assisted differential detection (CADD) has been proposed, in which the optical field of a complex-valued double sideband (DSB) signal is reconstructed without using a sharp-edge optical bandpass filter or local oscillator laser. The CADD receiver features a transfer function with periodical nulls in the frequency domain, while the signal-signal beat interference (SSBI) is severely amplified around the frequency nulls of the transfer function. Since the null magnitude at the zero frequency is inevitable, a guard band is required between the carrier and the signal, leading to a higher receiver bandwidth and implementation cost. To reduce the needed guard band, we propose a parallel dual delay-based CADD (PDD-CADD), in which an additional delay is placed parallel to the original delay in the conventional CADD. By this means, the modified transfer function has a sharper roll-off edge around the zero frequency. Consequently, the requirement on the guard band can be relaxed, which maximizes the bandwidth utilization of the system. The parallel delay is first optimized through numerical simulation. We then perform a proof-of-concept experiment to transmit a 100-Gb/s orthogonal frequency division multiplexing (OFDM) 16-ary quadrature amplitude modulation (16-QAM) signal over an 80-km single-mode fiber (SMF). After the fiber transmission, the proposed PDD-CADD can reduce the required guard band from 3 to about 1.2 GHz compared with the single delay-based conventional CADD. To our best knowledge, for the direct detection of a single polarization complex-valued DSB signal without using a sharp-roll-off optical filter, we achieve a record electrical spectral efficiency of 5.9 b/s/Hz.

Polarization-diversity receiver using remotely delivered local oscillator without optical polarization control.

Silicon photonics coherent transceivers have integrated all the necessary optics except the lasers. The laser source has become a major obstacle to further reduce the cost, footprint, power consumption of the coherent transceivers for short-reach optical interconnects. One solution is to utilize remotely delivered local oscillator (LO) from the transmitter, which has the benefits of relaxing the requirements of wavelength stability and laser linewidth and simplifying the digital signal processing (DSP) of carrier/phase recovery. However, a sophisticated adaptive polarization controller (APC) driven by a control loop in the electrical domain with a complicated algorithm is required to dynamically track and compensate for the polarization wandering of the received LO. In this paper, we propose a hybrid single-polarization coherent receiver and Stokes vector receiver (SVR) for polarization-diversity coherent detection without a need of optical polarization control for the remotely delivered LO. With such a scheme, we successfully received a 400-Gb/s dual-polarization constellation-shaped 64-QAM signal over 80-km fibers.

Carrier assisted differential detection with a generalized transfer function.

Direct detection capable of optical field recovery not only enables high-order modulation for high spectral efficiency (SE) but also extends the transmission reach by digital compensation of linear channel impairments such as chromatic dispersion. Recently, to bridge the gap between direct detection and coherent detection, carrier assisted differential detection (CADD) has been proposed for the reception of complex-valued double-sideband signals. In this paper, we extend the concept CADD to a general selection of the transfer functions, beyond the originally-proposed delay interferometer. To validate the proposed CADD approach, we utilize an optical filter based on silicon photonics microring resonator (MRR) as one realization of the generalized transfer functions. With the MRR based optical filter, both the required carrier-to-signal power ratio (CSPR) and the optical signal-to-noise ratio (OSNR) sensitivity are drastically improved over the conventional CADD due to the significantly suppressed signal-signal beating interference (SSBI). In addition, the proposed CADD is resilient to the wavelength offset up to several GHz between the transmitter laser and the center wavelength of the MRR based optical filter. With the proposed transfer function, CADD provides a novel approach for achieving high-SE transmission with superior receiver sensitivity and could be potentially useful for inter-/intra-datacenter or mobile front haul applications.

Cascade recurrent neural network-assisted nonlinear equalization for a 100 Gb/s PAM4 short-reach direct detection system.

We propose a novel, to the best of our knowledge, cascade recurrent neural network (RNN)-based nonlinear equalizer for a pulse amplitude modulation (PAM)4 short-reach direct detection system. A 100 Gb/s PAM4 link is experimentally demonstrated over 15 km standard single-mode fiber (SSMF), using a 16 GHz directly modulated laser (DML) in C-band. The link suffers from strong nonlinear impairments which is mainly induced by the mixture of linear channel effects with square-law detection, the DML frequency chirp, and the device nonlinearity. Experimental results show that the proposed cascade RNN-based equalizer outperforms other feedforward or non-cascade neural network (NN)-based equalizers owing to both its cascade and recurrent structure, showing the great potential to effectively tackle the nonlinear signal distortion. With the aid of a cascade RNN-based equalizer, a bit-error rate (BER) lower than the 7% hard-decision forward error correction (FEC) threshold can be achieved when the receiver power is larger than 5 dBm. Compared with traditional non-cascade NN-based equalizers, the training time could also be reduced by half with the help of the cascade structure.

Squeezing out the last few bits from band-limited channels with entropy loading.

The past decade witnessed the stirring development of advanced optical modulations and digital signal processing, which have been pushing optical transmission systems towards the capacity limit. Recent research has sought to squeeze out the last few bits from bandwidth-limited optical channels. One straightforward path is to expand the signal spectrum beyond the bandwidth limit while keeping the single-carrier modulation, which inevitably induces huge inter-symbol interference. To cope with such penalty, sophisticated digital nonlinear equalization on single-carrier signals should be exploited to reduce the burden of the subsequent forward error corrections (FEC). On the other hand, a more instinctive capacity-approaching method for bandwidth-deficient channels is the well-known water-filling realized by multicarrier modulation. As its approximation, bit loading (BL) has been a well-established algorithm to maximize the bit rate of a discrete multitone (DMT) channel with fixed-rate FEC. Built on probabilistic constellation shaping (PCS), multicarrier entropy loading (EL) goes beyond BL by continuous source entropy adaptation and has proven its superiority over the single-carrier PCS counterpart. In this paper, we reveal the EL advantage over BL on both achievable information rate (AIR) and FEC, aiming to prove EL as the optimum capacity-approaching solution for bandwidth-limited channels with frequency-selective fading. In a 100G direct detection system with a bandwidth-deficient directly modulated laser, EL improves the AIR by 5%-10% over BL using identical FEC overhead. EL will be critical for short-reach interconnects dominated by low-cost optical components to squeeze out the last few bits from the bandwidth-constrained system.

Computational complexity comparison of feedforward/radial basis function/recurrent neural network-based equalizer for a 50-Gb/s PAM4 direct-detection optical link.

The computational complexity and system bit-error-rate (BER) performance of four types of neural-network-based nonlinear equalizers are analyzed for a 50-Gb/s pulse amplitude modulation (PAM)-4 direct-detection (DD) optical link. The four types are feedforward neural networks (F-NN), radial basis function neural networks (RBF-NN), auto-regressive recurrent neural networks (AR-RNN) and layer-recurrent neural networks (L-RNN). Numerical results show that, for a fixed BER threshold, the AR-RNN-based equalizers have the lowest computational complexity. Amongst all the nonlinear NN-based equalizers with the same number of inputs and hidden neurons, F-NN-based equalizers have the lowest computational complexity while the AR-RNN-based equalizers exhibit the best BER performance. Compared with F-NN or RNN, RBF-NN tends to require more hidden neurons with the increase of the number of inputs, making it not suitable for long fiber transmission distance. We also demonstrate that only a few tens of multiplications per symbol are needed for NN-based equalizers to guarantee a good BER performance. This relatively low computational complexity signifies that various NN-based equalizers can be potentially implemented in real time. More broadly, this paper provides guidelines for selecting a suitable NN-based equalizer based on BER and computational complexity requirements.

Investigation of single- and multi-carrier modulation formats for Kramers-Kronig and SSBI iterative cancellation receivers.

The Kramers-Kronig (KK) receiver has recently attracted significant attention due to its capability of field recovery with direct detection. Under minimum phase condition, the KK receiver may use either single- or multi-carrier modulation formats. In this Letter, we investigate the appropriate modulation formats for both KK and signal-signal beat interference (SSBI) iterative cancellation (IC) receivers. It is shown that for the KK receiver, the single-carrier modulation format is superior to orthogonal frequency division multiplexing (OFDM), because the multi-carrier nature of OFDM signals increases the peak-to-average power ratio, which causes a violation of minimum phase condition. For the IC receiver, SSBI cancellation is more effective when the OFDM modulation format is adopted; thus, OFDM is the better fit for IC receivers than single carrier.

High-dimensional Stokes vector direct detection over few-mode fibers.

Direct detection attracts much attention for its simplicity compared with coherent detection. In this Letter, we propose for the first time, to the best of our knowledge, a high-dimensional Stokes vector direct detection (HD-SVDD) receiver for mode-division multiplexing transmission in few-mode fibers where the coupled modes can be recovered without resorting to coherent detection. To the best of our knowledge, the first high-dimensional Stokes vector reception based on the proposed HD-SVDD receiver has been successfully demonstrated with a dual-spatial and dual-polarization mode at 60 Gb/s over a 200 m two-mode fiber.

Multi-parameter distributed fiber sensing with higher-order optical and acoustic modes.

We propose a novel multi-parameter sensing technique based on a Brillouin optical time domain reflectometry in the elliptical-core few-mode fiber, using higher-order optical and acoustic modes. Multiple Brillouin peaks are observed for the backscattering of both the LP01 mode and LP11 mode. We characterize the temperature and strain coefficients for various optical-acoustic mode pairs. By selecting the proper combination of modes pairs, the performance of multi-parameter sensing can be optimized. Distributed sensing of temperature and strain is demonstrated over a 0.5-km elliptical-core few-mode fiber, with the discriminative uncertainty of 0.28°C and 5.81 µÎµ for temperature and strain, respectively.

.Maximizing the spectral efficiency of Stokes vector receiver with optical field recovery.

Stokes vector receivers (SVR) bridge the 4-D (i.e. dual-polarization complex signals) coherent detection and the conventional intensity-only 1-D direct detection (DD). By multi-dimensional polarization modulation in Stokes space, SVR maximizes the electrical spectral efficiency (ESE) of DD receivers by recovering at most 3-D signals. However, most 3-D schemes lack the capability of optical field recovery, an essential requirement for digital post-compensation of fiber dispersion that elongates the achievable distance. We propose a 3-D Stokes-space field modulation to enable 3-D signal field recovery, verified by a 3-D 32-Gbaud per dimension probabilistic-constellation-shaped 64-QAM transmission over 260-km fiber at C-band. This sets an ESE record of 16.5 (net ESE of 13.9) bit/s/Hz for DD receivers.

Direct detection of the optical field beyond single polarization mode.

Direct detection is traditionally regarded as a detection method that recovers only the optical intensity. Compared with coherent detection, it owns a natural advantage-the simplicity-but lacks a crucial capability of field recovery that enables not only the multi-dimensional modulation, but also the digital compensation of the fiber impairments linear with the optical field. Full-field detection is crucial to increase the capacity-distance product of optical transmission systems. A variety of methods have been investigated to directly detect the optical field of the single polarization mode, which normally sends a carrier traveling with the signal for self-coherent detection. The crux, however, is that any optical transmission medium supports at least two propagating modes (e.g. single mode fiber supports two polarization modes), and until now there is no direct detection that can recover the complete set of optical fields beyond one polarization, due to the well-known carrier fading issue after mode demultiplexing induced by the random mode coupling. To avoid the fading, direct detection receivers should recover the signal in an intensity space isomorphic to the optical field without loss of any degrees of freedom, and a bridge should be built between the field and its isomorphic space for the multi-mode field recovery. Based on this thinking, we propose, for the first time, the direct detection of dual polarization modes by a novel receiver concept, the Stokes-space field receiver (SSFR) and its extension, the generalized SSFR for multiple spatial modes. The idea is verified by a dual-polarization field recovery of a polarization-multiplexed complex signal over an 80-km single mode fiber transmission. SSFR can be applied to a much wider range of fields beyond optical communications such as coherent sensing and imaging, where simple field recovery without an extra local laser is desired for enhanced system performance.

Maximum likelihood sequence estimation for optical complex direct modulation.

Semiconductor lasers are versatile optical transmitters in nature. Through the direct modulation (DM), the intensity modulation is realized by the linear mapping between the injection current and the light power, while various angle modulations are enabled by the frequency chirp. Limited by the direct detection, DM lasers used to be exploited only as 1-D (intensity or angle) transmitters by suppressing or simply ignoring the other modulation. Nevertheless, through the digital coherent detection, simultaneous intensity and angle modulations (namely, 2-D complex DM, CDM) can be realized by a single laser diode. The crucial technique of CDM is the joint demodulation of intensity and differential phase with the maximum likelihood sequence estimation (MLSE), supported by a closed-form discrete signal approximation of frequency chirp to characterize the MLSE transition probability. This paper proposes a statistical method for the transition probability to significantly enhance the accuracy of the chirp model. Using the statistical estimation, we demonstrate the first single-channel 100-Gb/s PAM-4 transmission over 1600-km fiber with only 10G-class DM lasers.

Single-shot distributed Brillouin optical time domain analyzer.

We demonstrate a novel single-shot distributed Brillouin optical time domain analyzer (SS-BOTDA). In our method, dual-polarization probe with orthogonal frequency-division multiplexing (OFDM) modulation is used to acquire the distributed Brillouin gain spectra, and coherent detection is used to enhance the signal-to-noise ratio (SNR) drastically. Distributed temperature sensing is demonstrated over a 1.08 km standard single-mode fiber (SSMF) with 20.48 m spatial resolution and 0.59 °C temperature accuracy. Neither frequency scanning, nor polarization scrambling, nor averaging is required in our scheme. All the data are obtained through only one-shot measurement, indicating that the sensing speed is only limited by the length of fiber.

Complex imaging via coherent detection.

Complex imaging via coherent detection is proposed for acquiring two-dimensional (2-D) nearfield optical image that recovers amplitude and phase simultaneously. Based on the proposed complex imaging, we experimentally demonstrate the technique by detecting few-mode-fiber (FMF) modes with high extinction-ratio, and perform mode decomposition and differential mode delay (DMD) measurement.