Phase-retrieval (PR) schemes based on the modified Gerchberg-Saxton (GS) algorithm capture the full-field employing a dispersive element and intensity-only measurements to eliminate the use of local oscillator. In this work, we propose two carrier-assisted PR schemes, namely central carrier-assisted PR (CCA-PR) and edge carrier-assisted PR (ECA-PR), to improve the comprehensive performance of PR receiver in terms of convergence speed, redundancy, and computational complexity. The proposed CCA-PR recovers the electrical field employing a reference direct current carrier with several iterations between two projection planes. It avoids pilot symbols and digital backpropagation to the transmitter and offers a flexible electrical bandwidth requirement compared with conventional PR schemes. To lower the carrier-to-signal power ratio (CSPR) requirement and enable faster convergence for the carrier-assisted PR schemes, the ECA-PR is proposed to obtain the initial phase for the GS algorithm. We numerically characterize the performance of the two schemes and experimentally demonstrate them for 30 GBaud 16-quadrature amplitude modulation (16-QAM) transmission over 80 km single-mode fiber with a bit error rate (BER) below the threshold of 7% hard-decision forward error correction (HD-FEC). Several critical parameters are analyzed, including the applied dispersion value, CSPR, and electrical bandwidth. Moreover, we compare the optical signal-to-noise ratio (OSNR) sensitivity, required electrical bandwidth and hardware complexity of the proposed PR schemes with mainstream field recovery schemes.

Bandwidth limitation in optoelectrical components and the chromatic dispersion-induced power fading phenomenon cause severe inter-symbol interference (ISI) in high-speed intensity modulation and direct detection (IM-DD) optical interconnects. While the equalizer implemented in the receiver's digital signal processing procedure can mitigate ISI, it also inevitably enhances the noise located in the decayed frequency region, known as equalization-enhanced colored noise (EECN). Additionally, the nonlinear impairments of the modulator and photodetector also deteriorate the performance of the IM-DD system, especially for high-order modulation formats. In this work, we propose a gradient-descent noise whitening (GD-NW) algorithm to address EECN and extend it by introducing nonlinear kernels to simultaneously mitigate EECN and nonlinear impairments. The proposed algorithms are compared with conventional counterparts in terms of the achievable baud rate and the receiver optical power sensitivity. As a proof-of-concept experiment, we validate the principles of the proposed algorithms by successfully transmitting 360-GBd on-off-keying (OOK) and 180-GBd 4-level pulse-amplitude-modulation (PAM-4) signals in the back-to-back case under a 62-GHz brick-wall bandwidth limitation. 280-GBd OOK and 150-GBd PAM-4 transmissions are also demonstrated over 1-km standard single-mode fiber with a bit error rate below 7% hard-decision forward error correction aided by the proposed approach.

Phase retrieval (PR) schemes based on modified Gerchberg-Saxton (GS) algorithm using pilot symbol or pilot tone have recently attracted great attentions in self-coherent systems. In this work, we propose a dual-carrier-assisted phase retrieval (D-CAPR) algorithm and further fulfill a dual-polarization carrier-assisted PR (DP-CAPR) scheme. The polarization diversity is realized by transmitting a polarization-division-multiplexed (PDM) signal with orthogonal offset carriers, and the dual-polarization optical fields are recovered by the proposed D-CAPR algorithm. The D-CAPR scheme is able to directly retrieve the phases of optical field given the prior phase information of two carriers on each polarization without the use of any frequency guard band. We numerically characterize the performance of proposed DP-CAPR and experimentally demonstrate it for 30 GBaud dual-polarization-32-ary quadrature amplitude modulation (DP-32-QAM) transmission over 80 km single-mode fiber. The impacts of polarization rotation, polarization mode dispersion, and electrical noise on DP-CAPR have been investigated. Moreover, we compare the electrical bandwidth requirement, optical signal-to-noise ratio (OSNR) sensitivity, and hardware complexity of the DP-CAPR scheme with previously reported DP field recovery schemes.

Intensity-modulated direct-detection (IM/DD) optical systems are most widely employed in short-reach optical interconnects due to their simple structure and cost-effectiveness. However, IM/DD systems face mixed linear and nonlinear channel impairments, mainly induced by the combination of square-law detection and chromatic dispersion, as well as the utilization of low-cost non-ideal transceivers. To solve this issue, recent years have witnessed a growing trend of introducing machine learning technologies such as neural networks (NNs) into IM/DD systems for channel equalization. NNs usually present better system performance than traditional approaches, and various types of NNs have been investigated. Despite the excellent system performance, the associated high computational complexity is a major drawback that hinders the practical application of NN-based equalizers. This paper focuses on the performance and complexity trade-off of NNs employed in IM/DD systems, presenting a systematic review of the current status of NN-based equalizers as well as a number of effective complexity reduction approaches. The future trends of leveraging advanced NN in IM/DD links are also discussed.

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.

Data centers, the engines of the global Internet, rely on powerful high-speed optical interconnects. In optical fiber communication, classic direct detection captures only the intensity of the optical field, while the coherent detection counterpart utilizes both phase and polarization diversities at the expense of requiring a narrow-linewidth and high-stability local oscillator (LO). Herein, we propose and demonstrate a four-dimensional Jones-space optical field recovery (4-D JSFR) scheme without an LO. The polarization-diverse full-field receiver structure captures information encoded in the intensity and phase of both polarizations, which can be subsequently extracted digitally. To our knowledge, our proposed receiver achieves the highest electrical spectral efficiency among existing direct detection systems and potentially provides similar electrical spectral efficiency as standard intradyne coherent detection systems. The fully recovered optical field extends the transmission distance beyond the limitations imposed by fiber chromatic dispersion. Moreover, the LO-free advantage makes 4-D JSFR suitable for photonic integration, offering a spectrally efficient and cost-effective solution for massively parallel data center interconnects. Our results may contribute to the ongoing developments in the theory of optical field recovery and the potential design considerations for future high-speed optical transceivers.