Nowadays, Neural network (NN) has been proved to be an effective solution for nonlinear equalization in short reach optical systems. However, recent research has mainly focused on implementing more powerful NNs for equalization, while ignoring their adaptability to equalization tasks. In this paper, we propose Multi-Symbol Output (MSO)-Neural Networks (NN) for nonlinear equalization in high-speed short reach optical interconnects. The results show that the proposed MSO design works well on Deep Neural Networks (DNN), Long Short-Term Memory neural networks (LSTM) and Gate Recurrent Unit (GRU), which are the recent NN-based equalization structures. By increasing output symbols of the NNs, the number of slide windows in equalization can be sharply reduced, and so the complexity is reduced. By the same time, more information is brought to the MSO-NNs in back-propagations, therefore performance gain achieved. A 212-Gb/s 1-km Pulse Amplitude Modulation (PAM)-4 optical link is experimentally demonstrated as the target system, and the proposed MSO-NN equalizers are used to compare with traditional equalization algorithms including Volterra Nonlinear Equalizer (VNE) and single-symbol output NNs. Experimental results show that MSO design could help reduce the complexity of NN required for nonlinear equalization in the target system by around 2/3, and the proposed MSO-LSTM performs much better than VNE and 1 dB better than SSO-LSTM at the same time. Based on the proposed MSO-LSTM, transmission with BER under HD-FEC over 1 km NZDSF is achieved with a ROP at -2 dBm. Our work is well expandable and the proposed MSO design can be extended to other NN-based equalizers, which can help reduce complexity and learn more info from the training data and gain performance. The proposed MSO-NNs further enhance the performance and reduces the complexity of NN equalizers, provides assurance for future real-time high-speed short-range optical systems, and brings new ideas to NN-based equalizer design.

We provided a feasible solution for 800-Gb/s per carrier long-distance wavelength division multiplexing (WDM) coherent optical fibre transmission based on offline DSP. We experimentally demonstrate 5-carrier 125-GHz-spacing WDM coherent optical fibre transmission achieving 2000-km transmission distance and 800-Gb/s net bit rate per carrier. We utilized 100-Gbaud truncated probabilistically shaped (TPS) polarization-multiplexed 64QAM format in this work. In terms of advanced components, the high-speed digital-to-analog converter with 35-GHz 3 dB-bandwidth and Raman-amplified ultra-large-area fibre were utilized to achieve higher baud-rate and longer transmission distance. In terms of modulation format, we changed PS to TPS to obtain a more suitable shaping depth, and make the shaped signal better suited to the DSP process of coherent optical communication, including constant modulus algorithm (CMA) equalizer. Besides, our results show that the TPS-64QAM signal with 5-bit/symbol/polarization entropy outperforms the standard-32QAM with a same bit rate by around 1 dB sensitivity gain. Furthermore, we proposed a multiple-input multiple-output (MIMO) Volterra equalizer (VE), which consists of a 1 ^st -order 2 × 2 MIMO complex-valued widely linear (WL) equalizer and a 2 ^nd -order real-valued nonlinear equalizer. Our proposed MIMO VE can effectively resolve the impact of In-phase/quadrature (IQ) imbalance and IQ skew, and compensate linear and nonlinear impairments at the same time. We also utilized partial kernel VE to reduce the complexity by retaining part of the 2 ^nd -order kernels.

The radio-over-fiber (RoF) orthogonal frequency division multiplexing (OFDM) system at Terahertz (THz) band has been a promising solution to meet the demand for high capacity and flexibility. The signals transmitted in the RoF system will suffer severe impairments caused by the wireless multi-path effect, optical fiber transmission, and photoelectric device response. The time-frequency domain equalization (TFDE) based on the two-dimension convolution (Conv2D) neural network (NN) is proposed to resist the linear and nonlinear impairments of the RoF-OFDM system. Furthermore, complex convolution is applied to compensate for the complex channel response. Compared with several baseline models, the detailed performance improvement and model size discussion of the complex-valued Conv2D NN TFDE are investigated. With the aid of the complex-valued Conv2D NN TFDE, the 16 Gbaud 16-ary quadrature amplitude modulation (16QAM) signals are delivered over 54.6 m wireless distance and 20 km standard single mode fiber. The line rate of this RoF system achieves 53.5 Gbit/s.

We experimentally demonstrated a 10-channel 50-GHz-grid wavelength division multiplexing (WDM) signal transmission over 400-km standard single-mode fiber (SSMF) with the net bit rate of 614.4 Gbps/carrier and the spectral efficiency (SE) of 12.288 b/s/Hz, which is the highest SE for 256QAM to the best of our knowledge. Thanks to the joint pre-equalization and Volterra nonlinear equalization (VNLE), 49-Gbaud polarization division multiplexing (PDM) 256-ary quadrature amplitude modulation (256QAM) signal transmission with a novel constellation using probabilistic shaping (PS) and geometric shaping (GS) techniques is realized, considering the 0.828-normalized generalized mutual information (NGMI) low-density parity-check (LDPC) threshold with 25% overhead. Compared with the regular 256QAM at the same net bit rate, the designed hybrid PS/GS 256QAM at the expense of 1-Gbaud increase in the symbol rate obtains 1.7-dB and 1.5-dB shaping gain in single-channel case and WDM case, respectively. Meanwhile, an improvement of at least 0.6-dB in optical signal to noise ratio (OSNR) over the hybrid PS/GS 256QAM is achieved in comparison with PS-256QAM for both single-channel and WDM transmission.

Photonics-aided terahertz (THz) technologies in capable of supporting large signal bandwidths are promising in future ultrahigh-speed wireless communication systems, especially the THz-over-fiber (ToF) indoor applications. $2 \times 2$ multiple-input–multiple-output (MIMO) architecture for polarization-division multiplexing (PDM) can further double the system capacity with polarization dimension, while bringing more crosstalk and impairments to signal recovery. In this article, we propose to apply a MIMO equalizer with embedded adaptive phase recovery (eAPR) and independent channel processing (ICP) (MIMO-ICP-eAPR) digital signal processing (DSP) to better compensate for the crosstalk and impairments in a $2 \times 2$ MIMO PDM THz transmission system. With the novel MIMO-ICP-eAPR and photonics-aided THz-wave technologies, we experimentally demonstrate 60-GBaud probabilistically shaped (PS)-64QAM signal transmission over 20-km fiber and 3-m THz wave at 322 GHz in the air, empowered by a $2 \times 2$ MIMO antenna array for PDM technologies. The adaptive phase recovery (APR) integrated with MIMO equalizers can provide a better performance compared to separately applying MIMO equalizers followed by APR. Compared to the APR-separated counterpart, the proposed MIMO-ICP-eAPR can improve the input power sensitivity by 0.6 dB. Furthermore, even without ICP for mitigating IQ crosstalk, the MIMO-eAPR approach still shows performance enhancement compared to MIMO followed by APR. To the best of our knowledge, a record-breaking net rate of 510 Gbps per wavelength for a THz-wave transmission system with PS signals is reached. This work can provide fiber-THz architecture as well as a solution for future THz applications.

We proposed a low-complexity multi-input multi-output neural network integrated with a maximum likelihood phase recovery algorithm (MIMO-NN-BMLPR), which is adopted in long-haul coherent optical communication. Neural network based equalization can effectively overcome the nonlinear distortions induced during long-haul transmission. However, the forward neural network equalizer is difficult to track the phase of coherent optical signals. We integrate an additional maximum likelihood phase recovery layer with the MIMO-NN structure so that the phase noise can be compensated. In this work, 8-channel 100-GBaud dual-polarization (DP) PS-16QAM signals are successfully transmitted over 6400km and satisfy the normalized generalized mutual information (NGMI) threshold at 0.86. The proposed MIMO-NN-BMLPR integrates the low-complexity phase estimation with the NNE to improve the performance. Compared with the traditional DSP structure, the proposal prolongs the distance by 48.84% with a 39.80% complexity reduction.