Chromatic dispersion-enhanced signal-signal beating interference (SSBI) considerably affects the performance of intensity-modulation and direct-detection (IM/DD) fiber transmission systems. For recovering optical fields from received double sideband signals after propagating through IM/DD transmission systems, Gerchberg-Saxton (G-S) iterative algorithms are promising, which, however, suffers slow convergence speeds and local optimization problems. In this paper, we propose a multi-constraint iterative algorithm (MCIA) to extend the Gerchberg-Saxton-based linearized detection. The proposed technique can accelerate the convergence speed and realize nonlinear-equalization-free detection. Based on the data-aided iterative algorithm (DIA) and the decision-directed data-aided iterative algorithm (DD-DIA), the proposed technique reuses redundant bits from channel coding to not only correct decision errors but also enforce the constraints on the task function to further accelerate the whole optical field retrieval processing. Simulation results show that, compared with the DD-DIA, the MCIA reduces the received optical power (ROP) by about 1.5-dB for a 100-Gb/s over 50-km SSMF PAM-4 signal transmission at the symbol error rate (SER) of 2×10−2. For a 100-Gb/s over 400-km SSMF transmission system, just 30 MCIA iterations is needed, which is 30% reduction in iteration count compared with the DD-DIA. For further increased transmission capacities, the MCIA can improve the SER by two orders of magnitude compared with the conventional IA. To validate the effectiveness of the MCIA, we also conduct experiments to transmit 92-Gb/s PAM-4 signals over 50-km IM/DD fibre systems. We find that the MCIA has a 1-dB ROP improvement compared with the DD-DIA. Compared with Volterra nonlinear equalization, the BERs of the MCIA with a simple linear equalizer are reduced by more than one order of magnitude with only 52 MCIA iterations.

We propose a hybrid linearization algorithm combining the multi-constraint iteration and linear equalization. We experimentally demonstrate a 112-Gb/s PAM-4 signal transmission over 100-km SSMF in IM/DD optical transmission system with one single-ended photodiode.

We propose a low complexity transfer-learning assisted neural-network nonlinear compensation (TL-NN- NLC) scheme. The experimental results show 1.3-dB quality factor (Q-factor) improvement for 128 Gb/s polarization multiplexed (PM) 16-QAM coherent optical transmission over 800-km SSMF.

The severe band-limited effect resulted from the low-cost optical transceiver increases the channel memory length and the number of taps of the equalizers. Besides, the interaction of fiber dispersion and square-law detection introduce nonlinear distortions in intensity modulation and direct-detection (IM/DD) transmission systems. The serious band-limited effect and nonlinear distortions degrade the transmission performance and bring challenges to current equalizers for low-complexity implementation. In this paper, we propose a trellis-compression nonlinear maximum likelihood sequence estimation (TC-NL-MLSE) algorithm to compensate the linear and nonlinear distortions with lower complexity. In the TC-NL-MLSE, we introduce a polynomial nonlinear filter (PNLF) to partly compensate both the linear distortions and nonlinear distortions. Then, we establish a look-up-table (LUT) to calculate the nonlinear branch metric (BM). To simplify the calculation, two or three levels with the highest probabilities are selected according to decision thresholds for each symbol to compress the state-trellis graph (STG). This significantly reduces computational complexity on BM calculations especially for high-order modulations. We conduct experiments to transmit beyond the 200-Gb/s PAM-8 signal over 2-km standard single mode fiber (SSMF) at C-band. The TC-NL-MLSE outperforms the reduced-state MLSE with PNLF, and can reach the 7%-overhead hard-decision forward error correction threshold. Moreover, the TC-NL-MLSE reduces the complexity by 97% compared with standard LUT-MLSE, limiting the multipliers around 100 at the expense of only 0.2-dB receiver sensitivity penalty.

Maximum likelihood sequence estimation (MLSE) is the optimal signal sequence detection that can remove the inter-symbol interference (ISI). However, we find that the MLSE causes burst consecutive errors alternating between +2 and –2 in M-ary pulse amplitude modulation (PAM-M) IM/DD systems with large ISI. In this paper, we propose to use precoding to suppress the burst consecutive errors resulted from MLSE. A 2 M modulo operation is employed to guarantee that the probability distribution as well as the peak-to-average power ratio (PAPR) of encoded signal remain unchanged. After the receiver-side MLSE, the decoding process that involves adding the current MLSE output to the previous one and applying a 2 M modulo is implemented to break the burst consecutive errors. We conduct experiments to transmit 112/150-Gb/s PAM-4 or beyond 200-Gb/s PAM-8 signals at C-band to investigate the performance of the proposed MLSE integrated with precoding. The results show that the precoding can break burst errors effectively. For 201-Gb/s PAM-8 signal transmission, the precoding MLSE can achieve 1.4-dB receiver sensitivity gain and reduce the maximum length of burst consecutive errors from 16 to 3.