Symbol-level fiber-longitudinal power profile estimation.

Symbol-level fiber-longitudinal power profile estimation (PPE) greatly reduces the implementation complexity compared with the waveform-level PPE using oversampled data. However, symbol-rate data cannot account for the inter-sample interaction, which leads to inaccuracy of the absolute power estimation. To realize an accurate symbol-level PPE, we provide an in-depth analysis of the differences between symbol-level and waveform-level perturbation matrices and propose a power calibration method based on the trace of the inverse matrix. Evaluated in the probabilistic constellation shaping (PCS) 64QAM 130 Gbaud 5 × 50 km optical links, the root mean squared error (RMSE) of the symbol-level PPE decreases by 0.98 and 0.62 dB at erbium-doped fiber amplifier (EDFA) positions and all estimated positions with the aid of matrix calibration.

Low-complexity clustered polynomial nonlinear filter-based electrical dispersion pre-compensation scheme in IM/DD transmission systems.

A polynomial nonlinear filter (PNLF)-based electrical dispersion pre-compensation (pre-EDC) scheme assisted with Gerchberg-Saxton (GS) algorithm is proposed to compensate the chromatic dispersion (CD) for intensity-modulation and direct-detection (IM/DD) optical transmission systems, where PNLF is utilized to fit the nonlinear transfer function of the iterative GS algorithm-based pre-EDC scheme to realize a low-complexity non-iterative CD pre-compensation. The capability of PNLF to fit the nonlinear iterative process enables the PNLF-based pre-EDC scheme to compensate for CD-induced linear distortions and address CD-induced nonlinear distortions, which are typically captured through iterative approaches. Additionally, to further reduce the computational complexity, we also introduce the k-means clustering algorithm to eliminate the weight redundancy and propose a lower-complexity clustered PNLF-based pre-EDC scheme. Simulation results show that PNLF-based and clustered PNLF-based pre-EDC schemes save 76.0% and 97.5% complexity with only 0.3 dB receiver sensitivity penalty at 20% forward error correction (FEC) threshold, compared with GS-based pre-EDC scheme in C-band 56 GBaud 80-km on-off keying (OOK) system. Furthermore, the effectiveness of PNLF-based and clustered PNLF-based pre-EDC schemes is also evaluated through the experimental demonstration. Experimental results show that under C-band 32 GBaud 80-km OOK system, bit error ratio (BER) satisfying 20% FEC threshold is achieved by applying PNLF-based and clustered PNLF-based pre-EDC schemes, which save 78.3% and 94.2% complexity with only 0.4 dB receiver sensitivity penalty compared with GS-based pre-EDC scheme, respectively. The research results indicate that the (clustered) PNLF-based pre-EDC scheme has the great application potential for CD compensation in high-performance and low-cost IM/DD optical transmission systems.

Low-complexity optimized detection with cluster assisting for C-band 64-Gb/s OOK transmission over 100-km SSMF.

In this paper, a low-complexity optimized detection scheme consisting of a post filter with weight sharing (PF-WS) and cluster-assisted log-maximum a posteriori estimation (CA-Log-MAP) is proposed. Besides, a modified equal-width discrete (MEWD) clustering algorithm is proposed to eliminate the training process during clustering. After channel equalization, optimized detection schemes improve performance by suppressing the in-band noise raised by the equalizers. The proposed optimized detection scheme was experimentally performed in a C-band 64-Gb/s on-off keying (OOK) transmission system over 100-km standard single-mode fiber (SSMF) transmission. Compared with the optimized detection scheme with the lowest complexity, the proposed method saves 69.23% required number of real-valued multiplications per symbol (RNRM) at 7% hard-decision forward error correction (HD-FEC). In addition, when the detection performance reaches saturation, the proposed CA-Log-MAP with MEWD saves 82.93% RNRM. Compared with the classic k-means clustering algorithm, the proposed MEWD has the same performance without a training process. To the best of our knowledge, this is the first time clustering algorithms have been applied to optimize decision schemes.

Joint intra and inter-channel nonlinearity compensation based on interpretable neural network for long-haul coherent systems.

A novel joint intra and inter-channel nonlinearity compensation method is proposed, which is based on interpretable neural network (NN). For the first time, conventional cascaded digital back-propagation (DBP) and nonlinear polarization crosstalk canceller (NPCC) are deep unfolded into an NN architecture together based on their physical meanings. Verified by extensive simulations of 7-channel 20-GBaud DP-16QAM 3200-km coherent optical transmission, deep-unfolded DBP-NPCC (DU-DBP-NPCC) achieves 1 dB and 0.36 dB Q factor improvement at the launch power of -1 dBm/channel compared with chromatic dispersion compensation (CDC) and cascaded DBP-NPCC, respectively. Under the bit error rate threshold of 2 × 10-2, DU-DBP-NPCC extends the maximum transmission reach by 28% (700 km) compared with CDC. Besides, 3 different training schemes of DU-DBP-NPCC are investigated, implying the effective signal-to-noise ratio is not the proper evaluation metric of nonlinearity compensation performance for DU-DBP-NPCC. Moreover, DU-DBP-NPCC costs 26% lower computational complexity compared with DBP-NPCC, providing a better choice for joint intra and inter-channel nonlinearity compensation in long-haul coherent systems.

Raman/EDFA hybrid bidirectional amplifier for fiber-optic time and frequency synchronization.

Herein, we verify that a Raman/EDFA hybrid amplifier can improve the stability of fiber-optic time and frequency synchronization systems compared to the Er3+-doped fiber amplifier (EDFA), owing to its higher gain and lower noise figure (NF) performance. We studied the variation law of Raman gain efficiency for a fiber Raman amplifier (FRA) as a function of pump power and input signal power, designed a bidirectional Raman/EDFA hybrid amplifier, and proved that equivalent NF below 0 dB can be obtained. Finally, hybrid amplifiers were compared to EDFAs in a free-running frequency synchronization system. The transfer stabilities reached 1.9678 × 10-13/1 s and 2.0248 × 10-13/1 s when FRA + EDFA and EDFA + FRA configurations were used, respectively, both exhibiting better performance than the stability of 3.0905 × 10-13/1 s obtained by EDFA.

Low-complexity equalizer with a hybrid decision scheme for 50 Gb/s/λ PAM4-PON using a low-cost 10 G receiver.

In this Letter, we experimentally demonstrate a 50Gb/s/λ four-level pulse amplitude modulation-based passive optical network system with a 10 G class receiver. A memory polynomial equalizer (MPE) combined with a decision feedback equalizer (DFE) is applied to eliminate channel distortions in the system. To further improve the performance of the MPE-DFE, for the first time, to the best of our knowledge, a low-complexity hybrid decision scheme (HDS) is proposed, which consists of single-symbol decision (SSD) and multi-symbol decision (MSD). The SSD is exactly the conventional hard decision based on minimum Euclidean distance, whereas MSD is based on a simplified maximum likelihood detection principle with M-algorithm. In terms of complexity, MSD requires 19.1% more multiplications than SSD, but the symbol number of MSD only accounts for less than 20% of the total signal frame when the received optical power is greater than -27dBm. Experimental results show that the proposed MPE-DFE with HDS achieves a 0.7 dB and 1.3 dB sensitivity gain compared with conventional SSD, and up to 35.4 dB and 31.4 dB link power budget, regarding the forward error correction threshold of 10-2 and 10-3, respectively.

C-band 56-Gb/s PAM4 transmission over 80-km SSMF with electrical equalization at receiver.

In this paper, a memory polynomial equalizer combined with decision feedback equalizer (MPE-DFE) is proposed to eliminate channel distortions for intensity modulation and direct detection (IM/DD) systems. Compared with traditional feedforward equalizer and decision feedback equalizer (FFE-DFE), the proposed MPE-DFE introduces extra square terms and cubic terms to jointly equalize chromatic dispersion and nonlinear distortions. We demonstrated a C-band 56-Gb/s four-level pulse-amplitude modulation (PAM4) system over 80-km standard single mode fiber (SSMF) transmission. Experimental results show that the proposed MPE-DFE achieved up to 6.2 dB higher SNR than traditional FFE-DFE. Moreover, the achieved bit error ratio (BER) with MPE-DFE reaches 3.1 × 10-3, which is below 7% feedforward error correction (FEC) threshold of 3.8 × 10-3. To the best of our knowledge, we achieved a record transmission distance for C-band 56-Gb/s PAM4 signal with only electrical equalization at the receiver.

Equalization scheme of C-band PAM4 signal for optical amplified 50-Gb/s PON.

The bandwidth limit of devices and the chromatic dispersion (CD) of optical fiber severely distort the high-speed signal in a passive optical network (PON). In this paper, an efficient equalization scheme is proposed for optical amplified 50-Gb/s PAM4-PON with a 10G-class transmitter. The proposed equalization scheme is based on fast frequency domain equalization (FDE) with circular convolution, an optimized post-filter, and a low-complexity maximum likelihood sequence detector (MLSD), which requires only total 23 real-valued multiplications for each output symbol. Experimental results show that up to 33.2 dB power budget is successfully achieved over 20 km transmission without using any optical CD compensation module in the C-band. Moreover, there is only 0.5 dB penalty of receiver sensitivity compared to optical back to back (BTB) transmission. Therefore, the CD distortion has been nearly compensated for by the proposed equalization scheme. To the best of our knowledge, this is the best performance of an optical amplified 50-Gb/s PAM4-PON system in the C-band.

Joint Hartley-domain and time-domain equalizer for a 200-G (4×56-Gbit/s) optical PAM-4 system using 10G-class optics.

In this paper, we experimentally demonstrate a 200-G (4×56-Gbit/s) optical 4-level pulse-amplitude modulation (PAM-4) system using 10G-class optics over 10-km standard single-mode fiber and propose a joint Hartley-domain equalizer (HDE) and time-domain equalizer (TDE) algorithm for efficiently compensating the serious high-frequency distortions caused by the bandwidth-limited devices. To the best of our knowledge, the first HDE based on Hartley transform is designed for an optical PAM-4 system. Owing to the real-valued and self-inverse properties of the Hartley transform, the HDE has advantages in processing the real-valued PAM-4 signal. The experimental results show that the joint HDE and TDE algorithm has a better performance than only the HDE or only the TDE. Meanwhile, for obtaining a desired bit error rate, the computational complexity of the joint HDE and TDE algorithm is approximately 6% that of only the TDE with larger tap number. In conclusion, the joint HDE and TDE algorithm shows great potential for high-speed and cost-sensitive optical PAM-4 systems.

Capacity limit for faster-than-Nyquist non-orthogonal frequency-division multiplexing signaling.

Faster-than-Nyquist (FTN) signal achieves higher spectral efficiency and capacity compared to Nyquist signal due to its smaller pulse interval or narrower subcarrier spacing. Shannon limit typically defines the upper-limit capacity of Nyquist signal. To the best of our knowledge, the mathematical expression for the capacity limit of FTN non-orthogonal frequency-division multiplexing (NOFDM) signal is first demonstrated in this paper. The mathematical expression shows that FTN NOFDM signal has the potential to achieve a higher capacity limit compared to Nyquist signal. In this paper, we demonstrate the principle of FTN NOFDM by taking fractional cosine transform-based NOFDM (FrCT-NOFDM) for instance. FrCT-NOFDM is first proposed and implemented by both simulation and experiment. When the bandwidth compression factor α is set to 0.8 in FrCT-NOFDM, the subcarrier spacing is equal to 40% of the symbol rate per subcarrier, thus the transmission rate is about 25% faster than Nyquist rate. FTN NOFDM with higher capacity would be promising in the future communication systems, especially in the bandwidth-limited applications.

Interleaved single-carrier frequency-division multiplexing for optical interconnects.

In this paper, we propose a real-valued interleaved single-carrier frequency-division multiplexing (I-SC-FDM) scheme for intensity-modulation and direct-detection optical interconnects. By simplifying the encoding structure, the computational complexity can be reduced from Nlog2N complex multiplications to N complex multiplications. At the complementary cumulative distribution function of 10-2, a reduction of 10 dB and 7.5 dB for the peak-to-average power ratio (PAPR) of the I-SC-FDM is achieved than that of orthogonal frequency-division multiplexing modulated with QPSK and 16QAM, respectively, when the subcarrier number is set to 4096. We experimentally demonstrate the I-SC-FDM scheme for optical interconnects with data rates of 12 Gbit/s, 24 Gbit/s and 128 Gbit/s transmitted over 22.5-km, 22.5-km and 2.4-km standard single mode fiber, respectively. The I-SC-FDM scheme shows great potential for cost-sensitive and power-sensitive optical interconnects owing to its low computational complexity and low PAPR.

Faster-than-Nyquist non-orthogonal frequency-division multiplexing based on fractional Hartley transform: erratum.

This erratum is presented to correct the errors in our paper [Opt. Lett.41, 4488 (2016) OPLEDP0146-959210.1364/OL.41.004488].

Faster-than-Nyquist non-orthogonal frequency-division multiplexing based on fractional Hartley transform.

In this Letter, we propose, to the best of our knowledge, the first faster-than-Nyquist non-orthogonal frequency-division multiplexing based on fractional Hartley transform (FrHT). Different from the existing NOFDM signal, the real-valued FrHT-based NOFDM signal can be directly applied to an intensity-modulated/direct-detection optical system without upconversion, and it can achieve a transmission rate faster than the Nyquist rate, which is the up limit of orthogonal frequency-division multiplexing. For example, when bandwidth compression factor α is set to 0.4, the transmission rate is 20 percent faster than the Nyquist rate. Furthermore, we demonstrate simulations and experiments to verify the feasibility of FrHT-based NOFDM. After a 25 km standard single-mode fiber transmission, the bit error rate of FrHT-based DC-offset NOFDM can achieve a 7% and 20% forward error correction limit when α is set to 0.45 and 0.4, respectively.

Low-peak-to-average power ratio and low-complexity asymmetrically clipped optical orthogonal frequency-division multiplexing uplink transmission scheme for long-reach passive optical network.

In this Letter, we propose a discrete Hartley transform (DHT)-spread asymmetrically clipped optical orthogonal frequency-division multiplexing (DHT-S-ACO-OFDM) uplink transmission scheme in which the multiplexing/demultiplexing process also uses the DHT algorithm. By designing a simple encoding structure, the computational complexity of the transmitter can be reduced from O(Nlog(2)(N)) to O(N). At the probability of 10(-3), the peak-to-average power ratio (PAPR) of 2-ary pulse amplitude modulation (2-PAM)-modulated DHT-S-ACO-OFDM is approximately 9.7 dB lower than that of 2-PAM-modulated conventional ACO-OFDM. To verify the feasibility of the proposed scheme, a 4-Gbit/s DHT-S-ACO-OFDM uplink transmission scheme with a 1∶64 way split has been experimentally implemented using 100-km standard single-mode fiber (SSMF) for a long-reach passive optical network (LR-PON).

Digital pilot aided carrier frequency offset estimation for coherent optical transmission systems.

We present a digital pilot aided carrier frequency offset estimation (FOE) method for coherent optical transmission systems. Unlike the conventional pilot tone insertion scheme, the pilot of the proposed method is generated in a digital manner and can serve as a good FOE indicator. Aided by this kind of digital pilot, the FOE is implemented by determining the location of the digital pilot in the spectrum. Theoretical analysis and numerical simulations show that the proposed method has the advantages in wide range, high accuracy, modulation formats independent, no need to remove the modulation, and high tolerance to the residual chromatic dispersion (CD) and polarization mode dispersion (PMD).

An improved scheme for Flip-OFDM based on Hartley transform in short-range IM/DD systems.

In this paper, an improved Flip-OFDM scheme is proposed for IM/DD optical systems, where the modulation/demodulation processing takes advantage of the fast Hartley transform (FHT) algorithm. We realize the improved scheme in one symbol period while conventional Flip-OFDM scheme based on fast Fourier transform (FFT) in two consecutive symbol periods. So the complexity of many operations in improved scheme is half of that in conventional scheme, such as CP operation, polarity inversion and symbol delay. Compared to FFT with complex input constellation, the complexity of FHT with real input constellation is halved. The transmission experiment over 50-km SSMF has been realized to verify the feasibility of improved scheme. In conclusion, the improved scheme has the same BER performance with conventional scheme, but great superiority on complexity.

Statistical characterization of the nonlinear noise in 2.8 Tbit/s PDM-16QAM CO-OFDM system.

We show for the first time through comprehensive simulations under both uncompensated transmission (UT) and dispersion managed transmission (DMT) systems that the statistical distribution of the nonlinear interference (NLI) within the polarization multiplexed 16-state quadrature amplitude modulation (PM-16QAM) Coherent Optical OFDM (CO-OFDM) system deviates from Gaussian distribution in the absence of amplified spontaneous emission (ASE) noise. We also observe that the dependences of the variance of the NLI noise on both the launch power and the transmission distance (logrithm) seem to be in a simple linear way.