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.

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.

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.

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.