An iterative BP-CNN decoder for optical fiber communication systems.

The conventional belief propagation (BP) of the low-density parity-check (LDPC) is designed based on additive white Gaussian noise (AWGN) close to the Shannon limit; however, the correlated noise due to chromatic dispersion or square-law detection results in a performance penalty in the intensity modulation and direct-detection (IM/DD) system. We propose an iterative BP cascaded convolution neural network (CNN) decoder to mitigate the correlated channel noise. We use a model of correlated Gaussian noise to verify that the noise correlation can be identified by the CNN and the decoding performance is improved by the iterative processing. We successfully demonstrate the proposed method in a 50-Gb/s 4-ary pulse amplitude modulation (PAM-4) IM/DD system. The simulation results show that the proposed decoder can achieve a BER performance improvement which is robust to transmission distance and launch optical power. The experimental results show that the iterative BP-CNN decoder outperforms the standard BP decoder by 1.2 dB in received optical power over 25-km SSMF.

Multi-band DFT-S 100 Gb/s 32 QAM-DMT transmission in intra-DCI using 10 G-class EML and low-resolution DAC.

In this paper, 100 Gb/s/λ 32 quadrature amplitude modulation discrete multi-tone (QAM-DMT) transmission using 10 G-class electro-absorption modulated laser (EML) and 4/5-bit digital-to-analog converters (DACs) are experimentally demonstrated to meet the requirement of intra-datacenter interconnection (intra-DCI). Unequal length multi-band (ULM) discrete Fourier transform spread (DFT-S) precoding is investigated to alleviate the distortion induced by the high peak-to-average power ratio (PAPR) of DMT. The results show that the required computational complexity of ULM DFT-S precoding with 2-bands (k1=256, k2=64) decreases sharply compared to the traditional DFT-S technique with only about 0.5 dB receiver sensitivity penalty. In addition, compared to the equal length multi-band (ELM) DFT-S precoding, the ULM DFT-S precoding can bring about 2.5 dB receiver sensitivity improvement with slight added computational complexity. With the assistance of ULM DFT-S precoding and noise shaping (NS) technique, the bit-error ratio (BER) of 100 Gb/s 32 QAM-DMT signal generated by 5-bit DAC over 2-km single-mode fiber (SMF) transmission can reach the hard-decision forward error correction (HD-FEC) threshold with received optical power (ROP) of -6.5 dBm, with only additional 39.9% multiplier and 33.7% adder.

Design of fully interpretable neural networks for digital coherent demodulation.

In this paper, we propose a digital coherent demodulation architecture using fully interpretable deep neural networks (NNs). We show that all the conventional coherent digital signal processing (DSP) is deeply unfolded into a well-structured NN so that the established training algorithms in machine learning can be applied. In contrast to adding or replacing certain algorithms of existing DSP in coherent receivers, we replace all the coherent demodulation algorithms with a fully interpretable NN (FINN), making the whole NN interpretable. The FINN is modular and flexible to add or drop modules, including chromatic dispersion compensation (CDC), the digital back-propagation (DBP) algorithm for fiber nonlinearity compensation, carrier recovery and residual impairments. The resulted FINN can be quickly initialized by straightforwardly referring to the conventional DSP, and can also enjoy further performance enhancement in the nonlinear fiber transmissions by NN. We conduct a 132-Gb/s polarization multiplexed (PM)-16QAM transmission experiment over 600-km standard single mode fiber. The experimental results show that without fiber nonlinearity compensation, FINN-CDC obtains less than 0.06-dB SNR gain than chromatic dispersion compensation (CDC). However, with fiber nonlinearity compensation, 2-steps per span FINN-DBP (FINN-2sps-DBP) and FINN-1sps-DBP bring about 0.59-dB and 0.53-dB SNR improvement compared with the conventional 2sps-DBP and 1sps-DBP, respectively.

Demonstration of 100-Gbit/s 32-QAM signal transmission in a radio-over-fiber system with 2-bit DAC.

In this Letter, a low-cost radio-over-fiber (RoF) system at the Ka band based on a low-resolution digital-to-analog converter (DAC) is proposed and investigated. The noise shaping (NS) technique is adopted to suppress the in-band quantization noise induced by the low-resolution DAC. To evaluate the performance of the proposed RoF system, the transmission of a 80/100-Gbit/s dual-polarization 16/32-QAM signal over 20-km single-mode fiber (SMF) and 1-m 2 × 2 multi-in multi-out (MIMO) wireless link coupled with a 2/3/4-bit DAC is experimentally demonstrated. The results show that the bit error rate (BER) of the signal generated by the 2-bit DAC can be effectively reduced by more than one order of magnitude when noise shaping is applied.

Multi-constraint Gerchberg-Saxton iteration algorithms for linearizing IM/DD transmission systems.

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.

High-capacity bi-directional full-duplex transmission based on fiber-eigenmode multiplexing over a FMF with 2×2 MIMO.

We propose and experimentally demonstrate symmetrical (homo-modal) and asymmetrical (hetero-modal) full-duplex bi-directional architectures based on dual-vector eigenmodes multiplexing over a 3 km few mode fiber (FMF). Firstly, 4 vector modes (VMs) of 2 mode groups (MGs), l = 0 (HE11o and HE11e modes) and l = +2 (EH11o and EH11e modes), each carrying a 14 GBaud quadrature phase-shift keying (QPSK) signal, are utilized in the up and down links and a 224 Gb/s same-mode bi-directional transmission is successfully realized. The crosstalk between the VMs in l = 0 and l = +2 of this full-duplex system is less than -13.8 dB. To strengthen the immunity to performance degradation induced by connector reflection and back scattering, we propose an effective approach to mitigate impairments by using hetero-modes on two terminals of the bi-directional system. Then, 2 VMs of l = 0 and 2 VMs of l = +2 are respectively employed in the up and down streams. The channel isolation between the VMs in l = 0 and l = +2 of such full-duplex link is larger than 19 dB, which supports a 448 Gb/s bi-directional transmission with 28 GBaud 16-ary quadrature amplitude modulation (QAM) modulation over a 3 km FMF by using 2 × 2 MIMO. Moreover, mode-wavelength division multiplexing including 2 modes and 4 wavelengths in both up and down streams is implemented in the transmission system. A total capacity of the 1.792 Tb/s link with 28 GBaud 16-QAM signal over each channel is successfully realized over the 3 km FMF. The measured bit-error-ratios (BERs) of all channels are below the 7% hard decision forward error correction (FEC) threshold at 3.8 × 10-3. The experimental results adequately indicate that such a scheme has a great potential in high-speed bi-directional point-to-point (P2P) optical interconnects.

Influence of EEPN and P2A noise with CD pre- and post-compensation in optical SSB transmission and Kramers-Kronig receiver system.

We present a comparative study of equalization-enhanced phase noise (EEPN) and phase to amplitude (P2A) noise with chromatic dispersion (CD) pre- and post-compensation in single side-band (SSB) transmission and direct-detection (DD) systems, respectively. We analyze the interplay of laser phase noise and fiber dispersion on an optical SSB Nyquist shaped four-level pulse amplitude modulation (PAM-4) signal in a Kramers-Kronig (KK) receiver. Our main results show that the EEPN in a DD-KK receiver dominates the system noise with the relaxed signal-to-noise ratio (SNR). The P2A noise in CD post-compensation scheme is relaxed due to the complex filed recovery with KK receiver. The numerical simulations are implemented to illustrate the interplay of laser linewidth and fiber dispersion in both CD pre- and post-compensation scenarios. Compared with CD pre-compensation, 3-dB reduction of power spectral density (PSD) of P2A noise at the peak is alleviated with CD post-compensation. The laser linewidth has ~1 MHz release with CD post-compensation for a 56-Gbaud PAM-4 signal over 100-km standard single-mode fiber (SSMF) transmission.

Comparison of null-subcarriers reservation and adaptive notch filter for narrowband interference cancellation in intra-data center interconnect with DMT signal transmission.

In this paper, we experimentally compare the performance of two different narrowband interference suppression schemes in 120 Gb/s intensity modulation and direct detection (IM/DD) system with discrete multi-tone (DMT) signal transmission for intra-data center interconnect (Intra-DCI). Digital pre-equalization and DFT-spread techniques are applied for system bandwidth limitation induced signal distortion compensation and signal peak to average power ratio (PAPR) reduction, respectively. Null-subcarriers reservation (NSR) and adaptive notch filter (ANF) techniques are compared during the suppression of digital-to-analog convertor (DAC) clock leakage induced narrowband interference. 1.2 dB and 1.8 dB DMT receiver sensitivity improvements can be achieved at a bit-error rate of 3.8 × 10-3 in optical back-to-back (OBTB) transmission when optimized NSR and ANF schemes are applied for narrowband interference cancellation, respectively. After 2-km single mode fiber (SMF) transmission, the required received optical power (ROP) of DMT signal with optimized NSR and ANF for narrowband interference cancellation at BER of 3.8 × 10-3 are -6.5 dBm and -7.1 dBm, respectively. Obviously, ANF outperforms NSR scheme in narrowband interference cancellation for DMT system.

100 Gbit/s PAM4 signal transmission and reception for 2-km interconnect with adaptive notch filter for narrowband interference.

In this paper, we experimentally demonstrate the transmission of 56 Gbaud four-level pulse amplitude modulation (PAM4) signal over 2-km single mode fiber (SMF) with intensity modulation and direct detection (IM/DD) scheme, while the bit-error-ratio (BER) of the PAM4 signal is under hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10-3. Linear pre-equalization is implemented in the transmitter side with a 3-tap finite-impulse-response (FIR) filter to compensate for the intersymbol interference (ISI) induced by system bandwidth limitation. Receiver side equalization is realized with training sequence (TS) based feed-forward equalizer (FFE) with decision-feedback equalizer (DFE). Furthermore, an Adaptive Notch Filter (ANF) is proposed to suppress the digital-to-analog converter (DAC) clock leakage induced narrowband interference for the first time, and the bandwidth of the ANF is optimized to achieve the best BER performance.

Terabit optical OFDM superchannel transmission via coherent carriers of a hybrid chip-scale soliton frequency comb.

We demonstrate seamless channel multiplexing and high bitrate superchannel transmission of coherent optical orthogonal frequency division multiplexing (CO-OFDM) data signals utilizing a dissipative Kerr soliton (DKS) frequency comb generated in an on-chip microcavity. Aided by comb line multiplication through Nyquist pulse modulation, the high stability and mutual coherence among mode-locked Kerr comb lines are exploited for the first time, to the best of our knowledge, to eliminate the guard intervals between communication channels and achieve full spectral density bandwidth utilization. Spectral efficiency as high as 2.625 bit/Hz/s is obtained for 180 CO-OFDM bands encoded with 12.75 Gbaud 8-QAM data, adding to the total bitrate of 6.885 Tb/s within a 2.295 THz frequency comb bandwidth. This Letter confirms that high coherence is the key superiority of Kerr soliton frequency combs over independent laser diodes, as a multi-spectral coherent laser source for high-bandwidth high-spectral-density transmission networks.

Optical single side-band Nyquist PAM-4 transmission using dual-drive MZM modulation and direct detection.

We present the design and optimization of the optical single side-band (SSB) Nyquist four-level pulse amplitude modulation (PAM-4) transmission using dual-drive Mach-Zehnder modulator (DDMZM)modulation and direct detection (DD), aiming at the C-band cost-effective, high-speed and long-distance transmission. At the transmitter, the laser line width should be small to avoid the phase noise to amplitude noise conversion and equalization-enhanced phase noise due to the large chromatic dispersion (CD). The optical SSB signal is generated after optimizing the optical modulation index (OMI) and hence the minimum phase condition which is required by the Kramers-Kronig (KK) receiver can also be satisfied. At the receiver, a simple AC-coupled photodiode (PD) is used and a virtual carrier is added for the KK operation to alleviate the signal-to-signal beating interference (SSBI).A Volterra filter (VF) is cascaded for remaining nonlinearities mitigation. When the fiber nonlinearity becomes significant, we elect to use an optical band-pass filter with offset filtering. It can suppress the simulated Brillouin scattering and the conjugated distortion by filtering out the imaging frequency components. With our design and optimization, we achieve single-channel, single polarization 102.4-Gb/s Nyquist PAM-4 over 800-km standard single-mode fiber (SSMF).

Hilbert superposition and modified signal-to-signal beating interference cancellation for single side-band optical NPAM-4 direct-detection system.

We propose a Hilbert superposition and modified signal-to-signal beating interference (SSBI) cancellation scheme in an optical single side-band (SSB) modulation and direct-detection system. The optical SSB signal is generated by a relatively low-cost dual-drive Mach-Zehnder modulator (DDMZM). The two driving signals are a pair of Hilbert signals with Nyquist pulse-shaped four-level pulse amplitude modulation (NPAM-4). In addition to the transmitted baseband signal, both its Hilbert transform and the SSBI can also be detected by direct-detection, which introduce the interference to the transmitted signal. We use the first-stage Hilbert superposition cancellation (HSC) to cancel the unwanted Hilbert transform signal and a modified single-stage linearization filter which contains the second-stage HSC to deduct the SSBI in the receiver. We experimentally demonstrate that 40 Gb/s optical SSB NPAM-4 signal transmission over 80 km standard single mode fiber (SSMF).

Experimental characterization of an all-optical wavelength converter of OFDM signals using two-mode injection-locking in a Fabry-Pérot laser.

While optical OFDM has been demonstrated for superior transmission performance, its analogue waveform in the time domain challenges many conventional all-optical wavelength converters (AOWC) that are needed for future flexible optical networks. There only exist a few reports on AOWC of OFDM signals, which are mainly based on the low-efficient four-wave mixing. In this paper, we propose an AOWC for OFDM signals by using two-mode injection-locking in a low-cost Fabry-Pérot laser. The control signal and the probe signal at a milliwatt power level are combined and injected into the FP laser. By a proper control, they can be injection-locked to two longitudinal modes in the FP laser and subsequently, the transmission of the probe signal is conditioned by the control signal. We conduct an experimental study on various aspects of this AOWC. Despite a vendor-specified electrical-to-optical (E/O) modulation bandwidth of 2.5 GHz, we find that the optical-to-optical (O/O) modulation bandwidth of AOWC is free from this limit and can be much wider. We examine the linear transfer curve of the AOWC by simply using the OFDM waveforms as the stimulus. The performance tolerance to the wavelength detuning and injected power ratio is also measured. The proposed AOWC can provide a linear transfer function from the control signal to the probe signal to support the random-fluctuated OFDM waveform. We also investigate the maximum capacity of the AOWC by using the adaptive bit-loading OFDM. Finally, we measure the power penalty after the AOWC at two different bit rates to show the tradeoff between the penalty and capacity.

Blind polarization demultiplexing by constructing a cost function for coherent optical PDM-OFDM.

We propose a training symbols-free polarization demultiplexing method by constructing a cost function (CCF-PDM) for coherent optical PDM-OFDM. This method is applicable for high-speed, wide-bandwidth OFDM signals, different subcarrier modulation formats and long-haul transmission. It shows comparable performance with that of conventional method but without overhead and converges fast. Since the neighboring subcarriers experience similar polarization effects, we set the initial matrix parameters by the neighboring subcarrier to reduce the number of iteration for the gradient algorithm and prevent swapping the data of the two orthogonal polarizations. We verify this method in experiment by transmitting 66.6-Gb/s PDM-OFDM signal with 4QAM subcarrier modulation over 5440 km SSMF and 133.3-Gb/s PDM-OFDM signal with 16QAM subcarrier modulation over 960 km SSMF respectively. We compare its performance with that of training symbols. We also analyze the convergence speed of this method.

Digital coherent superposition of optical OFDM subcarrier pairs with Hermitian symmetry for phase noise mitigation.

Digital coherent superposition (DCS) provides an approach to combat fiber nonlinearities by trading off the spectrum efficiency. In analogy, we extend the concept of DCS to the optical OFDM subcarrier pairs with Hermitian symmetry to combat the linear and nonlinear phase noise. At the transmitter, we simply use a real-valued OFDM signal to drive a Mach-Zehnder (MZ) intensity modulator biased at the null point and the so-generated OFDM signal is Hermitian in the frequency domain. At receiver, after the conventional OFDM signal processing, we conduct DCS of the optical OFDM subcarrier pairs, which requires only conjugation and summation. We show that the inter-carrier-interference (ICI) due to phase noise can be reduced because of the Hermitain symmetry. In a simulation, this method improves the tolerance to the laser phase noise. In a nonlinear WDM transmission experiment, this method also achieves better performance under the influence of cross phase modulation (XPM).

Theoretical calculation on ICI reduction using digital coherent superposition of optical OFDM subcarrier pairs in the presence of laser phase noise.

Digital coherent superposition (DCS) of optical OFDM subcarrier pairs with Hermitian symmetry can reduce the inter-carrier-interference (ICI) noise resulted from phase noise. In this paper, we show two different implementations of DCS-OFDM that have the same performance in the presence of laser phase noise. We complete the theoretical calculation on ICI reduction by using the model of pure Wiener phase noise. By Taylor expansion of the ICI, we show that the ICI power is cancelled to the second order by DCS. The fourth order term is further derived out and only decided by the ratio of laser linewidth to OFDM subcarrier symbol rate, which can greatly simplify the system design. Finally, we verify our theoretical calculations in simulations and use the analytical results to predict the system performance. DCS-OFDM is expected to be beneficial to certain optical fiber transmissions.

High-resolution optical spectrum characterization using optical channel estimation and spectrum stitching technique.

A technique is proposed to measure the high-resolution and wide-band characterization of amplitude, phase responses, and polarization property of optical components. This technique combines the optical spectrum stitching and optical channel estimation methods. Two kinds of fiber Bragg grating based Fabry-Perot cavities with ultrafine structures have been characterized based on this technique. By using 1024 point fast Fourier transform and a narrow linewidth, wavelength-tunable laser source, a frequency resolution of ~10 MHz is realized with an optical measurement range beyond 250 GHz.

Polarization demultiplexing in stokes space for coherent optical PDM-OFDM.

We propose a polarization demultiplexing method for coherent optical PDM-OFDM based on Stokes space, without inserting training symbols. The proposed approach performs well for different modulation formats of OFDM subcarrier, and shows comparable performances with that of conventional methods, but with a fast convergence speed and reduced overhead. The OFDM signal in the time domain cannot satisfy the conditions of SS-PDM accurately. Therefore, we first digitally convert the received OFDM signals to the frequency domain using fast Fourier transform (FFT). Each subcarrier of the OFDM signal has a much lower speed and narrower bandwidth, the polarization effects that it experiences can be treated as flat. Consequently, we can apply the polarization demultiplexing in Stokes space (SS-PDM) on per subcarrier basis. We verify this method in experiment by transmitting 66.6-Gb/s PDM-OFDM signal with 4QAM subcarrier modulation over 5440km SSMF and 133.3-Gb/s PDM-OFDM signal with 16QAM subcarrier modulation over 960km SSMF respectively. We also compare the results with those of training symbols. Finally, we analyze of the convergence speed of this method.

Auto bias control technique for optical OFDM transmitter with bias dithering.

In coherent optical communication systems, the transmitter usually employs an optical in-phase and quadrature (IQ) modulator to perform electrical-to-optical up-conversion. However, some environmental factors, such as temperature and mechanical stress, strongly influence the stability. To stabilize the quality of the transmitted signal, auto bias control (ABC) is essential to keep modulator in optimum bias. In this paper, we present a novel method of ABC for the optical orthogonal frequency division multiplexing (O-OFDM) signal. In the proposed scheme, a small cosine/sine wave dither signal is added on to the I/Q baseband signal, respectively. Based on the power monitoring of the 1st and 2nd harmonics of the dither signal, the biases of the optical IQ modulator for O-OFDM system can be adjusted very precisely. The simulation and experimental results show good performance on locating the optimum bias voltages for the IQ modulator with high precision.

Characterization of passive optical components with ultra-fast speed and high-resolution based on DD-OFDM.

The passive optical components with very fine structures in wavelength domain are very sensitive to the mechanical vibrations or thermal fluctuations. If the measurement speed is lower than the temperature and mechanical fluctuation, we cannot measure the dynamic characteristics of the optical components. In this paper, we propose and demonstrate a novel method with ultra-fast measurement speed and high-resolution based on optical channel estimation using direct-detected orthogonal frequency division multiplexing (DD-OFDM) signal, which can be used to measure the dynamic characteristics and fine structure of the passive optical components. In experiment, by using fast Fourier transform (FFT) and a low-cost electro-absorption modulated laser (EML), we can achieve the transfer function characteristics with 3.9 MHz resolution. Compared with the optical channel estimation using coherent OFDM signal reported before, the proposed measurement technique is cost-effective.