1. Introduction

Beyond 100G, 400G per channel is one of the next desirable bit rates for optical wavelength-division-multiplexing (WDM) transmission systems and networks [1–3]. The generation and transmission of 400-Gb/s optical signal per channel has been reported using multiplexing and modulation techniques, such as optical time-division-multiplexing (OTDM) 16-ary quadrature amplitude modulation (16-QAM) [1], electrical time-division-multiplexing (ETDM) 16-QAM [2], Nyquist wavelength-division-multiplexing (N-WDM) 32-QAM [3] and so on. 10 × 456-Gb/s polarization-division-multiplexing (PDM) 16-QAM OTDM signal was transmitted over 800-km ultra-large-area fiber (ULAF) in [1], 10 × 448-Gb/s (56-Gbaud) PDM 16-QAM ETDM signal over 1200-km ULAF in [2], and 8 × 450-Gb/s PDM 32-QAM N-WDM signal over 400-km ULAF in [3]. However, these achievements relied heavily on the use of specialty fibers and Raman amplifiers, due to the fact that multi-level modulation not only requires larger optical signal-to-noise ratio (OSNR), but also is more sensitive to nonlinear propagation impairments and laser phase noise [1–7]. Adopting relatively simple quadrature-phase-shift-keying (QPSK) modulation makes possible long transmission distance and efficient digital-signal-processing (DSP) algorithms. However, 400-Gb/s optical PDM-QPSK signal will be subject to significant filtering penalty because of the expanded signal spectrum. Moreover, compared to multi-level modulation such as 16-QAM and beyond, increasing the baud rate of PDM-QPSK toward 100Gbaud is challenging, due to the limit of the electrical multiplexer and the limited bandwidth of analog-to-digital converters (ADCs).

The term N-WDM traditionally implies spectral filtering at the transmitter that meets the inter-symbol interference (ISI)-free Nyquist criterion while allowing channel spacing approximately equal to baud rate, for which the ideal optical filtering is necessary. However, the practical implementation of the optical filter still has a very long way to go before meeting the requirements for ideal Nyquist spectral shaping. In most cases, instead of adopting digital-to-analog converter (DAC) with large bandwidth and high sampling speed at the transmitter, optical multiplexer with narrow-band optical filtering function is used to perform aggressive spectral shaping and multiplexing function, in order to obtain N-WDM (channel spacing equal to symbol rate) or faster-than-N-WDM signals (channel spacing less than symbol rate). However, the severe ISI in the received signal, due to spectral shaping by optical multiplexer, would require very large computational resources to implement an optimal maximum-a-posteriori-probability (MAP) or maximum-likelihood-sequence-estimation (MLSE) receiver. The adaptive equalizer in current coherent receivers, which allows conventional carrier recovery algorithm to be used, also enhances intra-channel noise and inter-channel crosstalk when it tries to create an ISI-free channel. Thus, it means that innovative signal processing techniques are needed at the receiver, in order to realize high spectral efficiency (SE) as well as counter ISI, enhanced intra-channel noise and inter-channel crosstalk.

In the paper, by leveraging the widely recommended PDM-QPSK format for OTU-4, we experimentally generated 40 × 433.6-Gb/s N-WDM channels at an unparalleled symbol rate of 108.4Gbaud achieved by OTDM, which were then successfully transmitted over 2800-km single-mode fiber (SMF)-28 with 80-km per span and Erbium-doped fiber amplifier (EDFA)-only amplification. Each channel occupies 100GHz and yields a SE of 4.05b/s/Hz, assuming 7% forward-error-correction (FEC) overhead. The post filter and 1-bit MLSE adopted after carrier phase estimation (CPE) in the conventional DSP process at the receiver effectively suppresses the enhanced intra-channel noise and inter-channel crosstalk. To our best knowledge, this is the first ever demonstration of coherent optical PDM-QPSK transmission beyond 100Gbaud, which also gives the longest distance among 400G-per-channel WDM transmission proposals, even without the use of specialty fibers and Raman amplifiers.

2. The principle of digital post filtering

The idea of duo-binary signaling or correlative coding [8], which has only 1-bit memory length and is a specific class of partial response signaling, is to introduce a controlled amount of ISI into the signal instead of trying to eliminate it completely. The introduced ISI can be compensated in digital domain at the receiver. Thus, the ideal symbol-rate packing of 1 baud per Hertz per polarization can be achieved without the requirements for unrealizable filters based on the Nyquist theorem. Thus, it’s necessary for multi-symbol optimal decision schemes, such as MAP and MLSE, to take advantage of symbol correlation existing in the received partial response signals. The challenge is that the number of states and transitions grows exponentially with the involved memory length. For instance, the adopted MLSE length of 10 means 4¹⁰ states and 4¹¹ transitions in lane-dependent PDM-QPSK signals [9], and thus computational complexity significantly increases in practical implementation. On the other hand, in the bandwidth-limiting optical coherent system, the noise in high frequency components of the signal spectrum and the crosstalk are both enhanced after conventional linear equalization algorithm, such as classic constant modulus algorithm (CMA) [10].

2.1 Simulation results and discussions

A linear digital delay-and-add finite-impulse-response (FIR) filter, when added after CPE in the conventional DSP process at the coherent receiver, can provide a simple way to achieve partial response, which will effectively mitigate the enhanced crosstalk and noise [10]. At the same time, the MLSE algorithm, with a significantly reduced memory length, is employed to realize symbol decoding and optimal decision. Figure 1(a) gives the simulated electrical spectra after linear CMA equalization and post duo-binary filtering, respectively. The high frequency components are strongly recovered and mixed with the enhanced noise after linear equalization, while post filter introduces a filtering impact on the high frequency components. Figure 1(b) shows the transfer function of post filter. It is noted that the second tap coefficient of the post filter is adjusted to optimize the overall performance together with the following MLSE algorithm. It’s also worth noting that the normalized frequency of the horizontal axis in Figs. 1(a) and 1(b) is respectively calculated by the signal frequency divided by 28GHz and 10GHz, corresponding to the assumption that the baud rate of the PDM-QPSK signal is 28Gbaud. From the constellation point of view, the effect of the post filter transforms the 4-point QPSK signal into 9-point quadrature duo-binary one. The mechanism for the generation of ‘9-QAM’ signals can be considered as the superposition of two 3-ary amplitude shift keying (3-ASK) vectors on a complex plane [11–13].

 

Fig. 1 (a) Electrical spectra after CMA equalization and digital post duo-binary filtering, respectively; (b) Transfer function of digital post filter.

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2.2 Experimental results and discussions

We investigated the required ADC bandwidth for a 112-Gb/s PDM non-return-to-zero QPSK (PDM-NRZ-QPSK) single channel. Figure 2 shows measured BER versus ADC bandwidth for the 112-Gb/s PDM-NRZ-QPSK single channel. We can see that the optimum bandwidth is 12.5GHz. Thus, the optimum bandwidth is around 50GHz for the corresponding 448-Gb/s bit rate. In the experiment demonstrated in the next section, the adoption of carrier-suppressed RZ (CSRZ) can further reduce the requirement for ADC bandwidth, and therefore the 45-GHz ADC bandwidth is adequate for the 433.6-Gb/s PDM-CSRZ-QPSK signal. Furthermore, as shown in Fig. 2, for the BER below 3.8 × 10⁻³, the ADC bandwidth ranges from 16GHz all the way down to 11GHz, which is an important cost indicator for future hardware applications.

 

Fig. 2 BER performance as a function of ADC bandwidth.

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3. Experimental setup and results for 108.4-Gbaud PDM-QPSK transmission

Figure 3 shows the experimental setup for 40 × 433.6-Gb/s N-WDM OTDM on a 100-GHz grid over 2800-km SMF-28 transmission with EDFA-only amplification, adopting PDM-CSRZ-QPSK modulation as well as post filter combined with 1-bit MLSE.

 

Fig. 3 Experimental setup. Inset (a)-(c) show the eye diagrams of the single optical carrier after I/Q MOD, two cascaded IMs and OTDM, respectively. OC: optical coupler, I/Q MOD: I/Q modulator, EA: electrical amplifier, IM: intensity modulator, DL: delay line, ATT: optical attenuator, PBC: polarization beam combiner, WSS: wavelength selective switch, SW: switch, TOF: tunable optical filter, PBS: polarization beam splitter.

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At the transmitter, forty lasers, with the maximum output power of 13dBm, are divided into two groups and respectively used as the continuous-wavelength (CW) light source for the odd and even channels. The shortest and longest wavelength of all the lasers is 1532.65 and 1562.21nm, respectively. Each group of lasers includes ten distributed feedback (DFB) lasers with linewidth less than 1MHz and ten fully tunable C-band external cavity lasers (ECLs) with linewidth less than 100kHz, with 200-GHz neighboring frequency spacing. The odd and even groups of lasers are independently combined by two polarization-maintaining optical couplers (PM-OCs), and then modulated by two I/Q modulators (I/Q MODs). Each I/Q MOD is driven by a 54.2-Gbaud electrical binary signal, which, with 0.5-Vp-p amplitude and pseudo-random binary sequence (PRBS) length of (2¹³-1) × 4, is generated from a 4:1 electrical multiplexer. The 4:1 electrical multiplexer multiplexes four 13.55-Gb/s binary signals generated from a pulse pattern generator (PPG). For optical QPSK modulation, the two parallel Mach-Zehnder modulators (MZMs) in each I/Q MOD are both biased at the null point and driven at the full swing to achieve zero-chirp 0- and π-phase modulation. The phase difference between the upper and lower branches of each I/Q MOD is controlled at π/2. Inset (a) shows the eye diagram of the single optical carrier after I/Q MOD measured by 70-GHz oscilloscope. For each path, two cascaded intensity modulators (IMs) with 3-dB bandwidth of 38GHz and twice of half-wave voltage are respectively driven by two synchronized 27.1-GHz sinusoidal clock signals, in order to generate optical CSRZ-QPSK signal with 33% duty cycle and 3-dB pulse width of ~3.5ps. Each IM is DC-biased at the maximal output power point to double the frequency of the clock signal. Inset (b) shows the eye diagram of the single optical carrier after two cascaded IMs. For OTDM in each path, a PM-OC splits the 54.2-Gbaud optical CSRZ-QPSK signal into two branches, two optical delay lines (DLs) provide 20-bit de-correlation for two branches and a second PM-OC recombines the signal, in order to generate 108.4-Gbaud OTDM CSRZ-QPSK signal. Inset (c) shows the eye diagram of the single optical carrier after OTDM. The subsequent polarization multiplexing for each path is realized by polarization multiplexer, comprising a PM-OC to halve the signal into two branches, an optical DL to provide a 150-symbol delay, an optical attenuator to balance the power of two branches and a polarization beam combiner (PBC) to recombine the signal. The programmable wavelength selective switch (WSS) on a 100-GHz grid is used to combine and spectrally shape the odd and even channels. The WSS has an insertion loss of 7dB and a 3-dB bandwidth of ~72GHz. The SE is 433.6/100/1.07 = 4.05b/s/Hz, assuming 7% FEC overhead.

Then the WDM signal is launched into a recirculating fiber loop. This loop has five 80-km spans of SMF-28, and seven times of circulation yield to 2800-km transmission distance. Each span has 17.5-dB average loss without optical dispersion compensation. For each span, two-stage EDFA with mid-stage adjustable tilt filter is employed to compensate the fiber loss. Two acousto-optic (AO) switches control the loading and circulation of the signal. The total launch power (after EDFA) into each fiber span is 21dBm, corresponding to 5dBm (an optimal launch power) per 400G channel.

At the receiver, a tunable optical filter (TOF) with 3-dB bandwidth of 1nm is used to choose the desired channel. An ECL with linewidth less than 100kHz is used as the local oscillator (LO). A polarization-diversity 90° hybrid is used to realize polarization- and phase-diversity coherent detection of the LO source and the received optical signal before balanced detection. The analog-to-digital conversion is realized in the digital oscilloscope with 120-GSa/s sampling rate and 45-GHz electrical bandwidth. Strong filtering effect is introduced because the bandwidth of photo detectors (PDs) and ADC chips is not enough for the 108.4-Gbaud PDM-CSRZ-QPSK signal. Some special offline DSP procedure is employed for the captured data. Firstly, the clock is extracted using the “square and filter” method, and then the digital signal is re-sampled at twice of the baud rate based on the recovered clock. Secondly, a T/2-spaced time-domain FIR filter is used for chromatic dispersion (CD) compensation, where the filter coefficients are calculated from the known fiber CD transfer function using the frequency-domain truncation method. Thirdly, two complex-valued, 13-tap, T/2-spaced adaptive FIR filters, based on the classic CMA, are used to retrieve the modulus of the PDM-QPSK signal and realize polarization de-multiplexing. The subsequent step is carrier recovery, which includes frequency-offset estimation and CPE. A post filter is introduced after CPE to suppress the enhanced noise and crosstalk, and then the 1-bit MLSE is used for symbol decision. Finally, differential decoding is used to eliminate the π/2 phase ambiguity before BER counting. In this experiment, the BER is counted over 12 × 10⁶ bits.

Figure 4(a) shows the optical spectra of the single optical carrier before and after WSS, while Fig. 4(b) of all the 40 N-WDM channels before and after 2800-km SMF-28 transmission. In Fig. 4(a), the optical spectra both at 0.1- and 1-nm resolution are given for comparison. The spectrum obviously becomes narrow after optical filtering. In Fig. 4(b), the corresponding constellations before and after post filtering are respectively given after 2800-km SMF-28 transmission. The constellation is much better after post filtering. Figure 5(a) shows the measured BER versus OSNR for the single channel and the WDM channel both at 1540.56nm, respectively. The required OSNR at the BER of 3.8 × 10⁻³ is 22.7dB for the single channel without WSS. There is no obvious OSNR penalty after passing through 100-GHz WSS or in the WDM-channel case. Figure 5(b) shows the measured BER (an average of both X- and Y-polarization state) of all the WDM channels after 2800-km SMF-28 transmission. The BER for each of the forty WDM channels is less than the pre-FEC limit of 3.8 × 10⁻³.

 

Fig. 4 (a) Optical spectra of the single optical carrier before and after WSS; (b) Optical spectra of all the 40 N-WDM channels before and after 2800-km SMF-28 transmission.

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Fig. 5 Experimental results. (a) BER versus OSNR for the single channel and the WDM channel, (b) BER of all the WDM channels after 2800-km SMF-28 transmission.

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4. Conclusion

We have successfully demonstrated the generation and transmission of 40×433.6-Gb/s N-WDM OTDM over 2800-km SMF-28 with EDFA-only amplification, adopting PDM-CSRZ-QPSK modulation as well as post filter combined with 1-bit MLSE. The SE is 4.05b/s/Hz. The introduction of post filter combined with 1-bit MLSE effectively suppresses the enhanced intra-channel noise and inter-channel crosstalk, and gives a BER better than the pre-FEC limit of 3.8×10-3 after 2800-km SMF-28 transmission at a record of 108.4Gbaud, demonstrating the feasibility of future 400-Gb/s single-carrier channel with PDM-QPSK modulation without sacrificing the transmission distance. This work was partially supported by NNSF of China (No. 61107064, No. 61177071, No. 600837004), NHTRDP (863 Program) of China (2011AA010302, 2012AA011302), and the National Key Technology R&D Program (2012BAH18B00).