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We experimentally investigate digital intra-channel nonlinear impairment compensation and inter-channel crosstalk suppression for 4 × 160.8-Gb/s wavelength division multiplexing (WDM) polarization division multiplexing quadrature phase shift keying (PDM-QPSK) transmission over 1300-km single-mode fiber-28 (SMF-28) on a 50-GHz grid with the spectral efficiency of 3.21b/s/Hz, adopting simplified heterodyne coherent detection. By using nonlinear compensation based on DBP with crosstalk suppression based on post filter and maximum likelihood sequence estimation (PF&MLSE), the BER has been improved from 1.0 × 10−3 to 3.5 × 10−4 for 4 × 160.8Gb/s WDM PDM-QPSK with heterodyne detection after 1300km SMF-28 transmission.
©2013 Optical Society of America
1. Introduction
Thanks to the development of electronic analog-to-digital converters (ADCs) and photo detectors (PDs) in bandwidth and speed, both homodyne and heterodyne coherent detection with digital signal processing (DSP) has been attracting a great deal of interest again in recent years [1–6].With DSP technology, optical transmission impartments can be equalized in electrical domain [1,2]. Homodyne detection has been discussed and investigated a lot in recent coherent communication system [1–4]. However, inphase and quadrature (I/Q) signals should be separated in optical domain with full information. In this way, 4 balanced detectors with double hybrid structures and 4 channels ADCs are required. Heterodyne coherent detection can simplify the coherent receiver with only half of the PDs and ADCs [1,5–11]. However, this technique is limited by the bandwidth of PDs or ADCs which should have doubled bandwidth for intermediate frequency (IF) signals. Thanks to the development of the PDs and ADCs, it gives a possibility to achieve a simplified coherent receiver with heterodyne detection, which has been investigated in subcarrier multiplexing system [7,8], access network [9] and high capacity transmission [10]. However, some new problems, such as filtering crosstalk caused by limited transmission bandwidth and the fiber nonlinearity impairments have not been discussed in the heterodyne detection area.
Most recently, we have experimentally demonstrated a high-speed simplified coherent receiver with heterodyne detection of 8 × 50-Gb/s polarization division multiplexing quadrature phase shift keying (PDM-QPSK) WDM after 1040-km single-mode fiber-28 (SMF-28) transmission, based on IF down conversion in digital frequency domain [5]. In [6], we have shown the heterodyne detection of 4 × 196.8-Gb/s polarization division-multiplexing carrier-suppressed return-to-zero quadrature-phase shift-keying (PDM-CSRZ-QPSK) over 1040 SMF with reduced LO number. However, for high-speed heterodyne detection with density WDM (WDM), the severe crosstalk caused by filtering effect of arrayed waveguide grating (AWG) and ADC, as well as the fiber nonlinear impairment become two main limiting factors when further increasing the transmission capacity, which has been discussed a lot in both single-channel and WDM systems [12–16]. Due to the wider bandwidth requirement for heterodyne detection, the filtering effect cause by PDs and ADCs are even stronger. In heterodyne detection system, the performance of nonlinear compensation and cross talk suppression are still worthy of study.
In this paper, we experimentally investigate digital nonlinear impairment compensation and crosstalk reduction by post filter and maximum likelihood sequence estimation (MLSE) decision for 4 × 160.8-Gb/s WDM PDM-QPSK transmission over 1300-km SMF-28 on a 50-GHz grid with the spectral efficiency of 3.21b/s/Hz, adopting simplified heterodyne coherent detection. A digital post filter and 1-bit MLSE are introduced at the receiver DSP to overcome severe filtering effect, noise enhancement and crosstalk caused by AWG and limited ADC bandwidth. Combined with nonlinear impairment compensation based on digital backward propagation (DBP), we can further improve the transmission performance. Finally, the bit-error ratio (BER) performance for 4 × 160.8-Gb/s WDM PDM-QPSK signal with heterodyne detection has been improved from 1.0 × 10-3 to 3.5 × 10-4 after 1300-km SMF-28 transmission and Erbium-doped fiber amplifier (EDFA)-only amplification.
2. The principle of nonlinear compensation and crosstalk suppression
In this paper, the fiber nonlinear impairment can be compensated by digital backward propagation (DBP) method based on the solving of nonlinear Schrodinger (NLS) equations [12–17]. In our case, an improved DBP method for polarization multiplexed WDM system is used, which can be realized by solving Manakov function [14] as
Where Ex,y is the optical field of X- or Y-polarization signal, βi is the i-order dispersion, α is the fiber loss, γ is the nonlinear parameter, is the linear operator,is the nonlinear operator and z is the step fiber length. By using split-step method (SSM) as shown in Fig. 1, we can compensate the linear fiber chromatic dispersion (CD) and nonlinear impairment by backward solving the above-mentioned function. During each step length z, we first compensate the linear CD and fiber loss for the z/2 fiber length in the frequency domain by FFT as shown in Fig. 1(b). Then, we calculate the total power of the signal and compensate the nonlinear phase shift in the time domain as shown in Fig. 1(c). Finally, the CD and loss of the other half step length z/2 is compensated again in the frequency domain. For N spans of fiber, each M steps are used, and the total CDC and NLC computation are MN steps.
Fig. 1 (a)The main block of nonlinear compensation; (b) the process block of linear compensation for CD; (c) the process block of nonlinear compensation. (LC: linear compensation; NLC: nonlinear compensation; F and F−1: FFT and IFFT processing)
Figure 2(a) and 2(b) show the illustration of filtering effect caused by AWG channels and ADC bandwidth limitation. For WDM with heterodyne detection, one of the advantages is that, the local oscillator (LO) number can be reduced to half [6]. In this case, the symbol rate approaches to the channel spacing and the frequency offset between LO and signal carrier is one half of the channel frequency spacing. Thus, one LO laser can be used for two neighboring WDM channels. In this scheme, AWG is used at the transmitter to spectrally shape and multiplex the WDM signal.
Fig. 2 An illustration of filtering effect caused by AWG and ADC bandwidth limitation and the principle of 9-QAM signal generation by digital post filter
Due to the narrow pass-band of AWG channels and the limitation of ADC bandwidth, the filtering effect can cause severe noise enhancement and crosstalk. In the bandwidth-limiting optical coherent system, the noise in high frequency components of the signal spectrum and the inter-channel crosstalk are both enhanced after conventional linear equalization algorithm, such as conventional constant modulus algorithm (CMA) [18–20]. A digital delay-and-add post filter (PF) provides a simple way to achieve partial response, which can effectively mitigate the enhanced inter-channel crosstalk and intra-channel noise. 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 evolution of this transformation is illustrated in Fig. 2(c) and (d). As a result of the delay-and-add effect, the 2-ary amplitude shift keying (2-ASK) I and Q components disappear and are then independently converted into two 3-ASK symbol series [18–20]. Therefore, the adoption of the post filter also makes possible the use of multi-symbol optimal decision schemes, such as MLSE, to take advantage of symbol correlation existing in the received partial response signals. Here, we use PF and MLSE with merely 1-bit memory length to realize further error correction induced by inter-symbol interference (ISI) [18].
3. Experimental results
Figure 3 shows the experimental setup for 4 × 160.8-Gb/s WDM PDM-QPSK signal with heterodyne detection over 1300-km SMF-28 transmission on a 50-GHz grid. At the transmitter, four external cavity lasers (ECLs) with the linewidth less than 100 kHz and the output power of 14.5 dBm are used for 4 WDM channels. The operating wavelength of ECL 1 to ECL 4 ranges from 1549.0 nm to 1550.2 nm with carrier spacing of 50 GHz. The odd (ECL 1 and 3) and even (ECL 2 and 4) channels are implemented with two sets of polarization-maintaining optical couplers (PM-OCs) before independent I/Q modulation [21]. Each I/Q modulator is driven by a 40.2-Gbaud electrical binary signal, which, with 0.5Vp-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 10.05-Gb/s binary signals generated from pulse pattern generator (PPG). The polarization multiplexing of the signal is realized by the polarization-multiplexer, which comprises a PM-OC to halve the signal, an optical delay line to provide a delay of 150 symbols, and a polarization beam combiner (PBC) to recombine the signal. The odd and even channels are combined and amplified before the fiber transmission. After an OC for each path, four 40.2-Gbaud optical PDM-QPSK signals are spectrally filtered and combined using an AWG on the 50-GHz grid. The 3, 10, and 20-dB bandwidth of the 50-GHz AWG is 26.7, 44.9 and 59.6 GHz, respectively.
Fig. 3 The experimental setup for 4 × 160.8-Gb/s WDM PDM-QPSK signal with heterodyne detection over 1300-km SMF-28 transmission on a 50-GHz grid. (I/Q Mod.: I/Q modulator; Att.: Attenuation; EDFA: Erbium-doped fiber amplifier; LO: Local oscillator; PD: balanced photo detector; EA: electrical amplifier; WSS: wavelength selective switch)
The straight transmission link consists of 5 spans of 80-km SMF-28 and 10 spans of 90-km SMF-28 with EDFA-only amplification in the absence of optical dispersion compensation. Two band-pass optical filters (using wavelength selective switch (WSS)) with bandwidth of ~2nm are inserted in the transmission line to suppress the amplified spontaneous emission (ASE) noise accumulation of EDFAs. In order to investigate the nonlinear impairment, the output power of each EDFA can be adjusted. Figures 4(a) and 4(b) show the optical spectrum of all the 4 channels of 160.8-Gb/s PDM-QPSK signal after 50-GHz AWG and after 1300-km transmission, respectively. The resolution for Fig. 4 is 0.1 nm. At the simplified coherent receiver based on heterodyne detection, a tunable optical filter (TOF) with 3-dB bandwidth of 0.4 nm is used to choose the desired channel. An ECL with linewidth less than 100 kHz is used as the LO source, which has 25-GHz frequency offset relative to the received optical signal. In our experiment, we only use two LO sources, one at 1549.24 nm for channel 1 (1549.0 nm) and channel 2 (1549.4 nm) while the other at 1550.04 nm for channel 3 (1549.8 nm) and channel 4 (1550.2 nm). Two polarization beam splitters (PBSs) and two OCs are used to implement polarization diversity of the received optical signal together with the LO source in optical domain before balanced PDs each with 50-GHz bandwidth. The analog-to-digital conversion is realized in the real-time digital storage oscilloscope (OSC) with 120-GSa/s sampling rate and 45-GHz electrical bandwidth. Two ADC channels are enough for offline DSP.
Fig. 4 Optical spectrum of 4X160.8-Gb/s PDM-QPSK channels (a) after AWG; (b) after 1300-km transmission. (The optical spectrum of even and odd channels is a little different due to the different gain of the driver of the I (Q) electrical signals in the two sets of the transmitters, but we find that the receiver sensitivity of the two sets has no much difference); (c) Optical spectrum of PDM-QPSK signal with LO measured before balanced detectors after transmission; (d) Electrical spectrum of the received IF signals after balanced detector and 45GHz ADC.
Figure 4(c) shows the optical spectrum of channel 2 (1549.4 nm) of 160.8-Gb/s PDM-QPSK signals with LO (1549.24 nm) measured before the balanced PDs after transmission. The resolution here is 0.01 nm for more clear observation. The received IF signal after balanced PD and ADC is illustrated in Fig. 4 (d). The frequency offset of LO and signal is 25 GHz and the ADC bandwidth is 45GHz. We can see that, due to the ADC bandwidth limit, the signal spectrum wider than the 45-GHz ADC bandwidth is cut off, which causes severe filtering effect, noise enhancement and crosstalk.
The detailed offline DSP for received signals after ADCs is shown in Fig. 3. Firstly, the received signals are down-converted to the baseband by 25-GHz frequency shifting and resampled to the 2 Samples per symbol. Secondly, nonlinear compensation (NLC) and CD compensation (CDC) are implemented together by DBP method based on the solving of the Manakov function as Eq. (2) with SSM. Here, the average span loss is 0.26dB/km, CD is 17ps/km/nm and nonlinear parameter γ is 1.5W−1km−1. After CDC and NLC, two complex-valued, 13-tap, T/2-spaced adaptive finite-impulse-response (FIR) filters, based on classic CMA, are used to retrieve the modulus of the PDM-QPSK signal and realize polarization de-multiplexing. The carrier recovery is performed in the subsequent step, where the 4-th power Viterbi-Viterbi algorithm is used for the residual frequency offset estimation and phase recovery [2–4]. These algorithms can also estimate the slowly-changing dynamic frequency drift. Then, a delay-and-add post filter is adopted to convert the binary signal to the duo-binary. The final symbol decision is based on 1-bit MSLE. Finally, differential decoding is used to eliminate π/2 phase ambiguity before BER counting. In this experiment, the BER is counted over 10 × 106 bits (10 data sets, and each set contains 106 bits).
We first investigate the back to back BER performance of channel 2 for single-channel and 4-channle WDM, both using heterodyne detection, versus OSNR with and without post filter and MLSE process as shown in Fig. 5(a). The constellations channel 2 in WDM case at 23.7-dB OSNR before and after the post filter are inserted in Fig. 5(a) as (i) and (ii), respectively, showing how the 4 point QPSK signal is shaped into a 9QAM-like one after PF. By using PF and MLSE to suppress the inter-channel crosstalk and ISI, we can obtain more than 2-dB OSNR gain for BER at 1x10−3. The WDM signal shows 0.5-dB OSNR penalty to the single channel case for BER at 1x10−3, which is due to the crosstalk from other channels. The nonlinear compensation results based on DBP method for single channel over 850-km transmission are shown in Figs. 5(b) and 5(c). Here, we test the single channel over 5 spans of 80-km and 5 spans of 90-km SMF-28. Figure 5(a) shows the single-channel BER performance after 850-km SMF-28 transmission varying with fiber input power of each span for different processing schemes: with CDC only and with CDC + NLC. Post filter and MLSE are used in both cases for crosstalk suppression. The input power is simultaneously changed for each span and the step length is 5km. The results show that, by using nonlinear compensation based on DBP, we can improve the BER performance for heterodyne detection after transmission. The optimal input power can be increased from 3-dBm to 5-dBm with better OSNR and BER performance. In this way, the CDC and NLC with PF&MLSE give the best performance. Figure 5(b) shows the BER performance varying with the calculation step length from 1 to 80km in NLC when using DBP SSM. We can see that, for the larger input power (7dBm) with larger nonlinear impairment, it is more sensitive to the step length. It is worth noting that, the computation complexity of the nonlinear impairments compensation by DBP can be reduced by using a advanced back propagation methods, such as correlated DBP in [17], which will be investigated in future work.
Fig. 5 (a) The Back to back BER performance of single-channel and WDM channels varying with OSNR with and without post filter and MLSE. Inset (i) and (ii) show the X-polarization constellations of different cases; (b) Single-channel BER performance varying with input power for different processing schemes over 850-km transmission; (c) Single-channel BER performance for NLC varying with calculation step length for different input power.
Figure 6(a) shows the BER performance in the 4 × 160.8-Gb/s WDM signals varying with different input power after 850-km SMF transmission for different processing schemes. Here, we choose channel 2 as the test channel and 850-km transmission fiber consists of 5 spans of 80-km fiber and 5 spans of 90-km fiber. The input power is simultaneously changed for each span and the step length is also 5km. It shows that, CDC and NLC with PF&MLSE still give the best performance. We also find that, the optimal input power is 2-dBm/channel for 4 × 160.8-Gb/s WDM after 850-km SMF transmission. Compared with single-channel results in Fig. 5(a), the optimal input power is lower. Also, the performance of DBP is limited compared with single channel case since only intra-channel nonlinearity impairment is compensated. Inter-channel nonlinearity impairments such as cross-phase modulation and four-wave mixing get strong for large input power. Thus, the input power of each channel is quite lower than single channel signal and the gain of DBP performance drops with the number of WDM channels.
Fig. 6 (a) WDM channels BER performance of channel 2 in 4 × 160.8-Gb/s varying with input power for different processing schemes over 850-km transmission; (b) BER performance of channel 2 in 4 × 160.8-Gb/s WDM channels varying with transmission distance from 400 to 1300km for different processing schemes. Inset (i) and (ii) show the X-polarization constellations after 1300-km transmission for different schemes.
We extend the transmission distance to 1300km with 5 spans of 80-km SMF and 10 spans of 90-km SMF for the 4 × 160.8-Gb/s WDM channels. Figure 6(b) shows the BER performance of channel 2 varying with the transmission distance for different process schemes. Here, the transmission results of each different distance are under the optimal input power and the step length is 5km. Inset (i) and (ii) show the X-polarization constellations after 1300-km transmission using CDC + PF&MLSE and CDC + NLC + PF&MLSE, respectively. The results show that, we can further improve the BER performance by nonlinear compensation with crosstalk suppression. By using nonlinear impairment compensation based on DBP with crosstalk suppression based on PF&MLSE, the BER performance for 4 × 160.8-Gb/s WDM PDM-QPSK signal with heterodyne detection has been improved from 1.0 × 10−3 to 3.5 × 10−4 after 1300-km SMF-28 transmission. We also measured and confirmed that the BER performance of the other WDM channels after nonlinear compensation and crosstalk suppression is identical to Channel 2. Above results demonstrated the performance improvement based our proposed digital nonlinear impairment compensation and inter-channel crosstalk suppression scheme for WDM heterodyne detection system. It is worth noting that, the heterodyne detection has both advantages and disadvantages compared with homodyne detection [5,6]. However, in this paper, we focus on the nonlinear compensation and cross-talk suppression in heterodyne detection system.
4. Conclusion
We propose and experimentally investigate digital nonlinear impairment compensation and channel crosstalk suppression for 4 × 160.8-Gb/s WDM PDM-QPSK transmission over 1300-km SMF-28 on a 50-GHz grid with the spectral efficiency of 3.21b/s/Hz, adopting simplified heterodyne coherent detection. By using nonlinear compensation based on DBP with crosstalk suppression based on PF&MLSE, the BER has been improved from 1.0 × 10-3 to 3.5 × 10-4 for 4 × 160.8Gb/s WDM PDM-QPSK with heterodyne detection after 1300km SMF-28 transmission and EDFA-only amplification.
Acknowledgments
This work was partially supported by the NHTRDP (973 Program) of China (Grant No. 2010CB328300), and NNSF of China (No. 61107064, No. 61177071, No.61250018), NHTRDP (863 Program) of China (2011AA010302, 2012AA011302), the the National Key Technology R&D Program (2012BAH18B00), International Cooperation Program of Shanghai Science and Technology Association (12510705600), the Creative Talent Project Foundation for Key Disciplines of Fudan University, and the China Scholarship Council (201206100076)
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