We experimentally demonstrate 2 × 64 Gb/s PAM-4 transmission over a 70 km standard single-mode fiber (SSMF) using two O-band 18G-class directly modulated lasers (DMLs). Only one praseodymium-doped fiber amplifier (PDFA) at the receiver side is used to compensate the transmission loss. Meanwhile, transmission impairments are compensated by a sparse Volterra filter (SVF) equalizer, which can achieve similar system performance but with half the computational complexity (CC), in comparison with a traditional VF equalizer. Finally, we optimize the insignificant factor (IF) of SVF to identify the trade-off between the transmission performance and the CC. Thus, the redundancy of individual SVF kernels can be reasonably removed.
© 2017 Optical Society of America
With rapid development of cloud services, real-time video, and online social networks, there occurs an urgent requirement of transmission capacity for interconnection among data-centers. The interconnection operating at 100 Gb/s or 400 Gb/s has drawn significant research efforts as well as standardization activities, such as the IEEE 802.3bs 400G Ethernet Task Force . Since the data-center interconnection is particularly sensitive to cost, poweFvr consumption, and footprint, traditional intensity modulation and direct detection (IM-DD) are always attractive. Recently, advanced modulation formats such as pulse amplitude modulation (PAM), carrier-less amplitude and phase modulation (CAP), and discrete multi-tone modulation (DMT) are commonly used in current IM-DD system, because of their both great performance and high spectra efficiency [2–4]. Compared with the CAP and DMT, PAM-4 has advantages of low cost, free of digital to analog converter (DAC), and easy implementation. Furthermore, PAM-4 is chosen because of its potential applications in the metro network. Without using additional external modulator, directly modulated laser (DML) is also highly preferred, due to its low cost and simple configuration. In , single-lane 180 Gb/s PAM-4 transmission over 2 km standard single mode fiber (SSMF) using 30 GHz C-band dual-drive Mach-Zehnder modulator (DDMZM) is demonstrated. In , 100 GBaud PAM-4 is successfully transmitted over 500 m SSMF with C-band external modulation enabled by an integrated high-speed DAC. Meanwhile, 112 Gb/s PAM-4 signal can be successfully transmitted over 20 km SSMF using O-band silicon photonic MZM . As for the DML enabled PAM-4 transmission, 112 Gb/s duobinary PAM-4 signal can be successfully transmitted over 1 km SSMF with 18 GHz C-band DML . Meanwhile, 56Gb/s PAM-4 transmission over 15 km SSMF using 25 GHz O-band vertical cavity surface emitting lase (VCSEL) is also demonstrated . However, for data-center interconnection, the typical distances may range from 40 km to 80 km. The growing transmission distance and capacity result in severe impairments in term of loss and chromatic dispersion (CD). Generally, the SSMF at O-band has little chromatic dispersion (CD), but fiber loss is high, while C-band has low attenuation but high CD causes severe inter-symbol interference (ISI). In order to further extend the SSMF reach and transmission capacity without CD compensation, we have to choose the operation wavelength at O-band and increase the input power accordingly, only leading to severe transmission impairments arising from fiber nonlinearity. In , a feed-forward equalizer/decision-feedback equalizer (FFE/DFE) is used to achieve 28 Gb/s PAM-4 transmission over 40 km SSMF using 24.2 GHz C-band DML. In , a dedicated channel shortening filter (CSF) in combination with maximum likelihood sequence estimation (MLSE) is applied to achieve C-band 112 Gb/s PAM-4 transmission over 80 km SSMF. In our previous work , 2 × 56 Gb/s PAM-4 transmission at 1550nm over 100 km SSMF is demonstrated with the help of Volterra filter (VF) equalizer. However, those equalizers have high computation complexity (CC). In order to reduce the CC, simplified Volterra algorithm is proposed to achieve 4 × 56 Gb/s CAP-32 signal transmission over 60 km SSMF , which simplifies the third order kernels to cubic term and ignores the other terms. However, the effect of ignored terms has not been comprehensively discussed.
In this letter, to the best of our knowledge, it is the first time that 2 × 64 Gb/s O-band PAM-4 signal is transmitted over 70 km SSMF using DMLs with a bandwidth of 18 GHz. Furthermore, the sparse Volterra filter (SVF) is proposed to compensate the transmission impairments with substantial CC reduction. Finally, we optimize insignificant factor (IF) to investigate the trade-off between transmission performance and CC. Our discussions of the importance for individual kernels confirm that the redundancy of kernels can be reasonably identified and removed.
2. Principle of the sparse Volterra filter
For the DML-based IMDD transmission operating at O-band, the effect of CD can be ignored. Therefore, the transmission impairments mainly come from (1) limited bandwidth of the optoelectronic devices, (2) signal-to-signal beating noise (SSBN), (3) fiber nonlinearities, and (4) fiber attenuation. The input-output relationship of third-order VF is expressed as
The 1st order kernels of Volterra filter can be used to mitigate the linear impairments, because it is a FIR filter. The SSBN resulting from the square-law detection can be compensated by the 2nd order kernels of Volterra filter. Generally, the SSBN can be described as 15]. Normally, the optical interconnection is implemented without inline optical amplifier and the fiber attenuation is larger at O-band, we have to maximize the output power of DML, leading to severe fiber nonlinearities. The main fiber nonlinearity is self-phase modulation (SPM), while the cross-phase modulation (XPM) and four-wave mixing (FWM) are not severe due to the wide channel spacing. Therefore, the 3rd order kernels of Volterra filter can be used to deal with fiber nonlinearities . However, not all Volterra kernels have equal importance, and there exist some less important kernels . Therefore, less important kernels need to be identified and removed in order to reduce the CC, which is defined as SVF. Considering all inputs, Eq. (1) can be rewritten as vector formatEq. (3) into orthogonal domain asEq. (5), the kernels corresponding to larger have greater effect on NMSE. Thus, can represent the importance of the kernel. Insignificant factor (IF) is a threshold we set during the iteration process of removing the less important kernels. For each iteration, the kernels corresponding to largest are identified and set When the NMSE is less than the IF, the iteration process is ended. Therefore, all important kernels are identified, and the less important kernels are removed, leading to the reduction of CC. Obviously, the sum of NMSE due to the removed kernels is always less than IF, so IF can be referred as the upper boundary of the sum of NMSE due to the removed kernels. Then, recursive least square (RLS) algorithm is applied to determine the residual kernels by training symbols and carry out the SVF equalizer.
3. Experimental setup
The experimental setup is shown in Fig. 1. At the transmitter side, two independent pseudo-random bit sequences (PRBS) with a word length of are first generated using MATLAB software. After the bit to symbol mapping, we obtain two independent PAM-4 sequences. Then, those two independent PAM-4 sequences are loaded into a four-channel arbitrary waveform generator (AWG, Keysight M8195A) operated at 64 GSa/s. By setting the tunable symbol rate and the loading sequences of two channels, we can generate two independent electrical PAM-4 signals with tunable symbol rate. The outputs of AWG directly drive two 18 GHz DMLs which are operated at 1311.89 nm and 1313.51 nm without any electrical amplifier, respectively. Meanwhile, we set the output voltage of AWG to its maximum value of 1V. The measured extinction ratio of optical signal is 6 dB, under the condition of 10Gbps on-off-keying optical signal. The maximum output power of single DML is 7.5 dBm. The outputs of DMLs are wavelength-multiplexed by an optical coupler (OC) and the spectral of the wavelength-multiplexed signal is shown in the insert (i) of Fig. 1. After transmission over the 70 km SSMF with attenuation of 0.35 dB/km at the O-band, the signal is amplified by a Pasedymiun-doped fiber amplifier (PDFA, AMP-FL8611-OB-20) located at the receiver side. The gain and noise figure (NF) of PDFA are 19.5 dB and 6.5 dB,respectively. In order to characterize two channels separately, a tunable optical bandpass filter (TOBF) is used to select each channel individually. Then, single channel signal is detected by a PD with bandwidth of 40 GHz. The corresponding signal is sampled by a real-time oscilloscope (Tektronix DPO 73304D) operating at 100 GSa/s and processed offline. The flow of offline digital signal processing (DSP) is also shown in Fig. 1. In the offline processing, the transmission impairments are compensated by SVF equalizer. As for the SVF, training symbols are first used to estimate Volterra kernels. The memory length of three Volterra kernels is set to 21, 9 and 7, which is defined as (21, 9, 7), corresponding to 150 kernels in total. Modified Gram-Schmidt orthogonal search algorithm is applied to remove the insignificant kernels, which reduces the number of kernels to 75, indicating of half CC reduction in comparison with that of traditional VF. Eye-diagram of the PAM-4 signal before and after SVF equalizer is also shown in the insert (ii) and (iii) of Fig. 1.
4. Experimental results and discussion
First, we demonstrate 28 GBuad PAM-4 signal transmission over 70 km SSMF. Figure 2(a) shows the BER of 28 GBaud PAM-4 signal versus the received power after 70 km SSMF transmission for two channels. Since output power of single DML is 7.5 dBm and the insertion loss of O-band optical coupler is 3.6 dB, the total launch power of two-wavelength signal is 6.9 dBm. The BER of two-channel signal is similar, which is below 7% FEC threshold () after 70 km SSMF transmission, when the received power is larger than −13 dBm. Fig. 2(b) shows the BER of 28 GBaud PAM-4 signal at 1311.89 nm after 70 km SSMF transmission, using different equalization techniques. The used linear equalizer is a FIR filter with 21 taps, and recursive least square (RLS) algorithm is used to update the taps. The time spacing of the equalizer is half of the symbol period. For the purpose of fair comparison, the number of taps in linear equalizer is the same as the number of first order kernels of VF. The BER cannot reach the FEC threshold using linear equalizer because of its poor performance to mitigate the SPM-induced impairments. With the help of either VF or SVF equalizer, all BERs are below the threshold at the received power of −13 dBm. It is noted that the BER performance of SVF is similar to that of VF, while the CC is the half of VF.
Figure 3 shows BER of 28 GBaud PAM-4 signal versus the received power after various length SSMF transmissions. The parameters of equalizer remain the same for individual SSMF transmissions. The received power corresponding to the BER threshold is −14.8 dBm, −14.8 dBm, −14 dBm, and −13dBm, for the SSMF transmission of 40 km, 50 km, 60 km and 70 km, respectively. When the distance is 80 km, BER can’t reach the FEC threshold. Generally, the signal OSNR decrease linearly with the growing SSMF length . Meanwhile, it is experimentally found  that the BERs of PAM-4 signal don’t have a linear relationship with respect to its OSNR. When the OSNR of PAM-4 signal is high, the BER degrades slowly with the reduction of OSNR. However, the situation is different when OSNR is low. In our experiment, when PAM-4 signal transmission over less than 50 km SSMF, the OSNR after optical amplification are more than 29.1 dB. Within such OSNR range, little BER penalty occurs. When the transmission distance is longer than 50 km SSMF, the BER performance becomes very sensitive with the variation of OSNR. We infer that the SVF equalizer with the fixed parameters can’t function well due to the low OSNR value. Therefore, the penalty occurs when the SSMF transmission length is more than 50 km. Fig. 4 shows BER of PAM-4 signal at 1311.89 nm versus the transmission distance with various symbol rates. It is noted that BER cannot reach the threshold when the distance is 80 km, as a result of extremely low OSNR caused by fiber loss. As shown in Fig. 4, we can maximally achieve 32 GBaud PAM-4 signal transmission over 70 km SSMF, which verifies the functionality of SVF equalizer to effectively mitigate the distortions arising in the limited bandwidth, SSBN and fiber nonlinearities. Furthermore, the signal in another channel at 1313.51 nm has the similar performance, indicating that we can experimentally demonstrate O-band 2 × 64 Gb/s PAM-4 transmission over 70 km SSMF using two 1310 nm DMLs with a bandwidth of 18 GHz.
Furthermore, we discuss the effect of IF arising in the SVF. Figure 5 shows the BER of 28 GBaud PAM-4 and number of SVF kernels versus IF after 70 km SSMF transmission. As shown in Fig. 5, with the increment of IF, the number of SVF kernels decreases and the BER is degraded. We find that the reduction of the number of SVF kernels is nearly linear, but the BER is degraded exponentially. Therefore, we optimize the IF to , which can reduce by half the number of the kernels and BER is not degraded significantly.
For the second order kernels, we divide these kernels into two sets. The square term is the set of kernels which have the form of , and the cross term is the set of kernels which have the form of . For the third order kernels, we divide these kernels into three sets. The cubic term, square cross term and the cross term have the forms of , , and , respectively. For the second order kernels, both cross term and square term are combined to compensate the SSBN. Meanwhile, for the third order kernels, the cross term, square cross term, and cubic term are combined to compensate fiber nonlinearities. Fig. 6(a) shows the number of kernels in square term and cross term with respect to IF for second order kernels. As shown in Fig. 6(a), with the increment of IF, the number of kernels in square term decreases slowly, but the number of kernels in cross term decreases rapidly, indicating that the cross term have more redundancy. Thus, the used SVF equalizer can remove the less important kernels. However, the number of residual kernels in cross term is still more than that in square term, indicating of the vital function for the cross term, so we can’t simply ignore all the kernels in cross term. Fig. 6(b) shows the number of kernels in cubic term, square cross term and cross term versus IF for third order kernels. As shown in Fig. 6(b), although the redundancies of square cross term and the cross term are more than that of cubic term, the number of residual kernels in cross term and square cross term is still more than that in cubic term. Thus, we can’t completely ignore all the kernels in cross term and square cross term. Furthermore, by comparing Fig. 6(a) and 6(b), the third order kernels have more redundancy than the second order kernels, but the number of residual third order kernels are still similar to that of the second order kernels, indicating of the vital function for the third order kernels, so it is indispensable to include the third order kernels in SVF implementation.
We have experimentally demonstrated 2 × 64 Gb/s PAM-4 signal transmission over 70 km SSMF based on O-band 18G-class DMLs. The PDFA is applied at the receiver side to amplify the PAM-4 signal. Both linear and nonlinear transmission impairments can be compensated by SVF equalizer. Compared to the traditional VF equalizer, the SVF equalizer achieves the similar BER performance and half computational complexity. The importance of each term in second and third order SVF kernels is identified. The O-band DML-enabled PAM-4 transmission is a good candidate for future low cost optical interconnection.
National Natural Science Foundation of China (61711530043, 61575071); 863 High Technology Plan (2015AA015502); Key project of Natural Science Foundation of Hubei Province(CXZD 2016000277); and Natural Science Foundation of Hubei Province (ZRMS 2016001460).
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