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Abstract
The digital subcarrier multiplexing (DSCM) transmission scheme is expected for future ultra-large baud rate transmission. However, the phase noise and transmitter (Tx) IQ skew tolerance are decreased due to the narrow sub-band transmission and conjugated interference from symmetric subcarrier. In this paper, we propose a paired-subcarrier equalization scheme to jointly mitigate the phase noise and Tx IQ skew. We use a phase locking loop (PLL) embedded 4 × 4 MIMO equalizer to simultaneously realize polarization demultiplexing, phase noise and Tx IQ skew compensation. The 4 × 4 MIMO can deal with the paired-subcarrier interference in the DSCM transmission. Besides, since the inner subcarrier suffers smaller interference from its symmetric subcarrier, we estimate the phase noise by inner subcarriers and share the phase noise information with other subcarriers to reduce the overall complexity. Through simulations of 100-GBaud 64-QAM DSCM coherent optical fiber transmission consisting of eight 12.5-Gbaud subcarriers and experiment of 10-GBaud four-subcarriers PM-16QAM transmission, we find that the PLL embedded equalizer for DSCM scheme exhibits better skew and phase noise compensation ability compared with other equalizers. Additionally, we compare the performance of single-carrier and DSCM schemes with the proposed equalizers in simulation. The influence of phase noise and Tx IQ skew on DSCM transmission can be largely relaxed.
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1. Introduction
With the rapid development of the Internet, mobile broadband and data centers, the requirement of network transmission bandwidth has been explosive growth, promoting the development of ultra-large capacity optical transmission systems. Beyond 100 Tb/s transmissions in the C + L band of single-mode fiber have been demonstrated [1–3], where the transmission symbol rate is expected to be 100 Gbaud per channel. The single-carrier transmission scheme has achieved huge commercial success these years, the digital signal processing (DSP) algorithms are mature and have many advantages in signal recovery, e.g. dispersion compensation, carrier recovery and fast-tracking of the state of polarization (SOP). However, as the application of ultra-large bandwidth and higher spectral-efficiency modulated signal, the communication scheme and various linear impairments have to be reexamined. The complexity of dispersion compensation is greatly increased due to the ultra-high baud rate [4]. Besides, the equalization-enhanced phase noise (EEPN) impairment imposes a tighter constraint on the receiver laser phase noise for coherent systems with higher modulation format and large electronic-compensated dispersion [5]. In wideband single-channel transmission, the polarization mode dispersion (PMD) parameter is dependent on frequency, which implies that we have to cope with increasingly complicated PMD impairments in wideband channels [6]. In addition, the self-phase modulation penalty increases with the baud rate [7]. Therefore, DSCM has been attracting more attention to enable flexible data rate adaptivity and provide robustness against various linear impairments, such as dispersion compensation, EEPN and frequency-dependent PMD effect [8]. The cumulated dispersion compensation increases with the square of the baud rate and the variance of EEPN is inversely proportional to the symbol rate. This simplifies the chromatic dispersion compensation (CDC) and improves the EEPN tolerance. In the narrowband sub-channel transmission, the PMDs at different frequencies are strongly correlated, therefore, the traditional 2 × 2 MIMO equalizer is still feasible for polarization demultiplexing.
The DSCM is expected in the evolution of ultra-wideband signal transmission. However, when there exists IQ mismatch and skew, subcarriers suffer interference from their “symmetric” subcarriers [9]. Besides, the IQ skew introduces frequency-dependent interference which is larger at higher frequency bands [10,11]. Currently, numerous analog or digital domain calibration methods for the IQ skew estimation of coherent optical transceivers have been proposed for single-carrier transmissions [12–15]. However, the residual IQ skew after calibration or from some dynamic effects still needs to be mitigated, especially for the application of higher-level modulation format signals. Several adaptive equalization schemes have demonstrated their effectiveness to mitigate the dynamic receiver (Rx) IQ skew [16–22]. But in fact, the skew of the transmitter is more difficult to deal with since it impairs the whole DSP chain compared with Rx-side impairments [23]. Some algorithms for transmitter (Tx) IQ skew equalization have been proposed [24–26], where the 4 × 2 widely-linear (WL) MIMO equalizer has demonstrated its effectiveness to compensate the Tx IQ skew. However, these schemes are ineffective in DSCM transmission because of the conjugate interference resulting from the “symmetric” subcarrier. The 4 × 4 WL equalizer is useful to compensate for the Rx skew in the DSCM system, however, its performance is affected by the phase noise for Tx IQ skew compensation [27].
Since DSCM transmissions have longer symbol periods per subcarrier when compared to the equivalent-rate single-carrier transmissions, there is a performance degradation if a conventional per-subcarrier laser phase noise compensation method is employed [28,29]. In general, the carrier phase estimation (CPE) can be operated in data-aided or blind manner. By inserting pilot symbols, the phase noise can be directly estimated from the phase difference between the transmitted and received symbols. The extension of pilot-based joint CPE has already been proposed in [30], but the additional overhead reduces the net transmission rate. Blind CPE approaches include techniques such as the Viterbi-Viterbi (VV) algorithm and BPS, which provide an overhead-free scheme at the cost of increased complexity and modulation format dependence [29,31]. In addition, the training symbols used for de-polarization can similarly be used for digital PLL to achieve phase noise compensation. Since the accuracy of phase noise estimation affects the performance of Tx IQ skew compensation, we need to use a better phase noise estimation scheme that can mitigate the effect of Tx IQ skew. When the PLL is used, the carrier phase is updated by using the complex signals after MIMO equalizer and Tx impairment compensation filter. So carrier phase recovery is not contaminated by Tx impairments [26]. However, the phase offset increases at higher frequency bands due to the Tx IQ skew. It is difficult for PLL to obtain accurate phase tracking. Moreover, the PLL implemented on each subcarrier for the DSCM transmission increases the overall complexity.
In this paper, we propose a paired-subcarrier equalization scheme that uses the PLL embedded 4 × 4 equalizer to jointly compensate for laser phase noise and Tx IQ skew in DSCM transmission systems. We use training symbols from each pair of subcarriers as the input of 4 × 4 equalizer since the Tx IQ skew for each subcarrier suffers interference from the conjugate components of the “symmetric” subcarrier. To alleviate the complexity, we use a shared phase noise estimation scheme. We first estimate the phase noise by the inner paired subcarriers to reduce the frequency-dependent influence from the Tx IQ skew. This helps us have a more accurate phase noise estimation. Then, we share the estimated phase noise with other paired subcarriers. We conduct numerical simulations of 100-GBaud 64-QAM DSCM coherent optical fiber transmission that consists of eight 12.5-Gbaud subcarriers and experiment of 10-GBaud four-subcarriers PM-16QAM transmission. The simulation results show that the PLL embedded 4 × 4 equalizer can simultaneously compensate for the laser phase noise and Tx IQ skew. The scheme of shared phase noise estimation exhibits better skew tolerance and can reduce the complexity. Additionally, compared with the single-carrier system, it shows the same performance under varied optical signal-to-noise ratio (OSNR) and better performance on the tolerance of EEPN. The proposed equalization method can relax the phase noise and Tx IQ skew limitations for DSCM transmission schemes in ultra-large capacity transmission applications.
2. Principle of the proposed equalization
The IQ skew results from the misalignment of in-phase- and quadrature-component, e.g. the mismatch of the high-speed cable, group delay of DAC/ADC, drivers, etc. We use $x(t )\textrm{ } = \textrm{ }I(t )\textrm{ } + \textrm{ }jQ(t )$ to express the transmitted signal, so the distorted signal due to IQ skew can be expressed as, $y(t )$
In Eq. (5), each subcarrier experiences frequency up-conversion. The received signal after down-conversion consists of the useful signal and the interference from its “symmetric” subcarrier. These paired interfering subcarriers follow the relationship $n + m = N + 1$, where m is the index of “symmetric” subcarrier-n. There is no interference from other subcarriers except for the conjugate subcarrier.
Figure 1 illustrates the Tx IQ skew effect of a DSCM signal with eight subcarriers in the frequency domain. The amplitude of the spectrum is flat because the spectrum is the superposition of subcarriers and their conjugate interference. It is worth noting that the penalty caused by a certain skew varies periodically with the frequency of subcarriers [9,10]. This can be explained by the varied with $w\tau$ in Eq. (5). As the $w\tau$ increases, $1 - \cos w\tau$ is increased for $0 \le w\tau \le \pi$ and decreased for $\pi \le w\tau \le 2\pi$. Since the alias of a pair of symmetric subcarriers exists in the spectrum, the 2 × 2 real-valued equalizer used in single-carrier system after carrier recovery is unable to compensate for the Tx IQ skew. Thus, we have to use the 2 × 2 WL complex-value equalizer to compensate for the Tx IQ skew after depolarization or the 4 × 4 WL complex-valued equalizer to achieve joint depolarization and Tx IQ skew compensation. To facilitate explanation, we focus on two generic frequency-symmetric subcarriers in the following discussions. We use sub-n and sub-m, chosen such that ${f_n} ={-} {f_m}$.
Figure 2 shows four equalization configurations. Configuration I is a conventional de-polarization and phase noise compensation scheme [8]. The de-polarization is realized through a 2 × 2 strictly linear (SL) complex-valued equalizer for each subcarrier. Then, pilot symbols are used to estimate the laser phase noise. Configuration II is also a conventional de-polarization and phase noise compensation as Configuration I, and 2 × 2 WL complex-valued equalizer which has the same performance with 4 × 4 real-valued equalizer is used to compensate the Tx IQ skew [9]. Moreover, two 2 × 2 WL complex-valued equalizers can be substituted by a 4 × 4 WL equalizer and the phase noise is compensated independently [33]. They have similar performance, we attribute these two algorithms as one kind. Configuration III uses the PLL to track the phase noise and realizes the joint equalization to mitigate the Tx IQ skew [26]. Configuration IV is the proposed PLL embedded 4 × 4 WL equalizer for each pair of subcarriers. Since the existence of Tx IQ skew causes penalties for de-polarization and phase noise compensation, errors are accumulated in the following compensation. So we propose a PLL embedded 4 × 4 WL equalizer to jointly perform de-polarization, phase noise and Tx IQ skew compensation to reduce the error accumulation problem. The finite impulse response (FIR) structure of the equalizer is,
Fig. 2. The structure of four equalization configurations. Configuration I: 2 × 2 equalizer for de-polarization, phase noise compensation based pilot symbols; Configuration II: 2 × 2 equalizer for de-polarization, phase noise compensation based pilot symbols and Tx IQ skew compensation for each subcarrier by 2 × 2 equalizer independent; Configuration III: 2 × 2 equalizer for de-polarization and Tx skew compensation for each subcarrier by 2 × 2 equalizer combined with PLL; Configuration IV: PLL embedded 4 × 4 equalizer for joint equalization of polarization, phase noise and Tx IQ skew.
Correspondingly, the updated equations of the filter coefficients are obtained by the gradient descent method to minimize the cost function,
Since the Tx IQ skew leads to the phase offset increasing at higher frequencies, it is difficult for PLL to realize accurate phase tracking. Besides, the phase noise of subcarriers is approximately equal when the transmission distance is short. So, we use a shared architecture to realize the phase noise compensation, which can improve the anti-skew ability and reduce the complexity of DSP. First, we estimate the phase noise of the inner subcarriers using PLL, which is less affected by the skew, so the estimated phase noise is more accurate. Then, this phase noise is directly shared with other pairs of subcarriers. The walk-off effect is induced by the fact that different frequency components of the optical pulse have different group velocities, which leads to the time delay between subcarriers. So the phase noise for different subcarriers has a relative delay [34]. For longer transmission distances, we can increase the number of reference subcarriers for phase noise estimation to alleviate the influence of the walk-off effect.
3. Simulation setup and discussions
As shown in Fig. 3, we carry out numerical simulations by VPItransmissionMakerTM9.1 of 100-Gbaud PDM-64-QAM digital subcarrier multiplexing transmission consisting of eight subcarriers to investigate the performance of our proposed joint equalizer. At the Tx, the roll-off factor of the RRC spectral shaping is 0.1. And we also digitally emulate the Tx IQ skew. Then the transmitted signals are fed into a dual-polarization IQ modulator (DP-IQM). An external cavity laser (ECL) with a central wavelength of 1550 nm and a linewidth of 100 kHz is used as the optical carrier. After electrical-to-optical (E/O) conversion, an erbium-doped fiber amplifier (EDFA) is used for launched optical power (LOP) adjusting. The signal is transmitted over 100km-SSMF with an attenuation of 0.2 dB/km and a dispersion coefficient of 16.0 ps/nm/km. The loss of the SSMF is fully compensated by the EDFA. An optical AWGN source loads noise to the optical signal transmitted through the fiber in order to adjust optical signal’s OSNR. At the receiver, the linewidth and optical power of the local oscillator laser are 100 KHz and 10 dBm, respectively. The frequency offset (FO) is set to 200 MHz. Then, a coherent receiver is utilized for optical-to-electrical (O/E) conversion. Figure 3(b) shows the received spectrum with eight sub-bands. Figure 3 (c) depicts the DSP flow. After the FO compensation, the subcarriers are demultiplexed through down-conversion and matched filtering. Next, we compensate the CD for each subcarrier. Then, the proposed pair-subcarrier joint equalizer is used to realize the depolarization, carrier phase recovery and Tx skew compensation. Finally, the BER is measured by the direct counting method. The Q-factor is calculated from the measured BER $Q[{dB} ]= 20{\log _{10}}\left( {\sqrt 2 erf{c^{ - 1}}({2 \times BER} )} \right)$.
Fig. 3. (a)Simulation setup. PBS: polarization beam splitter, PBC: polarization beam coupler, SSMF: standard single mode fiber, EDFA: Erbium-doped optical fiber amplifier. (b)The spectrum of DSCM after the effect of Tx IQ skew (c) Tx DSP and Rx DSP.
3.1 Performance of the proposed algorithm in DSCM transmission
We first investigate the performance of the proposed equalizer in the DSCM system under optical back-to-back without phase noise. The equalization configurations are similar to that in Section 2, Configuration I only uses one 2 × 2 SL for each subcarrier. Configurations II and III have the same structure that one 2 × 2 SL equalizer is used for each subcarrier and two 2 × 2 WL equalizers are used for each pair of subcarriers for Tx IQ skew compensation since the phase noise is not considered. So we use Configuration II&III in Fig. 4(a) to represent it. Configuration IV uses the 4 × 4 WL equalizer for each pair of subcarriers. Figure 4(a) shows the Q-factor versus Tx IQ skew using different equalization configurations without phase noise. In Fig. 4(a), the performance of the four configurations is the same when the Tx IQ skew is 0ps because the depolarization in each configuration is not disturbed by skew and phase noise. We find that the penalty without equalizer is up to 9.4 dB within the case of 3-ps Tx IQ skew and only the Configuration IV can fully compensate the Tx IQ skew. Compared with the case without equalizer, Configuration I only reduces 1.4 dB penalty when the Tx IQ skew is 3 ps. This is because the 2 × 2 SL complex-valued equalizer cannot deal with the Tx IQ skew and the small gain comes from equalizing the divergent constellations caused by the Tx IQ skew. In addition, the Q-penalty is only 0.26 dB for Configuration II&III. It effectively compensates for most of the IQ-skew impairment, and the residual penalty comes from the insufficient equalization accuracy caused by the mutual influence of Tx IQ skew and polarization. Overall, the 4 × 4 WL equalizer is the best scheme to deal with the Tx IQ skew.
Fig. 4. Q-factor Vs Tx IQ skew for different equalization configurations in DSCM system (a) optical back-to-back without phase noise (b) transmission over 100 km SSMF with phase noise.
Figure 4(b) depicts the Q-factor versus Tx IQ skew after 100-km fiber transmission with phase noise. We compare the four equalization configurations defined in Fig. 2. The pilot insertion rate is 1/32 for all configurations. In Fig. 4(b), the difference of Q-factors at Tx IQ skew of 0ps is dependent on the phase noise tolerance of different configurations. We find that Configuration IV can almost completely compensate for Tx IQ skew while Configurations II and III have 1.50-dB and 1.15-dB Q-penalty at Tx IQ skew of 3ps, respectively. The penalty is due to the presence of Tx IQ skew which results in the inaccuracy of fully compensating for the polarization effect and phase noise. Therefore, the PLL embedded 4 × 4 WL equalizer can simultaneously achieve polarization demultiplexing, phase noise and Tx skew compensation that is more suitable for the large capacity and high-level modulated transmission systems.
Figure 5(a) shows the Q-factor versus Tx IQ skew with the two schemes of phase noise estimation. 1) independent mode: each subcarrier uses PLL to track the phase noise, 2) shared mode: only a pair of subcarriers use the PLL to track the phase noise, and other subcarriers use the estimated phase noise directly. The difference is that the phase noise is estimated in independent or shared mode, while they both use the same 4 × 4 equalizer architecture. The “Sub. m&n” or “Sub. m&n in shared mode” means the performance of each paired subcarriers in independent or shared mode, where the shared phase noise is estimated by Sub. 4&5. The Q-factor of Fig. 5 (a) is calculated from the average BER of both polarization states for each paired subcarrier. The Q-factor in all other figures is calculated from the average BER of both polarization states for all subcarriers. In Fig. 5(a), the inner subcarriers show better performance while the outer subcarriers sub-1&8 have over 0.23-dB Q-penalty than the inner subcarriers sub-4&5 with 3-ps Tx skew using independent phase noise compensation. This result is also consistent with Fig. 1, where the impairment of outer subcarrier is aggravated by Tx IQ skew, leading to a decrease in the accuracy of phase noise estimation. Therefore, when we share the phase noise estimation results from the inner two subcarriers with the minimum interference to the rest of the subcarriers, we can obtain overall better skew tolerance.
Fig. 5. (a) Q-factor Vs Tx IQ skew of PLL embedded 4 × 4 equalizer in independent and shared mode (b) Q-factor versus transmission distance of the overall performance of DSCM system with the PLL embedded 4 × 4 equalizer in independent mode and shared mode with different reference subcarriers.
Figure 5(b) shows the Q-factor versus transmission distance of the overall performance of DSCM system with the PLL embedded 4 × 4 equalizer in independent mode and shared mode with different reference subcarriers. The Tx IQ skew is 3 ps. In Fig. 5 (b), we find that the performance of Configuration IV in shared mode with Sub.4&5 as reference subcarriers degrades faster compared with Configuration IV in independent mode. Since there is a relative delay in the received phase of each subcarrier because of the existence of the walk-off effect, the phase offset is larger for outer subcarriers when we choose Sub.4&5 as the reference subcarriers to estimate the phase noise. In this case, we should use the other inner subcarrier pairs as reference subcarriers to estimate the phase noise or increase the number of reference subcarriers for phase noise estimation to alleviate the influence of the walk-off effect. To maintain a low-complexity compensation, we use Sub.2&7 as reference subcarriers for comparison. As the dash-dotted lines shown in Fig. 5(b), the overall performance with Sub.2&7 as reference subcarriers shows about 0.4-dB performance gain compared with Sub.4&5 as reference subcarriers in 3000-km transmission. Besides, the shared mode with both Sub.4&5 and Sub.2&7 as reference subcarriers shows better performance compared with only one paired reference subcarrier. The shared mode with both Sub. 4&5 and Sub. 2&7 is achieved through sharing the phase estimated from Sub. 4&5 to Sub. 3&6 and Sub. 2&7 to Sub. 1&8, respectively. Moreover, the shared mode with Sub.4&5 as reference subcarriers has a better performance compared with the independent mode when the transmission distance is within 150 km. So, the phase noise compensation in shared mode is more suitable for short-reach applications. For long-haul transmissions, we can use independent mode or more reference subcarriers.
3.2 Performance comparison of single-carrier and DSCM transmission
We also compare the transmission performance of DSCM system using the proposed joint equalizer and single-carrier system using the PLL embedded 4 × 2 WL equalizer [26]. The symbol rate and modulation format of the singe-carrier system are also 100GBaud and 64-QAM, respectively. Moreover, we also verify the DSCM system performance with independent and shared phase noise estimation modes, respectively. Figure 6 shows the Q-factor versus OSNR with or without 3-ps Tx IQ skew after transmission over 100-km SSMF. The performance of DSCM system with independent phase estimation or shared phase estimation mode embedded 4 × 4 equalizer is almost the same to that of the single-carrier system.
Fig. 6. Q-factor Vs OSNR for comparison of single-carrier and DSCM systems with/without 3ps Tx skew after transmission over 100 km SSMF.
Then, we compare the influence of EEPN on the two transmission systems. Figure 7 depicts the Q-factor of single-carrier and DSCM transmission systems with and without 3-ps Tx skew as a function of transmission distance. From Fig. 7, we can see that the performance of single-carrier system decreases sharply while the DSCM system has a penalty within 0.2 dB as transmission distance increases. This indicates that the DSCM system has a better tolerance to EEPN than the single-carrier system.
Fig. 7. Q-factor Vs transmission distance of single-carrier and DSCM systems with/without 3ps Tx IQ skew.
4. Experiment setup and results
We experimentally evaluate the effectiveness of the proposed method by testing a 40-GBaud PM-16QAM transmission consisting of four subcarriers. This mismatch of data rate with previous simulations is resulted from the limited band-width of transceivers. The 40-GBaud PM-16QAM transmission can also be used to verify the performance of the proposed algorithm. Figure 8 shows the experimental setup and offline DSP. On the Tx side, the 215 16-QAM symbols are pulse shaped by a root-raised cosine (RRC) filter with a roll-off factor of 0.1 for each subcarrier. The Tx IQ skew is digitally emulated in Tx DSP. Since the Tx IQ skew of the two polarizations is basically different in the real system, the Tx IQ skew of digital emulation in X-polarization is 2ps larger than that in Y polarization. They are uploaded to an 8-bit, four-channel, 120-GSa/s arbitrary waveform generator (AWG) to generate the driving signals. A tunable 100-KHz linewidth (ECL) operating at 1550 nm generates the optical signal at a power of 11 dBm. Then, a commercially available LiNbO3 dual-polarization IQ modulator with a 3-dB bandwidth of 23 GHz is used for electro-optic conversion.
During the transmission, an erbium-doped fiber amplifier (EDFA) with a noise figure of 5 dB is used to set the launch power. The signal is transmitted over 100-km-SSMF with an attenuation of 0.2 dB/km and a dispersion coefficient of 16.8 ps/nm/km. After compensating for the fiber loss through the post-EDFA, a variable optical attenuator (VOA) is used to control the received optical power (ROP). The LO laser is an ECL with 100-KHz linewidth operating at 1549.947 nm with a power of 9.5 dBm. After coherent detection and electrical amplification, the signal is digitized by a digital storage oscilloscope (DSO) operating at 256 GSa/s for offline DSP.
In the offline DSP, the Rx IQ skew is first compensated by a fixed Rx frontend filter [26]. Then the signal is resampled to 2 Sa/sym. The remaining DSP processes include frame synchronization, FO compensation, subcarrier demultiplexing and matched filter. The FO estimation is based on the fourth power of the inner subcarrier. Then we compensate for the FO for the DSCM signal in the frequency domain. After the CDC for each subcarrier, we compare the four equalizers as shown in Fig. 2. After demodulation, the BER is measured by directly counting and the Q-factor is calculated from the BER.
Figure 9 depicts the Q-factor versus Tx Y-IQ skew after 100-km fiber transmission for four equalizer configurations. Note that the Q-factor is averaged over two polarization signals. In Fig. 9, Configuration IV, i.e., the PLL embedded 4 × 4 WL equalizer, can almost completely compensate for the Tx skew and outperform other equalizers. Configuration I is used to measure the impact of Tx IQ skew, which linearly degrades the Q-factor. There is a large gap between Configuration I to others when the Tx Y-IQ skew is 0ps. Because the X-polarization is affected with a 2-ps Tx X-IQ skew. Compared with configuration IV, configurations II and III have 0.60-dB and 1.54-dB Q-penalty at Tx Y-IQ skew of 10ps, respectively. The trend of experiment results agrees well with simulation results. The proposed joint equalizer can simultaneously achieve polarization demultiplexing, phase noise and Tx IQ skew compensation that is suitable for large-capacity transmission systems.
Fig. 9. Q-factor Vs Tx Y-IQ skew for different algorithms in DSCM system transmission over 100 km SSMF.
5. Conclusion
In this paper, we have proposed a PLL-embedded paired-subcarrier equalization scheme for the joint equalization of polarization, phase noise and Tx IQ skew for DSCM transmission systems. The proposed PLL embedded 4 × 4 equalizer can deal with the paired-subcarrier interference in the DSCM transmission, so it has superior performance. Moreover, the comparison between the single-carrier and the DSCM system using the proposed equalizer illustrates that the influence of phase noise and Tx IQ skew on DSCM transmission can be largely relaxed.
Funding
National Natural Science Foundation of China (62111530150, U22A2086); Science and Technology Commission of Shanghai Municipality (SKLSFO2021-01); Fundamental Research Funds for the Central Universities (ZYGX2019J008, ZYGX2020ZB043).
Acknowledgments
This work was supported by National Science Foundation of China (NSFC) (U22A2086 and 62111530150), STCSM (SKLSFO2021-01), Fundamental Research Funds for the Central Universities (ZYGX2020ZB043 and ZYGX2019J008).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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