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Abstract
In this paper, we propose a novel transceiver in-phase/quadrature (I/Q) skew in-field calibration scheme with correlation-based method for the dual-polarization coherent optical system. Simultaneous dual-polarization calibration of transceiver I/Q skews after fiber transmission is experimentally performed. Rx/Tx correlation-based skew estimations (CBSEs) are proposed to accurately estimate the transceiver I/Q skews with dual-polarization OFDM signal. By simulation, the robustness of the Rx/Tx CBSEs is investigated against various transceiver I/Q imbalances and channel impairments including carrier frequency offset (CFO), phase noise (PN), and chromatic dispersion (CD). The simultaneous measurement of large transceiver skews is studied within a range of ±128 ps. The bit error rate (BER) improvement brought by the CBSEs is studied in 80 km single-mode fiber (SMF) transmissions under various Rx/Tx skews. In the experiments, the Rx/Tx skew is measured in the range of 1 to 128 ps w/ and w/o the presence of 5 ps Tx/Rx skew. Simultaneous dual-polarization measurements are performed with the X/Y polarization Tx/Rx skews set to 2.5 ps, 5 ps, 7.5 ps and 10 ps, respectively. The measurement errors are within ±0.2 ps. The 80 km SMF dual-polarization transmission after in-field calibration for inter-data center interconnection (inter-DCI) is implemented, with a data rate of 400 Gb/s for both 16QAM and 32QAM modulation formats.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The dramatic growth rate of Internet traffic is bringing the world into the Zettabyte Era, making the demands for data rate increase exponentially. The bandwidth-hungry industries such as the internet of things (IoTs), cloud computing, virtual reality, and the construction of smart cities, make the data center interconnections (DCIs) face the challenges of both providing higher transmission rate and dealing with more intricate network topologies [1–5]. In the coherent optical transmission systems of inter-DCIs, though higher modulation formats could be used to increase the data rate with limited available bandwidth, they are highly sensitive to the transceiver in-phase/quadrature (I/Q) skews. I/Q skew is the timing difference between the I/Q paths, which is a quasi-static impairment that variates slowly as the aging of devices and fluctuation of temperature, or changes with the replacing of radio frequency (RF) cables. Traditionally the skews of the transceivers are calibrated before deployment into service, by using some in-factory or laboratory calibration methods, such as using a vector network analyzer to measure the linear transfer function, measuring the skews with a high-resolution optical spectrum analyzer [6], or tuning the local oscillator (LO) frequency to estimate the skew by deriving the phase slope [7]. However, such laboratory methods require expensive equipment and labor-intensive complex operations, which are hardly available in an in-field scenario. In-field skew calibration is highly desirable, yet much more challenging since it requires minimizing additional resources and operations [8]. Thus, the in-field measurement of the transceiver I/Q skews simultaneously in the receiver-side digital signal processing (DSP) has become an attractive research topic [8–15].
Most of the existing works on I/Q skews only focus on one side of the transceiver. Some methods were studied to deal with the transmitter (Tx) I/Q skews [16–22], while some were proposed for the receiver (Rx) I/Q skews [23–28]. However, these works did not consider the interaction between Rx and Tx skews that might degrade or even incapacitate estimations. So far, a few works on simultaneous transceiver I/Q skew measurement have been proposed [9–15], as enumerated in Table 1. Part of the works are based on multiple-input multiple-output (MIMO) equalizers. In Ref. [9], Y. Fan et al. proposed a monitoring scheme for I/Q imbalances including skews, with a blind and a data-aided 4×4 MIMO equalizers respectively for Rx and Tx imbalances monitoring, and verified the scheme in fiber transmission system in Ref. [10]. In Ref. [11], C. Ju et al. demonstrated by simulation an in-service transceiver I/Q imbalance and skew monitoring scheme with 4×2 complex-valued radius directed equalizer (RDE) and a decision-directed least mean square (DD-LMS) equalizer. A 4×4 constant modulus algorithm (CMA) and minimum mean square error (MMSE) equalizers are used for Rx and Tx skew monitoring in Ref. [12] by J. Liang et al. In Ref. [13], M. Arikawa et al. proposed adaptive multi-layer linear and widely linear filter for the transceiver I/Q imbalances and verified it in transmission. The MIMO methods can be utilized conveniently in-service for simultaneous compensation and monitoring for I/Q imbalances including skews, along with other transceiver imperfections with adaptive control of filters, without using long training sequence (TS). However, even MIMOs have good accuracy for small skews, the estimation error of MIMOs increases as the skew values get larger. As given in the experiment of Ref. [9], when the Rx skew is 5.5 ps the estimation error can be up to 0.5 ps. The dynamic range of MIMO methods is limited by the equalizer capacity, and could not deal with possible large value skews of dozens of picoseconds. For a wider skew monitoring range, the Godard timing error detection [29] was implemented in [14] for the coherent transceiver skews, yet, with lower accuracy. With QPSK signal, the Rx skew error range can be up to ±0.65 ps in a dual-polarization situation, and the accuracy would be worse for higher modulation format as the comparisons given in Table 1 of Ref. [14]. Furthermore, when the skew value exceeds the single carrier symbol duration, the detection is hampered by phase ambiguity, thus the dynamic range is still limited. Given the above situation, calibrating the skews with accurate wide-ranged method before service is an attractive choice, while the slow drifting of skews can be monitored with in-service methods. For accurate skew measurement without range limitation, in Ref. [15], a specially designed multitone I/Q interleaved sequence is utilized to calibrate the transceiver skews by one measurement. However, since this skew estimation method is based on deriving the slope of the phase difference between frequencies, it would be highly sensitive to even slight residual chromatic dispersion (CD) in the in-field measurement over the fiber. On the other hand, this method could not calibrate the I/Q skews of two polarizations simultaneously. Though the multitone sequence could be transmitted twice respectively for the calibration of two polarizations, a polarization controller is required to deal with the polarization rotation, which is an additional device that requires manual manipulations. Given the above-described research status, wide-ranged simultaneous dual-polarization transceiver I/Q skew calibration method that could be utilized through the fiber links is still to be studied.
Table 1. Works On Transceiver Skew Calibration For Coherent Optical System
To our best knowledge, correlation-based dual-polarization transceiver I/Q skew calibration for the coherent transmission system is proposed in this paper for the first time. Calibration through the fiber transmission is experimentally performed. The methods of estimating time delays by the calculation of cross-correlation have already been discussed in some research fields such as zero-IF receiver under I/Q time delay [30], anti-sniper acoustic detection positioning [31], and acoustic source localization [32]. However, in a coherent optical system, the correlation methods are interfered by the existence of carrier frequency offset (CFO), phase noise (PN) and CD, while the polarization rotation needs to be carefully handled during the skew estimation in dual-polarization transmission system. In this paper, we propose a novel in-field correlation-based transceiver I/Q skew calibration scheme for dual-polarization coherent optical systems. The transceiver I/Q skews are measured by the proposed correlation-based skew estimations (CBSEs) utilizing OFDM signal. The Rx CBSE is performed for the Rx skew estimation in the aid of filtering for robustness against CFO, PN, and CD. The transceiver phase and amplitude imbalances are both compensated by the Gram-Schmidt orthogonalization process (GSOP) [33]. The Tx CBSE for the Tx skew estimation is implemented after compensating the other transceiver imbalances. In the simulations, the interferences from various transceiver I/Q imbalances on the Rx/Tx CBSEs are investigated. The wide dynamic transceiver skew measurement is performed within ±128 ps. The influences of channel impairments including residual frequency offset, PN, CD, and optical noise are discussed, and the BER improvement brought by the Rx/Tx CBSEs in the transmission over 80 km single-mode fiber (SMF) under various Rx/Tx skews is studied. In the experimental verifications, the dynamic ranges of the Tx/Rx CBSEs are measurement, the simultaneous transceiver measurement is implemented, and 80 km SMF transmissions after in-field calibration with CBSEs for inter-DCIs are performed, with both 50 GHz 16QAM and 40 GHz 32QAM dual-polarization OFDM signal to study the BER improvement under various optical signal to noise ratio (OSNR).
The rest of this paper is organized as follows: In Section 2, we introduce the mathematic model of the signal under the transceiver I/Q imbalances and the principle of the proposed Rx/Tx CBSEs. In Section 3, the simulation setups and results are given. In Section 4, the experimental verifications are demonstrated. Finally, the conclusion of this paper is drawn in Section 5.
2. Signal model and principle of proposed scheme
Section 2.1 describes the math model of the signal under the impairments of transceiver I/Q imbalances in the dual-polarization coherent system, Section 2.2 demonstrates the principle of the Rx/Tx CBSEs.
2.1 Signal model with transceiver I/Q imbalances
We generate the OFDM signal as the training sequence (TS), which would be used for skew estimation. For each polarization, denote the QAM symbols carried in the ${n^{th}}$ subcarrier of the positive and negative frequencies of the ${m^{th}}$ OFDM symbol as $d_{m,n}^{P + }$ and $d_{m,n}^{P - }$, respectively, where $P \in (X,Y)$ stands for X polarization or Y polarization. Assume each polarization has M OFDM symbols and $2N$ subcarriers, the subcarrier frequency spacing is $\Delta f$, the symbol period is $T = 1/\Delta f$, the cyclic prefix (CP) duration is ${T_{CP}}$, the length of the OFDM symbol is ${T_{OFDM}} = T + {T_{CP}}$, the starting frequency of the subcarriers is ${f_0}$ for the positive frequency and $- {f_0}$ for the negative frequency, then the baseband OFDM signal is:
To avoid the polarization crosstalk between X and Y polarization signals brought by the polarization rotation, the half loaded [34] structure dual-polarization OFDM signal is adopted as the TSs here. The X and Y polarization signals are interleaved in time domain, expressed as:
For the estimation of the CFO and PN, we insert RF-pilot (RFP) [35] by adding a tone in the middle of the OFDM band. The RFP has higher power than the OFDM subcarriers, such that we can estimate the CFO in the receiver side by finding the RFP in the signal spectrum.
Figure 1 shows the sources of transceiver imbalances. For simplicity, the I branches are taken as the reference, and the imbalances are described in the Q branches. Figure 1(a) demonstrates the appearance of Tx imbalances in the I/Q modulator. The Tx skew happens with the various delays of digital to analog converter (DAC) channels and the electrical amplifiers (EAs), the different gains of EAs bring on the Tx amplitude imbalance, and when the phase modulator deviates from ${90^\circ }$, the Tx phase imbalance occurs. On the receiver side as shown in Fig. 1(b), the lightwave of the LO is separated into two branches, one of which is rotated ${90^\circ }$. When the phase rotation angle is not perfect, the Rx phase imbalance emerges. The Rx amplitude imbalance comes from the unbalanced gains of the transimpedance amplifiers (TIAs). At last, the time delays of TIAs and ADCs induce Rx skews.
Now we discuss the mathematic model of the transceiver I/Q imbalances. In the presence of the transmitter imbalances of the I/Q modulator, assume the phase response of Q branch is $\varphi _{Tx}^P$, the amplitude response of the Q branch is $\alpha _{Tx}^P$ and the latency of Q branch is $\tau _{Tx}^P$, then the Tx phase imbalance is $\phi _{Tx}^P$, the amplitude imbalance in dB is $20{\log _{10}} \alpha _{Tx}^P$ and the Tx skew is $\tau _{Tx}^P$. Denote the base band signal under the Tx imbalances as $s_{TxIQI}^P(t)$, then we have:
Denote the LO frequency as ${f_{LO}}$, the PN of LO as ${\phi _{LO}}(t)$, then the CFO is ${f_{CFO}} = {f_c} - {f_{LO}}$ and the PN of the detected complex signal would be ${\phi _{PN}}(t) = {\phi _c}(t) - {\phi _{LO}}(t)$. For polarization P, without considering the Rx imbalances, we assume the output photocurrents from balanced the photodiodes (BPDs) of the receiver for the I/Q components of the optical signal are $I_I^P(t)$ and $I_Q^P(t)$, respectively, and the received complex field is ${r^P}(t) = I_I^P(t) + jI_Q^P(t)$, then:
Since the dual-polarization TSs are interleaved in time-domain, we can also understand how the TS of each polarization under the impairment of Tx skews undergoes the dual-polarization matrix by rewriting Eq. (4) as below:
Similarly, $r_{RxIQI}^P(t)$ could be divided to two time-interleaved portions $r_{RxIQI}^{PX}(t)$ and $r_{RxIQI}^{PY}(t)$. Graphical demonstration is given in Fig. 2 about how the signals undergo Tx Skews, polarization rotation and Rx skews, where the tags Tx/Rx Skew of X/Y Pol. indicate which portions of the received signal are these impairments of these transceiver skews distributed to.
Fig. 2. Graphical demonstration of how the TSs of the two polarizations undergo Tx skews, polarization rotation and channel effects, and Rx skews, and how the Tx/Rx skew impairments are distributed in the received signal.
The impairments of the Rx/Tx skews are shown in Fig. 3 by measuring the OSNR penalty at the soft decision forward error correction (SD-FEC) threshold of BER $\textrm{2} \times \textrm{1}{\textrm{0}^{\textrm{ - 2}}}$, which are simulated in BTB transmissions with 50 GHz OFDM signal. It could be observed that the higher is the modulation format, the more sensitive is the signal to the I/Q skews. With Rx skew of 2 ps, the OSNR penalty for 16QAM-OFDM is about 1 dB, for 64QAM-OFDM the OSNR penalty increases to about 5 dB, while a skew value of 2.5 ps could even degrade the BER of 64QAM to be higher than the SD-FEC threshold regardless of OSNR. The curves of the OSNR penalty versus Rx/Tx skews are generally consistent, where the OSNR penalty induced by Tx skew is slightly higher. Whereas when the skews are less than 0.2 ps, the OSNR penalty is negligible.
2.2 Principle of receiver/transmitter correlation-based skew estimations
We first demonstrate the principle of estimating time difference by the cross-correlation. Assume two functions ${f_1}(t)$ and ${f_2}(t)$ are of finite length in the time interval $t \in [0,{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {T_f}]$, we define the cross-correlation of two functions ${f_1}(t)$ and ${f_2}(t)$ as:
where $\tau$ is a variable of time delay and the superscript $^\ast $ means taking the conjugation of the signal. If ${f_2}(t)$ is a time-shifted version of ${f_1}(t)$ by the delay value ${\tau _ \circ }$, and is multiplied by an complex amplitude C, namely ${f_2}(t) = C{f_1}(t - {\tau _ \circ })$, by taking $\tau = {\tau _ \circ }$, we would derive the maximal absolute value of the cross-correlation R, namely $|C |{\int_{ - \infty }^{ + \infty } {|{{f_1}(t)} |} ^2}dt$. Thus, the principle of detecting time difference ${\tau _ \circ }$ by the cross-correlation is:The implementations of cross-correlation are demonstrated in Refs. [30–32]. Based on Eq. (8), we derive the CBSE for estimating I/Q path time difference. An illustration of CBSE is given in Fig. 4(a). The time delays with respect to the TS of received I/Q signals are estimated as ${\hat{\tau }_I}$ and ${\hat{\tau }_Q}$ by calculating the cross-correlations, then the I/Q skew is estimated as ${\hat{\tau }_{IQ}} = {\hat{\tau }_Q} - {\hat{\tau }_I}$. However, in the coherent optical system, the presence of CFO, PN and CD would degrade the time delay estimation by cross-correlation, thus we first estimate these impairments.
For CFO and PN estimation, after signal synchronization, RFP filtering is implemented. We derive an estimation of CFO ${\hat{f}_{CFO}}$ by finding the maximal power intensity in the frequency spectrum of the received signal:
Assume the length of the fiber link is L and the fiber dispersion coefficient is D, then the transform function of the CD is:
where c is the vacuum speed of light, and $\lambda$ is the central wavelength. Here f is the relative frequency to the optical carrier frequency. Denote $IFT({\cdot} )$ the inverse Fourier transform operator and ${h_{CD}}(t) = IFT({H_{CD}}(f))$, then the filter we use for the CD compensation (CDC) is ${h_{CDC}}(t) = h_{CD}^\ast ( - t)$.In the Rx skew estimation, ${r_{RFP}}(t)$ and ${h_{CD}}(t)$ would be utilized to impose the estimated CFO, PN and CD on the TS ${s^P}(t)$, thus approximately excluding these disturbing factors from the cross-correlations for timing differences. The graphical demonstration of the Rx CBSE in the aid of the RFP and CD filter is shown in Fig. 4(b), where the operator $angle({\cdot} )$ means taking the radian of the signal. Note that the CDC should be implemented after the Rx skews are compensated, since the convolution with complex-valued ${h_{CDC}}(t)$ leads to the interaction of Rx I/Q components. We perform Rx CBSE to estimate Rx skew as $\hat{\tau }_{Rx}^P$, in the aid of RFP ${r_{RFP}}(t)$ and CD filter ${h_{CD}}(t)$:
A graphical explanation about the signal portions utilized in Rx CBSE is given in Fig. 5(a). $r_{RxIQI}^{PX}(t)$ and $r_{RxIQI}^{PY}(t)$ go through the same Rx I/Q path delays, thus the two-norm of their cross-correlations with ${s^X}(t)$ and ${s^Y}(t)$ respectively is used to estimate the Rx I/Q path time latencies $\hat{\tau }_{I,Rx}^P$ and $\hat{\tau }_{Q,Rx}^P$, then we derive the Rx skew estimation $\hat{\tau }_{Rx}^P$ as the difference between them.
After Rx CBSE, the Rx skew and the CD are then compensated as:
Following, the Rx phase and amplitude imbalances are compensated by GSOP:
The Tx phase and amplitude imbalance are also compensated with GSOP:
The signal portions utilized by Tx CBSE is shown in Fig. 5(b). It could be understood from Eq. (5) that the Tx TS ${s^P}(t)$ of one polarization under the impairment of Tx skew $\tau _{Tx}^P$ is distributed by the dual-polarization channel matrix to both Rx polarizations, as $\tilde{r}_{TxSkew}^{XP}(t)$ and $\tilde{r}_{TxSkew}^{YP}(t)$, thus these two signal portions are utilized for Tx CBSE to estimate $\tau _{Tx}^P$, which is performed as:
Note that in the Tx CBSE in Eq. (16), the time shifting $\tau$ in the cross-correlation is imposed on the real/imaginary parts of ${s^P}(t)$, which is corresponding to the form of Tx I/Q path delays. The skew estimation process is now completed. In the actual transmission the Tx/Rx skews could be compensated by performing linear phase filters on the Q branches respectively in the Tx and Rx DSPs, for certain skew value $\tau$:
Since the CBSEs are based on the cross-correlation between TS and received signal, they are not limited by the signal type. Though OFDM signal is used for the verification of the CBSEs in this paper, the CBSEs could be also utilized by other signals that satisfy the time-interleaved structure for the two polarizations to avoid the influence of polarization cross talk, and have the pilot for the CFO and PN estimation.
3. Simulation investigations
The simulation/experimental setups are given in Section 3.1 along with the Tx and Rx DSP process, and Section 3.2 demonstrates the simulation results of the proposed scheme.
3.1 Simulation/experimental setups
The simulation/experimental setups are given in Fig. 6 along with the DSP scheme diagrams. The simulation is performed by VPI Transmissionmaker. The VPI simulation sampling rate is set to 64 GSa/s, while a Gaussian low-pass filter with 3 dB bandwidth of 15 GHz is used to emulate the bandwidth limitation of the system. The extinction ratio of the IQ Mach-Zehnder modulators (IQ-MZMs) is 25 dB. An external cavity laser (ECL) is working at 1552 nm to provide continuous wavelength (CW) lightwave with linewidth of 100 KHz as optical carrier signal. The lightwave from the ECL is divided by a polarization beam splitter (PBS) into two branches for two IQ-MZMs. After optical signal modulation, the output of the two IQ-MZMs are combined by a polarization beam combiner (PBC). The input and output optical powers of the transmitter are 12 dBm and -13 dBm, respectively. The optical signal is then amplified by an erbium doped optical fiber amplifier (EDFA), with launch power -2 dBm into 80 km SMF. In the receiver side, the optical signal from the fiber is amplified by another EDFA, then the receiving optical power (ROP) is controlled by a variable optical attenuator (VOA) at -12 dBm. After that, the optical signal is detected by an integrated coherent receiver (ICR). The LO is another ECL working at 16 dBm with 100 KHz linewidth and 1 GHz CFO.
In the experiment, an arbitrary waveform generator (AWG) with sampling rate 64 GSa/s is used to provide electrical driving signals to the modulators in the transmitter side. In the receiver side, the outputs of the ICR are captured by an 80 GSa/s oscilloscope. The system setups and DSP schemes are generally the same as the simulation, except that the linewidth of ECLs is less than 100 KHz.
The RFP is inserted by adding a DC to the baseband signal in the Tx DSP before optical modulation in the simulation. In the experiment, since the AWG is DC blocking, the RFP is inserted by adjusting the bias voltages of IQ-MZMs for the optical carrier power to be higher than OFDM subcarrier powers.
The DSP is done by the MATLAB software. The sampling rate of the digital signal is 64 GSa/s, thus in the experiment the 80 GSa/s signal from the oscilloscope is resampled to 64 GSa/s for the Rx DSP. For the transceiver skew measurement, in the Tx DSP, a random bit sequence is first generated and mapped into 4QAM symbols that are input into inverse fast Fourier transform (IFFT) of size 1024 to generate OFDM symbols, for each polarization as the TS for skew estimation. The CP length is 16 sampling points. The number of OFDM symbols for each polarization is $M = 10$, and the interval time between the two polarization signals is ${T_I} = 156.25$ ps. The starting frequency of the subcarriers is ${f_0}$=437.5 MHz, and the subcarrier spacing is 62.5 MHz, with 400 subcarriers respectively for positive and negative frequency, the bandwidth is thus 62.5 MHz × 400 × 2 = 50 GHz. Then the RFP is inserted. In the Rx DSP, after synchronization, RFP filtering with BPF width of 75 MHz is performed followed by Rx CBSE, then the Rx skews are compensated followed by CDC. After that, Rx GSOP is used to compensated Rx phase and amplitude imbalances, followed by CFO and PN compensation in the aid of RFP. Tx GSOP is then used to compensate Tx phase and amplitude imbalances. Finally, Tx CBSE is performed to derive the Tx skews.
In the transmission after skew calibration, the Tx DSP is generally the same as in the measurement process, except that the Tx skews are compensated with the estimated values, and the QAM symbols would be different formats depending on the need of the discussion. In the Rx DSP, the Rx skews are also compensated with the estimated values, followed by the filtering to derive RFP, then CDC are performed. After Rx GSOP, CFO and PN are compensated in the aid of RFP, and Tx GSOP is performed. Then, FFT is performed to derive the QAM symbols, followed by channel estimation (CE) and equalization. At last, QAM demapping and BER calculation are implemented.
The skews are emulated in the digital domain with the linear phase filter given in Eq. (17). Tx skews are imposed on the signals after Tx DSP, whereas Rx skews are imposed on the signals before Rx DSP. The time latency parameter searching of CBSEs in Eq. (11) and Eq. (16) is performed with a time resolution of 0.01 ps, except that in the simulation discussion of estimation errors versus impairments the resolution is set to 0.001 ps to observe the subtle change of the curve.
3.2 Simulation results
We investigate the accuracy of Rx/Tx CBSEs, under the impairments from the possible existing transceiver I/Q imbalances and channel imperfections. This part of simulation is done in BTB transmission without optical noise, to study precisely the interference from each factor.
The Rx CBSE could suffer the interference from all kinds of the other transceiver I/Q imbalances, since it is implemented before they have been compensated. Thus, we investigate Rx skew estimation errors under various I/Q imbalances within a wide range, as shown in Fig. 7. The Rx skew is preset to 5 ps. The Rx/Tx amplitude imbalances are swept in ranges of ${\pm} 10$ dB, the Rx/Tx phase imbalances in ${\pm} {20^\circ }$, and Tx skew in ${\pm} 10$ ps. The Rx amplitude imbalance does not affect accuracy of Rx CBSE as shown in Fig. 7(a), since the change of the amplitude of Rx I/Q branches would not change the peak position of cross-correlation amplitude. As we can see in Fig. 3, the OSNR penalty is negligible when the residual skew is less than 0.2 ps. Thus, we can conclude from Figs. 7(b)-(e) that the influences of Rx phase imbalance, Tx amplitude imbalance, Tx phase imbalance and Tx skew on Rx CBSE are negligible within the given range.
Fig. 7. Rx CBSE error under various kinds of I/Q imbalances: (a) Rx amplitude imbalance, (b) Rx phase imbalance, (c) Tx amplitude imbalance, (d) Tx phase imbalance and (e) Tx skew.
The Tx CBSE is implemented after all the other transceivers I/Q imbalances have been compensated, thus we consider the residual imbalances from the errors of Rx CBSE and Rx/Tx GSOPs. We preset the Tx skew to 5 ps and sweep these residual imbalances in ranges wider than they might actually be, to measure the Tx CBSE error, as plotted in Fig. 8. Each of these potential residual imbalances induces Tx CBSE error of less than 0.01 ps, and we could conclude that the Tx CBSE accuracy is hardly influenced by the residual imbalances.
Fig. 8. Tx CBSE error under various kinds of residual I/Q imbalances: (a) Rx amplitude imbalance, (b) Rx phase imbalance, (c) Rx skew, (d) Tx amplitude imbalance, and (e) Tx phase imbalance.
Further, we discuss the modification of Rx CBSE under large Tx skew. As shown in Fig. 9(a), the Rx CBSE error can be up to 0.73 ps without modification when Tx skew is 128 ps. Since an Rx skew of 0.73 ps has negligible influence on Tx CBSE as shown in Fig. 8(c), the Tx skew estimation is relatively accurate and could be utilized to modify the Rx CBSE. After the Tx CBSE, we impose the Tx skew estimated $\hat{\tau }_{Tx}^P$ on the TS ${s^P}(t)$ as ${s^{P\dagger }}(t) = real({s^P}(t)) + \delta (t - \hat{\tau }_{Tx}^P) \otimes imag({s^P}(t))$, and perform modified Rx CBSE which is Eq. (11) using ${s^{P\dagger }}(t)$ instead of ${s^P}(t)$, to approximately exclude the influence of Tx skew on Rx skew estimation. The error of modified Rx CBSE under large Tx skew is around 0 ps as shown in Fig. 9(a). We simulated the simultaneous large transceiver skew estimation with Tx CBSE and modified Rx CBSE, as shown in Fig. 9(b), the measured range of skews can be up to ±128 ps, where both Tx and Rx estimation errors are around 0 ps.
Fig. 9. (a) Estimation error of Rx CBSE w/o and w/ modification under large Tx skew. (b) Simultaneous estimation of large transceiver skew with Tx CBSE and modified Rx CBSE.
And then we demonstrate the robustness of the CBSEs against channel impairments including residual frequency offset, PN, optical noise measured by OSNR, residual CD and polarization rotation as given in Fig. 10. The error plotted is derived as the maximal error amplitude of Rx/Tx skews tested multiple times. In the Rx/Tx error measurement, one of the Rx and Tx skews are set to 5 ps, while the other set to 0 ps. The definition of residual frequency offset is ${\hat{f}_{CFO}} - {f_{CFO}}$, namely the difference of the estimated CFO and CFO. The accuracy of CFO estimation in the aid of RFP is limited by the spectrum resolution, such that residual frequency offset appears.
Fig. 10. Rx/Tx CBSE error versus (a) residual frequency offset, (b) laser linewidth, (c) OSNR, (d) residual CD and (e) polarization rotation.
It could be observed from Fig. 10(a) that with 5 MHz residual frequency offset, the estimation error is about 0 ps. When the residual frequency offset is less than 10 MHz, the error is less than 0.2 ps, and as the residual frequency offset increases to as large as 30 MHz, the error is about 1.2 ps. The estimation error versus linewidth is plotted in Fig. 10(b) to demonstrate the influence of PN. In this stage, the linewidth is set to a given value for one laser and 0 Hz for the other, and the PN is not compensated. In a coherent optical system, the laser linewidth is usually less than 100 KHz thus the combined linewidth of the transceiver lasers is less than 200 KHz, while the sweep range is 50∼500 KHz. It could be observed from Fig. 10(b) that linewidth within 500 KHz does not lead to estimation error. In Fig. 10(c), the error is about 0 ps with OSNR = 30 dB. The error falls within 0.2 ps when OSNR is higher than 16 dB. Even when the OSNR goes down to 0 dB, the maximal error is 1.2 ps. Figure 10(d) considers the case that residual CD exists in the in-field calibration through fiber transmission. The residual CD comes from the fluctuation of the total dispersion of the fiber link. When the residual CD is as large as about 135 ps/nm the estimation error is 0.2 ps, while when the residual CD is within 40 ps/nm, the error is less than 0.05 ps. In comparison, 40 ps/nm residual CD would induce an estimation error of 4.808 ps on the one measurement method in Ref. [15] that estimates the skew by averaging the phase slope within the frequency range 0-30 GHz. The error is calculated by ${\tau _{CD{\kern 1pt} {\kern 1pt} error}} = \frac{{\int_{{f_{start}}}^{{f_{end}}} {\left( {\frac{{d{H_{CD}}(f)}}{{df}}} \right)} df}}{{2\pi ({f_{end}} - {f_{start}})}}$, and $[{f_{start}},{f_{end}}]$ is the frequency range of the multitone signal in Ref. [15] where the central wavelength is 1550 nm. Figure 10(e) shows that polarization rotation does not induce estimation error. In the CBSEs in Eq. (11) and Eq. (16), each two-norm calculation involves two received TS. The existence of polarization rotation angle ${\theta _P}$ would make one received TS be multiplied by ${\pm} \sin {\theta _P}$ and the other multiplied by ${\pm} \cos {\theta _P}$. For the two-norm this rotation leads to an amplitude of ${({\sin ^2}{\theta _P} + {\cos ^2}{\theta _P})^{\frac{1}{2}}} = 1$, such that the CBSEs are not influenced by the polarization rotation.
Considering in the 80 km inter-DCI coherent optical transmission, typically, the linewidth is less than 100 KHz, the OSNR is higher than 16 dB, with residual frequency offset and CD controlled within 10 MHz and 135 ps/nm, the proposed estimation method is robust against these impairments.
Further, we study the BER improvement of 50 GHz dual-polarization 16QAM-OFDM signal brought by the CBSEs in 80 km transmission for inter-DCI, with various preset Rx and Tx skews w/ and w/o compensation, in OSNR of 34 dB. BER versus Rx/Tx skew curves are given in Fig. 11(a) and Fig. 11(b), respectively. As shown in Fig. 11(a), the increase of preset Rx skew leads to a sharp deterioration of BER performance. With Rx skew at about 2.5 ps, the BER goes up to hard decision forward error correction (HD-FEC) threshold of BER $3.8 \times {10^{ - 3}}$, and reaches SD-FEC with Rx skew of about 4 ps. With the Rx skew compensation, the BER is kept to about $5 \times {10^{ - 4}}$ with various preset Rx skew values, which is generally the same performance as when Rx skew = 0 ps. The curve of BER versus Tx skew is similar to the Rx skew case as shown in Fig. 10(b), where the constellation graphs w/o and w/ Tx skew compensation at Tx skew = 5 ps are also given.
Fig. 11. BER performance of 50 GHz dual-polarization 16QAM-OFDM versus (a) preset Rx skew and (b) preset Tx skew w/ and w/o skew compensation.
4. Experimental verifications
In Section 4.1, we measure the dynamic range and accuracy of the CBSEs. In Section 4.2, transmission after in-field calibration through 80 km SMF for inter-DCIs is experimentally verified with 16/32QAM dual-polarization OFDM signal.
4.1 Measurement of dynamic range and accuracy
The dynamic ranges of the Rx/Tx CBSEs are measured in BTB transmission with 4QAM-OFDM TSs. The Tx and Rx skews of the experimental devices are first adjusted to ∼0 ps, then the Rx/Tx skew is tuned from 1-128 ps with Tx/Rx skew = 0 ps or 5 ps, to test the dynamic ranges of the CBSEs. The results of one of the polarizations are plotted as Figs. 12(a)-(b), where both the estimated values and estimation errors are shown. It could be observed that the dynamic range of the Rx/Tx CBSEs can be up to 128 ps, and the error is generally unrelated to the preset skew value. Also, the Rx/Tx skew estimation is almost not interfered by the existence of Tx/Rx skew. The maximal estimation error is 0.17 ps.
Fig. 12. Dynamic range and accuracy measurement of Rx/Tx CBSEs: (a) Rx skew estimated and estimation error versus preset Rx skew, (b) Tx skew estimated and estimation error versus preset Tx skew, and (c) histogram of transceiver skews simultaneously estimated for both polarizations.
The simultaneous I/Q skew measurement for dual-polarization transceiver is verified. The X/Y polarization Tx/Rx skews are respectively preset as 2.5 ps, 5 ps, 7.5 ps and 10 ps. The skew estimation is repeated for 12 times and plotted as the histogram in Fig. 12(c). The averages of tested skews are 2.5625 ps, 5.0792 ps, 7.4604 ps and 9.9983 ps, and the maximal estimation error is 0.18 ps. From above measurement, the estimation error full within ±0.2 ps which has negligible influence on the system performance.
4.2 Signal transmission after in-field I/Q skew calibration
Finally, 80 km SMF dual-polarization transmission is demonstrated to experimentally verify the in-field calibration of CBSEs in the inter-DCI coherent optical system, with both 50 GHz 16QAM and 40 GHz 32QAM-OFDM signals, namely the data rate is 400 Gb/s. For both polarizations, the Tx skew is set to 2.5 ps and the Rx skew is set to 5 ps. Before each transmission, the CBSEs are performed to derive the transceiver I/Q skews, then in this transmission the transceiver skews are compensated with the estimated values. The BER versus various OSNR is measured for signals w/ and w/o skew compensation and plotted in Fig. 13, where the OSNR reference bandwidth is 0.1 nm. With proposed skew calibration, the 50 GHz 16QAM reaches SD-FEC and HD-FEC threshold at OSNR of about 23 dB and 30 dB respectively, while for the 40 GHz 32QAM 22.5 dB and 32 dB respectively. However, without skew compensation, both the 16QAM and 32QAM signal are seriously deteriorated by the transceiver skews and could not reach the SD-FEC threshold with OSNR of even up to 34 dB. The constellation graphs at OSNR of 34 dB are also plotted as Figs. 13(a)-(d) for the 16QAM/32QAM signals w/ and w/o skew compensation, which show that the CBSEs bring on significant performance improvement.
Fig. 13. Experimentally measured BER versus OSNR in 80 km SMF 400 Gb/s transmission and constellation graphs at OSNR of 34 dB: (a) 50 GHz 16QAM w/ skew compensation, (b) 50 GHz 16QAM w/o skew compensation, (c) 40 GHz 32QAM w/ skew compensation, and (d) 40 GHz 32QAM w/o skew compensation.
5. Conclusion
In this paper, we propose a novel in-field transceiver in-phase/quadrature (I/Q) skew calibration DSP scheme with correlation-based method. Simultaneous dual-polarization transceiver I/Q skew calibration through the fiber transmission is experimentally performed. The simulation and experimental results show that the Rx/Tx CBSEs are robust against the interference from transceiver I/Q imbalances and impairments from residual frequency offset, PN, optical noise, and residual CD. In the experimental verification, skew of one side of the transceiver is fixed at 0 ps or 5 ps, and the other side skew is tuned and measured from 1 ps to 128 ps. Simultaneous dual-polarization transceiver skew estimation is verified with the X/Y polarization Tx/Rx skews set to 2.5 ps, 5 ps, 7.5 ps and 10 ps, respectively. The measurement error is within ±0.2 ps. In the 80 km SMF transmission for inter-DCI coherent optical system in the presence of transceiver I/Q skews, the CBSE calibration method significantly improves the BER performance, with a Tx skew of 2.5 ps and a Rx skew of 5 ps at an OSNR of 34 dB, the BER of 50 GHz 16QAM signal is reduced from $\textrm{2}\textrm{.6} \times \textrm{1}{\textrm{0}^{\textrm{ - 2}}}$ to $\textrm{5}\textrm{.5} \times \textrm{1}{\textrm{0}^{\textrm{ - 4}}}$, and for 40 GHz 32QAM signal, the BER is reduced from $\textrm{4}\textrm{.5} \times \textrm{1}{\textrm{0}^{\textrm{ - 2}}}$ to $\textrm{2}\textrm{.9} \times \textrm{1}{\textrm{0}^{\textrm{ - 3}}}$.
Funding
Key-Area Research and Development Program of Guangdong Province (2020B0101080002); Local Innovation and Research Teams Project of Guangdong Pearl River Talents Program (2017BT01X121); the Fundamental and Applied Basic Research Project of Guangzhou City (202002030326); the Open Fund of IPOC (BUPT) (IPOC2020A010).
Disclosures
The authors declare no conflicts of interest.
Data availability
The 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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