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Abstract
The performance of the high-baud-rate and high-order-modulation-format short-reach coherent transmission systems is sensitive to the in-phase and quadrature (IQ) skew. The conventional receiver IQ skew compensation schemes based on adaptive equalizers (AEQs) suffer from the IQ skew enhanced timing jitter incurred by the clock recovery algorithm (CRA), resulting in a serious sensitivity degradation. In this paper, we first propose a novel multiplication-free timing phase error detector (TPED) with the gain insensitive to the receiver IQ skew and the capability to deal with the complex-valued Nyquist signal with an arbitrary roll-off factor and its real-valued IQ tributaries. Based on the TPED, we then propose a new all-digital feedback CRA able to compensate for the receiver IQ skew. With the novel CRA, the IQ skew enhanced timing jitter is eliminated and the receiver sensitivity can be improved by more than 1 dB for the 61 GBaud dual-polarization Nyquist 16QAM system for an IQ skew of 5 ps. Furthermore, the proposed CRA can reduce the computation complexity of the AEQ by more than 25% compared with the existing schemes by relieving the AEQ from IQ skew compensation. Both numerical simulations and experiments are carried out to validate the advantages of the proposed algorithms. The high-skew-tolerant and low-complexity CRA is a strong candidate for the power-sensitive high-speed short-reach coherent transmission systems.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
To meet the ever-growing demands for high-capacity optical networks, we can resort to more parallel light-paths or higher single-carrier date rate [1]. The former requires more transceivers, while the latter relies on digital coherent techniques supporting high-baud-rate and high-order-modulation-format signals. As the latter uses much fewer transceivers and thus can potentially reduce the power consumption, size and cost, it has been considered as a strong competitor for the high-speed datacenter intra- and inter-connects [1–4]. However, the performance of the high-baud-rate and high-order-modulation-format systems may be seriously degraded by the in-phase and quadrature skew (IQ skew) incurred by the separate I and Q paths with unequal lengths in the phase-diversity coherent receivers, and the total IQ skew may be as large as 10 ps [4–9]. The optical internetworking forum (OIF) has specified that the total IQ skew should be smaller than 4 ps (12% of the symbol period) in the 100 Gbps transmission [10,11]. In [12], it is reported that the IQ skew tolerances for the 16- and 64-ary quadrature amplitude modulation (QAM) signals with 1 dB signal to noise ratio (SNR) penalty are less than 11% and 4.2% of the symbol period, corresponding to 1.8/0.7 ps for the 61 GBaud signals, respectively. Although the receiver IQ skew can be measured and calibrated in the factory production stage [13–16], it may still vary due to component aging and temperature variations during the lifetime of deployment [17].
To solve this problem, the adaptive equalizer (AEQ) able to compensate various linear distortions has been used for the in-service IQ skew and imbalance compensation [18–26]. The well-known 4×4 real-valued (RV) AEQ, allowing for independent adjustment of the IQ tributaries, can compensate for the receiver IQ skew at the cost of high computation complexity [8,19]. Further deployment in the power-sensitive short-reach systems would require a simplified AEQ [22–26]. Recently, a two-section RV-AEQ is proposed to reduce the AEQ computation complexity and compensate for the IQ skew. It consists of two 2×2 N-tap RV-AEQs and one 4×4 1-tap RV-AEQs. It can reduce the computation complexity by about 60% compared with the traditional 2×2 complex-valued (CV) AEQ or the 4×4 RV-AEQ [25,26].
However, the conventional receiver IQ skew compensation methods based on the AEQ suffer from the IQ skew enhanced timing jitter incurred by the clock recovery algorithm (CRA) performed before the AEQ, resulting in a serious sensitivity penalty [9]. The CRA is generally performed before the AEQ in the DSP flow to realize synchronous sampling [26–28]. Otherwise, the sampling clock offset (SCO) induced misalignment between the received samples and the receiver clock will accumulate over time, and may finally disable the AEQ with a finite number of taps and thus limited misalignment compensation ability [29,30]. However, the CRA performed before the AEQ will be affected by the receiver IQ skew, and thus becomes unstable and exhibits an enhanced timing jitter [9]. The CRA relies on the timing phase error detector (TPED) to judge whether the sampling time is late or early relative to the best sampling instant [30–37]. It is found that the receiver IQ skew will change the TPED gain, thus affecting the CRA loop stability [9]. Furthermore, the IQ skew will enhance the TPED timing jitter which varies too fast to be compensated by the subsequent AEQ, leading to a serious receiver sensitivity penalty, especially for the high-baud-rate and high-order-modulation-format systems [9].
To solve this problem, the frequency-domain modified Godard’s TPED [31,36] and an extra specific circuit are used to monitor the receiver IQ skews, so as to compensate for them with the digital interpolator filters before the CRA [9]. However, this scheme is complex because the modified Godard’s TPED requires hundreds of real multiplications per timing phase error (TPE) estimation and an extra complex fast Fourier transform (FFT) operation to obtain the signal spectrum. As a side note, the modified Godard’s TPED is more suitable for the long-haul systems in which the signal spectrum has already been acquired in the receiver for the frequency-domain bulk CD compensation [9,31]. However, in the short-reach systems, the CD is small and often compensated with the AEQ in the time domain [22–26]. Therefore, the time-domain TPEDs, such as the Gardner’s and Lee’s TPEDs [32,33,36], are preferable as they don’t require the extra complex FFT. Another shortcoming of the scheme is that the modified Godard’s TPED fails for the Nyquist signals with a small roll-off factor (ROF) [36] which is widely used in the high-speed short-reach coherent transmission [23–26,36].
In this paper, we propose a novel low complexity multiplication-free time-domain TPED with the gain insensitive to the receiver IQ skew and the capability to handle the Nyquist signal with an arbitrary ROF and its real-valued IQ tributaries. Based on the TPED, we propose a novel all-digital feedback CRA to compensate for the receiver IQ skew and eliminate the IQ skew enhanced timing jitter. Taking advantage of the CRA, we also reduce the tap numbers of the two-section simplified RV-AEQ to further reduce the computation complexity. Numerical simulations and experiments are carried out to demonstrate the effectiveness and efficiency of the proposed algorithms.
2. Working principle
The widely used all-digital feedback CRA consists of a TPED, a loop filter (LF), a numerically controlled oscillator (NCO) and a digital interpolator filter (DIF) as shown in Fig. 1(a) [31,36]. Figure 1(b) shows the structure of the LF which mitigates the phase noise of the TPED output and extracts the stable component to control the NCO. The two key LF parameters, i.e. the proportional and integral element gains K1 and K2, should be carefully selected according to the TPED gain ${k_d}$ as follows [37,38]
Here $\xi $ is the damping factor and ${\omega _n}$ is the natural frequency. The NCO controls the DIFs by the two parameters, the base point index ${m_k}$ and the fractional interval ${\mu _k}$ with which the DIF can calculate the sample at the instant of ${m_k}T + {\mu _k}T$. Here T stands for the symbol period.
The most well-known time-domain and frequency-domain TPEDs are the Gardner’s and Godard’s TPED, respectively [31,32]. They both require two samples per symbol. The two traditional TPEDs are not suitable for the small ROF Nyquist signals [36]. To solve this problem, a new kind of fourth-power TPEDs have been proposed. They apply the traditional TPEDs on the power of received sample sequence [34–36]. The well-known fourth-power Gardner’s TPED (hereinafter referred to as TPEDFG) has the following form [34]
Here M is the total number of the samples used in the estimation. $P(n) = {|{x(n)} |^2}$ stands for the signal power and $x(n)$ represents the CV signal field samples. It also requires two samples per symbol. Equation (3) indicates that the TPEDFG requires 2.5M real multiplication per estimation. Typically, hundreds of samples are required per estimation to average out the noise impact [36]. Thus, the TPEDFG requires approximately three hundred real multiplications per TPE estimation. This high computation load incurs both a high hardware complexity and a significant latency in the feed-back CRA, thus reducing the TPE tracking speed [37]. We also note that the TPEDFG fails for the Nyquist signals with a large ROF and non-Nyquist signals [39,40]. Most of the other existing TPEDs are approximately equivalent to the Godard’s, Gardner’s or the fourth power Gardner’s TPEDs as they have similar expressions in the frequency domain [36], and thus also have the high computation complexity and poor versatility issues [40]. Therefore, it is desirous to design a TPED with low computation complexity and good versatility.Recently, we proposed a multiplication-free TPED as follows (hereinafter referred to as the TPEDsgn-sgn) [37]
Here $\textrm{csgn(}\cdot \textrm{)}$ stands for the complex sign function defined by $\textrm{csgn}({\cdot} ) = {\mathop{\rm sgn}} [Re ({\cdot} )] + j \cdot {\mathop{\rm sgn}} [{\mathop{\rm Im}\nolimits} ({\cdot} )]$, where $Re ({\cdot} )$ and ${\mathop{\rm Im}\nolimits} ({\cdot} )$ represent the real and imaginary parts of the operand within the brackets. The TPEDsgn-sgn is a modified version of the Lee’s TPED and also requires two samples per symbol [33,37]. But the TPEDsgn-sgn has much lower computation complexity and much better versatility than the Lee’s TPED [40]. The TPEDsgn-sgn only involves the multiplications of the four complex values (i.e. ${\pm} 1 \pm j$). Thus, the multiplications can be replaced by a simple look-up-table (LUT) operation with four outputs (${\pm} 2$ and ${\pm} 2j$). In [40], we proved that the TPEDsgn-sgn is versatile for signals with different pulse-shaping schemes including the Nyquist signals with arbitrary ROFs and non-Nyquist signals. However, a shortcoming of the TPEDsgn-sgn is that it is not suitable for the RV signals, and thus cannot be used to estimate the TPE of the IQ tributaries, individually. The reason can be explained by the so-called S-curves of the TPED.
The S-curve is an important TPED characteristic revealing the variations of the estimated TPE versus the real TPE. The timing jitter which is the most important TPED performance metric is defined as the variance of the zero crossing positions of the S-curve given by
where $\delta t$ is the standard deviation of the zero-crossing positions normalized to one symbol period. Figure 2 shows the ideal S-curves of the different TPEDs when no noise is present and the appropriate signals are used. The optical signals used include the 16QAM non-Nyquist signals and Nyquist signals with ROF = 0.As we can see from Fig. 2(a), for the CV signals, the TPEDFG has S-curves with a S-type profile, while the TPEDsgn-sgn has an approximately linear S-curve as the Lee’s TPED. Figure 2(b) show the S-curves for the RV signals. In this case the TPEDsgn-sgn outputs only three possible values (-0.25, 0 and 0.25). Therefore, its S-curve has a step-like profile and is not continuous at the zero-crossing point as shown in Fig. 2(b). This characteristic makes it difficult for the CRA to find the zero-crossing point.
To get a smooth S-curve, we propose the following TPED (hereinafter referred to as the TPEDsgn)
Here only one $\textrm{csgn(}\cdot \textrm{)}$ operation is applied to ensure that ${\varepsilon _{sgn}}$ varies continuously at the zero-crossing point for both the CV and RV signals. We note that the TPEDsgn also requires two samples per symbol and is still multiplication-free as one of the two factors in the multiplication is ${\pm} 1 \pm j$ and thus the multiplications can be performed with only additions. Figure 2(a) and 2(b) show that its S-curves for both the CV field samples and the RV IQ tributaries of the Nyquist signals with a ROF = 0. They are continuous for both cases, indicating that the TPEDsgn is versatile for the CV and RV signals, and, as will be shown later, the TPEDsgn also inherits the versatility of the TPEDsgn-sgn for different pulse shaping schemes.
Utilizing the novel TPEDsgn, we can develop a new CRA to compensate for the IQ skew and thus mitigate the IQ skew enhanced timing jitter. For the feedback CRA, the sign of the TPE estimate is adequate to control a feedback loop to find the zero-crossing point corresponding to the best sampling instant. In Fig. 3, the first and third rows show the waveforms of the I and Q signals, respectively. The second, fourth and fifth rows show the S-curves obtained with the I, Q and CV signals, respectively (hereinafter referred to as I, Q and CV S-curves). It is noteworthy that, as we plot three successive symbol slots in the figure (T stands for the symbol period), three S-curves with the period of T are cascaded in series. Without loss of generality, the S-curves plotted here have a typical S-type profile. The first column represents the case where no receiver IQ skew exists, whereas the second one refers to the case where receiver IQ skew is present. As we can see, when the IQ skew is not present, the best sampling instants of the I and Q signals, as well as the zero-crossing points of the I, Q and CV S-curves, are aligned as expected. However, as shown by the second column, when the IQ skew is present, the zero-crossing point of the CV S-curve drifts to somewhere between the zero-crossing points of the I and Q S-curves to balance the I and Q TPEs, so that the total TPE of the CV field signals is the smallest. Therefore, when only one TPED is used, the timing jitter will be enhanced because of the random competition of the I and Q tributaries.
Fig. 3. The first and third rows show the waveforms of the I and Q signals, respectively. The second, fourth and fifth rows show the I, Q and CV signal S-curves, respectively. S1, S2 and S3 stands for three neighboring symbols. T stands for the symbol period.
To solve this problem, we can use two CR units for the I and Q signals, respectively. But this scheme may incur one symbol period IQ misalignment as illustrated by the third and fourth columns in Fig. 3. In case 1 (the third column), fortunately, the initial I and Q samples acquired at the sampling instant belong to the same symbol. If two separate CR units are used, they can adjust the I and Q sampling instants, individually, to acquire the best I and Q samples (I1 and Q1) belong to the same symbol. As a byproduct, the receiver IQ skew is also compensated. In case 2 (the fourth column), unfortunately, the initial I and Q samples acquired at the sampling instant belong to two neighboring symbols due to the IQ skew. The two separate CR units will move the I and Q sampling instants to the right and left, respectively, toward the best sampling points of the two different symbols (S1 and S2) according to the S-curve zero-crossing points in the two symbol slots. Although, the best I and Q samples (I2 and Q1) can still be obtained, they belong to different symbols, resulting in one symbol period IQ misalignment. We note that the IQ skew compensation method proposed in [9] may fail in this case because it cannot ensure the initial I and Q samples belong to the symbol, and thus the TPEs calculated for the I and Q tributaries, respectively, may belong to different symbol slots. To solve this problem, in the preliminary stage, we use one CR unit to adjust the sampling instant in only one direction toward one symbol, so that I and Q samples acquired after this stage belong to the same symbol as shown in the fifth column of Fig. 3. In the second stage, we use separate CR units to finely tune the I and Q sampling instants and compensate for the receiver IQ skew. It is noteworthy that, all samples output in the preliminary stage are discarded, and only the samples output in the second stage will be saved for subsequent processing.
According to the above principle, we propose a novel CRA as shown in Fig. 4(a). There are four separate clock recovery (CR) units with the same configuration as in Fig. 1 and all are enabled by the TPEDsgn. The I and Q tributaries from the X and Y channels are input into the four CRA units via three 1×2 switches. In the preliminary stage, the switches are pushed up. The four tributary signals are only input into the first CR unit. The other three CR units don’t work. After the first CR unit converges and finds the sub-optimal sampling instant, the other three CR units with the same configuration can initialize all their parameters with those acquired by the first CR unit, including the parameters of the LF, NCO and the taps of the DIF. The initialization guarantees that the samples acquired by the four CR units at the beginning of the second stage belong to the same symbol. After the initialization, the three switches are pulled down. The four tributaries are processed by the four CR units, independently. As the TPEDsgn can deal with both CV and RV signals, the first CR unit can be reused to deal with the RV I tributary. We note that in the convergence process, the four CR units may discard different numbers of samples because their convergence speeds may be different as the I and Q tributaries carry different data information and may have different impairments. However, the numbers of the discarded samples can be known from the base point index ${m_k}$ output of the four CR units. Therefore, the four resampled sequences outputted by the four CR units can be aligned by discarding the same number of samples which is performed in the alignment unit in Fig. 4(a). It is noteworthy that the prerequisite for the alignment is that the I and Q samples input into the second stage belong to the same symbol which is ensured by the preliminary stage. The flow chart of the proposed two-stage CRA is plotted in Fig. 4(b).
Fig. 4. (a) The structure of the proposed CRA and the subsequent DSP flow consisting of the RV-AEQ and carrier recovery unit. (b) The flow chart of the proposed two-stage CRA.
With regard to the computation complexity, as the effort for a multiplier is much higher than for an adder, the number of real multiplications required is used as the figure of merit to measure the complexity. The proposed TPEDsgn is multiplication-free. Therefore, in the CRA, the DIF is the main contributor to the computation complexity. Typically, the DIF is implemented with the cubic Lagrange interpolator and the Farrow architecture. To reduce the complexity, we use a simple linear DIF with only two RV taps equal to $1 - {\mu _k}$ and ${\mu _k}$. In the four CR units shown in Fig. 4, there are two such DIFs per polarization, and thus 4 real multiplications are required as the input signal is RV. If the IQ skew compensation was not required, one DIF would be required per polarization which also requires 4 real multiplications as the input signal is CV. In other words, the DIF computation complexity is not increased for the IQ skew compensation. The small interpolation error due to using the linear DIF instead of the cubic DIF can be readily compensated by the subsequence two-section RV-AEQ. What is more, as the IQ skew has been compensated with the proposed CRA, the RV-AEQ can reserve its capability for the CD and other forms of ISI compensation, and thus the tap numbers of the FIR filters can be reduced. This can further reduce the computation of the simplified RV-AEQ.
3. Numerical simulations and experiments
The setup of the numerical simulation system is shown in Fig. 5(a). The optical signal transmitted is the 61 GBaud dual-polarization Nyquist 16QAM (DP-Nyquist-16QAM) signals with a ROF of 0.1. The received signal power (ROP) is adjusted by a variable optical attenuator (VOA). The integrated coherent receiver (ICR) is a conventional intradyne coherent receiver [6]. The receiver IQ skew, amplitude imbalance and phase mismatch are added onto the signals Ix,in, Qx,in, Iy,in and Qy,in before they are input into the DSP system.
Fig. 5. (a) The setup of the numerical simulation system. (b) The structure of the two-section RV-AEQ.
First, we investigate the effect of the receiver IQ skew on the TPED gain. Figure 6(a) and 6(b) show the S-curves of the well-known TPEDFG and the proposed TPEDsgn obtained by numerical simulations. To focus on the effect, no noise is considered in this figure. The IQ skew varies from 0 to 8 ps. As we can see, the S-curve of the TPEDFG changes with the IQ skew, while that of the TPEDsgn remains nearly the same as it has a linear S-curve. For comparison, the variations of the TPED gain defined as the slope of the S-curve at the zero-crossing point [9] are plotted in Fig. 6(c). The results are normalized by the value without the IQ skew. As we can see, the TPEDFG gain is sensitive to the IQ skew. It drops from 1 to about 0.38 when the IQ skew increases from 0 to 8 ps. Thus, the LF parameters K1 and K2 of the CRA based on the TPEDFG have to be adjusted periodically with Eqs. (5) and (6) by monitoring the IQ skew on-line [9]. On the contrary, the proposed TPEDsgn gain is insensitive to the IQ skew. Thus, the CRA based on the TPEDsgn can work in a set-and-forget manner.
Fig. 6. The S-curves of the well-known TPEDFG (a) and the proposed TPEDsgn (b). The variations of the TPED gain versus the receiver IQ skew.
We then investigate the IQ skew enhanced timing jitter for the conventional TPEDFG and the proposed TPEDsgn. Figure 7 shows the variations of the timing jitter versus the IQ skew obtained by numerical simulations. In the figure, the SNR is set to be 16.5 dB with which the bit error rate (BER) is close to 1${\times} $10−3. Here M = 1024 samples are used in drawing the S-curve and 1000 S-curves are used to calculate the timing jitter for each IQ skew value. As we can see, the timing jitter of the TPEDFG is enhanced by about 13 dB when the IQ skew increases from 0 ps to 8 ps. By contrast, the IQ skew enhanced timing jitter is avoided by the proposed CRA using the TPEDsgn to process only the I or Q tributary in the second stage. Its timing jitter is mainly caused by the noise and keeps about -33 dB which is about 12 dB lower compared with the TPEDFG when the IQ skew is 8 ps. To show the IQ skew enhanced timing jitter visually, 100 S-curves of the two TPEDs are plotted in Fig. 7. As we can see from Fig. 7(a), for the TPEDFG, the zero-crossing points is well concentrated in a small area when the IQ skew is 0 ps. By contrast, the zero-crossing area is much larger when the IQ skew is 5 ps as shown in Fig. 7(d), showing the timing jitter performance is poor.
Fig. 7. The variations of the timing jitter against the IQ skew for the conventional TPEDFG handling the CV signals and the proposed TPEDsgn handling the RV IQ tributaries.
We also investigate the versatility of the TPEDsgn for the Nyquist signals with different ROFs. Figure 8 shows the variations of the timing jitter versus the ROF when the IQ skew is 0 ps. Here the SNR is also set to be 16.5 dB, M = 1024 and the ROF is varied from 0 to 1. As we can see, the timing jitter of the TPEDFG increases to about -16 dB when the ROF increases to 1. While the timing jitter of the TPEDsgn remains below -25 dB over the whole range. Such a low timing jitter will not incur any sensitivity penalty as the signal quality is dominated by the SNR when operating at the BER of 10−3 [41]. The results demonstrate that the proposed TPEDsgn is suitable for all ROFs.
To investigate the effect of the IQ skew on the receiver sensitivity, a 2-km short-reach 61 GBaud DP-Nyquist-16QAM transmission system is simulated using the commercial software VPI TransmissionMaker V. 9.7. The ROF is still 0.1. The initial TPE is randomly selected and the SCO is set to be 50 ppm. The ROP is varied by adjusting the attenuation of the VOA. The total laser linewidth and laser frequency offset are set to be 200 kHz and 1 GHz, respectively. The electrical signals output by the ICR are filtered with the Butterworth low-pass filters with a 3-dB bandwidth of 24.5 GHz. The DSP chain performs clock recovery, adaptive equalization, carrier recovery, symbol de-mapping and the final bit error calculation. As for the implementation of the clock recovery and adaptive equalization, we investigate the performance of the four schemes listed in Table 1. The existing schemes include schemes 1, 2 and 3 investigated in [27,19,25]. As for the clock recovery, the existing schemes use the traditional feedback all-digital CRA shown in Fig. 1. While for the proposed scheme, the novel CRA shown in Fig. 4 is used. As for the TPED, the traditional CRA uses the well-known TPEDFG, while the proposed CRA uses the proposed TPEDsgn. As for the adaptive equalization, schemes 1 and 2 use the 2×2 CV-AEQ and 4×4 RV-AEQ, respectively. While scheme 3 and the proposed scheme use the two-section RV-AEQ shown in Fig. 5(b). For schemes 1, 2 and 3, we use the tap update methods given in [27], [8] and [25], respectively. In the two-section RV-AEQ, the number of the cross-FIR-filter taps (N2) can be trimmed to be smaller than the number of the straight-FIR-filter taps (N1) to reduce the computation complexity, considering that N2 is determined by the CD incurring IQ crosstalk which is small in the short-reach transmission [25]. It is reported that the optimal (N1, N2) is (25, 11) for the 2-km 61 GBaud PDM-16QAM transmission system [25]. For the convenience of comparison, the same (N1, N2) is used here. For schemes 1 and 2 which are used as benchmarks, the tap numbers (N) are set to be 25 for both the cross and straight FIR filters as in the traditional manner.
Table 1. Comparison of different schemes (assuming one CV multiplication requires four RV ones)
Figure 9 (a) shows the variations of the receiver sensitivity penalty (at the BER of 10−3) versus the receiver IQ skew. As we can observe, scheme 1 cannot compensate for the IQ skew as expected. Schemes 2 and 3 can compensate for the IQ skew, but due to the IQ skew enhanced timing jitter incurred by the traditional CRA, the receiver sensitivity penalty increases by about 1.3 dB when the IQ skew is 5 ps. By contrast, when the proposed scheme is used, the receiver sensitivity is not degraded by the IQ skew. The impact of the XY skew is similar to that of the IQ skew [26], and is also investigated here. As we can observe from Fig. 9(c), although schemes 1, 2 and 3 can compensate for the XY skew, the receiver sensitivity penalty still increases by about 0.8 dB when the XY skew is 5 ps because of the XY skew enhanced timing jitter. By contrast, when the proposed scheme is used, no receiver sensitivity penalty occurs.
Fig. 9. The variations of the receiver sensitivity penalty (at the BER of 10−3) versus the IQ skew (a) and XY skew (c). The variations of the BER versus the ROP when the IQ skew (b) and XY skew (d) are 5 ps, respectively.
It is noteworthy that, in the conventional DSP flow, the Gram-Schmidt orthogonalization procedure (GSOP) algorithm is used to compensate for the receiver IQ amplitude imbalance and phase mismatch before the CRA and AEQ [5,25]. In our simulations, the GSOP algorithm is removed from the DSP flow because the GSOP can only compensate for receiver IQ imbalance, while the RV-AEQ can compensate for the IQ imbalance, CD and various inter-symbol-interference (ISI). Therefore, with the RV-AEQ, the GSOP is not necessary. Furthermore, the performance of the GSOP degrades when the IQ skew and laser frequency offset are present [42]. Figure 10 shows that the proposed scheme, as well as schemes 2 and 3, is still robust to the IQ amplitude imbalance and phase mismatch. By contrast, very serious sensitivity penalty occurs when scheme 1 is used. The reason is that scheme 1 doesn’t allow for independent adjustment of the IQ tributaries, while the other schemes do.
Fig. 10. The variations of the receiver sensitivity penalty (at the BER of 10−3) versus the IQ amplitude imbalance (a) and IQ phase mismatch (b).
With the help of the proposed CRA, we also try to reduce the computation complexity of the two-section RV-AEQ considering that the receiver IQ skew has been compensated beforehand. Figure 11(a) and 11(b) show the variations of the required ROP (for the BER of 10−3) versus N1 and N2, respectively. To optimize N1 and N2, respectively, in Fig. 11(a) N2 is not changed, while in Fig. 11(b) N1 is not changed. Here the IQ skew is set to be 5 ps. We note that, the 1.3 dB sensitivity advantage of the proposed scheme over scheme 3 is owing to the IQ-skew-induced timing jitter as illustrated in Fig. 9(b). Figure 11(a) shows that, with the proposed scheme, the required ROP is nearly the same when N1 is reduced from 25 to 15 (the difference is less than 0.08 dB). By contrast, with scheme 3, the required ROP increases by about 0.4 dB when N1 is reduced from 25 to 15. This is because, with the proposed CRA, the AEQ doesn’t need to compensate for the IQ skew, and thus N1 can be reduced further. Figure 11(b) shows that, when N2 is reduced, the required ROPs increase nearly by the same amount for the two schemes, and thus N2 cannot be reduced by taking advantage of the proposed CRA. This is because N2 is mainly determined by the CD-induced IQ crosstalk [25]. When (N1, N2) is (25, 11), the two-section RV-AEQ requires 160 real multiplications, while when (N1, N2) is (15, 11), it requires only 120 real multiplications. This means that, with the proposed CRA, the AEQ computation complex can be reduced by 25% compared with scheme 3 when the IQ skew is 5 ps. Compared with scheme 2 which require 400 real multiplications, the AEQ computation complex is reduce by 70%. Meanwhile with the proposed scheme the sensitivity can be improved by about 1.3 dB, compared with schemes 2 and 3. Noting that, for the short-reach transmission, the power consumption of the AEQ is the highest among the DSP flow except the FEC decoder [28], the improvement is a valuable step in reducing the power consumption of the coherent transceivers.
Fig. 11. The variations of the required ROP (at the BER of 10−3) versus N1 and N2. In (a) N2 = 11 while in (b) N1 = 25.
We also investigate the performance of the proposed scheme through experiments. The setup of the experimental system is shown in Fig. 12. Two external cavity lasers with the linewidth of 100 kHz and wavelength of 1550 nm are used as the signal carrier and local oscillator, respectively. A 65 GSa/s arbitrary waveform generator (AWG, Keysight M8195A) with a 3-dB bandwidth of 25 GHz is used to generate the four tributaries of the 45 GBaud DP-Nyquist-16QAM signal with a ROF = 0.01. The generated signals are amplified by the radio-frequency amplifier (CENTELLAX, OA3MHQM) with a 3-dB bandwidth of 30 GHz, and then modulated onto the optical carrier using a dual-polarization optical IQ modulator (Fujitsu, FTM7977HQA) with a 3-dB bandwidth of 23 GHz. At the receiver side, a VOA is used to control the ROP. An ICR (Fujitsu FIM24706) with a 3-dB bandwidth of 22 GHz is used to reconstruct the optical signal field. The four output signals of the ICR are captured by a 50 GSa/s digital sampling oscilloscope (DSO, Tektronix DPO73304D) with a 3-dB bandwidth of 23 GHz for offline processing. For the convenience of setting different levels of the receiver IQ skew and imbalance accurately, the original IQ skew and other imperfections of the transmitter and receiver are calibrated and compensated with the method proposed by us [16], and then the required receiver IQ skew and imbalance are added digitally. The transmission fiber is a standard single-mode-fiber (SSMF) with a length of more than 2 km. For the 2 km transmission scenario, the excess fiber dispersion is pre-compensated digitally at the transmitter.
The flow chart of the DSP chain is also plotted in Fig. 12. After resampling to 2 samples per symbol (SPS), the CRA and AEQ are first implemented. Then, the carrier recovery algorithm is performed to remove the frequency offset and phase noise before the final BER calculation. We firstly investigate the receiver IQ skew tolerance of different schemes. We set (N1, N2) to be (15, 11) for the proposed scheme. For comparison, scheme 3 has (N1, N2) of (25, 11) [25]. As for schemes 1 and 2, the tap numbers of all the FIR filters are set to be 25. Figure 13 shows the variations of the receiver sensitivity penalty versus the receiver IQ skew obtained from the experiments. As we can see, the performance of scheme 1 degrades significantly with increasing IQ skew, as expected. Scheme 2 and 3 can compensate for the IQ skew, but due to the IQ skew enhanced timing jitter incurred by the traditional CRA, the receiver sensitivity penalty increases by about 1 dB when the IQ skew is 5 ps. By contrast, there is no receiver sensitivity penalty due to the IQ skew when the proposed scheme is used. Figure 14 shows the variations of the receiver sensitivity penalty versus the receiver IQ amplitude imbalance and phase mismatch obtained from the experiments. As we can see, the proposed scheme without the GSOP algorithm is still robust to the IQ amplitude imbalance and phase mismatch. In summary, the experimental results also validate the advantages of the proposed scheme.
Fig. 14. Receiver sensitivity penalty against the receiver-side IQ amplitude imbalance (a) and IQ phase mismatch (b).
4. Conclusions
In this paper, a novel multiplication-free TPED is proposed. It has the detector gain insensitive to the IQ skew and can deal with the Nyquist signal with an arbitrary roll-off factor and its real-valued IQ tributaries. Based on the TPED, a new all-digital feedback CRA is proposed. It can compensate for the receiver IQ skew and eliminate the IQ skew enhanced timing jitter. With the proposed CRA, the receiver sensitivity can be significantly improved when the receiver IQ skew is present. What is more, the computation complexity of the subsequent AEQ can be reduced significantly as the IQ skew is compensated beforehand. The advantages of the proposed scheme are validated by both numerical simulations and experiments. The proposed high receiver skew-tolerant and hardware-efficient CRA is a strong competitor for the high-speed short-reach coherent transmission systems with strict power-consumption limits.
Funding
National Natural Science Foundation of China (61975059, 61975063); Foundation of Chinese Science and Technology on Electro-Optical Information Security Control Laboratory (2021JCJQLB055017).
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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