Multi-parameter estimation resistant to the random polarization effect for coherent optical receivers

Meng Qiao; Yingyu Chen; Dawei Wang; Dawei Wang; Zhaohui Li; Zhaohui Li

doi:10.1364/OE.489827

1. Introduction

Dense wavelength division multiplexing (DWDM) optical coherent transmission in large-scale optical fiber networks is a key solution to meet the increasing demand for global data traffic. Optical coherent receivers employing DSP to demodulate polarization multiplexed quadrature modulated signals enable high spectral efficiency optical transmission systems [1–3]. The receiver’s task to restore the original signal through various equalization processes requires it to retrieve information about the optical channel impairments during the demodulation of the received signal. As a result, OPM inside digital coherent receivers attracts considerable attention [4]. OPM technology can offer uninterrupted and up-to-the-minute data on the physical state of optical networks, thus enabling accurate identification of the location and cause of any failures that may occur. Moreover, it can determine the degree of individual impairments caused by the network and their distribution. This information empowers network providers to detect early signs of data signal deterioration and take timely preventive measures before faults have a significant impact on system performance. This can ensure a reliable network operation and minimize service disruptions [5]. The key parameters of OPM, including CD, PMD, FO and OSNR, are essential for the receivers to function properly, i.e., they are the critical values to trigger or configure algorithms in the DSP chain.

The CD effect is well known as one of the most important signal impairments in optical fiber transmission systems. It can limit the transmission distances and capacities of long-haul fiber links. CD arises from the variation in propagation velocity with wavelength. An initially sharp pulse is thus dispersed and begins to overlap with adjacent pulses resulting in degraded signal quality [6]. Traditional CD estimation techniques rely on many samples and have to scan through the possible CD values. In [7], a method of auto-correlation of signal power waveform to estimate CD is proposed, and [8] proposed a two-stage fast and adaptive CD estimation algorithm. The first stage uses signal power auto-correlation function for the coarse estimation while the second stage utilizes a modified constant modulus algorithm to obtain much more accurate accumulated CD. These CD estimation algorithms have high estimation accuracy, a large dynamic range, and a short estimation time. However, in order to eliminate the influence of PMD, these method adopts a series of complex operations. [9] proposed a CD estimation method based on fractional Fourier transformation. The algorithm is robust to amplified spontaneous emission noise and nonlinear interference, but obviously it is sensitive to PMD. PMD is a stochastic effect resulting from fiber inhomogeneity, which can be introduced either at fiber manufacturing or during cabling [10]. The differential group delay (DGD), which serves as an instantaneous measure of PMD, can be approximated by a Maxwellian probability distribution. However, the DGD may occasionally exhibit large values. When the cross-talk caused by the DGD surpasses the equalizer’s capacity, the resulting system penalty associated with PMD can cause rapid degradation of system performance [11]. Thus, the influence of PMD on the system algorithm deserves our attention.

FO is an important impairment in coherent transmission systems induced by wavelength mismatch of transmitter laser and the local oscillator (LO). Thus the relatively large frequency offset at the receivers should be removed before running other DSP modules. Various FO estimation (FOE) methods have been proposed for single carrier systems in [12–14]. The classic FOE is based on the fast Fourier transform (FFT), where the peak of the spectrum of the fourth powered signal is searched to locate the FO value [12]. The sparse FFT-FOE method in [14] utilizes the FFT approach on downsampled data to decrease the complexity of FOE, it can effectively reduce the complexity of FO monitoring, while mandating that the FO should not be overly large. An FO estimation method based on linear frequency modulated signal and fractional fourier transform is proposed in [15]. It can be performed before CD compensation. Additionally, it has strong resistance to additional emission noise. But it is also sensitive to PMD.

The OSNR monitoring enables network operators to evaluate the quality of transmission (QoT) and take necessary actions based on the OSNR values detected. Various techniques have been proposed to estimate the in-band OSNR, which is often considered to be the basic performance indicator of the DWDM transmission. They include the high-order statistical moment-based monitoring [16], the amplitude histograms [17], the Stokes parameters [18], the random forest based ensemble learning [19], the period training sequence-based [20], the pilot-assisted [21], and the cyclostationarity-based [22]. However, the mentioned OSNR estimation algorithms are often limited by the impact of optical fiber channel effects such as CD, FO, and PMD. Thus, their performance under realistic transmission scenarios is questionable. To achieve a robust OSNR estimation, it is critical to model the effects of optical fiber channels and to study their impact on specific OSNR estimation algorithms. In recent years, many Machine-learning(ML) based OPM estimation methods have been proposed [23–25]. They are considered promising solutions to add intelligence to optical network nodes. ML techniques can help network nodes learn from network conditions and use this knowledge to optimize network resources. An important advantage of ML-based algorithms is that they provide better results when dealing with nonlinear behaviors. Moreover, deep learning techniques have the ability to solve complex models without the need to build exhaustive analytical models [26]. However, acquiring high-quality training datasets and having higher computational complexity remains challenging.

We previously proposed [27] a CD and PMD insensitive timing recovery method based on the signal’s cyclostationarity. This paper extends the theory further to formulate a new joint CD, OSNR, and FO estimation strategy resistant to the polarization effect. Thus, the joint estimation of these critical parameters can be achieved before the DSP pipeline. The estimation is insensitive to random polarization drift and 1st-order PMD. The developed model of channel effect is also expected to be applicable to other cyclostationarity-based algorithms.

2. Operation principle

2.1 Cyclostationarity functions

The prevalent signal format in optical DWDM systems, such as PDM-QPSK and PDM-16QAM, can be modeled for each polarization with a random process $x(t)$, which is said to be cyclostationary in the wide sense if both its mean and autocorrelation function (ACF) is periodic. Namely, the mean $m_x(t+T_0)=m_x(t)$ and the ACF $R_x(t_1,t_2)= E\{x(t_1)x^*(t_2)\}$ are periodic with period $T_0$. The cyclic autocorrelation functions (CAF) are defined as the Fourier coefficients of the ACF, i.e.,

(1)$$R_x^\alpha(\tau) =\frac{1}{T_0}\int_{{-}T_0/2}^{T_0/2}R_x\left(t+\frac{\tau}{2},t-\frac{\tau}{2}\right)e^{{-}i2\pi\alpha t}dt$$

which are nonzero only at $\alpha = {k}/{T_0}$. The Fourier transform of CAF is termed spectral correlation function (SCF), i.e.,

(2)$$S_x^\alpha(f)=\int_{-\infty}^{\infty}R_x^\alpha(\tau)e^{{-}i2\pi f\tau}d\tau$$

which described the correlation between two spectral components with frequency difference $\alpha$. The SCF is a generalization of power spectral density (PSD). For practical reasons, we consider only one CAF-SCF pair with $k=1$ and $\alpha =1/T_0$. It can be shown that the signal needs to have nonzero excess bandwidth in order to have a meaningful SCF.

2.2 Modeling CD and PMD effects

We consider the impact of optical fiber transmission effects, such as CD, PMD, and polarization drift on the SCF of polarization multiplexed signal. We proceed first with extending the definition of both CAF and SCF to the two orthogonal polarizations x and y, namely,

(3)$$S_{xx}^\alpha(f)=\int_{-\infty}^{\infty}R_{xx}^\alpha(\tau)e^{{-}i2\pi f\tau}d\tau$$

(4)$$S_{xy}^\alpha(f)=\int_{-\infty}^{\infty}R_{xy}^\alpha(\tau)e^{{-}i2\pi f\tau}d\tau$$

(5)$$S_{yx}^\alpha(f)=\int_{-\infty}^{\infty}R_{yx}^\alpha(\tau)e^{{-}i2\pi f\tau}d\tau$$

(6)$$S_{yy}^\alpha(f)=\int_{-\infty}^{\infty}R_{yy}^\alpha(\tau)e^{{-}i2\pi f\tau}d\tau$$

where $R_{xx}^\alpha (\tau )$ and $R_{yy}^\alpha (\tau )$ are simply the CAFs of signals in the x- and y-polarization, respectively, whereas $R_{xy}^\alpha (\tau )$ is the Fourier coefficient of $R_{xy}(t_1,t_2)= E\{x(t_1)y^*(t_2)\}$ and likewise $R_{yx}^\alpha (\tau )$ the Fourier coefficient of $R_{yx}(t_1,t_2)= E\{y(t_1)x^*(t_2)\}$. Clearly, they are generalizations of ordinary cross-correlation functions. Group these definitions into matrices to obtain

(7)$$C(\tau)=\begin{bmatrix} R_{xx}^\alpha(\tau) & R_{xy}^\alpha(\tau) \\ R_{yx}^\alpha(\tau) & R_{yy}^\alpha(\tau) \\ \end{bmatrix}$$

and

(8)$$S(f)=\begin{bmatrix} S_{xx}^\alpha(f) & S_{xy}^\alpha(f) \\ S_{yx}^\alpha(f) & S_{yy}^\alpha(f) \\ \end{bmatrix}$$

which are termed the CAF and SCF matrix, respectively. Ideally, the SCF matrix should be an identity matrix due to the independent statistical properties of dual polarization signals.

Considering the first-order PMD effect, characterized by a unitary matrix $U$,

(9)$$\underbrace{ \begin{bmatrix} X(f+\alpha/2) \\ Y(f+\alpha/2) \end{bmatrix}}_{E_1}=e^{{-}j\phi_0}U \underbrace{ \begin{bmatrix} X(f-\alpha/2) \\ Y(f-\alpha/2) \end{bmatrix}}_{E_2}$$

where $X$ and $Y$ are the spectra of the x- and y-polarization signals at the receiver, respectively, and $E_1$ and $E_2$ are the Jones vectors of the signals spectral components at frequencies $f\pm \alpha /2$. Assuming no polarization-dependent loss, the matrix $U$ satisfies the relation

(10)$$U=\begin{bmatrix} a & -b^* \\ b & a^* \end{bmatrix},\quad a a^{*}+b b^{*}=1.$$

Similar to the case of using the periodogram as a practical estimation of the true PSD, the practical estimation of SCF is called cyclic periodogram. Let $E_{1,2}$ be the two output Jones vectors at frequencies $f\pm \alpha /2$ when this is no PMD and polarization rotation. Namely, they should coincide with their input states except for a common phase change. Using the relations ${E_1}=e^{-j\phi _0}E_2$, $E'_2=VE_2$ and (9), we obtain the cyclic periodogram

(11)$$P'=E'_1(E'_2)^H=UV(E_1(E_2)^H)V^H=UVPV^H\,$$

where $V$ is a unitary matrix describing the global polarization rotation of the fiber. The matrix $P$ is the cyclic periodogram without polarization rotation and PMD. By taking the expectation of both sides of (11), or by averaging both sides of (11) over all frequencies, we see that

(12)$$\hat{C}(0) = \bar{P'} = UV\bar{P}V^H \approx e^{{-}j\phi_0}U$$

because $\bar {P}\approx e^{-j\phi _0}I$ and the first equality is due to the Fourier relation between CAF and SCF. Namely, the frequency averaged cyclic periodogram matrix $\bar {P'}$, or the estimated CAF matrix $\hat {C}$ at $\tau =0$, is in fact an estimate of the PMD matrix $U$, with a common phase related to the group delay. Based on this conclusion, we can easily obtain the quantity that is insensitive to the polarization effect, i.e.,

(13)$$R(\tau) = |R_{xx}^\alpha (\tau)|^2+|R_{xy}^\alpha (\tau)|^2 +|R_{yx}^\alpha (\tau)|^2+|R_{yy}^\alpha (\tau)|^2$$

which is independent of both $U$ and $V$. This quantity will be used in the subsequent CD, FO and OSNR estimation algorithm. Since CD will introduce a time shift in all elements of the CAF matrix, it is easy to verify that the estimate of $U$ should be replaced by $\hat {C}(\tau _{cd})$, where $\tau _{cd}$ is the proper delay that maximizes $R$.

2.3 CD estimation

The CD effect of optical fiber can be modeled as a filter with a quadratic-phase frequency response $H = \operatorname {exp} (jKf^2)$ with $K=\pi \lambda ^2DL/c$, where $\lambda$ is the wavelength, $D$ dispersion coefficient, $L$ fiber length, and $c$ the speed of light. By making use of (1) and (2), it can be shown that the CD effect results in a linear phase change in the SCF with the change rate over frequency equal to $2K\alpha$, which then produces a constant time shift in the CAF due to their Fourier relation. The CAF is a pulse-like function; hence, the time shift can be identified by peak searching of $|R_{xx}^\alpha |^2$, the 1st element of the CAF matrix (Fig. 1(b)). Thus, a previous work [28] proposed a CD estimator

(14)$$\widehat{DL} = \frac{cT_0}{\lambda^2}\cdot\tau_\text{CD}\,$$

where $\tau _\text {CD} = {\operatorname {arg}\mathop {\operatorname {max}}}|R_{xx}^\alpha (\tau )|^2$. That is, the 1st element of the CAF matrix is first utilized to find the proper delay $\tau _\text {CD}$, then the CD is estimated by (14). According to (10) and (12), however, using $|R_{xx}^\alpha |^2$, or any other element of the CAF matrix, alone will be affected by PMD. Based on the above analysis of the PMD effect and making use of the property of the PMD matrix (10), we can still use (14) but with a new delay estimator

(15)$$\tau_\text{CD} = {\operatorname{arg}\mathop{\operatorname{max}}_{\tau}}\{|R_{xx}^\alpha(\tau)|^2+|R_{xy}^\alpha(\tau)|^2+|R_{yx}^\alpha(\tau)|^2+|R_{yy}^\alpha(\tau)|^2\}\,.$$

It is easy to verify that the new method is PMD-resistant. Note that combine only two terms, such as $R_{xx}^{\alpha }$ and $R_{xy}^{\alpha }$, or $R_{yx}^{\alpha }$ and $R_{yx}^{\alpha }$, is also PMD-resistant. But combining all four elements of the CAF matrix improves the estimator’s SNR. We show in section 3 that this CD estimator is essentially penalty-free from the frequency offset, for it uses the squared modulus of the CAF.

Fig. 1. (a) Simulated signal spectrum and edge filter response, and (b) simulated SCF and CAF based on a 32 GBaud PDM-16QAM system with the cyclic frequency equal to the baudrate, 18 dB OSNR, 100 kHz laser linewidth, $\pm$8.5 ns/nm CD, and 512 symbols. The dashed CAF curve is for negative CD. The SCF is obtained by calculating the cyclic periodogram of the edge-filtered signal, and the CAF is obtained by taking the inverse Fourier transform of the estimated SCF.

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2.4 FO estimation

The SCF is defined for any frequency pairs that are separated by baudrate, and the SCF is nonzero for those frequency pairs within the signal’s bandwidth. The frequency offset does not change the overall shape of the signal’s spectrum. However, it shifts the SCF curve, and if the offset is too large, the spectral correlation is suppressed since the signal is severely filtered. Similar to the FO estimation method proposed in [29], we adopt the idea of sweeping the FO to maximize the spectral correlation. In our case, the correlation strength is indicated by the maximum of (13), or simply $R(\tau _\text {CD})$. However, based on the CD and PMD model given above, we formulate a normalized correlation coefficient in contrast to (18),

(16)$$\gamma = \sqrt{\frac{|R_{xx}(\tau_\text{CD})|^2+|R_{xy}(\tau_\text{CD})|^2+|R_{yx}(\tau_\text{CD})|^2+|R_{yy}(\tau_\text{CD})|^2}{2P_{1}P_{2}}}\,$$

where $\tau _\text {CD}$ is the CAF time-shift caused by CD obtained via (15), $P_1$ ($P_2$) is the average power of the upper (lower) subband in $x$- and $y$-polarization. Note that the value of $R(\tau _\text {CD})$ is actually independent of CD; hence is also the FO estimation. After collecting the value of $R(\tau _\text {CD})$ for each FO setting, we perform a quadratic fitting to the data as a function of FO. The peak location of the quadratic curve corresponds to the estimated value of FO (Fig. 2). Because of the new formulation of the correlation strength, our FO estimation is not affected by PMD, in contrast to the method in [29]. The sweep interval $\Delta f$ should not be overly large to limit the algorithm’s complexity. This paper uses $\Delta f=250$ MHz. Thus, this step should be considered as a coarse FO estimation, but it ensures the accuracy of the subsequent OSNR estimation and reduces the complexity of the fine FO estimation based on, for example, the $4^{th}$-power FFT algorithm [14].

Fig. 2. An example case of FO estimation using $\gamma$ value searching method and quadratic curve fitting method. The FO is set to −1GHz.

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2.5 OSNR estimation

An optical fiber transmission system’s most significant noise source is the amplifier’s spontaneous emission, also known as ASE noise. When polarization-dependent loss is ignored, the coherent optical channel has the all-pass characteristic. We can regard the symbol and noise amplitude as random independent variables with a zero-mean value. The CAF $R_x^\alpha (\tau )$ of the signal is periodic within the periodic interval of the signal duration $T_0$, as long as $\tau$ is less than $T_0$, whereas the ASE noise is not periodic. In the signal spectrum, the periodicity of $R_x^\alpha (\tau )$ reveals a strong correlation between the time-varying amplitudes of certain spectral component pairs and the phase sequence, which does not exist in the case of ASE noise. By exploiting this property, the SNR can be calculated by measuring the correlation between the upper and lower sidebands of the signal spectrum. The SCF $S_x^\alpha$ can be obtained practically by,

(17)$$S_x^\alpha(f)=\frac{1}{W}X(f+\frac{\alpha}{2})X^*(f-\frac{\alpha}{2})$$

where $X(f)$ is the Fourier transform of a finite signal segment with time duration $W$. The length of the signal segment should be much larger than a symbol duration $T_0$. The normalized spectral correlation coefficient can be expressed as

(18)$$\eta =\frac{\int X(f+\alpha/2) X^*(f-\alpha /2)\,df}{\sqrt{\int|X(f+\alpha/2)|^2\,df}\cdot \sqrt{\int|X(f-\alpha/2)|^2\,df}}\,$$

where the integration is performed over a small frequency range. For noiseless signals, the normalized coefficient $\eta = 1$ when $\alpha =1/T_0$ and the two frequencies $f-\alpha /2$ and $f+\alpha /2$ are within the signal bandwidth. Based on the analysis above, the level of the ASE noise influences the value of the normalized coefficient, and as the SNR increases, the ASE noise decreases, and the value of $\eta$ theoretically approaches unity without limit. Based on the principles mentioned above, a previous work [29] formulates an SNR estimator based on $\eta$, namely $\text {SNR} = {\eta }/(1-\eta )$, where $\eta$ is obtained based on the data from a single polarization. Since the CD effect incurs a quadratic phase change across the signal spectrum, the magnitude of the upper and lower sideband correlation calculated from the spectrum will be significantly impacted. In addition, the effect of PMD and SOP drift will randomize the correlation and render the SNR estimation unstable. As a result, the SNR estimation proposed by [29] must be applied after the CD and PMD compensation modules. Note that the PMD effect is not investigated in [29]. In practical optical fiber links, the uncompensated or any residual CD and PMD will significantly affect the OSNR and FO estimation accuracy, as discussed in the next section. Based on the analysis of the CD and PMD impact on the signal’s cyclostationarity in Section 2.2, we revise the SNR estimator by using the new normalized correlation coefficient $\gamma$, namely

(19)$$\text{SNR} = \frac{\gamma}{1-\gamma}\,$$

where $\gamma$ is defined by (16) and taken as the value returned by the FO estimation (i.e., the peak value of the quadratic curve). The calculation of OSNR needs to take into account the ratio of the power of the whole receiving bandwidth to the noise power within the reference bandwidth $B_{n}=0.1$ nm. The conversion from SNR to OSNR is also affected by the bandwidth of the upper and lower band [29]. Therefore, a proportional coefficient $k$ is calibrated for a fixed width of the upper and lower band before the actual OSNR estimation is conducted. It is important to note that in the above analysis, we have only considered the case when the ASE noise is linear. In [30], the authors mentioned the effect of nonlinear and linear noise on SNR estimation. Since nonlinear noise will increase the correlation of the upper and lower sidebands, we regard that nonlinear noise will increase our OSNR estimate errors.

To summarize the operation principle of the developed multi-parameter estimation, the joint CD, FO, and OSNR estimation schematic is shown in Fig. 3. Based on the data after resampling and matched filtering, the CD estimation is performed according to (15). Then, the FOE based on frequency sweeping and curve fitting the new spectral correlation coefficient $\gamma$ is performed. Note that the computation of $\gamma$ requires the CD estimation. Next, the SNR is calculated based on (19) by using the peak $\gamma$ determined by the FOE curve-fitting. Finally, the OSNR is obtained from the SNR estimate based on the proportional constant $k$ calibrated beforehand. The new method enables joint estimation of multiple parameters prior to the complex equalization in the DSP pipeline. Thus, critical information about the received signals can be obtained regardless of the primary channel effects.

Fig. 3. DSP receiver and multi-parameter estimation flow block diagram.

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3. Numerical simulation

To assess the performance of the proposed estimation algorithms, we conducted a comprehensive coherent optical communication simulation featuring a 32 GBaud PDM-16QAM system as illustrated in Fig. [3]. A series of devices and channel effects are simulated, including optical pulse shaping, optical signal modulation, CD, PMD, PDL, SOP, and ASE. At the receiving end, the proposed estimation algorithms immediately follow the normalization and resampling of the signal. Thus, the joint estimation requires no CD and PMD compensation, unlike the SCF method developed in [29], which needs to run after proper CD and PMD equalization.

We simulate the performance of the different CD estimation algorithms. Figure 4(a) shows the CD estimation performance of the algorithm (15) and the algorithm (14) mentioned in [28] with 15.6ps PMD, and block size is 4096. The data for each point were averaged 50 times. The results confirm that our CD estimation method is not sensitive to PMD. Figure 4(b) shows the proposed CD estimation error with different ROF and FO settings. As the ROF increases, more information about the excess bandwidth can be utilized by the spectral correlation, and hence more FO tolerance. The ROF is set to be 0.3 in most simulations.

Fig. 4. (a) CD estimation performance simulation under different fiber distance with 15.6ps/nm PMD, (b) CD estimation error with different ROF and FO.

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Then, we compare the performance of two FO and OSNR estimation methods in various system conditions, such as CD, PMD, laser linewidth, ROF, and subband bandwidth. We first introduce a total CD of 1.7 ns/nm and a 15.6 ps PMD with scrambled SOP. Figure 5(a) shows the estimated OSNR with the presence of both CD and PMD, whereas Fig. 5(b) shows the OSNR estimation with PMD while CD is absent. Clearly, the method given in [29] is severely affected by both CD and PMD, whereas our method shows robust performance. Noticeably, the PMD alone still affects the previous method. Similarly, Fig. 5(c) shows the estimated FO with the presence of both CD and PMD, whereas Fig. 5(d) shows the FO estimation with PMD while CD is absent. It can be seen that after CD compensation, the accuracy of the SCF method in the FO estimate increases a lot, but it is still poor compared with the proposed FO method. The proposed method shows robust performance.

Fig. 5. OSNR and FO estimation performance simulation under CD and PMD condition, (a) with CD and PMD, (b) with PMD w/o CD, (c) with CD and PMD and (d) with CD w/o PMD.

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We proceed to study the performance of the proposed FO estimation method under different system parameter settings. Figure 6(a) shows the impact of ROF. The method works well for ROF greater than 0.3. Fig. 6(b) confirms the resistance to laser phase noise. Figure 6(c) compares various data block sizes and Fig. 6(d) shows the impact of different edge filter bandwidths from 1GHz to 4GHz, a narrower subband is preferred.

Fig. 6. Proposed FO estimation performance simulation under different system parameters, (a) with different Rof, (b) with different laser linewidth, (c) with different block size and (d) with different filter bandwidth.

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Figure 7 shows the performance of the proposed OSNR estimation method under different system parameter settings, where Fig. 7(a) the ROF of the system is from 0.1 to 1, Fig. 7(b) different lasers linewidths from 1KHz to 1000KHz, Fig. 7(c) data lengths range from $2^{13}$ to $2^{16}$ and Fig. 7(d) different signal filter bandwidths from 1G to 4G. It can be observed that when the block size is $2^{13}$, jitter occurs when estimating a large OSNR, which is because the noise of the system is sensitive to the effect of m for a large OSNR. And the calibration coefficients $k$ for OSNR are slightly different for different bandwidths. Figure 7(d) shows if calibration coefficients with 1G filter bandwidth are used, the OSNR estimates are slightly reduced when the filter bandwidth is increased.

Fig. 7. Proposed OSNR estimation performance simulation under different system parameters, (a) with different Rof, (b) with different laser linewidth, (c) with different block size and (d) with different filter bandwidth.

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4. Experimental verification on DWDM system

To further investigate the performance of the proposed algorithms in a realistic optical system, we carry out experimental verification on a DWDM system with field-deployed optical fiber cable. The block diagram of the experimental setup is shown in Fig. 8. At the transmitter, we used an external cavity laser (ECL) with a linewidth of 100 kHz to carry the signal in the test channel. The DFB laser array produces the wavelengths for the dummy channels. The two IQ-modulators were driven by two arbitrary waveform generators (AWGs), operating at a sampling rate of 64 GSa/s, which generated Root Raised Cosine shaped Dual-Polarization (DP) PDM-16QAM signals at 32 GBaud with a roll-off factor of 0.3. The dummy channels are subject to a waveshaper (WSP) to flatten the spectrum and carve a spectral notch at the test band. The test and dummy channels are combined and launched into the field deployed standard single-mode fiber (SSMF). The deployed fiber link is about 99 km long. The PCD is a polarization synthesizer for adding randomly varying PMD and SOP. The ASE noise is loaded from an EDFA along with a variable optical attenuator (VOA). The VOA is used to adjust the OSNR value. At the receiver, the signal is detected by an optical coherent receiver (OCR) and converted to electrical baseband. The signal is then captured by a digital storage oscilloscope (DSO) at 80 G samples/s. The OSNR of the data series obtained is then analyzed by subsequent offline DSP.

Fig. 8. Block diagram of the experimental system; DP: dual-polarization; VOA: variable otpical attenuator; PCD: polarization scrambler ; WSP: waveshaper LO: local oscillator; OCR: optical coherent receiver.

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Figure 9(a) shows a one-hour estimation performance comparison of different CD estimation methods under polarization disturbance. No large error is observed for the new algorithm, whereas the old method (utilizing only one element of CAF matrix) has large error spikes. Figure 9(b) confirms the estimation accuracy versus different fiber lengths with polarization disturbance. Since the deployed fiber cable is of fixed length, several bundles of 20 km lab fiber are used to vary the total link length. Again, the new CD estimation is more stable and more accurate.

Fig. 9. (a) with PMD filed-test results of a 1-hour CD estimation results (b) with PMD conditions for CD estimation performance under different fiber length.

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Figure 10(a) shows the one-hour FO estimation based on the proposed method under polarization disturbance. Clearly, the method works stably over a long period and since it is a coarse estimation step, a finer step based on 4th power FFT tends to compensate for any residual FO (the lab laser has a decent frequency stability). Figure 10(b) shows the same one-hour test based on the SCF scheme with the same polarization disturbance after CD compensation. There are some large residual FO spikes and with little probability, the FO estimation failed completely.

Fig. 10. with CD and PMD filed-test results of a 1-hour FO estimation results (a) the proposed estimation scheme (b)SCF estimation scheme.

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Figure 11(a) shows the one-hour test of OSNR estimation with polarization disturbance. After CD compensation, the SCF method still generates a more fluctuated result. Figure 11(b) shows the estimation results without any CD compensation and polarization scrambling for different fiber lengths. The results confirm once again the robustness of the new OSNR estimation. Figure 12(a) shows the impact of FO on the OSNR estimation performance. It confirms that the FO estimation and compensation are critical for obtaining accurate OSNR estimates. This also validates the correctness of FO estimation. Figure 12(b) shows the BER calculation based on the two FO estimation schemes. The SCF method has chances for producing extreme BER due to FO estimation failure.

Fig. 11. (a) with CD and PMD filed-test results of a 1-hour OSNR estimation results (b) without Polarization disturbance different fiber length estimation results.

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Fig. 12. (a) OSNR monitoring performance with various FOC schemes (b) BER versus OSNR using the proposed scheme and SCF scheme with various FO settings.

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5. Conclusion

We study the impact of both CD and PMD on signal cyclostationarity. Based on the analysis result, we develop a multi-parameter (including CD, FO, and OSNR) estimation algorithm robust against the polarization effect. This is achieved by combining all elements of the CAF matrix to formulate a new normalized spectral correlation coefficient. It facilitates a high-performance CD and FO estimation via simple peak searching. An accurate OSNR estimation can be obtained after CD and FO estimation, prior to all equalization processes. Both numerical simulation and field cable experiment confirm the robustness and superiority of the proposed method compared to the state-of-the-art.

Funding

National Key Research and Development Program of China (2018YFB1801800); National Natural Science Foundation of China (62227819, U2001601); Science and Technology Planning Project of Guangdong Province (2020B0303040001).

Disclosures

The authors declare no conflicts of interest.

Data availability

All data included in this study are available upon request by contact with the corresponding author.

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Multi-parameter estimation resistant to the random polarization effect for coherent optical receivers

Abstract

1. Introduction

2. Operation principle

2.1 Cyclostationarity functions

2.2 Modeling CD and PMD effects

2.3 CD estimation

2.4 FO estimation

2.5 OSNR estimation

3. Numerical simulation

4. Experimental verification on DWDM system

5. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (12)

Equations (19)

Optics Express