Pilot-symbols-aided cycle slip mitigation for DP-16QAM optical communication systems

Haiquan Cheng; Yan Li; Fangzheng Zhang; Jian Wu; Jianxin Lu; Guoyi Zhang; Jian Xu; Jintong Lin

doi:10.1364/OE.21.022166

1. Introduction

In recent years, various carrier phase estimation (CPE) for coherent quadrature phase shift keying (QPSK) transmission systems have already been demonstrated to compensate for the laser and nonlinear phase noise in digital coherent receivers [1]. Multilevel modulation format, in particular 16-ary quadrature amplitude modulation (16-QAM), has gained a lot of interest for coherent optical transmission, which allows an improved bandwidth utilization of existing optical fiber. The major challenge of coherent 16-QAM transmission is the laser linewidth combined with phase noise tracking algorithm. Recently several blind CPE algorithms, such as blind-phase-search (BPS) and QPSK partitioning [2, 3], have been proposed and verified for 16-QAM system. However, these non-data aided (NDA) algorithms are vulnerable to the cycle slip (CS), which is an inherent property of NDA CPE without differential bit-encoding [4], especially at low optical signal-to-noise ratio (OSNR). CS can be caused by ASE, laser phase noise and nonlinear phase noise [5]. After a CS occurs, all detected symbols are erroneous and cannot be corrected by forward error correction (FEC) codes.

A common approach to deal with CS is to use differential encoding [5]. Differential encoding provides CS mitigation by turning the permanent phase errors into instantaneous ones but at the cost of additional OSNR penalties [6].To avoid the disadvantages produced by differential modulation format, pilot-symbols-based CPE with BPS for dual-polarization QPSK (DP-QPSK) has been proposed to prevent CS in [7]. In [5,6] and [8] a forward and backward (FWBW) method is used to detect the CS’s position and correct CS for DP-QPSK and dual-polarization 16-ary quadrature amplitude modulation (DP-16QAM) system, but it cannot detect and correct multiple CS in one pilot period [6], and it cannot work as expected when the phase changes severely within one pilot period due to large laser linewidth. Joint polarization carrier phase estimation (JP-CPE) has also been proposed to reduce the CS probability [8–10].

In this paper we propose a simple pilot-symbols-aided cycle slip mitigation scheme by pilot-symbols-aided phase unwrapping (PAPU). Simulations of a 10Gbaud DP-16QAM system demonstrate that this pilot-symbols-based CS mitigation scheme can significantly eliminate the performance degradation by CS maintaining a CS probability lower than 10⁻³. It can tolerate large laser linewidth up to 6 MHz with only 1.56% overhead and 15 dB OSNR, and achieve a bit-error-rate (BER) performance below soft-decision FEC limit 2 × 10⁻².

2. Pilot-symbols-aided cycle slip mitigation scheme

At the transmitter there are P-length pilot symbols with known data information as headers that are periodically inserted after D-length data payload symbols, with a frame length $L$ equals $P + D$ and a $P / (P + D)$ overhead in both orthogonal polarization tributaries. At the receiver, assuming all linear optical impairments have been completely compensated (as well as ideal timing recovery and synchronization as in [11]) the received symbols of x-polarization (y-polarization) $s_{x (y)} (k)$ can be described as a sequence of complex numbers with time index $k$ as in [10]:

s_{x (y)} (k) = c_{x (y)} (k) \cdot \exp (j θ_{x (y)} (k)) + n_{x (y)} (k)

where

c_{x (y)} (k)

is the complex-valued transmitted symbol at the k^-th time instant,

n_{x (y)} (k)

is the additive channel noise, and

θ_{x (y)} (k)

is the cumulated phase laser noise phase which is usually modeled as a Wiener process with variance

2 π Δ ν T

(

Δ ν

:combined linewidth of the transmitter and local oscillator laser,

T

: symbol duration). As mentioned in [12] an empirical model of using Wiener process for reproducing fiber nonlinearities has been experimentally verified at low signal-to-noise ratio. This suggests that we can put linear and nonlinear phase noise together in simulation with only the following two parameters: linewidth of the carrier and the signal-to-noise ratio.

Either blind or pilot-symbols-based methods can be used for CPE. Unlike the method in [7] we only use the QPSK partitioning to do CPE, and the estimated phase by pilot symbols is used as an absolute phase reference to do CS mitigation. Based on Eq. (2) the estimated carrier phase ${\hat{ϕ}}_{x (y)} (m)$ of x-polariztion (y-polarization) for the m^th frame at the headers can be obtained by correlating the received symbols with the known pilot sequences $d$ . It is necessary to interpolate ${\hat{ϕ}}_{x (y)} (m)$ to get the continuous phase reference $\hat{ϕ}'_{x (y)} (k)$

{\hat{ϕ}}_{x (y)} (m) = \arg (\sum_{i = 0}^{P - 1} d^{*} (m - i) \cdot s_{x (y)} (m - i))

where

d^{*}

denotes complex conjugation of the known pilot symbols in the k^th frame.

P

is the header length per frame. However, both the blind and pilot-symbols-based CPE can only estimate a range of phase, a phase unwrap operation is required to recover the phase wandering trajectory according to (3) and (4) assuming that the small phase noise steps are more likely than large ones [10].

{\hat{φ}}_{k, x (y)}^{u} = {\hat{φ}}_{k, x (y)}^{r} + r n g \cdot f ({\hat{φ}}_{k, x (y)}^{r} - {\hat{φ}}_{k - 1, x (y)}^{u})

f (z) = {\begin{matrix} + 1 \\ 0 \\ - 1 \end{matrix} \begin{matrix}  \end{matrix} \begin{matrix}  \end{matrix} \begin{matrix} (z < - \frac{r n g}{2}) \\ (| z | < \frac{r n g}{2}) \\ (z > \frac{r n g}{2}) \end{matrix}

where

{\hat{φ}}_{k, x (y)}^{r}

is the raw estimated phase right after the CPE,

{\hat{φ}}_{k - 1, x (y)}^{u}

is the reliable reference phase,

r n g

is the angle range of the CPE algorithm.

For non-data aided CPE CS is a persistent phenomenon. CS must be mitigated to prevent error propagation without differential coding [4,5]. As in [5,8] a forward and backward (FWBW) method is proposed to mitigate CS. Firstly a forward blind and pilot-symbols-based CPE is performed. A CS detector follows to detect the frame number by comparing the phase of blind CPE with the estimated phase by pilot symbols at header position. If the two phases differ by more than a predefined value i.e. pi/3 [5], somewhere in the previous frame is considered to be corrupted by CS. Then a backward CPE is performed to detect the exact position in the previous frame by comparing the forward and backward estimated phase. The CS position is where the forward and backward CPE converge. Then CS is mitigated by replacing carrier phase after the CS position with backward estimated carrier phase.

As indicated in [4,9] CS is generated by the nonlinear unwrap procedure at the low signal-to-noise ratios and high laser phase noise. We modify the usual phase unwrap procedure to make it immune to CS. The key point of the proposed CS mitigation scheme, as shown in Fig. 1(b), is the pilot-symbols-aided phase unwrapping (PAPU), which do CS detection and correction in a completely feed forward way and combine itself with the usual phase unwrapping. Without loss of generality, we use QPSK partitioning [3] as the CPE, and the PAPU is implemented as the following procedure.

Fig. 1 The QPSK partitioning based blind CPE with (a) usual phase unwrap, (b) pilot-symbols-aided CS mitigation scheme, and (c) the pilot-symbols-aided phase unwrapping (PAPU).

Download Full Size | PDF

At the start of the PAPU, as shown in Fig. 1(c), we get a reliable reference phase noted as ${\hat{θ}}_{k - 1, x (y)}^{u}$ , and the raw estimated phase ${\hat{θ}}_{k, x (y)}^{r}$ .Through comparing ${\hat{θ}}_{k, x (y)}^{r} - {\hat{θ}}_{k - 1, x (y)}^{u}$ with $\frac{π}{4}$ we get the usual unwrapped ${\hat{θ}}_{k, x (y)}^{u 0}$ according to (3) and (4). But ${\hat{θ}}_{k, x (y)}^{u 0}$ may also have experienced a CS. Actually we can know whether ${\hat{θ}}_{k, x (y)}^{u 0}$ has experienced an integer $\frac{π}{2}$ CS through directly comparing it with the interpolated phase $\hat{ϕ}'_{x (y)} (k)$ by pilot symbols and obtain a CS corrected phase ${\hat{θ}}_{k, x (y)}^{u}$ according to (5).

{\hat{θ}}_{k, x (y)}^{u} = {\hat{θ}}_{k, x (y)}^{u 0} - \frac{π}{2} \cdot r o u n d (\frac{3}{π} \cdot [{\hat{θ}}_{k, x (y)}^{u 0} - \hat{ϕ}'_{x (y)} (k)])

where

r o u n d

is a function to do round toward the nearest integers. According to our observations when CS happens there is a transition, we can set a threshold, e.g. pi/3 [5], to the round function corresponding to SNR to avoid the false CS fluctuation. The accuracy of this CS mitigation scheme depends on the accuracy of the interpolated carrier phase by pilot symbols. Then there is a trade-off between the accuracy and the overhead introduced by the pilot symbols. The advantage of the proposed scheme is that it does symbol-by-symbol CS mitigation and avoids the complex procedure to locate the CS position in FWBW. In addition we can refine the CPE with joint polarization as in [10] so we can expect JP-CPE with PAPU behaves a CS-free performance.

3. Simulation results and discussions

In order to investigate the performances of the proposed CS mitigation scheme, firstly a single polarization 10Gbaud 16-QAM simulation is performed with 2.4 MHz combined laser linewidth. We just select one pilot header per frame with 1.56% overhead similar to [5]. We choose to test the algorithm’s performance at around 16.5 dB, which is the required OSNR for 16-QAM at BER of 10⁻³ with an ideal additive channel noise [2]. 2¹⁶ symbols are used for each simulation. Figure 2 shows comparisons of the block averaging QPSK partitioning [3] with the usual phase unwrap, PAPU (as shown in Fig. 1(a) and 1(b)) and FWBW algorithm. We can see that the CS is completely mitigated by PAPU, and there are some residual cycle slips left with FWBW algorithm.

Fig. 2 Unwrapped and estimated phase by PAPU and FWBW

Download Full Size | PDF

The CPE averaging filter length, pilot-rate and OSNR strongly influence both the phase tracking capability and CS probability [6]. 30 independent simulations are performed to calculate the mean CS probability for each different configuration. Detection of CS follows the rule: if the absolute phase difference between the estimated phase and its actual phase is larger than a predefined threshold value, e.g. pi/2 [5], a sequence of CS is detected until the phase difference is smaller than the threshold. In order to investigate relationship between the accuracy of this CS mitigation scheme and the pilot-rate (as well as pilot arrangement), different frame structures with various pilot-rate for FWBW and PAPU are configured for simulations. For example 1/64 means one header with frame length 64. Figure 3 depicts the mean CS probability versus averaging filter length with various pilot-rate and pilot arrangement. We can see in Fig. 3(a) and 3(b) that PAPU and FWBW tends to use more evenly distributed pilot arrangement to obtain a lower CS probability. As shown in Fig. 3(c) and 3(d) increasing the overhead for a frame length 64 only reduces the mean CS probability slightly with 2.4 MHz linewidth and 17.5 dB OSNR. For simplicity only one header with frame length 64 is used in the following simulations.

Fig. 3 Mean CS probability versus averaging filter length with various pilot-rate and pilot arrangement,17.5 dB OSNR and 2.4 MHz combined laser linewidth by 30 independent simulations. (a-b) Mean CS probability versus averaging filter length with the same pilot-rate but different pilot arrangement for PAPUand FWBW; (c-d) Mean CS probability versus averaging filter length with different pilot-rate for PAPUand FWBW.The four subgraphs share the same coordinate and scale on the horizontal and vertical axis.

Download Full Size | PDF

Figure 4 depicts the mean CS probability versus averaging filter length and OSNR respectively for the usual phase wrap with CS, the CS mitigation by FWBW and PAPU. In [6] using the usual phase unwrapping longer filter length and higher OSNR leads to lower CS probability in Fig. 4, but our results further show that even with optimized filter length CS probability cannot be zero with combined linewidth up to 2.4 MHz. CS mitigation by FWBW can effectively eliminate CS especially at higher OSNR(17.5 dB). The proposed PAPU can mitigate CS and maintain a low CS probability as low as 10-3 at OSNR larger than 16.5dB, and less influenced by filter length than the FWBW. In real optical transmission system, it is difficult to find an optimum filter length for the CPE due to the varying OSNR and laser phase noise [3], and our PAPU algorithm with CPE can maintain a lower CS probability for a larger range of filter length.

Fig. 4 Mean CS probability versus averaging filter length with the usual phase wrap with CS, the CS mitigation by FWBW and PAPU. 30 independent simulations is performed with 16 dB, 16.5 dB and 17.5 dB OSNR and 2.4 MHz combined laser linewidth.

Download Full Size | PDF

Secondly we perform a polarization-multiplexed 10Gbaud 16-QAM simulation (the simulation results for single polarization are calculated from one polarization of the polarization-multiplexed signal) to show the BER performance versus different OSNR with 3.2MHz combined laser linewidth in Fig. 5. In addition, signals from both polarizations are impaired by identical laser phase noise, phase information from both polarizations is jointly processed for better CPE accuracy [3] and the joint polarization CPE used is similar to the method in [10]. FWBW/PAPU mitigating approaches with block averaging QPSK partitioning CPE of single/joint polarization, and differential coding [2] are simulated with their optimized filter length. Differential coding is implemented on the most significant two bits of one symbol with a rotationally invariant bits-to-symbol mapping as in [2]. The BER performance of single polarization CPE with differential coding is too large for OSNR lower than 16.5 dB and the results are not shown in Fig. 5. It can be seen that single or joint polarization with PAPU achieves a better BER performance compared with FWBW and differential coding especially at low OSNR. Joint polarization CPE with FWBW even show worse BER than single polarization CPE with PAPU at OSNR lower than 15.5 dB.

Fig. 5 BER versus different OSNR for single/joint polarization and differential coding CPE with FWBW/PAPU CS mitigation, the simulated OSNR is from 14.5 dB to 19 dB with 0.5 dB spacing, and the combined laser linewidth is 3.2MHz.

Download Full Size | PDF

Figure 6 shows the required OSNR versus different combined laser linewidth for single/joint polarization and differential coding CPE and two CS mitigating methods. From Fig. 6 we can see that single/joint polarization CPE with PAPU always requires lower OSNR than with FWBW and differential coding at the soft-FEC limit of 2 × 10⁻² [8]. Similar to case with Fig. 5 the required OSNR for joint polarization CPE with FWBW is larger than single polarization CPE with PAPU for linewidth larger than 3.2 MHz. Joint polarization CPE with PAPU can tolerate large laser linewidth up to 6 MHz with OSNR lower than 15 dB, which is about 1dB lower than the case with FWBW.

Fig. 6 Required OSNR versus different combined laser linewidth for single/joint polarization and differential coding CPE with FWBW/PAPU CS mitigation, The combined linewidth of the transmitter laser and local oscillator are 0 MHz, 0.6 MHz, 1.4 MHz, 2.4 MHz, 3.2 MHz, 4 MHz, 5 MHz, and 6 MHz.

Download Full Size | PDF

4. Conclusions

We have proposed and demonstrated a pilot-symbols-aided cycle slip mitigation scheme though a simple pilot-symbols-aided phase unwrapping (PAPU) algorithm. Simulation results show that this scheme enables coherent DP-16QAM system with 6 MHz linewidth tolerance and OSNR lower than 15 dB under soft decision FEC without differential coding. In addition other CPE method can work with this simple PAPU algorithm to reduce the CS probability.

Acknowledgments

This work was partly supported by 863 program 2013AA014202, 2012AA011303, 2012AA050801, NSFC program 61001121, 60932004, 61006041, 61205031, 973 program 2011CB301702, the Fundamental Research Funds for the Central Universities and Fund of State Key Laboratory of IPOC (BUPT), P. R. China.

References and links

1. Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1201–1209 (2010). [CrossRef]

2. T. Pfau, S. Hoffmann, and R. Noé, “Hardware-effcient coherent digital receiver concept with feed forward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(8), 989–999 (2009). [CrossRef]

3. Y. Gao, A. P. T. Lau, S. Yan, and C. Lu, “Low-complexity and phase noise tolerant carrier phase estimation for dual-polarization 16-QAM systems,” Opt. Express 19(22), 21717–21729 (2011). [CrossRef] [PubMed]

4. E. Ip and J. M. Kahn, “Addendum to ‘Feedforward Carrier Recovery for Coherent Optical Communications’,” J. Lightwave Technol. 27(13), 2552–2553 (2009). [CrossRef]

5. H. Zhang, Y. Cai, D. G. Foursa, and A. N. Pilipetskii, “Cycle Slip Mitigation in POLMUX-QPSK Modulation,” in Optical Fiber Communication Conference and Exposition (OFC/NFOEC), Los Angeles, CA, 2011, OMJ7.

6. C. R. S. Fludger, D. Nuss, and T. Kupfer, “Cycle-slips in 100G DP-QPSK transmission systems,” in Optical Fiber Communication Conference and Exposition (OFC/NFOEC), Los Angeles, CA, 2012, OTu2G.1.

7. M. Magarini, L. Barletta, A. Spalvieri, F. Vacondio, T. Pfau, M. Pepe, M. Bertolini, and G. Gavioli, “Pilot-symbols-aided carrier-phase recovery for 100-G PM-QPSK digital coherent receivers,” IEEE Photon. Technol. Lett. 24(9), 739–741 (2012). [CrossRef]

8. Y. Gao, A. P. T. Lau, and C. Lu, “Cycle-slip resilient carrier phase estimation for polarization multiplexed 16-QAM systems,” in Opto-Electronics and Communications Conference (OECC), Busan, 2012, 4B2–4 [CrossRef]

9. A. Bisplinghoff, C. Vogel, T. Kupfer, S. Langenbach, and B. Schmauss, “Slip-reduced carrier phase estimation for coherent transmission in the presence of non-linear phase noise,” in Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC) Anaheim, CA 2013, OTu3I.1. [CrossRef]

10. Fangrong Peng, “Phase Noise Estimation for Coherent Fiber-Optic Communication,” Master’s thesis, Chalmers Univ. of Technology, Gothenburg, Sweden, (2010).

11. X. Zhou, X. Chen, and K. P. Long, “Wide-range frequency offset estimation algorithm for optical coherent systems using training sequence,” IEEE Photon. Technol. Lett. 24(1), 82–84 (2012). [CrossRef]

12. M. Magarini, A. Spalvieri, F. Vacondio, M. Bertolini, M. Pepe, and G. Gavioli, “Empirical modeling and simulation of phase noise in long-haul coherent optical transmission systems,” Opt. Express 19(23), 22455–22461 (2011). [CrossRef] [PubMed]

Pilot-symbols-aided cycle slip mitigation for DP-16QAM optical communication systems

Abstract

1. Introduction

2. Pilot-symbols-aided cycle slip mitigation scheme

3. Simulation results and discussions

4. Conclusions

Acknowledgments

References and links

Cited By

Figures (6)

Equations (5)

Optics Express