Channel estimation and synchronization for polarization-division multiplexed CO-OFDM using subcarrier/polarization interleaved training symbols

Chun Ju Youn; Xiang Liu; S. Chandrasekhar; Yong-Hwan Kwon; Jong-Hoi Kim; Joong-Seon Choe; Duk-Jun Kim; Kwang-Seong Choi; Eun Soo Nam

doi:10.1364/OE.19.016174

1. Introduction

Coherent optical orthogonal frequency-division multiplexing (CO-OFDM) is a promising technology for high speed optical communication systems since it offers high spectral efficiency and high tolerance to chromatic dispersion and polarization mode dispersion [1, 2]. Using polarization division multiplexing (PDM), the transmission rate of CO-OFDM system can be readily doubled by allocating different data to two orthogonal polarization components of the signal. As a result, PDM CO-OFDM has actively been investigated for applications in future high-speed optical transport systems.

In OFDM, channel estimation and synchronization, including synchronization in time and frequency, are important and essential digital signal processing (DSP) processes [3,4]. In PDM CO-OFDM, the channel can be especially considered as a 2 × 2 multiple-input multiple-output (MIMO) system, and the goal of channel estimation is to find the 2 × 2 inverse channel matrix for each signal frequency component. For PDM CO-OFDM, time-interleaved single-polarization training symbols (TSs) [5] and correlated dual-polarization (CDP) TSs [6] have been proposed for DSP-efficient channel estimation. The use of CDP TSs makes the average power of the TSs equal to that of the payload symbols, thereby offering an additional benefit of reduced cross-phase modulation (XPM) penalty to other wavelength channels [6,7]. We recently proposed a novel channel estimation and synchronization scheme based on subcarrier/polarization-interleaved dual-polarization (SI-DP) TSs [8].

In this paper, we describe in detail the concept of SI-DP TSs, which offers doubled tolerance to the frequency offset between the transmit laser and the optical local oscillator (OLO) as compared to the previous methods reported in Refs. 5 and 6, while attaining the same high computational efficiency. The proposed method also allows the TS power to be equal to the average payload symbol power for reduced XPM penalty as reported in CDP TSs [6, 7]. We experimentally confirm the doubled frequency-offset tolerance of the proposed method in 43-Gb/s PDM CO-OFDM transmission over 5,200-km of ultra-large-area fiber (ULAF).

2. Principle

PDM CO-OFDM systems require the synchronization in time and frequency to find the OFDM frame boundaries and the frequency offset between the transmit laser and the receiver’s OLO. In addition, channel estimation is required to obtain the channel response, which is the basis for channel compensation, compensating for transmission impairments such as chromatic dispersion (CD), polarization rotation, and polarization-mode dispersion (PMD). We propose to use three SI-DP TSs, t₁, t₂, and t₃, for synchronization and channel estimation [8]:

[\begin{array}{l} t_{1 x} t_{2 x} ​ t_{3 x} \\ t_{1 y} t_{2 y} t_{3 y} \end{array}] = [\begin{array}{l} E O E \\ E E O \end{array}]

where subscript x and y denote the x and y polarization components of the signal to be transmitted, respectively, and E (O) is a symmetric (anti-symmetric) symbol whose even (odd) subcarriers are modulated with known pseudo-random bit sequences (PRBS) while the odd (even) subcarriers are unfilled or have zero power. The amplitude of the filled subcarriers of E and O are scaled up by 2 in order for the average power of each SI-DP TS to be the same as that of the payload symbols.

Figure 1(a) shows the structure of the subcarrier allocation using CDP-TSs [6] in PDM CO-OFDM. The channel estimation and synchronization method based on CDP-TSs can give substantial improvement in the signal tolerance to WDM nonlinear effects, such as inter-channel cross-phase modulation (XPM), since the mean power of the CDP-TSs is the same as that of the payload symbols [7, 9]. In the CDP-TSs, the autocorrelation with one symbol delay can be used for the frame synchronization and frequency offset estimation since the first and second DP TSs are the identical patterns. In addition, the normalized frequency offset (ε) can be estimated by [3, 8]

ε = \frac{f_{o f f s e t}}{Δ f_{s c}} = \frac{1}{2 π} \arg [\sum_{n = 0}^{N - 1} r * (n) r (n + N)]

where f_offset and

Δ f_{s c}

denote the frequency offset and subcarrier spacing, respectively, N is the number of fast Fourier transform (FFT) points used, and r(n) and r*(n) is the n-th received time sample and its complex conjugate, respectively. The phase difference between the received time samples

r (n)

and

r (n + N)

caused by a frequency offset is equal to

2 π ε

, as shown in Eq. (2). The frequency-offset tolerance of CDP-TSs is

\pm 0.5 Δ f_{s c}

because the output of the function arg[] in Eq. (2) ranges from

- π

to π. Note that the subcarrier spacing

Δ f_{s c}

equals R_s/N, where R_s is the sampling rate. Figure 1(b) shows the structure of the subcarrier allocation using the proposed SI-DP TSs in PDM CO-OFDM. The SI-DP TS based method can also provide the reduced WDM nonlinear effects since there is no difference between the average power of the TSs and that of the payload symbols. The first TS consists of identical E symbols in both x- and y-polarization states. The first and second halves of the first TS E are identical since only even subcarriers of the E symbol are modulated [3]. Thus, the autocorrelation of the first TS with ½-symbol delay results in a maximum that can be used for frame synchronization. In addition, the phase difference between the received time samples

r (n)

and

r (n + N / 2)

caused by frequency offset is equal to

π ε

. Thus, the frequency offset estimation can be performed based on the autocorrelation function with N/2 samples instead of N samples in Eq. (2), and the normalized frequency offset can be estimated by

Fig. 1 Illustration of PDM CO-OFDM subcarriers allocation. (a) The previous synchronization and channel estimation method using CDP-TSs. A is symbol with all subcarriers filled. (b) The proposed synchronization and channel estimation method using SI-DP TSs. (t₁, t₂, t₃) are training symbols, and d_n is n-th payload symbol. E(O) is a symbol whose even (odd) subcarriers are filled.

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ε = \frac{1}{π} \arg [\sum_{n = 0}^{N / 2 - 1} r * (n) r (n + N / 2)]

This results in a frequency-offset tolerance of $\pm Δ f_{s c}$ , which is twice as large as that in the case of one-symbol-delay based autocorrelation [5, 6]. We will experimentally confirm this in the next section. Note that one can further increase the frequency-offset tolerance by using TSs with even shorter periodicity. For example, the quadrupled frequency-offset tolerance can be obtained by using a TS consisting of four identical patterns. However, the accuracy of the frequency offset estimation using shorter TS would be reduced in the presence of noise, so TS with sufficient length, e.g., larger than 32, would be preferred.

The 2^nd and 3^rd SI-DP TSs are subcarrier/polarization interleaved symbols. This facilitates the decomposition of the 2×2 Jones matrix, [a(k) b(k); c(k) d(k)] as follows.

[\begin{array}{l} a (k) b (k) \\ c (k) d (k) \end{array}] = {\begin{matrix} [\begin{array}{l} r_{2 x} (k) / O (k) r_{3 x} (k) / O (k) \\ r_{2 y} (k) / O (k) r_{3 y} (k) / O (k) \end{array}] if k = k_{o d d}, \\ [\begin{array}{l} r_{3 x} (k) / E (k) r_{2 x} (k) / E (k) \\ r_{3 y} (k) / E (k) r_{2 y} (k) / E (k) \end{array}] if k = k_{e v e n} \end{matrix}

where r₂ and r₃ are the received training symbols, x and y denotes the x- and y-polarizations defined at the receiver, and k_odd and k_even are respectively the indices for the modulated odd and even subcarriers in the two SI-DP TSs defined in Eq. (1). As can be seen in Eq. (4), each channel matrix coefficient for a given subcarrier is efficiently obtained through a single complex division. The previous channel estimation methods such as those reported in Refs. 5 and 6 also require a single complex division per subcarrier. Thus, the required computational complexity of the channel estimation using two SI-DP TSs is essentially the same as those reported in Refs. 5 and 6.

3. Experimental Setup

Figure 2 shows the schematic of the experimental setup used to evaluate the transmission performance of PDM CO-OFDM signals using the proposed channel estimation method. At the transmitter, offline digital signal processing (DSP) was performed to generate the OFDM baseband signals, which were stored in a 10-GS/s arbitrary waveform generator (AWG). A transmitted data stream consisting of a PRBS of length 2¹⁵-1 was mapped onto 72 subcarriers with 16-QAM modulation, together with 8 pilot subcarriers, one unfilled DC subcarrier, and 47 unfilled edge subcarriers. The time domain signal was generated through an inverse fast Fourier transform (IFFT) operation of size 128, and a small guard interval (GI) of length 4 was inserted, resulting in an OFDM symbol size of 132. Four training symbols, [E E O E] were inserted at the beginning of each OFDM frame. After a PDM emulator with one symbol delay between the two polarizations, three SI-DP TSs as described earlier were obtained for frame synchronization, frequency offset estimation, and channel estimation. Each OFDM frame consisted of the four TSs and 300 OFDM payload symbols, as shown in inset (b) of Fig. 2. The real and imaginary parts of the OFDM time waveform were amplified and used to drive an optical I/Q modulator whose sub-Mach-Zehnders were biased at the transmission null. An external-cavity laser (ECL) with 100-kHz linewidth was used as transmit laser at 1550 nm. The data rate and subcarrier spacing of the PDM CO-OFDM signal were 43 Gb/s (=10GS/s*8*72/132*300/304) and 78.1 MHz (=10 GHz/128), respectively. The optical bandwidth of the 43-Gb/s signal was only 6.3 GHz. The signal was launched into a recirculating loop [10]. It consisted of four Raman-amplified 100-km spans of ULAF. The fiber loss, dispersion, and effective area were 0.185 dB/km, 19.9 ps/nm/km, and 120 μm², respectively. The loop contained a 50-GHz-grid wavelength-selective-switch (WSS) and an acousto-optic switch (SW) that shifted the optical signal frequency by 25 MHz every round trip, which allowed us to accurately assess the frequency-offset tolerance of the PDM CO-OFDM system. Another SW with a 25-MHz frequency shift was used before the signal entered the loop.

Fig. 2 Experimental setup of a 43-Gb/s PDM-OFDM-16QAM system using the proposed channel estimation and synchronization method. Insets: (a) Offline digital signal processing at the transmitter; (b) OFDM frame structure; and (c) Offline digital signal processing at the receiver. AWG: arbitrary waveform generator. PBC: polarization beam combiner. OC: optical coupler. SW: acousto-optic switch.

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At the receiver, the 43-Gb/s PDM CO-OFDM signal was detected by a digital coherent receiver consisting of a 2x8 polarization-diversity optical hybrid, four balanced detectors, and four 50-GS/s analog-to-digital converters (ADCs) which were embedded in a real-time digital oscilloscope. The detected and digitized waveforms were processed offline, as shown in the inset (c) of Fig. 2. Compensation of chromatic dispersion and self-phase modulation (SPM) were performed using a multi-step FFT-based algorithm [11, 12]. Frame synchronization, frequency offset estimation, and channel estimation were accomplished by the proposed method using the SI-DP TSs. The data subcarriers were recovered through channel and phase compensation after the FFT. The bit error ratio (BER) was obtained by direct error counting.

4. Experimental results

Figure 3 shows the measured timing metrics of the x- and y-polarization components of the PDM CO-OFDM signal, defined as

Fig. 3 Measured timing metric using the proposed synchronization method. (a) X-polarization components,(b) Y-polarization components, (c) PDM components

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M_{x (y)} (d) = {| \sum_{n = 0}^{N / 2 - 1} r_{x (y)}^{*} (d + n) r_{x (y)} (d + n + N / 2) |}^{2} / {| \sum_{n = 0}^{N / 2 - 1} r_{x (y)}^{*} (d + n) r_{x (y)} (d + n) |}^{2}

The measured timing metric of each polarization component shows four peaks, as shown in Fig. 3(a) and (b). This is because the E and O symbols are symmetric and anti-symmetric about their symbol centers, respectively, and produce maximum autocorrelation when the sample index d coincides with the starting position of these symbols. We introduce a joint timing metric for the PDM CO-OFDM signal as

M_{x + y} (d) = \frac{{| \sum_{n = 0}^{N / 2 - 1} r_{x}^{*} (d + n) r_{x} (d + n + N / 2) + \sum_{n = 0}^{N / 2 - 1} r_{y}^{*} (d + n) r_{y} (d + n + N / 2) |}^{2}}{{| \sum_{n = 0}^{N / 2 - 1} r_{x}^{*} (d + n) r_{x} (d + n) + \sum_{n = 0}^{N / 2 - 1} r_{y}^{*} (d + n) r_{y} (d + n) |}^{2}}

Figure 3(c) shows the joint timing metric, which shows a single distinct main peak that can be used for accurate and reliable frame synchronization. Note that the two side peaks in Fig. 3(c) are due to the use of the PDM emulator which causes a leftover E symbol in each polarization. These side peaks are much weaker than the main peak, so they will not affect the accuracy of the synchronization. Note also that in real PDM systems where only three DP symbols, as defined in Eq. (1), are used, there will be no such side peaks.

Figure 4 shows the subcarrier index correction needed at the OFDM receiver to correctly recover the OFDM subcarriers versus frequency offset. Increasing the subcarrier index by 1 leads to an effective signal frequency shift of one subcarrier spacing, which is 78.1 MHz in this experiment. The frequency offset can increase by 25 MHz every round trip due to an acousto-optic switch (SW) within the loop, and is easily compensated with the help of the subcarrier index correction at the receiver. The frequency-offset tolerance can be seen from the frequency range over which the subcarrier index correction is unchanged. Evidently, the frequency-offset tolerance of the proposed method is about ±78 MHz (or ±Δf_SC), which is twice as large as that of the previous methods [5, 6].

Fig. 4 Subcarrier index correction versus frequency offset using (a) The previous methods^{5, 6} and(b) The proposed method.

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Figure 5(a) shows the Q² factor, derived from the measured BER, as a function of the signal launch power after 3200-km transmission. Without nonlinearity compensation (NLC), the optimum launch power and the Q² factor were around −9 dBm and ~8.5 dB, respectively. With the use of multi-step NLC [11–13], the optimum signal launch power was significantly increased by 6 dB to −3 dBm, and the Q² factor was increased by 1.6 dB to 10.1 dB. The multi-steps NLC was performed at the receiver and the number of steps used was the same as the number of the transmission spans. The inter-polarization cross phase modulation (XPM) was taken into consideration by using an inter-polarization XPM factor of 1 [13]. Note that the optimum signal launch power decreases slightly with the increase of the transmission distance. Figure 5(b) shows the Q² factor as a function of the transmission distance when the signal launch power is fixed at −6 dBm. The Q² factor values shown in Fig. 5 were obtained by averaging over two polarization components of the signal, which performed very similarly. Without NLC, the BER of the 43-Gb/s PDM CO-OFDM signal after 2,400-km transmission is below 3.8x10⁻³, the threshold of enhanced hard-decision forward-error correction with 7% overhead [14]. With the use of multi-step NLC, the BER of the 43-Gb/s signal is below 3.8x10⁻³ after 5,200-km transmission, more than doubling the transmission distance achieved without using NLC.

Fig. 5 (a) Measured Q² factor as a function of signal launch power after 3,200-km transmission; (b) Measured Q² factor as a function of the transmission distance with the signal launch power fixed at −6 dBm.

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5. Conclusions

We have presented a novel channel estimation and frame synchronization method for PDM CO-OFDM by using subcarrier/polarization interleaved training symbols. This new method provides high tolerance to the frequency offset between the transmit laser and the receiver’s OLO and high computational efficiency in obtaining the 2×2 frequency-dependent optical channel matrix. We further experimentally confirmed its doubled frequency-offset tolerance over previously reported methods in long-haul 43-Gb/s PDM CO-OFDM transmission over 5,200-km of ULAF.

Acknowledgments

The authors wish to thank B. Zhu and D. W. Peckham of OFS labs for providing the ULAF used in this experiment. This work was partially supported by the IT R&D Program of MKE/KEIT (KI002037, coherent optical OFDM technologies for next generation optical transport networks), Republic of Korea.

References and links

1. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-2-841. [CrossRef] [PubMed]

2. S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “121.9-Gb/s PDM-OFDM Transmission With 2-b/s/Hz Spectral Efficiency Over 1000 km of SSMF,” J. Lightwave Technol. 27(3), 177–188 (2009). [CrossRef]

3. T. M. Schmidl and D. C. Cox, “Robust Frequency and Timing Synchronization for OFDM,” IEEE Trans. Wirel. Comm. 45(12), 1613–1621 (1997).

4. X. Hu, Y. Huang, and Z. Hong, “Residual Synchronization Error Elimination in OFDM Baseband Receivers,” ETRI J. 29(5), 596–606 (2007). [CrossRef]

5. S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “Long-haul transmission of 16 x 52.5 Gbits/s polarization-divisionmultiplexed OFDM enabled by MIMO processing (Invited),” J. Opt. Netw. 7(2), 173–182 (2008). [CrossRef]

6. X. Liu and F. Buchali, “A Novel Channel Estimation Method for PDM-OFDM Enabling Improved Tolerance to WDM Nonlinearity,” in Proc. Optical Fiber Commun. Conf. (OFC) 2009, Paper OWW5, http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2009-OWW5.

7. X. Liu, F. Buchali, and W. Robert, “Tkach, “Improving the Nonlinear Tolerance of Polarization-Division-Multiplexed CO-OFDM in Long-Haul Fiber Transmission,” J. Lightwave Technol. 27(16), 3632–3640 (2009). [CrossRef]

8. C. J. Youn, X. Liu, S. Chandrasekhar, Y.-H. Kwon, J.-H. Kim, J.-S. Choe, K.-S. Choi, and E. S. Nam, “An Efficient and Frequency-Offset-Tolerant Channel Estimation and Synchronization Method for PDM CO-OFDM Transmission,” in Proc. European Conf. Optical Commun. 2010, Paper P4.06.

9. S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, “Coherent Optical 25.8-Gb/s OFDM Transmission Over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008). [CrossRef]

10. S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of a 1.2-Tb/s 24-Carrier No-Guard-Interval Coherent OFDM Superchannel over 7200-km of Ultra-Large-Area Fiber,” in Proc. European Conf. Optical Commun. 2009, post-deadline paper PD2.6.

11. D. S. Millar, S. Makovejs, V. Mikhailov, R. I. Killey, P. Bayvel, and S. J. Savory, “Experimental Comparison of Nonlinear Compensation in Long-Haul PDM-QPSK Transmission at 42.7 and 85.4 Gb/s,” in Proc. European Conf. Optical Commun. 2009, Paper 9.4.4.

12. X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “Transmission of a 448-Gb/s Reduced-Guard-Interval CO-OFDM Signal with a 60-GHz Optical Bandwidth over 2000 km of ULAF and Five 80-GHz-Grid ROADMs,” in Proc. Optical Fiber Commun. Conf. (OFC) 2010, post-deadline paper PDPC2. http://www.opticsinfobase.org/abstract.cfm?URI=NFOEC-2010-PDPC2

13. X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “448-Gb/s Reduced-Guard-Interval CO-OFDM Transmission Over 2000 km of Ultra-Large-Area Fiber and Five 80-GHz-Grid ROADMs,” J. Lightwave Technol. 29(4), 483–490 (2011). [CrossRef]

14. ITU-T Recommendation G.975.1, 2004, Appendix I.9.

Channel estimation and synchronization for polarization-division multiplexed CO-OFDM using subcarrier/polarization interleaved training symbols

Abstract

1. Introduction

2. Principle

3. Experimental Setup

4. Experimental results

5. Conclusions

Acknowledgments

References and links

Cited By

Figures (5)

Equations (6)

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