Intra-symbol frequency-domain averaging based ... - OSA Publishing

Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM Xiang Liu1* and Fred Buchali2 1

Bell Laboratories, Alcatel-Lucent, 791 Holmdel-Keyport Road, Holmdel, New Jersey 07733, USA 2 Bell Laboratories, Alcatel-Lucent, 70499 Stuttgart, Germany * Corresponding Author: [email protected]

Abstract: We present an efficient channel estimation method for coherent optical OFDM (CO-OFDM) based on intra-symbol frequency-domain averaging (ISFA), and systematically study its robustness against transmission impairments such as optical noise, chromatic dispersion (CD), polarization-mode dispersion (PMD), polarization-dependent loss (PDL), and fiber nonlinearity. Numerical simulations are performed for a 112-Gb/s polarization-division multiplexed (PDM) CO-OFDM signal, and the ISFAbased channel estimation and the subsequent channel compensation are found to be highly robust against these transmission impairments in typical optical transport systems. ©2008 Optical Society of America OCIS codes: (060.1660) Coherent communications; (060.5060) Phase modulation; (060.2330) Fiber optics communication.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

See, for example, IEEE standards 802.11a, 802.11g, and 802.16. A. J. Lowery, L. Du, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” OFC’06, post-deadline paper PDP39. W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42, 587-589 (2006). I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express 14, 3767–3775 (2006). S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka; “20-Gb/s OFDM transmission over 4,160-km SSMF enabled by RF-Pilot tone phase noise compensation,” OFC’07, post-deadline paper PDP15. W. Shieh, H. Bao, and Y. Tang, "Coherent optical OFDM: theory and design," Opt. Express 16, 841-859 (2008). A. J. Lowery, "Amplified-spontaneous noise limit of optical OFDM lightwave systems," Opt. Express 16, 860-865 (2008). S. L. Jansen, I. Morita, T. C. Schenk, and H. Tanaka, "Long-haul transmission of 16×52.5 Gbits/s polarization-division- multiplexed OFDM enabled by MIMO processing (Invited)," J. Opt. Netw. 7, 173182 (2008). W. Shieh, X. Yi, Y. Ma, and Q. Yang, "Coherent optical OFDM: has its time come? [Invited]," J. Opt. Netw. 7, 234-255 (2008). E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, "Coherent detection in optical fiber systems," Opt. Express 16, 753-791 (2008). S. J. Savory, "Digital filters for coherent optical receivers," Opt. Express 16, 804-817 (2008). H. Sun, K. Wu, and K. Roberts, "Real-time measurements of a 40 Gb/s coherent system," Opt. Express 16, 873-879 (2008) X. Liu and F. Buchali, “Improved nonlinear tolerance of 112-Gb/s PDM-OFDM in dispersionuncompensated transmission with efficient channel estimation,” ECOC’08, paper Mo.3.E.2. Q. Yang, N. Kaneda, X. Liu, and W. Shieh, “Demonstration of frequency-domain averaging based channel estimation for 40-Gb/s CO-OFDM with high PMD,” OFC’09, paper OWM6. M. Shtaif, “Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss,” Opt. Express 16, 13918-13932 (2008). A. Mecozzi and M. Shtaif, “Signal-to-noise-ratio degradation caused by polarization-dependent loss and the effect of dynamic gain equalization,” J. Lightwave Technol. 22, 1856 - 1871 (2004). W. Shieh, "PMD-supported coherent optical OFDM systems," IEEE Photon. Technol. Lett. 19, 134-136 (2007). A. J. Lowery, S. Wang, and M. Premaratne, "Calculation of power limit due to fiber nonlinearity in optical OFDM systems," Opt. Express 15, 13282-13287 (2007).

#101682 - $15.00 USD Received 16 Sep 2008; revised 14 Nov 2008; accepted 15 Dec 2008; published 18 Dec 2008

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19. M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, and I. Shpantzer, "The FWM impairment in coherent OFDM compounds on a phased-array basis over dispersive multi-span links," in Coherent Optical Technologies and Applications, (Optical Society of America, 2008), paper CWA4. 20. K. Forozesh, S. L. Jansen, S. Randel, I. Morita, and H. Tanaka, “The influence of the dispersion map in coherent optical OFDM transmission systems,” in Coherent Optical Communications Systems, (IEEE LEOS Summer Topic Meetings, 2008), paper WC2.4. 21. J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communications systems using linear amplifiers,” Opt. Lett. 15, 1351–1353 (1990). 22. R.-J. Essiambre and P J Winzer, “Fibre nonlinearities in electronically pre-distorted transmission,” ECOC’05, paper Tu3.2.2.

1. Introduction Orthogonal frequency-division multiplexing (OFDM) is a widely used modulation/multiplexing technology in wireless and data communications [1]. With recent advances in high-speed CMOS technologies and optical modulation and detection technologies, optical OFDM at 40-Gb/s or even 100-Gb/s information rate becomes feasible [2-9]. Together with digital coherent detection, coherent optical OFDM (CO-OFDM) brings similar benefits such as high spectral efficiency and high receiver sensitivity as coherent single-carrier transmission [10-12]. A key feature of CO-OFDM is its capability to insert training symbols (TS’s) at the transmitter to facilitate channel estimation, which provides crucial information about the transmission channel and enables efficient digital compensation of optical transmission impairments such as chromatic dispersion (CD) and polarization-mode dispersion (PMD). In optical transmission, the accuracy of channel estimation is often limited by the presence of optical noise. To increase the accuracy of channel estimation, a timedomain averaging method that averages the channel matrices estimated by multiple TS’s for each frequency subcarrier was used [5,6,8]. Recently, we proposed the use of an intra-symbol frequency-domain averaging (ISFA) based method [13] where the averaging is over the estimated channel matrices for multiple adjacent frequency subcarriers in the same TS. This method offers the benefits of overhead reduction and reaction speed improvement. In this paper, we systematically study the robustness of the ISFA-based channel estimation against transmission impairments such as optical noise, CD, PMD, polarization-dependent loss (PDL), and fiber nonlinearity. This paper is organized as follows. In Section 2, we describe the architecture of a 112Gb/s polarization-division multiplexed (PDM) CO-OFDM system. Section 3 presents the concept of the ISFA-based channel estimation method and its performance in optical noise limited transmission. Section 4 discusses the impact of CD on the channel estimation. Section 5 shows the robustness of the channel estimation against PMD and the performance of digital PMD compensation. Section 6 discusses the impact of PDL, without and with PMD. Section 7 investigates the impact of fiber nonlinearity. Section 8 concludes this paper. 2. Architecture of a 112-Gb/s PDM CO-OFDM system Figure 1 shows the schematic of a 112-Gb/s PDM CO-OFDM transmitter and receiver setup [13]. The original 112-Gb/s data were first divided into x- and y-polarization branches, each of which was mapped onto 1280 frequency subcarriers with QPSK modulation, which, together with 16 pilot subcarriers, were transferred to the time domain by an IFFT of size 2048 with a filling ratio of ~63%. A cyclic prefix of length 512 was used to accommodate dispersion of up to ~20,000 ps/nm, resulting in an OFDM symbol size of 2560 time samples. The time-domain samples were then serialized and converted by two 56-GS/s DACs before driving two I/Q modulators. The modulated optical signals were combined by a polarization beam splitter (PBS) for polarization multiplexing. TS’s were inserted periodically into the OFDM symbol sequence after every 20 payload symbols. At the receiver, digital coherent detection with polarization diversity was used to sample the fields of two orthogonal components of the received optical signal. Symbol synchronization was then performed, and TS’s were extracted for channel estimation for each frequency subcarrier. To increase the accuracy of channel estimation in the presence of noise, previous authors [5,6,8] used a time-


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domain averaging algorithm that averages over multiple TS’s. Here, we used the intra-symbol frequency-domain averaging (ISFA) based method briefly described in [13] where the averaging was over the estimated channel matrices for multiple adjacent subcarriers in the same TS. ISFA offers the benefits of overhead reduction and reaction speed improvement. To save computational efforts, the channel estimation process can update the channel information at a speed that is much slower than the real-time data speed, but much faster than the speed of channel physical changes, which is usually in the order kilohertz. Other signal processing needed to recover the original data was similar to that described in [5,6,8]. Detailed descriptions of the channel estimation and compensation methods will be given in the following section. Figure 2 shows the allocations of the OFDM data subcarriers and pilot subcarriers. 16 pilot subcarriers were uniformly distributed among the data subcarriers. Table 1 summarizes key OFDM design parameters. A clipping ratio of 6 was chosen so that in DAC and ADC, the samples whose powers were more than 6 times of the mean signal power were clipped to 6 times the mean power.

Fig. 1. Schematic of a 112-Gb/s PDM CO-OFDM system architecture. PMDC: PMD compensation. EDC: electronic dispersion compensation. PA-CPEC: pilot-assisted common phase error compensation. DAC: digital-to-analog converter. ADC: analog-to-digital converter, PBS: polarization beam splitter.

Fig. 2. Allocations of the OFDM data subcarriers and pilot subcarriers.


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Table 1. OFDM design parameters used in this study. FFT/IFFT length (Nfft) 2048 Data rate 112-Gb/s

Symbol size Ns 2560 Sampling speed 56-GS/s

Number of pilot subcarriers (Np) 16 DAC/ADC 5 bits

Number of data subcarriers (Nd) 1280 Clipping ratio 6

Modulation PDM QPSK Laser linewidth 100 kHz

3. ISFA-based channel estimation method In OFDM, a large number of subcarriers are usually used so that the frequency-domain transfer function of a given transmission channel for each subcarrier can be regarded as constant or flat. The combined effect of CD, PMD and PDL on an optical OFDM signal can be generally expressed as ⎡ s' x ⎢ ⎢ ⎣s' y

( k ) ⎤ ⎡ a ( k ) b( k ) ⎤ ⎡ s x ( k ) ⎤ ⎥= ⎢ ⎥, (k ) ⎥⎦ ⎢⎣ c (k ) d ( k ) ⎥⎦ ⎢⎣ s y ( k )⎥⎦

(1)

where the 2x1 vectors in the equation respectively represent the received and the transmitted OFDM signals for the k-th subcarrier each of which contains two orthogonal polarization components, and the 2x2 matrix is the channel matrix representing linear channel effects. To simplify the channel estimation, a pair of time-multiplexed TS’s across the two polarization branches, t1 and t2, is inserted into the OFDM symbol sequence at the transmitter [8]. We can write t1 and t2, as ⎡t ⎤ ⎡0⎤ t1 = ⎢ x ⎥, t2 = ⎢ ⎥, ⎣0⎦ ⎣t y ⎦

(2)

where tx and ty are two known symbols, preferably with low peak-to-average-power-ratios (PAPR). Note that the pair of TS’s need to be periodically inserted into the OFDM symbol sequence in order to capture dynamic channel behaviors. Assuming that the two training symbols experience the same channel effect, the received training symbols are ⎡t '2 x (k ) ⎤ ⎡ b(k )t y ( k ) ⎤ ⎡ t ' ( k ) ⎤ ⎡ a ( k )t x ( k ) ⎤ t '1 (k ) = ⎢ 1 x ⎥=⎢ ⎥. ⎥=⎢ ⎥ , t '2 ( k ) = ⎢ ⎥ ⎣ ⎥ ⎢t '2 y (k ) ⎦ ⎢ d ( k )t y ( k ) ⎦ ⎢t '1 y ( k ) ⎦ ⎥ ⎣ c( k )t x ( k ) ⎦ ⎣ ⎣

(3)

The channel matrix can then be obtained as ⎡a(k) ⎢ ⎣c(k)

⎡t'1x (k) / tx (k) ⎥=⎢ d(k)⎦ ⎣t'1y (k) / tx (k)

b(k)⎤

t'2x (k) / ty (k)⎤

t'2 y (k) / ty (k)⎥⎦

.

(4)

To improve the accuracy of channel estimation in the presence of noise, the ISFA process is applied such that for each modulated subcarrier, its channel matrix is an average of the channel matrices estimated for itself and its multiple adjacent subcarriers according to Eq. (4). Typically, for subcarrier k, the averaging can be performed over subcarrier k and its m left neighbors and/or m right neighbors, or totally up to (2m+1) adjacent subcarriers. The improved channel matrix for subcarrier k’ after the ISFA process can be expressed as ⎡a (k ' ) ⎢ ⎣ c (k ' )

b (k ' ) ⎤

d ( k ' ) ⎥⎦ ISFA

=

∑

k '+ m

1 min( k max , k ' + m ) − max( k min , k ' − m ) +1

⎡a (k ) ⎢ k =k '− m ⎣ c(k )

b(k ) ⎤

d ( k ) ⎥⎦

,

(5)


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where kmax and kmin are the maximum and minimum modulated subcarrier indexes, respectively. In Eq. (5), the elements of the estimated channel matrix for k outside [kmin, kmax] are not available and thus are set to zero in the averaging process. Once the improved channel matrices for all the modulated subcarriers are obtained, they can be inverted and applied to the corresponding received subcarrier vectors in the payload symbols to obtain the original subcarrier vectors. This in effect realizes polarization demultiplexing and compensation of linear channel effects such as CD, PMD, and PDL. Simulations were performed to illustrate the effect of the ISFA process. A 112-Gb/s PDMOFDM signal was passed through a dispersive transmission link having a PMD with a mean differential group delay () of 100 ps. The original data were 211-1 pseudo random bit sequences. The loss of the transmission link was compensated by optical amplification and the optical signal to noise ratio (OSNR) of the received signal, defined with the common 0.1-nm noise bandwidth, was 15.5 dB. Figure 3 shows the first two channel matrix coefficients as a function of the modulated subcarrier index before and after the ISFA process with m=6. Evidently, the estimated channel coefficients without the ISFA process exhibit high-frequency fluctuations due to the presence of optical noise. With the ISFA, the noise-induced highfrequency fluctuations are removed.

Fig. 3. Channel matrix coefficients as a function of the modulated subcarrier index without (left) and with (right) the ISFA process. =100 ps. OSNR=15.5 dB.

Fig. 4. Simulated BER of the 112-Gb/s PDM-OFDM signal vs. OSNR in the back-to-back case.

To quantify the benefits of the ISFA process, we first performed simulations in the backto-back case where the channel is only affected by optical noise. 20 OFDM symbols were simulated in order to be able to count ~100 errors at a bit error ratio (BER) of 10-3, a typical #101682 - $15.00 USD Received 16 Sep 2008; revised 14 Nov 2008; accepted 15 Dec 2008; published 18 Dec 2008

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forward error correction (FEC) threshold. Figure 4 shows the back-to-back BER performance of the 112-Gb/s PDM-OFDM signal under different channel estimation (CE) conditions. Ideal CE refers to the case where the channel matrices are obtained in the absence of optical noise. The required OSNR for BER=10-3 is 15.2 dB in the ideal CE case. Direct CE refers to the case with noise but without the ISFA, the OSNR performance at BER=10-3 is ~5 dB worse. With the ISFA over 5 (m=2), 9 (m=4), and 13 (m=6) adjacent subcarriers, the channel estimation penalties with respect to the ideal CE case at BER=10-3 are significantly reduced to 1, 0.4, and 0.2 dB, respectively, showing substantial performance improvement achieved by the ISFA. Further increasing m in the ISFA process brings diminishing improvement in the BER performance and reduces the frequency resolution of the channel estimation, which may put a limit on the magnitude of frequency-dependent channel effects that the ISFA-based channel estimation can tolerate. In a recent experiment [14], the performance of the ISFA-based CE in linear transmission was found to be similar to that of the time-domain averaging based CE with the same averaging window size. The detailed comparison between these two CE approaches, however, is beyond the scope of this paper. We will investigate the impact of CD and PMD, which are frequency-dependent effects, on the ISFA-based channel estimation in the following two sections.

CD=6,800 ps/nm

CD=21,760 ps/nm

Fig. 5. The phases of the subcarriers estimated by the ISFA-based channel estimation process using m=6 when the OFDM signal experiences 6800-ps/nm (upper) and 21,760-ps/nm (lower) dispersion. The dashed curves are based on the calculations from the theory.

4. Impact of CD on the ISFA-based channel estimation In the presence of large CD, there is a large phase variation across the subcarriers, particularly near the edges of the OFDM spectrum, and the ISFA process may cause inaccurate estimation of the channel matrices. As a design rule, it is desired that the CD-induced phase difference between the center subcarrier and the farthest subcarrier in the averaging process of the ISFA to be less than about 1 rad. After some derivations, it is found that the residual CD prior to the ISFA, denoted as DISFA, is desired to be limited such that

| DISFA ( ps / nm) |