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Field trial of distance-adaptive optical transmission with digital in-band OSNR estimation

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Abstract

We present a feasible distance-adaptive optical transmission system that selects the optimum modulation format by referencing the estimated optical signal to noise ratio (OSNR) information transmitted from an opposing transceiver via a feedback channel. A modulation format free time-domain-multiplexed pilot sequence enables OSNR estimation and feedback channel transmission. Thanks to a feedback channel transmission, this system does not need to pass through a control plane in optimizing scheme. Using this system, we demonstrated 106.6 Gb/s QPSK and 213.3 Gb/s 16 QAM distance-adaptive optical transmission in a fully automatic manner in a field-installed fiber of 70.4 to 211.2 km.

© 2016 Optical Society of America

1. Introduction

Network flexibility in optical communications has received much attention in recent years because it enables the spectral efficiency in limited optical bandwidth resources to be increased. A distance-adaptive optical network have been proposed as a detailed architecture of a flexible optical network [1–4]. The purpose of the distance-adaptive optical network is to minimize the transport excess margins resulting from the worst case design of the current optical network. With the conventional rigid system design, the all signal’s forms such as spectral bandwidth, modulation format, forward error correction (FEC) overhead, and subcarriers of orthogonal frequency division multiplexing (OFDM) are determined by the transmission quality of the worst channel such as the channel at longest pass in the ring network. In contrast, with distance-adaptive optical network, appropriate signal forms are allocated to decrease the excess margin to each channel according to each transmission quality derived from such as a path length. There have been several computational simulation reports discussing the capacity gain by introducing the distance-adaptive optical network in a various network condition [5,6]. However, not many reports have been conducted transmission experiments in which the signal form was adaptively shifted in accordance with the dynamically changing physical information in each channels.

As an experimental report showing a dynamical signal form optimization scheme, a flexible-bandwidth testbed demonstration using a real-time adaptive control plane was presented [7]. Another study reported a bit error rate (BER)-adaptive modulation format optimization experiment performed by using a flexible-format transmitter [8]. The aim in these experiments were to adjust the modulation format and spectrum positioning to maintain quality of service in a fully automatic manner by monitoring the BER of a supervisory channel or demodulated signal. In these cases, BER is used for estimating the excess margin of the optical signal to noise ratio (OSNR) of the transmission line. BER can reflect the OSNR in the short term, while it fluctuates in long term operations. This is because it contains the whole impairment effects, not only the degradation of OSNR, which is time constant, but also polarization mode dispersion and nonlinear optical effect, which vary with time. Thus, it is preferable to use OSNR, which is time constant, as an indicator for signal form allocation, especially for the carrier network design that is required for long term stable operation. In light of another experiment aspect of [7], the optimum signal form of all wavelength division multiplexing (WDM) channels of all transmission links are calculated at the control plane, however, it leads to a considerably increased computation cost against current operational cost. To introduce the system in a cost effective manner, the signal form optimization scheme should be closed in a physical layer. In the experiment reported in [8], a proper modulation format was directly fed back from the PC at a receiver to a flexible transmitter via GPIB. However it is difficult to directly connect over GPIB in a real network, therefore it is necessary to arrange the way to feed back the signal form information.

In this paper, we describe a practical distance-adaptive transmission system that optimizes signal form according to the in-band OSNR in the transmission path and eliminates the control plane by using a polarization modulated feedback channel that communicates the path condition information between transceivers. The estimation of in-band OSNR and the transmission of the feedback channel are enabled by a pilot sequence (PS) that is time division multiplexed into a data frame sequence at a rate below 1%. Using these techniques, we experimentally demonstrated the distance-adaptive transmission through adaptively allocating the modulation format of 106.6 Gb/s QPSK or 213.3 Gb/s 16QAM including 20% FEC overhead in a fully automatic manner in a field-installed fiber. In addition to the previous report [9], we discuss about the feedback channel transmission technique in detail: the formula for the demodulation, the Q factor derived from frequency distribution of the demodulated output after 600km transmission and the tolerable frequency against polarization rotation effect calculated from the ratio of a pilot sequence to data sequence. Moreover, we additionally confirmed dynamic operation of modulation format allocation while changing the OSNR using OSNR estimation and feedback channel transmission techniques in back to back condition.

2. System configuration

Figure 1 shows a schematic of the proposed distance-adaptive optical transmission system and the procedure for signal form optimization. There are two opposing transceivers in the system; each comprise a transmitter (Tx.) and a receiver (Rx.). Tx. 1 and Rx. 1 in transceiver 1 are respectively connected to Rx. 2 and Tx. 2 in transceiver 2. The signal form such as modulation format, signal bandwidth, or FEC overhead is adaptively allocated as follows. First, a signal frame that contains data and a PS is transmitted from Tx.1 to Rx.2 through fiber 1. Next, the in-band OSNR of fiber 1 is estimated in Rx.2. Here, in-band OSNR means that its noise component is measured at the same frequency as that of the signal spectrum. Then, the proper signal form for fiber 1 is selected by comparing the estimated in-band OSNR with an OSNR threshold that represents the criterion to change the signal form. The OSNR threshold is designed before transmission in back-to-back condition. After that, signal form information is sent back from Tx. 2 to Rx. 1 through fiber 2 via a feedback channel. Next, the information is demodulated from the feedback channel in Rx. 1 and fed to Tx. 1. Finally, the proper signal form for fiber 1 is set in Tx. 1. When optimizing the signal form in Tx. 2, the above scheme should be started from Tx. 2. In this scheme, the signal form information determined by the estimated OSNR is sent back directly from the receiver to the transmitter via the feedback channel. This enables the system to operate without additional processing in the control plane.

 figure: Fig. 1

Fig. 1 System configuration and signal form optimization process.

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3. OSNR estimation

We estimate OSNR by using the pilot sequence in the scheme given in [10]. Signal power and noise power are respectively calculated from the data sequence spectrum and the pilot sequence spectrum. Figure 2(a) shows the frame structure of the transmitted signals. The pilot sequence is constructed of alternating binary symbols of 0s and 1s whose complex amplitudes are arbitrary value of S and –S. Figure 2(b) indicates the spectrum of the pilot sequence. Since the pilot sequence can be seen as a BPSK-modulated signal, its spectrum has two peak components with noise elements. When the cycle of the pilot sequence is four such as an alternate of S, S, –S, –S, the peak components are at +/− Rs/4, where Rs is the baud rate. Figure 2(c) is a spectrum of a data sequence. The OSNR estimation process is as follows. After detecting the transmitted signals in a receiver, chromatic dispersion (CD) is compensated for by using frequency-domain equalization (FDE). Then frame synchronization is achieved by searching for the peak power timing of the pilot sequence. Figures 3(a) and 3(b) depict time dependence of the signal spectrum before band pass filtering and the signal power after passing through a band pass filter. Since the average power in the pilot sequence and data sequence is equal, the power at two peak frequencies in pilot sequence is larger than that in data sequence. Therefore, by extracting the peripheral frequency of the peak components with a band pass filter as shown in Fig. 3(a), the phase of the pilot sequence can be found by searching the large power time of the signals as shown in Fig. 3(b). Then, the pilot sequence can be retrieved from the received sequence, and the noise power can be calculated from the frequency elements around DC. The signal power is obtained from the data sequence spectrum, which is extracted at another time with PS.

 figure: Fig. 2

Fig. 2 Pilot sequence and its spectrum for in-band OSNR estimation. (a) Frame structure, (b) spectra of pilot sequence and (c) data sequence.

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 figure: Fig. 3

Fig. 3 Time dependence (a) of the signal spectrum and (b) the power after band pass filtering.

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This estimation technique is a benefit for distance-adaptive optical transmission for two reasons. First, it is applicable to any modulation format because the estimation is conducted using time domain multiplexed pilot sequence which does not depend on a signal form. Second, we can estimate the OSNR prior to demodulating the signal or sampling timing synchronization by time-domain adaptive filter. This is because this method does not use the information about the complex amplitude of the transmitted signal; rather, it uses the information about the power spectral density. In addition, this method is suitable for dense WDM or the severe pass band narrowing condition caused by passing through the multistage wavelength selective switch (WSS). In the situation, out-of-band OSNR that calculates the noise power from an interspace of WDM channels decays by filtering effect. However this estimation can measure in-band OSNR whose noise elements are in the same bandwidth as that of the signal spectrum, thus it is not affected by pass band narrowing effect.

4. Feedback channel transmission

A feedback channel can transmit arbitrary data in addition to client data from receiver to transmitter by modulating the PS polarization [11]. We modulate the PS polarization to two orthogonal states at a transmitter and demodulate it by taking the inner product between two PS in successive frames at a receiver. Figure 4(a) shows the combination of pilot sequences for feedback channel modulation. The X sequence is always the same; in contrast, the Y sequence is selectively chosen in accordance with the bit information for feedback channel transmission. Figure 4(b) is the parallel state of the pilot sequence; it is set to be the same sequence in X and Y polarization. As a result, its combined state becomes single polarization. Figure 4(c) is the orthogonal state of the pilot sequence; it can be modulated to orthogonal state by inverting the Y sequence of PS to negative as shown in Fig. 4(a). This makes it possible to transmit bit information that corresponds to the inner product of two consecutive PS by selecting the Y sequence of PS. Equations (1) and (2) show a scheme for detection in parallel and orthogonal condition of PS modulation. Here, R(n-1) and R(n) are received signals composed of the complex amplitude of X and Y polarization signals, and x(n) and y(n) are signals in the n-1th and nth frames. In the parallel condition, PS of both polarizations are the same; in contrast, the Y sequence of latter PS is inverted in orthogonal state. When the pilot sequences of both frames are the same, the output becomes 2|x(n-1)|2 as shown in Eq. (1). On the other hand, if the combined polarization state is orthogonal compared with the previous frame, their inner product becomes 0 as shown in Eq. (2).

 figure: Fig. 4

Fig. 4 Pilot sequence and combined polarization statement for feedback channel modulation. (a) Combination of X and Y pilot sequences, (b) parallel polarization state and (c) orthogonal polarization state.

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Although the polarization of the PS is modulated for feedback channel transmission as described above, we can estimate OSNR in the previously described scheme at the same moment because its spectrum does not change in either polarization state. Thus we can effectively share the pilot sequence for OSNR estimation and feedback channel transmission.

R(n1)R(n)=x(n1)xn*+y(n1)yn*=x(n1)x(n1)*+y(n1)y(n1)*=|x(n1)|2+|x(n1)|2=2|x(n1)|2
R(n1)R(n)=x(n1)xn*+y(n1)yn*=x(n1)x(n1)*+y(n1)(y(n1)*)=|x(n1)|2|x(n1)|2=0

5. Distance-adaptive optical transmission experiments in a field fiber

We conducted a distance-adaptive optical transmission experiments in which a QPSK or 16 QAM modulation format was allocated depending on estimated OSNR over field installed fibers of different length. The experimental setup is shown in Fig. 5. We placed two opposing transmitter-receiver sets like those shown in Fig. 1. The transmitter for the main signal is comprised an external cavity laser (ECL) operating at 1577.025 nm, an IQ modulator (IQM), an arbitrary waveform generator (AWG) operating at 64 Gsample/s, an EDFA and an attenuator. The baud rate was 32 Gbaud and the bit rate was 106.6 Gb/s in QPSK or 213.3 Gb/s in 16 QAM extracting 20% FEC overhead. The Nyquist filter roll-off factor was 0.1. To maintain OSNR consistency between the two modulation formats, we normalized the root mean square value of QPSK to be the same as that of 16QAM in the AWG. The frame length was 32,768 symbols and the PS length was 256. The main signals were combined with 20 WDM signals whose even and odd channels were respectively generated at 50 GHz spacing. Then, they were transmitted at −3 dBm/Ch. The lower middle inset in Fig. 5 is the spectrum of 21 WDM signals before transmission. The main signals were set at the center channel. The transmission link comprised 3 spans and each span comprised a 70.4 km field-installed DSF, an EDFA and an attenuator. The optical fiber was installed between the NTT-EAST Yokosuka office and the NTT Yokosuka R&D Center, Kanagawa, Japan as shown at the lower right in Fig. 5. The average fiber loss was 0.35 dB/km. At the receiver side, the transmitted signals were coherently detected in an integrated coherent receiver (ICR) following the band-pass filter, and digitized in a digital signal oscilloscope (DSO). Finally, accumulated data in the DSO were demodulated by offline digital signal processing (DSP). In the DSP, at first, in-band OSNR in the transmission link from Transceiver 1 to Transceiver 2 was estimated. Then, the appropriate modulation format, either QPSK or 16QAM, was selected by comparing the estimated OSNR with the OSNR threshold that was defined in back-to-back condition. When the estimated OSNR exceeded the threshold 16QAM was selected, and when it fell below the threshold QPSK was chosen. After that, DSP provided the modulation format information to the AWG at Transceiver 2 as shown by a double line in Fig. 5. Depending on the modulation format information, the PS polarization was modulated to parallel or orthogonal state at the AWG as described in the previous chapter. When 16 QAM was appropriate for the transmission link, we assigned the inner product between two consecutive PS to 1 and when QPSK was suitable we set it to 0. At the receiver of Transceiver 1, the appropriate modulation information was demodulated by taking the inner product between PS in two frames. Then, the information was sent to AWG as shown by a double line. Finally, the signals from Transceiver 1 were modulated in an optimum modulation format. These operations were automatically performed by using offline DSP for hardware control.

 figure: Fig. 5

Fig. 5 Experimental setup

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Prior to the transmission, we designed the OSNR threshold in back-to-back condition. This threshold represents the minimally necessary OSNR for 16 QAM transmission. We compared the estimated OSNR to this threshold to decide the proper modulation format. From here on, we call estimated OSNR “equivalent OSNR (e-OSNR).” The e-OSNR contains both the optical and electrical noise components of a 0.1 nm bandwidth. In general, OSNR only represents the signal quality vis-a-vis optical noise; however, it is essential to take electrical noise into consideration in digital coherent transmission. This is because electrical noise can produce severe degradation when higher signal quality is required, for example, when a higher order modulation format is adapted. Thus we use e-OSNR as the criterion for changing the modulation format. Figure 6 shows e-OSNR as a function of OSNR measured by an optical spectrum analyzer (OSA). Each e-OSNR value is averaged for 200 frames. Since e-OSNR contains additional electrical noise, it is always lower than measured OSNR. The difference between estimated e-OSNR and measured OSNR became bigger as the measured OSNR increased; this is because electrical noise, such as quantization error in a digital-analog or analog-digital converter, is constant under any OSNR condition. This OSNR estimation can be performed even at OSNR of 10 dB.

 figure: Fig. 6

Fig. 6 The equivalent OSNR (e-OSNR), which contains optical and electrical noise within 0.1 nm bandwidth, as a function of OSNR measured by OSA.

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Figure 7 shows Q factors of QPSK and 16QAM as a function of OSNR and e-OSNR with theoretical curves as a function of OSNR. Outlined circles and squares are the Q factors as a function of e-OSNR. Filled circles and squares are the Q factors as a function of measured OSNR. The Q factors as a function of e-OSNR were obtained by shifting the horizontal axis of the Q factors as a function of OSNR in a parallel fashion, referencing the relation of Fig. 6. The slopes of the theoretical curve and Q factors as a function of e-OSNR were consistent within 1 dB accuracy in a range where e-OSNR is from 10 to 22 dB. Conversely, the difference between theoretical curve and Q factors as a function of OSNR became bigger at higher OSNR. This is because e-OSNR includes the total amount of noise power, unlike the OSNR, which reflects only optical noise power. The 1 dB penalty factors between theoretical curves and Q factors as a function of e-OSNR are demodulation algorithm imperfection and OSNR estimation error. We assumed the FEC threshold as 5.7 dB Q [12]. Theoretically, minimum OSNR where 16 QAM signal can be transmitted above FEC threshold is approximately 16.2 dB; therefore, we defined the e-OSNR threshold as 17.2 dB including 1 dB margin in consideration of estimation accuracy described in Fig. 6. The area filled in gray in Fig. 7 represents the area where 16QAM transmission is available.

 figure: Fig. 7

Fig. 7 Q factors of QPSK and 16 QAM as a function of OSNR and e-OSNR. Those of e-OSNR are obtained by shifting the horizontal axis of those of OSNR referencing the relation of Fig. 6. The e-OSNR threshold is a criterion where Q factor of 16 QAM exceeds the FEC threshold.

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Then we measured the performance of feedback channel transmission. Figure 8(a) and (b) show histograms of demodulation output of feedback channel transmission in orthogonal and parallel polarization states. We measured them at a condition of 600 km SMF transmission where each span was composed of a 100 km SMF and an EDFA and an attenuator, to ascertain the overload degradation effect. No measureable error was found in 900 frames after transmission. Assuming these demodulation output variations were Gaussian distribution, we found their average and standard deviation were 0.0050 and 0.0013 for orthogonal polarization state and 0.8646 and 0.0042 for parallel polarization state. Accordingly, the Q factor derived from average and standard deviation was 43.9 dB. This feedback transmission is able to tolerate OSNR degradation, due to the technique of averaging the inner product of all PS samples in a frame. However, it severely degrades when the polarization scrambling occurs since it modulates the polarization state of PS. Limitation of scrambling speed can be derived from the baud rate and the frame length. In this experiment the baud rate was 32 Gbaud and the frame length was 32,768. Errors occur when the polarization state rotates π/2 until the next frame comes. Therefore it is tolerable up to 244 kHz as shown in Eq. (3).

 figure: Fig. 8

Fig. 8 Demodulation output of feedback channel. (a) Orthogonal polarization state and (b) parallel polarization state.

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π2×32×10932768×12π244×103[Hz]

Using OSNR estimation and feedback channel transmission techniques, we ascertained the direct operation of modulation format allocation in back-to-back condition while changing the OSNR. In Figs. 9(a)-9(c) respectively depict e-OSNR, feedback channel output, and Q factor as a function of measured samples. It took about two seconds to measure each sample. Estimated OSNR and Q factor were obtained at Transceiver 2, while feedback channel output was demodulated at Transceiver 1. We first added a certain amount of noise so that the estimated OSNR would be higher than the OSNR threshold and then transmitted 16 QAM signals. At that time, the feedback channel output was 1 and the Q factor was approximately 12.5 dB. Then we dropped the OSNR using an attenuator when the 22nd sample was being measured. After that, the estimated OSNR fell below the OSNR threshold. At the same time, the feedback channel output went down to below the feedback channel threshold of 0.5. This was the indicator to change the modulation format from 16 QAM to QPSK. After demodulating the feedback channel at the receiver in Transceiver 1, the Q factor fell to around 3 dB, then it went up to around 9 dB. The time it took to validate the Q factors was equal to that required to measure three samples. This is because it was necessary to transmit the feedback channel signals through the fiber and set the modulation format at the AWG in Transceiver 1.

 figure: Fig. 9

Fig. 9 (a) The e-OSNR, (b) Feedback channel output, and (c) Q factor as a function of measurement sample. The OSNR was degraded when the 22nd sample was measured.

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Finally, we conducted a distance-adaptive optical transmission experiment while changing the transmission length. Figure 10 shows Q factor and e-OSNR as a function of transmission span in each span. In addition to ASE, phase modulation caused by nonlinearity of the optical fiber is added to the signal during transmission. After the transmission, the bottom shapes of the PS spectrum are broadened as shown in [13]. In the OSNR estimation scheme, we acquired the frequency elements around DC to calculate the noise power as described in section 3. Its frequency range was selected with the intention to exclude not only the PS spectrum but also other unnecessary spectrum such as broadened element caused by nonlinear optical effect or residual DC element caused by imperfect bias controlling in the IQ modulator. As depicted in the figure, e-OSNR degraded from 18.4 to 17.5 to 16.3 dB as the span increased. As the e-OSNR of span 3 dropped below the e-OSNR threshold of 17.2 dB which was defined in Fig. 7, the modulation format shifted from 16 QAM to QPSK at span 3. Then the Q factor successfully transited from 6.90 dB for span 1 to 5.86 dB for span 2 with 16QAM and 11.57 dB for span 3 with QPSK.

 figure: Fig. 10

Fig. 10 Q factor and e-OSNR as a function of transmission span.

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6. Conclusion and discussion

We described a distance-adaptive optical transmission system that flexibly assigns modulation format in accordance with the estimated or equivalent OSNR (e-OSNR) information transmitted via a feedback channel. Using a time division multiplexed pilot sequence enables OSNR estimation and feedback channel transmission. Since these methods do not depend on the data sequence format, they are applicable to any modulation format and baud rate. They can also be conducted before the time-domain adaptive filter is converged or before polarization demultiplexing. These features are benefit for selecting the appropriate modulation format at the beginning of a transmission. Using the system, we successfully demonstrated 106.6 Gb/s QPSK and 213.3 Gb/s 16 QAM distance-adaptive optical transmission in a fully automatic manner in a field-installed DSF of 70.4 to 211.2 km. Optimum modulation formats were chosen by comparing the e-OSNR to the OSNR threshold of 17.2 dB, which represents the minimally necessary OSNR for 16 QAM transmission in this system. We used QPSK and 16 QAM in this paper, however, we can cover additional modulation formats by setting proper e-OSNR thresholds and increasing the bit rate of feedback channel to be able to transmit the information of multi modulation formats.

In a real network, the modulation format is carefully chosen on the basis of the calculated system design, including all possible degradations in each field fiber. Hence, estimating other degradation effects such as nonlinear effect, polarization dependent loss, and pass band narrowing effect, in addition to OSNR, poses a good challenge to us to further improve the present system so that it can be introduced into a real network.

As a whole, however, our system’s features, i.e., the ability to estimate OSNR in a transmission link and optimize the modulation format without passing through a control plane thanks to a format independent time domain multiplexed pilot sequence, are benefit for introducing elasticity into a real network that requires stable operation and reduced operational cost.

Acknowledgments

This work is partly supported by the R&D project on “Research and Development of Ultra-high-speed and Low-power-consumption Optical Network Technologies” of the Ministry of Internal Affairs and Communications(MIC)of Japan and the R&D project on “Lambda Reach” of the National Institute of Information and Communications Technology (NICT).

References and Links

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6. T. Takagi, H. Hasegawa, K. Sato, T. Tanaka, B. Kozicki, Y. Sone, and M. Jinno, “Algorithms for maximizing spectrum efficiency in elastic optical path networks that adopt distance adaptive modulation,” in Proceedings of ECOC2010 (2010), paper We.8.D.5. [CrossRef]  

7. D. J. Geisler, R. Proietti, Y. Yin, R. P. Scott, X. Cai, N. K. Fontaine, L. Paraschis, O. Gerstel, and S. J. B. Yoo, “The first testbed demonstration of a flexible bandwidth network with a real-time adaptive control plane,” in Proceedings of ECOC2011 (2011), paper Th.13.K.2. [CrossRef]  

8. H. Y. Choi, T. Tsuritani, and I. Morita, “BER-adaptive flexible-format transmitter for elastic optical networks,” Opt. Express 20(17), 18652–18658 (2012). [CrossRef]   [PubMed]  

9. S. Okamoto, K. Yonenaga, F. Hamaoka, and Y. Kisaka, “Field experiment of OSNR-aware adaptive optical transmission with pilot-aided bidirectional feedback channel,” in Proceedings of OFC2016, (2016), paper Th2A.2. [CrossRef]  

10. S. Okamoto, Y. Kisaka, K. Ishihara, E. Yamazaki, and M. Tomizawa, “Digital In-band OSNR Estimation for Polarization-Multiplexed Optical Transmission,” in Proceedings of OECC2013 (2013), paper TuR2–4.

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13. L. Dou, Z. Tao, Y. Zhao, S. Oda, Y. Aoki, T. Hoshida, and J. C. Rasmussen, “Differential pilot aided in-band OSNR monitor with large nonlinear tolerance,” in Proceedings of OFC2015 (2015), paper W4D.3. [CrossRef]  

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Figures (10)

Fig. 1
Fig. 1 System configuration and signal form optimization process.
Fig. 2
Fig. 2 Pilot sequence and its spectrum for in-band OSNR estimation. (a) Frame structure, (b) spectra of pilot sequence and (c) data sequence.
Fig. 3
Fig. 3 Time dependence (a) of the signal spectrum and (b) the power after band pass filtering.
Fig. 4
Fig. 4 Pilot sequence and combined polarization statement for feedback channel modulation. (a) Combination of X and Y pilot sequences, (b) parallel polarization state and (c) orthogonal polarization state.
Fig. 5
Fig. 5 Experimental setup
Fig. 6
Fig. 6 The equivalent OSNR (e-OSNR), which contains optical and electrical noise within 0.1 nm bandwidth, as a function of OSNR measured by OSA.
Fig. 7
Fig. 7 Q factors of QPSK and 16 QAM as a function of OSNR and e-OSNR. Those of e-OSNR are obtained by shifting the horizontal axis of those of OSNR referencing the relation of Fig. 6. The e-OSNR threshold is a criterion where Q factor of 16 QAM exceeds the FEC threshold.
Fig. 8
Fig. 8 Demodulation output of feedback channel. (a) Orthogonal polarization state and (b) parallel polarization state.
Fig. 9
Fig. 9 (a) The e-OSNR, (b) Feedback channel output, and (c) Q factor as a function of measurement sample. The OSNR was degraded when the 22nd sample was measured.
Fig. 10
Fig. 10 Q factor and e-OSNR as a function of transmission span.

Equations (3)

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R ( n 1 ) R ( n ) = x ( n 1 ) x n * + y ( n 1 ) y n * = x ( n 1 ) x ( n 1 ) * + y ( n 1 ) y ( n 1 ) * = | x ( n 1 ) | 2 + | x ( n 1 ) | 2 = 2 | x ( n 1 ) | 2
R ( n 1 ) R ( n ) = x ( n 1 ) x n * + y ( n 1 ) y n * = x ( n 1 ) x ( n 1 ) * + y ( n 1 ) ( y ( n 1 ) * ) = | x ( n 1 ) | 2 | x ( n 1 ) | 2 = 0
π 2 × 32 × 10 9 32768 × 1 2 π 244 × 10 3 [ H z ]
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