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In this paper long-haul, single channel, polarization multiplexed 16-state quadrature amplitude modulation (PDM-QAM-16) transmission at 112Gbit/s is investigated. Novel digital signal processing techniques are used to perform carrier phase estimation and symbol estimation, in combination with nonlinear digital backpropagation. The results obtained demonstrate that the use of digital nonlinear backpropagation increases the optimum launch power from −4dBm to −1dBm with a consequent increase in maximum reach from 1440km to 2400km, which is a record transmission distance for QAM-16 reported to date for an SMF link with EDFAs only. Furthermore, experimental measurements are supported by simulations, based on the link used in the experiment.
©2010 Optical Society of America
1. Introduction
Quadrature amplitude modulation (QAM) format can achieve high spectral efficiency when used in combination with wavelength division multiplexing (WDM) on a dense grid with polarization division multiplexing (PDM). QAM-16 modulation is particularly promising, as it allows for doubling the overall bit rate, compared with quadrature phase-shift keying (QPSK) format for the same symbol rate, and is an effective solution to obtain a 100G bit rate required in future optical systems (14Gbaud with polarization multiplexing, including FEC overhead). QPSK transmission at 112Gbit/s has been demonstrated and characterized in various single-channel and WDM long-haul transmission experiments [1,2]; however, to date, little research on long-haul QAM-16 transmission has been carried out. The two examples of QAM-16 transmission exceeding 1000km are [3,4]. While 112Gbit/s QAM-16 transmission has been previously demonstrated to achieve 1022km WDM transmission using EDFA and distributed Raman amplification [3], there has been little investigation into long-haul transmission over EDFA-only links. A notable exception is [4], although this experiment was performed at 160Gbit/s (20Gbaud) and, therefore, has different nonlinear transmission characteristics than 112Gbit/s.
A possible reason for this lack of research is the complexity associated with the generation of the high-quality QAM-16 signal. Compared with QPSK, a QAM-16 transmitter is still at a relatively early stage of its development, with several electrical and optical QAM-16 generation techniques (denoted, as E-QAM-16 and O-QAM-16, respectively) demonstrated at various symbol rates.
E-QAM-16 generation requires two 4-level electrical signals to drive an I-Q modulator; these may be synthesized using a pulse pattern generator (PPG) in combination with a passive RF network [3,4] or an arbitrary waveform generator (AWG) [5]. However, as shown in [6], the PPG-generated 4-level electrical signal requires a complex arrangement of RF components in a driving circuitry and can suffer from the finite signal-to-noise ratio (SNR). To solve the problem of the limited SNR, a 4-level signal has been recently obtained optically with subsequent conversion into an electrical domain [7]; however, no transmission was demonstrated. In addition, the electrical noise of a 4-level electrical signal is linearly translated into the optical domain, due to the operation on the linear part of an I-Q modulator transfer function. The use of currently available AWGs is complicated by their limited analogue bandwidth (8GHz at 3dB) and low output voltage (1Vp-p).
Several solutions for O-QAM-16 have been also proposed. One of them involves the interferometric processing of two QPSK signals with different amplitude levels, which concept was first suggested in [8] and realized in optical domain in a planar lightwave circuit (PLC)-type interferometer to demonstrate 50km transmission [9]. The potential disadvantage of this approach is that lower amplitude level in one of the QPSK signals is obtained by underdriving the I-Q modulator, which results into electrical noise translation into optical domain. Also, the skewed QAM-16 constellation suggests the phase mismatch between two QPSK signals, resulting in higher BER. Significant improvements to this QAM16 transmitter have been recently made to show the record capacity of 69.1-Tb/s over 240km, proving a great potential of optically generated QAM16 [10]. A similar technique, but involving an additional PLC-type interferometer, has been also used to obtain a QAM-64 signal; however, no transmission was demonstrated [11]. A promising approach using a monolithic electroabsorption-based InP QAM-16 modulator [12] has also not been proven in transmission, mainly due to high insertion loss (theoretical loss of the design is 12.1dB), distorted characteristics at high input powers and chirp. Finally, a generation technique involving a cascade of three modulators under specific driving conditions was successfully demonstrated; however, again, with no associated transmission [13].
In this paper we used a novel QAM-16 generation technique, which is simple to implement, reduces the electrical complexity at the transmitter and reduces the transfer of electrical noise into the optical domain [6]. After characterizing the transmission performance over a set of fixed distances, we have measured the impact of the input launch power on the maximum reach (assuming an FEC limit of 3x10−3) achieving a maximum distance of 1440km. We have also quantified the maximum benefit available from the use of digital nonlinearity compensation (NLC) achieving the reach of 2400km. Comparison with simulations yielded excellent agreement with the experiments.
2. PDM-QAM-16 generation and transmission set-up
The experimental set-up to generate and transmit a PDM-QAM-16 signal was similar to [6,14]. First, a QPSK signal at 14Gbaud was generated using a Bookham GaAs I-Q modulator (Fig. 1 ). For this two 215-1 PRBS outputs of the 14Gbit/s PPG were decorrelated by half a pattern length and amplified to 7Vp-p (2Vπ of the modulator) to drive the I-Q modulator at its null transmittance point. An external cavity laser (ECL) operated at 1554nm with output power of 6dBm and linewidth of 100kHz (measured using a self-heterodyne technique).
Fig. 1 Experimental set-up to generate and transmit 112Gbit/s (14Gbaud) PDM-QAM-16 signal (PD – photodetector, dB – attenuator, ∆t – delay line, Φ – phase shifter).
The generated QPSK signal was then launched via a polarization controller (PC) into a phase-stabilized fiber interferometer, assembled from polarization-maintaining (PM) fiber-coupled components. The phase stabilization of the interferometer is described in [6,15]. Theoretically, the relative phase between the two arms can be set to either 0° or 90° (Fig. 2 ); however, we used a 90° phase shift to avoid phase ambiguity during phase-locking at extreme values (0° or 180°) [15]. The signals in the two arms were decorrelated by 17 symbols, using an additional spliced PM fiber, aligned in time and attenuated by 6dB with respect to each other. The interference of the two signals with different amplitude levels yielded a QAM-16 signal containing every possible combination of three consecutive symbols, and therefore may be used to investigate the transmission properties of QAM-16.
To obtain a polarization multiplexed signal, a passive delay-line stage with adjustable states of polarization for signals in each arm was used; the two QAM-16 signals were decorrelated by 32 symbols with respect to each other (due to slightly different optical paths in the polarization multiplexing stage). Eye diagrams of single polarization and PDM-QAM-16 signals are shown in Fig. 3(a) and Fig. 3(b), respectively. Note, that the eye diagram for PDM-QAM-16 contains five power levels, which arises from summation of two QAM-16 signals with two orthogonal polarizations at the polarization beam splitter (PBS). The resultant QAM-16 signal was launched into a recirculating loop consisting of an 80.2km SMF span with an overall chromatic dispersion of 1347ps/nm and loss of 15.4dB. Polarization mode dispersion of the fiber was not measured. The noise figure of the EDFAs used in the loop was ~4.5dB. The EDFA1 and attenuators 1 and 3 (dB1 and dB3) were used to balance the loop, the EDFA2 and attenuator 2 (dB2) were used to set the launch power to the fiber, the EDFA3 was used to compensate for the fiber loss. The optical filters (OF) used in the experiment had a bandwidth of 0.8nm. At the receiver we used a polarization and phase diverse coherent receiver to detect the in-phase and quadrature components of two orthogonal polarizations. The power difference between the signal and local oscillator (LO), which also had the measured linewidth of 100kHz, was set to 20dB, according to [16]. The beating signal was detected with single-ended PINs (11GHz bandwidth at 6dB), digitized using a 16GHz bandwidth Tektronix real-time scope at 50GSamples/s with 8 physical bits of resolution, and processed offline in Matlab.
Fig. 3 Eye diagrams of a QAM-16 signal at 14Gbaud. (a) Single polarization. (b) Polarization multiplexed.
3. Digital signal processing (DSP) for PDM-QAM-16
In the DSP, the captured digital signal was first de-skewed, normalized to unit power per polarization and re-sampled to 2Samples/symbol. The signal was then filtered by a stationary approximation of the inverse of the optical channel. In the case of linear compensation, this consisted of a single finite impulse response (FIR) filter with a length equal to the signal length to compensate for chromatic dispersion only. Nonlinearity compensation was performed as in [17], by solving the Manakov equation with a single asymmetric step per span. The nonlinear phase shifting coefficient was determined by maximizing Q-factor. Equalization was then performed using a constant modulus algorithm (CMA) equalizer with least-mean squares (LMS) updating for pre-convergence, before switching to a radially directed CMA with LMS updating, described in detail in [18]. All equalizers consisted of 15 taps; the convergence parameter was reduced iteratively from 10−3 to 10−4. To estimate the intradyne frequency offset, the complex symbol sequence at the output of the equalizer was raised to the 4th power to reduce spectral broadening due to modulation. The offset was then determined by finding the peak power in the FFT of the signal [19]. The frequency estimation was performed over the average of both signal polarizations and applied uniformly to both polarizations.
Carrier phase was estimated using a decision-directed feed-forward estimator of the differential phase (Fig. 4 ). To implement this, the equalizer output symbols in the feed-forward window (25 symbols long) are pre-rotated by the previous phase estimate. The symbols in the window are then de-rotated by the arguments of their respective decisions to remove the influence of modulation on the phase estimate. The de-rotated symbols are then summed and the argument of the result is found to find a maximum likelihood estimate of the change in carrier phase [20]. This differential phase is then added to the previous phase estimate to provide a new absolute estimate of phase; the advantage of estimating the differential phase is that no unwrapping is needed.
Fig. 4 Block diagram of carrier phase estimation algorithm. Block arrows indicate element-wise register operations while solid arrows indicate single element operations.
The transmitted symbol sequence was determined by correlating the received symbol sequence with the PRBS data, and calculating the delays and phase rotations in the transmitter and channel. The transmitted symbol sequence was transformed into a Gray coded bit sequence, as previously described in [6], which was subsequently used to calculate the BER.
Maximum likelihood (ML) symbol estimation was then performed in order to reduce the symbol error rate (SER) compared with rectangular decision boundaries. The received symbols were compared to the complex mean of each of the 16 transmitted symbols per polarization, and the Euclidean distance for each possible symbol calculated. By choosing the symbol with the minimum Euclidean distance, it is possible to perform maximum likelihood symbol estimation. While this decision paradigm is identical to rectangular decision boundaries for perfectly square constellations, ML symbol estimation performs better in the presence of modulation distortions and can, therefore, reduce the overall BER. This is illustrated in Fig. 5 , where a QAM-16 signal has been deliberately distorted to demonstrate the benefit of using the minimum Euclidean distance boundaries for the BER estimation. This type of ML symbol decision may be performed without the knowledge of the transmitted data using the k-means clustering algorithm [21]. Alternative approach was suggested in [22], which uses quadrilateral decision regions to counteract quadrature imbalance at the transmitter. The advantage of the ML symbol estimation is the fact that it is a more general technique since no assumption regarding the geometry of the underlying distortion is made.
Fig. 5 Illustration of two different BER calculation methods. (a) With theoretical rectangular decision boundaries. (b) With optimized rectangular decision boundaries. (c) With minimum Euclidean distance decision boundaries. Bit error rates are reduced from 2.0x10−3 (a) to 5.3x10−4 (b) and 1.2x10−4 (c).
4. Configuration for QAM-16 transmission simulations at 112Gbit/s
Simulations in Matlab were performed to model the transmission link as used in the experiment. The limited transmitter bandwidth was emulated using a 5th order electrical Bessel filter with a 3dB bandwidth of 26 GHz. Laser phase noise was modeled as a random walk process and the transmitter laser linewidth was set to 100kHz. Relative intensity noise (RIN) was considered to cause only minor distortions and was neglected throughout the simulations. The implementation penalty was modeled by adding appropriate electrical noise power to the electrical driving signals. Note that adding electrical noise at the receiver (as opposed to transmitter added noise) would give similar back-to-back performance, but would underestimate the nonlinear penalty due to less nonlinear interaction between signal and noise during transmission.
Table 1 shows the parameters set in the simulation to mimic the behavior of the experimental transmission. Only the EDFA to compensate for the fiber loss was simulated, as this was the one that produced most of the ASE noise and, therefore, significantly degrades the performance. The EDFAs were set to operate in saturation with a fixed output power of 17dBm; further attenuations were simulated to obtain the required power levels. Signal propagation in the fiber was modeled with the symmetrical split-step Fourier method to include the effect of chromatic dispersion, 1st order polarization mode dispersion, power dependence of the refractive index (Kerr effect) and nonlinear polarization scattering. The optical loop filter was modeled as a 2nd order Gaussian filter with a 3dB bandwidth of 100GHz.
Table 1. Fiber and link parameters
At the receiver, the power difference between the signal and LO was set to 20dB, according to the experiment. The linewidth of the LO was set to 100 kHz and the frequency offset between transmitter and LO-laser was set to 0 GHz. The limited receiver bandwidth was modeled with 5th order Bessel filters, employing a 3dB bandwidth of 10 GHz. Afterwards, the signal was digitized by ADCs with an effective resolution of 4bits, to include the influence of additional quantization noise. Subsequent DSP including chromatic dispersion compensation (if applicable, nonlinear compensation), equalization and digital phase estimation was performed as discussed in section 3. Monte-Carlo error counting was performed to determine the BER, which serves as performance metric for these simulations.
5. Back-to-back and transmission results at 112Gbit/s
To perform the back-to-back measurements, the set-up was modified to bypass the recirculating loop and place an additional EDFA at the receiver with attenuators for noise loading. Figure 6 shows the measured receiver sensitivity curve (BER versus OSNR) and simulated receiver sensitivity with noise loading at the transmitter to match the back-to-back behavior to the one obtained in the experiment. The plot covers those BER values close to the FEC limit, hence, are computationally reasonable. The penalty with respect to the theoretical OSNR sensitivity was found to be 4.5dB for a BER of 1x10−3, decreasing to 3.6dB at a BER of 3x10−3. The back-to-back BER was less than 10−5 (corresponding to the Q-factor higher than 12.6dB), calculated over 216 symbols and averaged over several runs.
To characterize the transmission performance of PDM-QAM-16, the Q-factor was measured as a function of input launch power for several fixed transmission distances with a step of 5 spans (Fig. 7 ). Figure 7(a) shows that the optimum launch power for all measured distances was approximately −4dBm. For the lower input powers the main source of degradation is OSNR degradation due to accumulated ASE noise from the EDFAs in the link, while for higher input powers the performance is degraded due to intra-channel nonlinearity. Applying nonlinearity compensation (NLC) allowed for an increase in the optimum launch power by 3dB for the distances measured [Fig. 7(b)]. This also resulted in the increase of input launch power margin from approximately 4dB to more than 9dB at 1200km with an FEC limit of 3x10−3. The nonlinear phase shifting constant (given as χ in [17]) was found to be optimal at 11.3x10−3 at −1dBm launch power for all distances considered in Fig. 7(b). The reason for a limited increase in the optimum launch power and, hence, Q-factor is that the nonlinearity cannot be compensated completely and can in fact be only mitigated. This is due to the fact that the nonlinear Manakov equation cannot be solved analytically, which means that any nonlinear mitigation schemes have to rely on an approximate numerical solution of the Manakov equation. In addition, such effects as nonlinear phase noise and interactions between nonlinearity and polarization mode dispersion are extremely hard to compensate for.
Fig. 7 Experimentally measured impact of the input launch power on the Q-factor for several fixed distances. (a) With linear compensation only. (b) With nonlinearity compensation
To assess the performance of nonlinearity compensation, Q-factor was plotted as a function of the transmission distance at the optimum launch power (denoted as optimum Q-factor). Figure 8(a) demonstrates that the use of NLC yielded an improvement in optimum Q-factor by 1 dB at 1200km and 1.3dB at 2000km. The maximum reach at the FEC limit of 3x10−3 was determined to be 1440km (18 spans) with linear compensation only and 2400km (30 spans) when nonlinearity compensation was applied. This corresponds to an increase in optimum reach of approximately 65%. Furthermore, we measured the maximum reach dependence on the input launch power at the FEC = 3x10−3 with and without nonlinearity compensation and plotted the simulation results [Fig. 8(b)], showing an excellent agreement between experiment and simulations (the discrepancy was less than 1dB). Constellation diagrams back-to-back and after 1440km and 2400km transmission (both with and without NLC) are shown in Fig. 9 .
Fig. 8 Performance comparison of transmission with and without NLC. (a) Experimentally measured optimum Q-factor versus transmission distance. (b) Impact of input launch power on the maximum reach at the FEC limit of 3x10−3.
Fig. 9 Experimental PDM-QAM-16 constellation diagrams at 112Gbit/s. (a) Back-to-back without noise loading. (b) 1440km without NLC at −4dBm. (c) 1440km with NLC at −4dBm. (d) 2400km without NLC at −1dBm. (e) 2400km with NLC at −1dBm.
6. Conclusions
The distance-dependent performance and maximum reach of single-channel PDM-QAM-16 112Gbit/s transmission over an uncompensated SMF link with all Erbium amplification was investigated. Over the range of distances examined, the optimum launch power was found to be −4dBm with compensation of linear effects only. This corresponded to the maximum reach of 1440km (for an FEC limit of 3x10−3). We also studied the maximum benefit available from digital nonlinearity compensation for single-channel transmission and found an increase in optimum launch power from −4dBm to −1dBm, with consequent increase in maximum reach by 65% to 2400km. The use of nonlinearity compensation yielded an improvement in the optimum Q-factor by 1dB at 1200km and 1.3dB at 2000km. We also showed that symbol estimation based on minimum Euclidian distance decisions can improve BER. This is particularly relevant for various optically generated QAM-16 signals, where deterministic modulation distortion (resulting in constellation asymmetry) may be a limiting factor. Experimental results were also verified by simulations, where excellent agreement with experimental results was obtained.
Acknowledgments
The work described in this paper was carried out with the support of the BONE-project (“Building the Future Optical Network in Europe”), a Network of Excellence funded by the European Commission through the 7th ICT-Framework Programme, Yokogawa Electric Corporation, EPSRC, Huawei, and The Royal Society.
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