## Abstract

A 448 Gbit/s single-carrier dual-polarization 16-ary quadrature-amplitude-modulation (DP 16-QAM) signal and a 1.206 Tbit/s three-carrier DP 16-QAM signal are demonstrated using look-up table (LUT) correction and optical pulse shaping. The LUT correction is used to mitigate the effects of transmitter-based pattern-dependent distortion due to the high symbol rates. A programmable optical filter is employed to narrow the modulated signal spectrum and thereby enhance the spectral efficiency and reduce the requirements on the receiver bandwidth and analog-to-digital converter sampling rate. By combining these techniques, the back-to-back required optical signal-to-noise ratios are 26.6 dB and 27.2 dB for BER = 10^{−3}, and transmission over 1200 and 1500 km of standard single-mode fiber with EDFA amplification was achieved for the 448 Gbit/s signal (12% forward error correction (FEC) overhead) and 1.206 Tbit/s signal (20% FEC overhead), respectively.

© 2013 Optical Society of America

## 1. Introduction

With the deployment of 100 Gbit/s systems and the increasing demand for data transmission capacity, systems with bit rates of 400 Gbit/s and 1 Tbit/s are now being investigated [1]. Possible solutions include single-carrier multi-level modulation with a high symbol rate [2–6] for a bit rate of 400 Gbit/s, and multi-carrier modulation with a low symbol rate for each subcarrier, such as Nyquist wavelength division multiplexing (WDM) [7] and coherent optical orthogonal frequency division multiplexing [8], for bit rates of 400 Gbit/s and 1 Tbit/s. Single carrier solutions for a bit rate of 400 Gbit/s are attractive because of the simple structure in the transmitter and a receiver complexity that is similar to those for multi-carrier solutions [9]. For a bit rate of 400 Gbit/s, single-carrier dual-polarization 16-ary quadrature-amplitude-modulation (DP 16-QAM), combined with coherent detection and digital signal processing provides a high spectral efficiency and reasonable optical signal-to-noise ratio (OSNR) requirement. Experiments for single-carrier 448 Gbit/s DP 16-QAM systems have used either optical time division multiplexing (OTDM) or electrical time division multiplexing (ETDM). By using OTDM at the transmitter, a 456 Gbit/s DP 16-QAM signal has been transmitted over 800 km of ultra large area fiber (ULAF) using Raman amplification [3], and a 448 Gbit/s DP 16-QAM signal has been transmitted over 250 km of ULAF using erbium doped fiber amplifiers (EDFAs) [4]. While OTDM overcomes the bandwidth limitations of electrical and opto-electronic components, ETDM is seen as a more practical approach [10]. Transmission over 1200 km of 448 Gbit/s DP 16-QAM has been achieved using ETDM signal generation and interleaved return-to-zero symbols [11].

A per-channel bit rate of 1 Tbit/s can be achieved using a superchannel comprised of several modulated optical subcarriers that are considered as a single entity for network routing [12–16]. This allows the subcarriers to be more closely spaced together compared to the individual channels in a conventional wavelength division multiplexed system. The number of optical carriers, the bit rate per carrier, and the modulation format are key aspects of the system design. Superchannels with a bit rate of 1 Tbit/s have been demonstrated using DP 8-QAM and 9 subcarriers with bit rates of 138 Gbit/s [14], DP 16-QAM and 4 subcarriers with bit rates of 320 Gbit/s [15], and DP 64-QAM and 10 subcarriers with bit rates of 128.4 Gbit/s [12]. Transmission of a 1.28 Tbit/s dual-carrier DP 16-QAM signal has been achieved over 3200 km of ULAF using hybrid Raman/EDFA amplification [16].

In this paper we demonstrate transmission of a 448 Gbit/s single-carrier DP 16-QAM signal and a 1.206 Tbit/s three-carrier DP 16-QAM superchannel signal using a look-up table (LUT) correction for pattern-dependent distortion and optical pulse shaping [17]. The LUT correction is used to mitigate the effects of transmitter-based pattern-dependent distortion due to the high symbol rates (56 and 50.25 Gsym/s for the 448 Gbit/s single-carrier and 1.206 Tbit/s three-carrier signals, respectively). A programmable optical filter is employed to narrow the modulated signal spectrum and thereby enhance the spectral efficiency and reduce the requirements on the receiver bandwidth and analog-to-digital converter sampling rate. For the 448 Gbit/s single-carrier signal (400 Gbit/s plus 12% forward error correction (FEC) overhead) the back-to-back OSNR sensitivity is 26.6 dB at a BER of 10^{−3} using a 7-symbol LUT. Using a four-span recirculating loop, transmission over 1200 km of standard single-mode fiber (SMF) with EDFA amplification is achieved with a bit error ratio (BER) below the forward error correction (FEC) threshold of 3.8 × 10^{−3}. For the 1.206 Tbit/s three-carrier super-channel signal (3 × 335 Gbit/s plus 20% FEC overhead), the back-to-back OSNR sensitivity is 27.2 dB for a BER of 10^{−3} using a 7-symbol LUT. Transmission over 1500 km of SMF with EDFA amplification is achieved with a BER below the FEC threshold of 2 × 10^{−2}.

## 2. Look-up table correction

Due to the limitations of high-speed linear drive amplifiers and optical modulators, 56 and 50.25 Gsym/s four-level in-phase and quadrature signals (corresponding to 448 and 402 Gbit/s 16-QAM signals, respectively) can exhibit pattern-dependent distortion or non-linear intersymbol interference with memory [11]. Figure 1 illustrates the function of the LUT correction used to separately mitigate the pattern-dependent distortion of the in-phase and quadrature signals. The LUT contains the required amplitude correction for the center symbol within each possible symbol sequence$S(k-n:k:k+n)$of length $2n+1$ Initially the LUT amplitude corrections are all zero. A sliding window is used to identify the known $2n+1$ symbol sequence to form the address of the LUT. The amplitude correction for the center symbol $\Delta A(k)$ is the difference between the symbol value $S(k)\in \{\pm 1,\pm 3\}$ and the actual sample value for the signal $A(k)$ ($\Delta A(k)=S(k)-A(k)$). As the window moves forward, each time a specific symbol sequence appears, the amplitude correction $\Delta A(k)$ is accumulated at the corresponding LUT entry. A LUT counter ($C$) is used to track the number of updates for each specific entry. The average correction $\overline{\Delta A(k)}$ is applied to the actual sample value for the signal $A(k)$ to produce the corrected output amplitude. In practice, the LUT correction could be pre-calculated or determined in real time based on considering the relevant tradeoffs in performance and complexity.

## 3. Optical pulse shaping

Raised-cosine optical pulse shaping was employed to narrow the modulated signal spectrum and thereby enhance the spectral efficiency and reduce the requirements on the receiver bandwidth and analog-to-digital converter (ADC) sampling rate. A programmable optical filter (POF) with a frequency resolution of 1 GHz was used to shape the modulated signal spectrum [14]. The POF response was set based on obtaining raised-cosine spectra with a specified roll-off factor and included pre-emphasis to compensate for (i) non-ideal features in the output spectra that result from the sharp roll-off of the desired response and the POF resolution, and (ii) the bandwidth of the coherent receiver (32 GHz). The pre-emphasis (inverse Gaussian) was 3.3 dB optical at ± 25.125 GHz from the carrier. Modulated signal spectra before and after the POF are shown in Fig. 2 for the 448 Gbit/s single-carrier DP 16-QAM signal with a roll-off factor *r* of 0.2. The single channel net spectral efficiency is 5.33 b/s/Hz (bit rate of 400 Gbit/s and a bandwidth of 75 GHz, although an assessment of WDM transmission performance is needed to properly specify the spectral efficiency). The received electrical signal has a raised-cosine spectrum as shown in Fig. 3.

For the 1.206 Tbit/s three-carrier DP 16-QAM superchannel signal, the modulated signal spectra for the even channel and two odd channels were separately shaped using two POFs in a manner similar to the 448 Gbit/s single-carrier DP 16-QAM signal. Figure 4 shows the optical spectrum for the 1.206 Tbit/s signal with a roll-off factor of 0.6. The single superchannel net spectral efficiency is 4.47 b/s/Hz (bit rate of 1.005 Tbit/s and a bandwidth of 225 GHz).

## 4. Experimental set-up

A DSP/DAC capability operating at the symbol rate is required to implement the LUT correction in the transmitter. Since this was not available, for demonstration purposes the LUT correction was implemented using off-line DSP of the received signals. For the 448 Gbit/s single-carrier DP 16-QAM signal, the entries for one LUT were obtained based on the received signal for a back-to-back system configuration. For the 1.206 Tbit/s three-carrier DP 16-QAM superchannel signal, the entries for three LUTs were obtained based on the received signal for a back-to-back system configuration. These fixed LUTs were used for all operating conditions (e.g., varying OSNR and fiber length) and represent a practical approach to implementing LUT correction of pattern-dependent distortion. This approach is a nonlinear version of previous work that considered pre-compensation based on a linear characterization (i.e., frequency response) of a back-to-back system [18]. It accurately emulates correction in the transmitter since the effects of additional noise are mitigated by the averaging used to obtain the corrections $\overline{\Delta A(k)}$ and the receiver performs linear detection. For comparison, the LUT entries were also determined for each captured data file for a given operating condition and the resultant LUT was applied to the same data file. These updated LUTs yield the best possible performance using this approach but are less amenable to a practical implementation.

Figure 5 shows the experimental set-up for the 448 Gbit/s single-carrier DP 16-QAM and 1.206 Tbit/s three-carrier DP 16-QAM superchannel transmission systems. For the single-carrier system, an external cavity laser with a linewidth of 100 kHz was used to generate the optical carrier. Four copies of a 56 Gbit/s 2^{15}-1 pseudorandom bit sequence signal were attenuated and combined to generate two four-level drive signals that were applied to an IQ modulator (25 GHz 3-dB bandwidth). After polarization multiplexing emulation, the signal was amplified by an EDFA and applied to a POF to create a raised-cosine spectrum.

For the three-carrier system, three external cavity lasers with linewidths of 100 kHz were used to generate the optical carriers with a channel spacing of 75 GHz. Four copies of a 50.25 Gbit/s 2^{15}-1 pseudorandom bit sequence signal were attenuated and combined to generate two four-level drive signals that were split and applied to two IQ modulators (25 GHz 3-dB bandwidth) with delays for de-correlation of the symbol patterns. The splitting of the four-level signals for the two modulators degraded the signal quality somewhat and would have been avoided had a second pulse pattern generator been available. One modulator was used for channels 1 and 3, and one modulator was used for channel 2. After polarization multiplexing emulation, the signals were amplified, applied to two POFs to create raised-cosine spectra, and then combined.

An EDFA, optical bandpass filter (OBPF) and variable optical attenuator (VOA) were used to set the input power for the re-circulating loop. The loop was comprised of four 75 km spans of standard SMF with a dispersion coefficient of 17 ps/km/nm at 1550 nm and an attenuation of 0.19 dB/km. An EDFA and optical bandpass filter (OBPF, bandwidth of 1.6 nm and 13 nm for the single-carrier and three-carrier signals, respectively) was used in each span. The OBPF removed noise and avoided saturation of the EDFAs. A polarization synthesizer (PS) was used in the loop to scramble the state-of-polarization of the re-circulating signals. The received signal was amplified and filtered (1.3 nm bandwidth) before detection by a polarization- and phase-diverse coherent receiver with 32 GHz bandwidth. The local oscillator laser had a nominal linewidth of 100 kHz. The four signals from the balanced photodetectors were digitized by 80 GSa/s ADCs using two synchronized real-time sampling oscilloscopes (33 GHz bandwidth). For back-to-back measurements, amplified spontaneous emission noise was added to the signal in order to measure the dependence of the BER on OSNR.

The off-line signal processing included (i) quadrature imbalance compensation [19], (ii) re-sampling to two samples per symbol, (iii) fixed frequency domain equalization for chromatic dispersion in the case of fiber transmission, (iv) digital square and filter clock recovery [20], (v) polarization recovery and residual distortion compensation using 25-tap adaptive equalizers in a butterfly configuration, (vi) carrier frequency offset recovery using a spectral domain algorithm [21], (vii) carrier phase recovery using a sliding window two-stage simplified QPSK partitioning and QPSK constellation transformation algorithm [22], (viii) look-up table correction for pattern-dependent distortion and (ix) symbol decisions. The adaptive equalizer used a constant modulus algorithm for pre-convergence followed by a radius directed algorithm [23]. The BER was obtained by direct bit error counting using rectilinear decision boundaries.

## 5. Results

#### 5.1. 448 Gbit/s single-carrier DP 16-QAM signal

To illustrate the LUT correction, a 3-symbol LUT (*n* = 1) is used as an example. Figure 6 shows the average corrections of a fixed LUT for each 3-symbol pattern. The corrections are clearly pattern-dependent and range from −0.4 to 0.4 relative to the symbol values { ± 1, ± 3}. Figure 7 shows a histogram for the corrections for the different occurrences of the symbol sequence [1 1 3]. The variation about the average value (0.4) is due in part to the pattern-dependent distortion depending on more symbols than the nearest neighbours (*n* = 1); the variation is smaller for 5- and 7-symbol LUTs. Constellation diagrams without and with 7-symbol fixed and updated LUT corrections (*n* = 3) are shown in Fig. 8. The 7-symbol LUT correction yields a significant reduction in the error vector magnitude (EVM) from 14.1% to 9.6% for the fixed LUT and 8.8% for the updated LUT.

Figure 9 shows the dependence of the BER on OSNR for the 448 Gbit/s DP 16-QAM back-to-back system without and with fixed LUT correction. Without correction, a BER floor larger than 10^{−3} is observed. With the LUT correction, the BER improves as the number of symbols (2*n* + 1) increases from 3 to 7. For BER = 10^{−3}, the required OSNRs using 3-, 5- and 7-symbol LUT corrections are 27.6, 27.2 and 26.6 dB, respectively. The 7-symbol LUT offers a significant improvement as no BER floor is observed (at least above BER = 10^{−5}).

For comparison, the dependence of the BER on OSNR is shown in Fig. 10 without LUT correction and with 7-symbol fixed and updated LUT corrections. The small difference between the results for the fixed and updated LUTs demonstrates that the practical implementation (fixed LUT) almost achieves the maximum improvement in performance possible with this approach to mitigating pattern-dependent distortion.

To demonstrate the role of the symbols adjacent to the center symbol for 3-, 5- and 7-symbol sequences, the fixed LUT corrections for the center 3-symbol pattern [1 1 3] are shown in Fig. 11. The 4^{4} possibilities of the 7-symbol patterns [*c a* 1 1 3 *b d*] are numbered sequentially on the abscissa, where *a*, *b*, *c* and *d* assume all possible values { ± 1, ± 3}. The 4^{2} possibilities of the 5-symbol patterns [*a* 1 1 3 *b*] and 1 possibility for the 3-symbol pattern [1 1 3] are shown as subsets. Compared with the 5-symbol LUT correction patterns [*a* 1 1 3 *b*], the additional symbols *c* and *d* in the 7-symbol patterns need to be included in order to determine the correction accurately. For each specific value of *a* and *b*, the LUT corrections [*c a* 1 1 3 *b d*] for different values of *c* and *d* vary significantly from the correction for [*a* 1 1 3 *b*]. Thus, the 7-symbol fixed LUT correction provides a more significant benefit than the 5-symbol fixed LUT correction.

The received optical spectra for the back-to-back system and for transmission over 1800 km of fiber are shown in Fig. 12. The optical filters in the loop do not affect the modulated signal spectrum because of their flat passband responses. Therefore, the spectrum specified at the output of the POF is preserved after transmission.

Figure 13 illustrates the dependence of the BER on launch power for transmission of the 448 Gbit/s DP 16-QAM signal over 900 and 1200 km of SMF without and with 7-symbol fixed LUT correction. Without the LUT correction, the BER curves are all above the FEC threshold of 3.8 × 10^{−3}. The 7-symbol fixed LUT correction significantly improves the BER performance allowing transmission over 1200 km with a launch power range of 2 dB.

Figure 14 shows the dependence of the BER on the fiber length for the 448 Gbit/s DP 16-QAM signal with a launch power of 1 dBm without and with 7-symbol fixed LUT correction. Without the LUT correction, the BER is above the FEC threshold. With the 7-symbol fixed LUT correction a maximum transmission distance of 1200 km can be achieved at the FEC threshold.

#### 5.2. 1.206 Tbit/s three-carrier DP 16-QAM* s*uperchannel signal

The OSNR sensitivity (0.1 nm noise bandwidth) for BER = 10^{−3} as a function of the roll-off factor *r* is shown in Fig. 15 for the superchannel with a channel spacing of 75 GHz. This result is for channel 2 only with 7-symbol fixed LUT correction. The best back-to-back performance is obtained for *r* = 0.6. The increase in the required OSNR for *r* < 0.6 is attributed to the limitations in achieving raised-cosine spectra with sharp roll-off using the POF and the increase for *r* > 0.6 is attributed to inter-channel crosstalk. The constellation diagram for *r* = 0.6 is shown as an inset in Fig. 15. The EVM is 11.3%.

The dependence of the BER on OSNR is shown in Fig. 16 for *r* = 0.6 without and with 7-symbol fixed LUT correction. Results are shown for the three individual channels comprising the superchannel, the superchannel (average of the three individual channels), and for comparison, the case of just a single channel (channel 2). Without LUT correction, a BER floor larger than 10^{−3} is observed. The 7-symbol LUT offers a significant improvement and yields an OSNR sensitivity of 27.2 dB for BER = 10^{−3}. The improvement is less for 3- and 5-symbol LUTs indicating a memory of 3 symbols (2*n* + 1 = 7) for the pattern-dependent distortion. The performance of the superchannel with 7-symbol LUT correction is similar to that of the single channel for BER values larger than 3 × 10^{−4} and slightly worse otherwise.

For comparison, the dependence of the BER on OSNR is shown in Fig. 17 without LUT correction and with 7-symbol fixed and updated LUT corrections. While the difference between the results for the fixed and updated LUTs is larger than that for the single-carrier signal, the fixed LUT nonetheless yields a significant improvement in performance. This larger difference is due, in part, to the degradation in the signal quality arising from the additional splitting of the four-level signals for the two modulators.

Figure 18 shows the dependence of the BER (average of the three channels) on the per-channel launch power for transmission of the 1.206 Tbit/s DP 16-QAM signal over 1500 km of SMF with 7-symbol fixed LUT correction. Results are presented for different values of the roll-off factor *r*. The optimum launch power is 1.5 dBm for all values of *r*. For this superchannel configuration, the effects of inter-channel crosstalk and fiber nonlinearities yield the best results for *r* = 0.8.

## 6. Conclusion

Single-carrier 448 Gbit/s DP 16-QAM and three-carrier 1.206 Tbit/s DP 16-QAM superchannel transmission has been demonstrated using 7-symbol LUT correction for the transmitter pattern-dependent distortion and optical pulse shaping to enhance the spectral efficiency and reduce the requirements on the receiver bandwidth and ADC sampling rate. By combining these techniques, the back-to-back OSNR sensitivities were 26.6 dB and 27.2 dB (BER = 10^{−3}) and transmission over 1200 (FEC threshold of 3.8 × 10^{−3}) and 1500 km (FEC threshold of 2 × 10^{−2}), respectively, of SMF with EDFAs was achieved.

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