We describe a 2048 QAM single-carrier coherent optical transmission over 150 km in detail. The OSNR at the transmitter was increased by 5 dB and the phase noise at the receiver was reduced from 0.35 to 0.17 degrees compared with a previous 1024 QAM transmission. Furthermore, we employed an A/D converter with a higher ENOB (7 bit) to guarantee the SNR of the digital QAM data, and introduced a polarization-demultiplexing algorithm to fast track the polarization state transition. As a result, a 66 Gbit/s polarization-multiplexed 2048 QAM signal was successfully transmitted within an optical bandwidth of 3.6 GHz including a pilot tone, and a potential SE of 15.3 bit/s/Hz under a 20% FEC overhead was achieved.
© 2015 Optical Society of America
Increasing the spectral efficiency (SE) toward the Shannon limit has been an important research subject with a view to meeting the growing demand for higher transmission capacity in optical backbone networks . Higher-order quadrature amplitude modulation (QAM) and orthogonal frequency-division multiplexing (OFDM) have been adopted to achieve an SE exceeding 10 bit/s/Hz [2–8], which makes it possible to realize an ultra-large wavelength-division multiplexing (WDM) capacity of > 100 Tbit/s by fully utilizing the finite bandwidth over the C- and L-bands in a single core . Recently, 512 QAM single-carrier transmission over 44 km was reported by employing an ultra large area fiber (ULAF) , where fiber nonlinearities were not compensated. 2048 QAM transmission was also reported , however the transmission distance was limited to only 3 km. To expand the transmission distance in such an extremely high-order QAM, further careful handling of both phase noise and the optical signal-to-noise ratio (OSNR) is essential.
In this paper, we describe in detail our realization of 2048 QAM single-carrier coherent optical transmission over 150 km. In contrast to our previous report , we removed the guard band between the QAM signal and the tone, and then a 66 Gbit/s polarization-multiplexed signal was transmitted within an optical bandwidth of 3.6 GHz including the pilot tone, resulting in a potential SE of 15.3 bit/s/Hz under a 20% soft-decision FEC overhead . This paper also elaborates on the preliminary report  by providing detailed information about this ultra-multilevel QAM transmission technique. We improved our coherent optical detection system with respect to the OSNR at the transmitter and the phase noise in the optical phase locked loop (OPLL) circuit at the receiver. To guarantee the SNR of the digital QAM data, we employed a digital oscilloscope with a higher effective number of bits (ENOB) of 7 bits. Furthermore, we introduced a polarization demultiplexing algorithm that does not depend on the multiplicity of the QAM signal for fast tracking the polarization state transition in the Stokes space . Finally, we discuss the issues that must be dealt with if we are to achieve 4096 QAM coherent transmission.
2. Experimental setup
Figure 1 shows our experimental setup for polarization-multiplexed, 3 Gsymbol/s, 2048 QAM coherent optical transmission. As a transmitter, we used a 1.5 µm acetylene frequency-stabilized fiber laser with a linewidth of 4 kHz. The coherent light from the laser passed through an erbium-doped fiber amplifier (EDFA) and was coupled to an IQ modulator, where the light was modulated with a 3 Gsymbol/s, 2048 QAM baseband signal and a tone signal generated by an arbitrary waveform generator (AWG, M8190A). The AWG was running at 9 Gsamples/s with a 12-bit resolution. At the AWG, we adopted a Nyquist filter with a roll-off factor of 0.2 to reduce the bandwidth to 3.6 GHz, and we also employed frequency-domain pre-equalization (pre-FDE) with an FFT size of 16384 to compensate for distortions caused by hardware imperfections in the transmitter. The tone signal, whose frequency was shifted by 1.8 GHz against the carrier frequency, was used for the optical phase tracking of the local oscillator (LO) under OPLL operation. We set the power ratio of the tone signal to the QAM data signal at −20 dB. The QAM data and the tone signals were orthogonally polarization-multiplexed and coupled into two 75 km spans of super large area (SLA) fiber, whose loss was 0.20 dB/km and whose Aeff was 106 µm2. The fiber loss was compensated for by using EDFA and Raman amplifiers. The Raman amplifiers were backward pumped and provided a 9.5 dB gain that contributed to the total gain of 15.0 dB in each span.
At the receiver, the signal was homodyne-detected with an LO whose phase was locked to the tone signal via an OPLL. The detected signals were A/D-converted at 40 Gsample/s (DSO 91304A) and processed with an offline digital signal processor (DSP). In the DSP, the Pol-Mux QAM data were polarization-demultiplexed with an algorithm based on the Stokes vectors . Then, we compensated for fiber nonlinearities and dispersion simultaneously by using a digital back-propagation (DBP) method . We employed a split-step Fourier analysis of the Manakov equation  with a 9.375 km step size. After that, we adopted FDE to compensate for residual distortions caused by hardware imperfections in the receiver. We also used an adaptive 99-tap FIR filter to remove the residual polarization cross-talk by minimizing the error vector magnitude (EVM) with a decision directed least mean square (DD-LMS) algorithm. The clock recovery was used to compensate for the desynchronization of the clock between the A/D and D/A converters. Finally, the compensated QAM signal was demodulated into binary data, and the bit error rate (BER) was measured. In Fig. 1, the inset shows the electrical spectrum of the demodulated signal at the DSP. There was no guard band between the QAM signal and pilot tone, and the signal bandwidth including the pilot tone was 3.6 GHz due to the adoption of a Nyquist filter.
3. Performance improvements of coherent optical transmission system
Since a 2048 QAM format requires a high SNR for the QAM signal and precise phase control in a coherent detection system, we increased the OSNR and reduced the phase noise in the OPLL circuit compared with those in the 1024 QAM experiment . Furthermore, we employed a digital oscilloscope with a higher ENOB to guarantee the SNR of the digital QAM signal and introduced a polarization demultiplexing algorithm in the DSP.
Figures 2(a) and 2(b) show the configurations of the previous  and present transmitters, respectively. To increase the OSNR of the QAM signal, we removed the optical couplers and reduced the insertion loss compared with  by generating a pilot tone signal and a QAM signal simultaneously at the AWG. We also increased the input power into the IQ modulator by 3 dB. Figures 3(a) and 3(b) show the optical spectrum before and after the improvements, respectively. After the improvements, the OSNR of the output signal from the transmitter increased from 40 to 45 dB as shown in Fig. 3. It should be noted that a 2048 QAM signal requires a theoretical Eb/N0 value as high as 30.4 dB to achieve a BER below 5.5x10−6, whichwas the minimum BER value per polarization that could be measured in our system with a data length of 4096 x 4. The data length of 4096 was the maximum length at which we could demodulate the QAM signals at one time in our off-line DSP. The value of Eb/N0 corresponds to OSNR = (R/Δν) Eb/N0 = 34.6 dB, where R ( = 33 Gbit/s) is the bit rate per single polarization and Δν ( = 12.5 GHz) is the bandwidth used for optical signal detection. This indicates that the present OSNR is sufficient for achieving a BER below 5.5x10−6 under a back-to-back condition.
Figures 4(a) and 4(b) show the configurations of the previous  and present receivers, respectively. The phase noise is inversely proportional to the OPLL bandwidth in accordance with the following equation 
Figures 5(a) and 5(b) show the SSB phase noise power spectrum before and after the improvement, respectively. As a result, the phase noise in the OPLL circuit was reduced from 0.35 to 0.17 degrees. The phase tolerance for 2048 QAM, determined by the phase difference between the two neighboring symbols, is ± 0.87 degrees. Therefore, the phase noise in the OPLL circuit was successfully reduced to less than 20% of the phase tolerance.
Figures 6(a) and 6(b) show the constellation maps of a 2048 QAM signal under back-to-back conditions obtained using two types of digital oscilloscopes with ENOBs of 5.8 and 7 bits, respectively. By employing the digital oscilloscope with a higher ENOB, the EVM of the constellation map was reduced from 0.76 to 0.59%, and the BER was improved from 1.78x10−3 to 1.2x10−4. Here, we calculated the BER by averaging 4096 x 4 symbols. This indicates that it is necessary to increase not only the OSNR but also the SNR of the digital QAM data by using an A/D converter with a higher ENOB.
Figure 7 shows the principle of a polarization-demultiplexing algorithm based on Stokes vectors for resolving a Pol-Mux QPSK signal . The four QPSK symbols from the complex plane can be described in the Stokes space. The data transition clearly defines a plane whose normal line J1-J2 contains information about the polarization states of the transmitted signal. Here, J1 and J2 represent the orthogonal Jones vectors, which are labeled H and V in the top left of Fig. 5 for ideal linear horizontal and vertical polarization states. This plane could be found by adapting a least square fitting of the Stokes vectors for QAM signals in the Stokes space. Therefore, by finding the least square plane and the normal line J1-J2, and aligning it with the H-V by multiplying a unitary matrix calculated from the normal vector , we can realize polarization demultiplexing.
Figure 8(a) shows the demodulated signals with the polarization demultiplexing algorithm based on the Stokes vectors, for 4, 16, and 2048 QAM signals under a back-to-back condition. Here, we also applied a conventional extended Kalman filter (EKF) algorithm  to the QAM signals, and the corresponding demodulated signals are also shown in Fig. 8(b) for comparison. As seen in Fig. 8(a), the Stokes space technique is independent of the modulation format since this technique does not require carrier phase recovery or data demodulation. Furthermore, the convergence speed is very fast (µs-order) and sufficient for tracking a dynamic change of polarization in field installed fibers . On the other hand, the EKF algorithm provides an optimal estimation of the physical quantities under feedback control from the error of the demodulated signal. The EKF algorithm can track the polarization state transition at a rate as fast as 6.8 Mrad/s . However, the convergence depends on the degree of multiplicity of the QAM signal, therefore the filter coefficients cannot be properly fixed for the high-order QAM as shown in Fig. 8(b). By using the Stokes space technique in the DSP, we were able to track the polarization state transition even with a QAM multiplicity as high as 2048.
4. Experimental results for 3 Gsymbol/s, Pol-Mux, 2048 QAM coherent optical transmission
Figure 9 shows the BER characteristics as a function of the launched power after a 150 km transmission with and without compensation for XPM between the two polarizations using the DBP method. We set the fiber launched power at −2 dBm to maximize the OSNR and minimize nonlinear impairments. For this launched power, we obtained an OSNR of 36.5 dB after a 150 km transmission. Among various linear and nonlinear transmission impairments, we can easily pre-compensate for chromatic dispersion and SPM without the DBP method. However, the distortions caused by XPM between the two polarizations still remains and degrades the performance of a 2048 QAM transmission. As shown in Fig. 9, compensation for XPM is important for 2048 QAM transmission. Figures 10(a) and 10(b) show the BER characteristics and the constellation map of 2048 QAM signal after a 150 km transmission respectively. As shown in Fig. 10(a), we achieved a BER lower than the FEC threshold (2x10−2) under a 20% overhead. Thus, in this experiment, 66 Gbit/s data were transmitted within an optical bandwidth of 3.6 GHz including the pilot tone, resulting in a potential SE of 15.3 bit/s/Hz.
5. Remaining issues for 4096 QAM coherent transmission
Below we describe the issues that must be overcome if we are to achieve 4096 QAM coherent transmission. The 4096 QAM format requires a theoretical Eb/N0 value as high as 33.0 dB to achieve a BER below 5.5x10−6. This Eb/N0 value corresponds to OSNR = (R/Δν) Eb/N0 = 37.6 dB and SNR = (log2 M) Eb/N0 = 45.0 dB, where M ( = 4096) is the multiplicity of the QAM signal. This indicates that the present OSNR ( = 45 dB) under a back-to-back condition is sufficient for achieving a BER below 5.5x10−6. On the other hand, we obtained an OSNR of 36.5 dB after a 150 km transmission. The OSNR exceeded the value of 29.0 dB for 4096 QAM needed to achieve a BER lower than the FEC threshold (2x10−2). Furthermore, the phase noise in the OPLL circuit ( = 0.17 deg.) is less than the phase tolerance of ± 0.45 degrees for the 4096 QAM format. This indicates that we still have a margin of the phase stability for 4096 QAM transmission. On the other hand, an SNR of 45.0 dB in the 4096 QAM data requires an ENOB of 7.2 bits in the A/D converter, in accordance with the following equation ,
This value is very close to that of our present digital oscilloscope (7 bits). Therefore, we must employ an A/D converter with an ENOB that exceeds 7 bits. In addition, a digital oscilloscope with a higher ENOB is also indispensable in terms of realizing more precise nonlinear compensation for XPM in the DBP method. This precise nonlinear compensation may improve the OSNR of the QAM signal after the transmission by increasing the launched power into the fiber link.
We described a 2048 QAM coherent optical transmission technique in detail, in which we grately improved the OSNR at the transmitter and the phase noise in the OPLL circuit. We showed experimentally that increasing both the SNR of the digital QAM data and the OSNR is indispensable for a 2048 QAM signal. We also introduced a polarization demultiplexing algorithm based on the Stokes vectors that enabled the fast tracking of the polarization state transition even for such a high multiplicity. With these techniques, we succeeded in transmitting a Pol-Mux 3 Gsymbol/s, 2048 QAM (66 Gbit/s) signal over 150 km with an optical bandwidth of 3.6 GHz including a pilot tone, resulting in a potential SE of 15.3 bit/s/Hz under a 20% FEC overhead. Finally, we discussd the issues that remain with respect to realizing 4096 QAM coherent optical transmission.
We sincerely thank Agilent Technologies for supporting our experiment.
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