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Abstract
We describe the first observation of guided acoustic-wave Brillouin scattering (GAWBS) phase noise in a digital coherent optical fiber transmission. GAWBS noise, which is a forward lightwave generated by thermally excited vibration modes in a cylindrical fiber structure, occurs coherently not only in a signal at a single carrier frequency, but also in modulated wide-band optical signals. Since the signal-to-GAWBS-noise ratio is independent of signal power, it has caused problems in various fields including quantum optics. We point out that GAWBS noise exists even in a digital coherent transmission system such as quadrature amplitude modulation (QAM) and degrades the transmission performance since the phase noise is inevitably included within the bandwidth of the transmitted data. We propose two analogue and one digital method to compensate for the GAWBS noise and demonstrate improved performance in a QAM digital coherent transmission.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Digital coherent optical transmission technology has become a very popular way of increasing the total information capacity of data with a high spectral efficiency [1–6]. In such a system, it is essential that we understand and suppress fiber nonlinearities if we are to improve transmission performance. A digital back propagation (DBP) method associated with a coupled Manakov equation plays an important role in removing cross-phase and self-phase modulation [7,8]. Similarly, as an analogue method, since both fiber dispersions and Kerr nonlinearities are deterministic, the signal distortion induced by such parameters can be exactly compensated for by adopting optical phase conjugation [9] or mid-span spectral inversion [10]. However, in principle the random phase fluctuation that occurs as the result of a nonlinear interaction between a noise such as amplified spontaneous emission (ASE) from erbium-doped fiber amplifiers (EDFAs) and a data signal cannot be completely removed, and we call this the Gordon-Mollenauer effect [11].
Although we have been mitigating various fiber nonlinearities to improve transmission performance, there is another important nonlinear effect, namely guided acoustic-wave Brillouin scattering (GAWBS) noise [12,13], which is inevitably generated in a fiber since it occurs as the result of steady-state thermal vibration in a cylindrical fiber structure. GAWBS noise was discovered by Shelby et al. in 1985 [12,13] and several groups subsequently reported that it degrades the squeezing of quantum states and precise optical measurements [14–16]. Stimulated Raman scattering (SRS) [17,18] and stimulated Brillouin scattering (SBS) [19–22] occur at thresholds of a few hundred mW and 10 mW, respectively, whereas GAWBS noise occurs at any power level. In addition, the lightwaves induced by SRS propagate in a forward direction and those induced by SBS propagate backwards thus satisfying the phase matching condition. Although SBS occurs through an interaction with an ordinary longitudinal acoustic wave, GAWBS is non-stimulated scattering in a forward direction and occurs as a result of the interaction of light with a transverse acoustics vibration in a thermally steady-state condition. Since GAWBS noise is an optical phase fluctuation that occurs coherently with acoustic waves, independent of input power through the thermal fluctuation of a cylindrical structure, and propagates in the transmission direction, it may degrade the quality of the transmitted optical data signal. That is, when GAWBS noise, which contains many frequency components offset from the optical carrier, penetrates the bandwidth of a transmitted coherent signal, it degrades that signal. If the transmission fiber can be cooled to liquid nitrogen temperature and the acoustic vibrations stopped, it may be possible to remove the noise. However, it appears to be unrealistic in ordinary optical fiber transmission cables.
In the process of GAWBS noise generation, a light beam with a single-frequency optical spectrum is generally coupled into a fiber and randomly modulated with many thermal vibration modes. This process generates many discrete optical frequencies over a bandwidth of 500 MHz [12,13]. Surprisingly, we were able to observe GAWBS noise even when the light beam was data-modulated for example, with a quadrature amplitude modulation (QAM) format that had a broad spectral profile. GAWBS noise occurs through a linear interaction with the vibration of the fiber structure, and so the optical signal-to-GAWBS-noise ratio is unrelated to the input power, that is, there is no threshold power for the GAWBS noise excitation. Therefore, it is very important to mitigate the GAWBS noise in a coherent fiber transmission system because it is generated at the power level of ordinary optical transmission.
In this paper, we first describe two cases where we observed GAWBS noise in a digital coherent transmission, namely with a single carrier and with QAM data. We then propose two analogue and one digital method designed to compensate for GAWBS noise. We cannot remove the GAWBS noise itself, but we can compensate for the effect after the transmission by using the following techniques, which are divided into two parts. In the first part, we describe two analogue methods which we call the reverse phase modulation (RPM) method and the injection locking (IL) method. In the latter part, we propose a digital compensation (DC) method, in which an analog-to-digital (A/D) converted data signal is divided with an A/D converted temporal phase fluctuation of GAWBS noise. With both the analogue and digital methods, we show that it is possible to improve the error vector magnitude (EVM) of the constellations of the transmitted QAM data.
2. Observation of GAWBS noise in digital coherent transmission
First, we prepared a simple heterodyne detection system with an intermediate frequency (IF) of 1 GHz for GAWBS noise observation, which is shown in Fig. 1. The light source and local oscillator (LO) were external cavity laser diodes (ECLD) with a linewidth of 4 kHz and an oscillation wavelength of 1539 nm. The frequency difference between them was set at approximately 1 GHz by tuning the temperature and the driving current of the LO ECLD. The 160 km-long fiber we used consisted of two 80 km spans of standard single-mode fiber (SSMF) with a loss of 0.2 dB/km and a dispersion of 18 ps/nm/km, respectively. The input power level into the test fiber was set at 0 dBm for both the first and second spans, which is sufficiently lower than the SBS threshold of 10 dBm.
Fig. 1 Observation of GAWBS noise in a heterodyne coherent optical fiber system. The light source is an ECLD with a linewidth of 4 kHz. The fiber is a standard single-mode fiber (SSMF) with a length of 160 km. The IF beat signal between the signal beam and the local oscillator (LO) beam was set at 1 GHz. EDFA: erbium-doped fiber amplifier, PD: photo detector, RF: radio frequency.
Figures 2(a) and 2(b) show the changes in the IF frequency spectrum under a back-to-back condition (before propagation) and after propagation over 160 km, respectively. Figure 2(c) shows the radio frequency (RF) spectrum of the transmitted signal with direct detection after propagation over 160 km. In Fig. 2(a), we cannot see any beat signals in the 1 GHz IF signal (center position). However, after the propagation it changes to that shown in Fig. 2(b), where there are many spectral components over a bandwidth of 500 MHz. The power level of the phase noise per mode is approximately 50-60 dB below the input power level. It is also clearly seen in Fig. 2(c) that there are no amplitude modulation (AM) noise components after the propagation. These results allow us to conclude that the noise appearing in Fig. 2(b) is phase noise as it is expected from GAWBS and possibly includes polarization noise due to TR2m modes.
Fig. 2 Changes in the heterodyne-detected intermediate frequency (IF) frequency spectrum before and after propagation (radio bandwidth (RBW): 100 kHz). (a) Under a back-to-back condition and (b) after 160 km propagation. (c) Radio frequency (RF) spectrum of the propagated light beam obtained with direct detection.
There are two important acoustic modes responsible for the GAWBS noise, R0m and TR2m, that cause spectral modulations as shown in Figs. 3(a) and 3(b), respectively, in which the R01 and TR21 vibrational modes are shown as an example. The R0m mode vibrates in the radial direction of the fiber cross-section and induces a pure optical phase modulation in the transmitted light signal. TR0m vibrates in the torsional and radial directions and causes phase modulation and polarization modulation, simultaneously. The resonant frequencies of such transverse vibration modes are determined by the diameter and acoustic-wave velocity of the silica fiber neglecting small inhomogeneities caused by the fiber core or the dopant profile. Therefore, a 125 μm step-index fiber generates the same vibration frequency regardless of type of fiber e.g. single-mode fiber (SMF), dispersion-shifted fiber (DSF), and dispersion compensation fiber (DCF). Figures 4(a) and 4(b) compare the noise spectra of SMF (red) and DSF (blue) and of SMF (red) and SMF + DCF (blue), respectively. It is clearly seen that the noise frequencies are independent of fiber type. We then compared the noise frequencies with theoretical results for the GAWBS noise obtained from a 125 μm silica fiber [12, 13]. The results are shown in Table 1, where 1(a) and 1(b) correspond to the R0m and TR2m modes, respectively. It is clearly seen that they agree well. Therefore, the phase noise that we observed is GAWBS noise.
Fig. 4 Comparison of noise spectra in different fibers (radio bandwidth (RBW): 100 kHz). (a) Comparison of SMF (red) and DSF (blue) and (b) of SMF (red) and SMF + DCF (blue). SMF: single-mode fiber, DSF: dispersion-shifted fiber, and DCF: dispersion compensation fiber. It is clearly seen that the noise frequencies are independent of fiber type.
Table 1. Comparison of experimentally detected noise frequencies in a 125 μm fiber and their theoretical values from ref [12]. (a) R0m mode and (b) TR2m mode.
As a next step, we investigated how the GAWBS noise evolves over the transmission distance. Figures 5(a)-5(e) show the evolution of the GAWBS noise for transmission fiber lengths in the 5 to 150 km range. It is seen that the noise power increases with an increase in fiber length. In Fig. 6(a), we summarize the evolution of the GAWBS noise as a function of the fiber length, where we selected three GAWBS frequencies of 139.3 MHz (TR2m), 321.2 MHz (R0m), and 464.2 MHz (R0m) as parameters. We find that the power level increases linearly with length. Since this process is not an exponential gain process, the GAWBS power increases linearly with fiber length. Figure 6(b) shows the power distribution of the GAWBS noise spectra, in which the noise power decreases at higher GAWBS frequencies. This may be attributed to the fact that the GAWBS-induced phase modulation is cancelled out locally in the radial direction as the frequency of the acoustic mode increases [12]. In addition, the guided acoustic modes at higher frequencies experience greater damping.
Fig. 5 GAWBS noise evolution for fiber lengths in the 5 km to 150 km range (radio bandwidth (RBW): 100 kHz). DSF: dispersion-shifted fiber.
Fig. 6 GAWBS noise characteristics. (a) Power increase in GAWBS noise spectra as a function of fiber length. Three frequencies of 139.3 MHz (TR2m), 321.2 MHz (R0m), and 464.2 MHz (R0m) are chosen as parameters. (b) Power distribution of GAWBS noise spectra.
Since the phase and amplitude information in the GAWBS noise spectrum is reflected completely in the IF heterodyne signal in the time domain, it appears to be possible to compensate for the GAWBS noise by applying reverse phase modulation derived from the GAWBS noise information itself. The RPM is applied through a phase modulator to the transmitted data signal as shown in Fig. 7, where a single-frequency carrier from an ECLD was transmitted over 160 km without QAM modulation. The transmitted signal was heterodyne-detected with an IF frequency offset of 10 GHz and it was possible to extract the GAWBS information with a double balanced mixer (DBM) by mixing the signal with a 10 GHz synthesizer signal, and finally only the baseband GAWBS noise components were fed back to the phase modulator. To maintain 10 GHz phase locking between the transmitted data signal and LO, an optical voltage-controlled oscillator (OVCO) [23] was used that can provide the LO ECLD output with an instantaneous frequency shift. A phase modulator and an optical narrowband filter are used in combination to extract the first order side-band of the phase modulation so that the output signal can be directly frequency-shifted in proportion to a voltage error signal from the DBM. The loop filter is a low-pass filter with a 3 dB roll-off frequency of 10 MHz. Note here that since the bandwidth of the OVCO was ~4 MHz, the OVCO output does not contain the GAWBS noise information. It is also important to note that the reverse phase modulation must be strictly inverted with the GAWBS noise in the time domain so that the GAWBS noise is completely cancelled out. Therefore, we installed an optical delay line before the phase modulator to obtain perfect timing between the GAWBS noise and the transmitted data. Assuming a highest GAWBS frequency of 500 MHz, the timing mismatch must be much smaller than 2 ns, which corresponds to a fiber length of 0.4 m. In the present experiment, the fiber length was adjusted in steps of as small as 4 mm. Furthermore, the whole optical path length in the receiver is designed to be less than 10 m so that the change in the optical path length caused by ambient conditions such as temperature drift is negligibly small thus allowing us to avoid any interferometric instability.
Fig. 7 Reverse phase modulation (RPM) method for GAWBS noise compensation. No QAM modulation was applied to detect pure GAWBS noise. The optical voltage-controlled oscillator (OVCO) was adopted for phase locking between the transmission signal and the local oscillator (LO) ECLD. A grating filter with a 5 GHz bandwidth was used as a narrow band optical filter in the receiver. EDFA: erbium-doped fiber amplifier, PC: polarization controller, SSMF: standard single-mode fiber, PD: photo detector, A/D: analog-to-digital converter, DBM: double balanced mixer, LN: lithium niobate, RF: radio frequency, VCO: voltage controlled oscillator.
Figure 8 shows how the GAWBS noise can be suppressed with the RPM method. Figure 8(a) shows the case before compensation, and Fig. 8(b) shows that after compensation. It is clearly seen that the GAWBS noise is successfully compensated for. Specifically, when we compare the integrated GAWBS noise in Figs. 8(a) and 8(b), we find that the noise power decreased to 7% after compensation. We also evaluated the GAWBS noise compensation performance by using the EVM of a carrier constellation without modulation, as shown in Figs. 9(a)-9(c). Figure 9(a) shows a constellation under a back-to-back condition, 9(b) shows that after transmission without phase compensation, and 9(c) shows that after compensation. Here, the phase fluctuation of the received IF signal was analyzed with a digital signal processor (DSP). The received optical power was 0 dBm. No other compensation of nonlinear impairments associated with transmission was adopted when measuring the IF signal. Here we use the EVM as a parameter for GAWBS noise evaluation, where the EVM is defined by the ratio of the noise variance to the optical amplitude. The EVM was increased to 1.6% after the propagation as shown in 9(b) from the original EVM of 0.9% shown in 9(a). However, as shown in Fig. 9(c), it recovered to 1.0% with the RPM method. This means that the RPM method presented here is very effective in compensating for GAWBS noise.
Fig. 8 GAWBS noise compensation with the reverse phase modulation (RPM) method: (a) before compensation and (b) after compensation (radio bandwidth (RBW): 100 kHz).
Fig. 9 Evaluation of degree of GAWBS noise compensation by using the error vector magnitude (EVM) of a carrier constellation. (a) Constellation under a back-to-back condition, (b) after transmission without phase compensation, and (c) with compensation.
Thus far, we have investigated a single carrier GAWBS effect without data modulation. Although the peak power of the GAWBS noise may be reduced when actual data modulation is applied, the GAWBS noise still remains because the data signal is also coherently modulated with the thermal acoustic vibration regardless of the linewidth of the light beam. This is entirely different from SBS [19,20], which has a clear threshold, and the gain of SBS can be reduced by applying a small frequency modulation to the carrier signal. With silica fiber, the SBS threshold is approximately 10 mW, the Stokes shift is approximately 11 GHz and the linewidth is approximately 10 MHz. It should be noted that SBS usually has one strong Stokes mode, which is different from the multiple modes caused by GAWBS.
Figure 10 shows how the GAWBS noise is generated even in a QAM coherent transmission, where 10(a)-10(e) correspond to a 30 Mbaud to 3 Gbaud range. The QAM multiplicity was set at 64. To investigate the GAWBS noise evolution in detail, the QAM transmission symbol rate was first deliberately reduced to 30 Mbaud 64 QAM whose bandwidth then became narrower than a typical frequency separation of the GAWBS modes of 50 MHz (see Table 1). In this case, a QAM electrical signal was supplied by an arbitrary waveform generator (AWG) as shown in Fig. 7. In Fig. 10, a QAM data spectrum is placed at the center, and on both sides we clearly see modulated and broadened GAWBS noise components, (especially in Fig. 10(a)). The GAWBS power level was approximately 50 dB down from the data signal peak. The original GAWBS noise for a single carrier signal has a linewidth of less than 10 MHz, but it becomes broader due to QAM modulation. When the symbol rate exceeds 60 Mbaud, the GAWBS noise components start to overlap each other as seen in Figs. 10(b)-10(d), and form a widely broadened phase noise. It is important to note that such GAWBS noise also pervades the original QAM data spectrum and degrades the transmission quality. Note here that the band edges of the QAM spectrum have small spectral shoulders, which are due to self-phase modulation through the transmission fiber with an input power of 0 dBm, not GAWBS noise.
Fig. 10 Generation of GAWBS noise in a QAM coherent transmission (radio bandwidth (RBW): 100 kHz). The symbol rate of the QAM transmission started from 30 Mbaud, which is narrower than the typical frequency separation of the GAWBS modes of 50 MHz. (a) to (d) correspond to data speeds of 30 Mbaud, 60 Mbaud, 100 Mbaud, and 3 Gbaud, respectively. The absolute center frequency of the IF spectrum is 3 GHz.
3. Suppression of GAWBS noise in digital coherent transmission and improvements in transmission performance
In this section, we describe three methods designed to compensate for the GAWBS noise in a digital coherent transmission. Section 3-1, 2, and 3 describe reverse phase modulation (RPM), injection locking (IL), and digital compensation (DC) methods, respectively. As regards the RPM and IL methods, which are analogue methods, IL is easier and more cost effective than the RPM method since there is no need to employ a phase modulator to compensate for the GAWBS noise. The DC method is much easier than the analogue methods since there is no need to use a phase modulator or an injection locking technique, but the insufficient resolution of A/D convertor may limit the performance. In all our experiments, the input power level to the transmission fiber was set at 0 dBm for both the first and second spans.
3.1 Reverse phase modulation (RPM) method
In this method, we first extract the GAWBS noise phase information using a tone signal, then reverse phase modulation is applied to the transmitted data with appropriate timing adjusted by the delay line using an LiNbO3 (LN) phase modulator so that the GAWBS noise can be compensated for. It is important to note that the tone signal and the QAM data signal are simultaneously and coherently modulated with the same GAWBS noise, as the GAWBS noise is determined by the thermal acoustic vibrations of the silica structure itself, and therefore, any light beam is affected in the same manner. In section 2, we showed that the RPM is effective in compensating for the GAWBS in a single carrier. Here, we show that the RPM method is effective even in an actual data transmission.
Figure 11 shows a transmission setup with 3 Gbaud 64 QAM, in which we incorporated the RPM method. A pilot tone signal is generated by splitting a part of the ECLD output with a coupler and applying a frequency downshift of 10 GHz with a single-sideband (SSB) modulator used as an optical frequency shifter (OFS). The spectrum of the QAM and tone signals are shown schematically in the inset. The QAM data and the tone signal are combined and coupled into a transmission fiber. A tone signal can be used not only for phase locking the OVCO to the data signal, but also for detecting the GAWBS noise. The GAWBS noise components within the QAM data bandwidth can be compensated for by the RPM signal, which is detected by a beat note between the tone signal (fs-10 GHz) and the LO ECLD signal (fLO). Figure 12 shows experimental results obtained (a) before and (b) after GAWBS compensation. Here, a 99-tap finite impulse response (FIR) filter and clock recovery are adopted for DSP when demodulating the QAM signals. The EVM can be reduced from 2.2%to 1.9%, which indicates that GAWBS noise compensation is also possible even in the QAM data transmission. Since QAM modulation largely broadens the spectral width, the level of the GAWBS noise can be widely broadened in the QAM bandwidth, which may result in a weaker phase compensation performance than that in Fig. 9.
Fig. 11 Experimental setup for 3 Gbaud 64 QAM digital coherent transmission with the reverse phase modulation (RPM) method. The tone signal can be used for both optical voltage controlled oscillator (OVCO) and for detecting the GAWBS phase fluctuation. A grating filter with a 5 GHz bandwidth was used as a narrow band optical filter in the receiver. EDFA: erbium-doped fiber amplifier, PC: polarization controller, OFS: optical frequency shifter, SSMF: standard single-mode fiber, PD: photo detector, B-PD: balanced photo detector, A/D: analog-to-digital converter, DSP: digital signal processor, DBM: double balanced mixer, LN: lithium niobate, RF: radio frequency, VCO: voltage controlled oscillator.
Fig. 12 Experimental results with the reverse phase modulation (RPM) method. (a) Before GAWBS compensation and (b) after compensation. The error vector magnitude (EVM) was reduced from 2.2% to 1.9%.
3.2 Injection locking (IL) method
The IL method makes it possible to directly copy the GAWBS noise information into an LO signal. Since the LO signal completely reflects the GAWBS information, there is no need to use a phase modulator as we employed in the RPM method. Figure 13 show GAWBS noise compensation using an IL method. A tone signal, which accompanies the GAWBS noise, is used for the injection locking of a distributed feedback laser diode (DFB LD) serving as the LO [24] and we make a copy of the noise, namely a random temporal phase fluctuation of GAWBS noise. Then, both the data signal after a proper time delay and the LO signal, whose frequency is returned to fs with an optical frequency shifter (OFS), are coupled into a photo detector for homodyne detection. This process makes it possible to remove the GAWBS noise from the transmitted signal.
Fig. 13 GAWBS noise compensation using the injection locking (IL) method. A grating filter with a 5 GHz bandwidth was used as a narrow band optical filter in the receiver. EDFA: erbium-doped fiber amplifier, PC: polarization controller, OFS: optical frequency shifter, SSMF: standard single-mode fiber, B-PD: balanced photo detector, A/D: analog-to-digital converter, DSP: digital signal processor, DFB LD: distributed feedback laser diode, LO: local oscillator.
Figure 14 shows how the EVM can be improved with the IL method. The experiment consists of 3 Gbaud 64 QAM transmissions over 160 km. By tuning the time delay properly to remove the GAWBS noise, the EVM after the compensation was effectively reduced from 2.3% to 2.0%. This result indicates that the IL method is also useful for GAWBS noise compensation with the same level of performance as the RPM method.
Fig. 14 Changes in the error vector magnitude (EVM) with the injection locking (IL) method. The constellation is for a 3 Gbaud 64 QAM transmission over 160 km. The EVM without delay tuning was 2.3% and appropriate delay tuning improved the value to 2.0%.
3.3 Digital compensation (DC) method
In previous sections, we described RPM and IL methods, which are analogue methods. In this section, we describe GAWBS noise compensation using a DSP, which we call the DC method. The observation and compensation of GAWBS noise using a DSP are shown in Fig. 15 and Fig. 17, respectively. The continuous wave (CW) light source for the transmitter is a narrow linewidth ECLD and the LO is another ECLD. Both lasers are mutually phase-locked by using an OVCO, where the frequency offset between the two lasers is removed with a radio frequency voltage-controlled oscillator [23].
Fig. 15 Experimental setup for the observation and compensation of GAWBS noise using a digital signal processor. To show the principle of the digital compensation (DC) method, no QAM modulation was applied. Heterodyne detection was used for GAWBS noise detection (IF = 1 GHz). The tone signal was shifted by 10 GHz from the carrier frequency. A grating filter with a 5 GHz bandwidth was used as a narrow band optical filter in the receiver. EDFA: erbium-doped fiber amplifier, PC: polarization controller, OFS: optical frequency shifter, SSMF: standard single-mode fiber, PD: photo detector, A/D: analog-to-digital converter, DSP: digital signal processor, LN: lithium niobate, LO: local oscillator, OVCO: optical voltage controlled oscillator, RF: radio frequency.
Initially, the CW light beam was not modulated as shown in Fig. 15, and we investigated the way in which the single carrier spectrum was modified by the fiber transmission. The IF frequency for heterodyne detection was set at 1 GHz. In this scheme, the GAWBS noise was digitally extracted from the IF signal by using an A/D converter, and we first obtained the random phase fluctuations of GAWBS noise in the time domain at an IF of 1 GHz (ωIF2). The data signal with the GAWBS noise was also digitized at an IF of 1 GHz (ωIF1) and then divided by the temporal phase fluctuations of GAWBS noise by using a DSP with an appropriate timing control, and finally we obtained a GAWBS noise-free transmitted data signal. The resolution of the timing control was set at 25 ps, which is approximately 1% of the period (2 ns) corresponding to the highest GAWBS frequency of 500 MHz, whereas the path length accuracy of 4 mm in the RPM and IL methods corresponds to a 1% accuracy of the optical path length of 0.4 m corresponding to 2 ns (L = (c/n)T = 2x108 x 2x10−9 = 0.4 m).
Here, first we show that a carrier signal and a tone signal shifted by 10 GHz from the carrier have the same phase fluctuations of GAWBS noise. Here S1 is an IF signal between the carrier and the LO signal, which is given as
where ωIF1 is the IF frequency and ϕG(t) is the random temporal phase fluctuations of GAWBS noise. S2 is another IF signal that can be obtained between the 10 GHz shifted tone and the LO signal, which is expressed asIf the temporal phase fluctuation of the GAWBS noise is the same in both the IF signals, we can easily obtain a GAWBS noise-free transmitted data signal by processing the digital signal as follows.
In the present case, S1/S2 = 1. The results are shown in Figs. 16(a)-16(c), which correspond to S1 and S2 after fast Fourier transformation (FFT), and data after signal processing using Eq. (3), respectively. In both Figs. 16(a) and 16(b), the GAWBS noise is clearly observed over 500 MHz. The fiber we used was a 160 km-long SSMF and we did not observe any phase noise components in this frequency band in a back-to-back condition. After signal processing, these GAWBS resonant spectra were completely removed as seen in Fig. 16(c). This indicates that a 10 GHz shifted tone signal has the same random time-dependent phase modulation with GAWBS. Here it is important to note that since the same phase modulation caused by the GAWBS noise is applied not only to the tone but also to the QAM data signal, we can obtain GAWBS noise-free transmitted data using Eq. (3). This is quite plausible since the GAWBS noise is determined by the thermal acoustic vibrations of the silica structure itself, and therefore, any light beam is affected in the same manner.Fig. 16 Experimental results for the compensation of GAWBS noise with the digital compensation (DC) method. (a) and (b) are S1 and S2 after fast Fourier transformation (FFT), respectively, and (c) is the data after GAWBS noise compensation.
In the next step, we carried out a QAM data transmission with DSP for GAWBS noise compensation as shown in Fig. 17. Here, we employed a single-polarization 3 Gbaud 64 QAM data modulation and a 10 GHz-shifted tone signal. The transmission distance was 160 km. The QAM data, SQAM (t), was homodyne detected with an OVCO and the tone signal was heterodyne detected with an IF of 1 GHz as ωIF for GAWBS noise detection. In this case, S1 and S2 are modified as and , respectively, and therefore, QAM without GAWBS noise can be obtained simply by calculating . Figures 18(a) and 18(b) show the change in the constellations before and after GAWBS compensation, respectively. The EVM in Fig. 18(a) was 2.2%, which was successfully reduced to 1.9% in Fig. 18(b). This result indicates that it is possible to digitally compensate for the GAWBS noise effect with the same performance levels as the RPM and IL methods.
Fig. 17 Experimental setup for GAWBS noise compensation in a 3 Gbaud 64 QAM transmission over 160 km. Homodyne detection was used for the data transmission and heterodyne detection was used for the GAWBS noise detection. A grating filter with a 5 GHz bandwidth was used as a narrow band optical filter in the receiver. EDFA: erbium-doped fiber amplifier, PC: polarization controller, OFS: optical frequency shifter, SSMF: standard single-mode fiber, PD: photo detector, B-PD: balanced photo detector, A/D: analog-to-digital converter, DSP: digital signal processor, DBM: double balanced mixer, LN: lithium niobate, LO: local oscillator, OVCO: optical voltage controlled oscillator, RF: radio frequency.
Fig. 18 Change in the constellation with the digital compensation (DC) method: (a) before GAWBS compensation and (b) after GAWBS compensation. The error vector magnitude (EVM) in (a) was 2.2%, which was reduced to 1.9% in (b).
4. Summary
We described our observation of GAWBS noise and its compensation in a QAM digital coherent transmission. GAWBS noise occurs coherently not only in a single carrier signal but also in QAM data transmission. We demonstrated that the adverse effect of GAWBS noise on transmitted data can be compensated for with three methods. Analogue methods named the reverse phase modulation (RPM) method and injection locking (IL) method realize optical direct compensation of the GAWBS noise. The IL method is simpler since no additional phase modulator is needed for GAWBS noise compensation. Lastly, a digital compensation (DC) method was presented in which an A/D converted phase fluctuation of GAWBS noise was removed from the A/D converted data signal. That is, an A/D converted data signal with GAWBS noise was divided by the A/D converted phase fluctuations of GAWBS noise. We demonstrated with three methods that it is possible to improve the EVM of the transmitted constellations with the same performance levels.
The existence of GAWBS noise may limit the ultimate performance of a digital coherent system since it occurs in an acoustic vibration in thermal equilibrium in a silica fiber structure. The modulation formats with higher multiplicity levels may suffer greatly from the noise as we require a higher OSNR.
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