We propose the precise and wideband compensation of the nonlinear phase noise caused by cross-phase modulation (XPM) among WDM channels using a pilot tone (PT) and injection locking for short-reach, higher-order QAM transmission. A high spectral efficiency is maintained by sharing a single PT among multiple channels. We describe a 60 ch, 3 Gbaud PDM−256 QAM transmission over 160 km, where the bit error rate was improved from 6 × 10−3 to 2 × 10−3 by employing the proposed XPM compensation technique, with a spectral efficiency of 10.3 bit/s/Hz. We also analyze the influence of the group delay caused by fiber chromatic dispersion that determines the compensation range achievable with a single PT. We obtained good agreement with the experimental results.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
To meet the increasing demand for broader data traffic, considerable attention has been paid to increasing in the multiplicity in digital coherent quadrature amplitude modulation (QAM) transmission [1–4]. In a dense wavelength division multiplexing (DWDM) transmission with a high QAM multiplicity of, for example, 256 levels, nonlinear phase noise induced by inter-channel cross-phase modulation (XPM) is a major signal impairment, and the development of a high-precision nonlinearity compensation scheme has been an important subject.
Among various approaches, a digital back-propagation (DBP) method has been widely used as a digital signal processing (DSP)-based nonlinearity compensation technique [5,6]. This method is particularly useful for compensating for self-phase modulation (SPM) and XPM between two polarizations in a single channel. However, inter-channel XPM is generally difficult to compensate for as multiple WDM channels cannot be handled in DSP due to the limited A/D bandwidth. In addition, DBP requires a long computation time for improving the compensation accuracy by increasing the resolution.
A simple alternative approach has been proposed that involves the extraction of phase noise from a pilot tone (PT) co-propagating with a data signal . During transmission the PT captures the same nonlinear phase noise from adjacent WDM channels as the co-propagating data signal. The phase noise can be cancelled by extracting it from the PT and applying it in reverse to the transmitted signal. The phase cancellation can be carried out either digitally [8,9] or optically by employing an injection locking method . This scheme is attractive because of its simple configuration and short computation time. With the PT-based digital phase compensation, the 56 ch (7 wavelength × 8 subcarrier) transmission of 5.6 Gbaud polarization division multiplexed (PDM)-64 QAM signals was demonstrated, where a 0.4 dB Q improvement was obtained in a 1200 km transmission . In this experiment, PTs were placed adjacent to every subcarrier with a 3 GHz offset from the carrier frequency. In addition, 7 ch, 25 Gbaud orthogonal frequency domain multiplexing (OFDM) transmission was demonstrated, where Q was improved by 1 dB at 2880∼3520 km with QPSK and by 0.8 dB at 1600∼1920 km with 16 QAM . Here a residual DC carrier obtained by adjusting the DC bias was used as a PT.
An important issue with the PT-based compensation scheme is that it requires a guard bandwidth around the PT to detect XPM phase noise. The bandwidth of XPM phase noise is mainly determined by the walk-off between WDM channels and becomes narrower as the transmission distance increases . Therefore, it is possible to reduce the guard bandwidth in a long-haul transmission over several thousand kilometers [9,10]. In the PT-based XPM compensation demonstrated for a 64 QAM-1200 km transmission , a Q improvement of 0.4 dB was achieved with a guard bandwidth of only 90 MHz. Also, in a demonstration of a 25 Gbaud QPSK-2880∼3520 km / 16 QAM-1600∼1920 km transmission , the guard bandwidth was set at 2.5 GHz. In this demonstration, a substantial Q improvement of 1 dB (for the QPSK) was successfully achieved.
On the other hand, in a higher-order QAM transmission, the transmission distance is generally shorter because the demodulation of higher-order QAM signals requires a relatively higher SNR. In such a case, XPM occurs over a relatively wide bandwidth because the walk-off is still small at short distances. Therefore, a broad guard band is required around a PT for wideband XPM detection. This inevitably sacrifices the SE.
In this paper, we propose a new technique for PT-based wideband XPM compensation based on injection locking for short-reach, higher-order QAM transmission. It features a high compensation performance by setting the guard bandwidth sufficiently broad to fully detect the XPM phase noise and by using a local oscillator (LO) with a broad locking range. In addition, unlike previous studies where every WDM channel was accompanied by its own PT, only a single PT is used to deal with the XPM compensation for 20 channels so that a high SE can still be maintained. In a preliminary work reported in , we applied this scheme to a 60 ch, 3 Gbaud PDM-256 QAM transmission, and successfully achieved an SE of 10.3 bits/s/Hz. However, certain issues remained unaddressed including the potential frequency range for XPM compensation that can be covered by a single PT, since it was limited solely by the tunability of the optical frequency shifter (OFS) used in our experiment. Here, we elaborate on the proposed scheme in great detail and include experimental and analytical studies related to the influence of the polarization relationship between PT and QAM data, the fiber group delay due to chromatic dispersion, and QAM data pattern, on the compensation performance. These studies enabled us to clarify the frequency range for XPM compensation achievable with a single PT, which is found to be determined dominantly by the fiber group delay.
2. Inter-channel XPM noise compensation with injection locking in a 60 ch, 3 Gbaud pol-mux 256 QAM WDM 160 km transmission
2.1 System design
We first describe the channel configuration that we used for our proposed PT-based XPM compensation scheme. Figure 1 shows the configuration of the WDM channel and PT. We used 3 Gbaud 256 QAM as data signals. The baud rate was set at 3 Gbaud by considering the dynamic locking range of the LO (6.8 GHz) as described later in this section. The bandwidth of the QAM data signal was reduced to 3.15 GHz by adopting a Nyquist filter with a roll-off factor of 0.05. The WDM channel spacing was set at 3.33 GHz. A PT was inserted between ch. 1 and −1 (namely ch. 0 is replaced by PT), with a guard band of ± 5 GHz on both sides. The guard bandwidth of 10 GHz is broad enough to detect all the XPM-induced phase noise. It should be noted that there is a frequency offset Δf between the PT and the QAM data. This indicates that, once XPM-induced phase noise information is transferred from the PT to the LO by injection locking at the receiver, the frequency of the injection-locked LO has to be shifted back by Δf using an OFS, so that it matches the original carrier frequency of the data channel for homodyne detection. Because of the limited frequency range of the OFS (± 40 GHz), we defined a bandwidth of 80 GHz as a unit block that contains 20 WDM channels. Here, we consider 20 channels controlled by a single PT to be a superchannel. We prepared three blocks with an 86.7 GHz spacing, and we accommodated a total of 60 WDM channels, where the guard band between the blocks was 10 GHz.
In this experiment, 20-channel 3 Gbaud QAM signals correspond to an aggregate baud rate of 60 Gbaud. Although there are commercially available systems with the baud rate up to 64 Gbaud, it is difficult to achieve such a high multiplicity at high baud rates. Our experiments exploit the concept of superchannel considering a tradeoff against the use of 20 separate receivers and frequency-shifted LOs.
With the present method, since the XPM-induced phase noise is transferred from the PT to the LO via injection locking, the injection locking performance of the LO plays a very important role. As an LO, we employed a tunable distributed feedback (DFB) laser array  with a linewidth of 2.7 MHz. Injection locking can be achieved when the frequency detuning between the PT and original LO frequencies is within the locking range. The injection power was optimally set at –5 dBm to obtain a wideband locking range while maintaining a stable locking condition. Here, the locking range was 8.2 GHz . Since the light sources of the PT and LO were temperature-controlled, the frequency drift of the light sources was suppressed to within 100 MHz. Under this condition, low noise carrier-phase locking with a phase noise of less than 0.25 deg. can be achieved. This is sufficiently small to demodulate the 256 QAM data . Here we focus on the dynamic injection-locking characteristics, rather than the static characteristics. We evaluated the dynamic phase response of the LO by using the measurement setup shown Fig. 2(a). The output of the ECLD , which was used as a seed light, was phase modulated by a sinusoidal wave. The LO was injection-locked to the seed light and the phase modulation components were transferred to the LO. If the phase modulations of the seed light and injection-locked LO are in-phase, they can be cancelled. This can be observed with a sideband suppression of X dB in an electrical spectrum analyzer. From X, we obtained the phase response as R = 1 − 10−X/10. With a high suppression ratio such as X = 20 dB, R approaches 1. On the other hand, when there is no cancellation effect, namely where X = 0 dB, R becomes 0. Figure 2(b) shows the measured phase response of the tunable DFB-LD array. From this result, the controllable 3 dB bandwidth of the LO was 6.8 GHz.
We have experimentally confirmed that the dynamic injection locking property can respond to a bandwidth of at least 3 GHz by actually injecting XPM-imposed PTs into the LO. On the other hand, for a bandwidth of 6.8 GHz obtained from the evaluation of Fig. 2, it should be noted that the slight difference in the LO response between single and multiple tones should be taken into account .
2.2 Detailed experimental setup
Figure 3 shows the experimental setup for a 60 ch, 3 Gbaud PDM-256 QAM WDM transmission with XPM compensation using injection locking. The transmitter comprises two parts, namely the main block and the dummy block. In the main block, we used a tunable ECLD  for the PT and the test channel sources. Here we fixed the PT wavelength and tuned the test channel to the carrier frequency of the corresponding channel accordingly with OFS-1. The OFS we used in this experiment consisted of an LiNbO3 (LN) intensity modulator and an optical filter. The polarization of PT and data was adjusted with a polarization controller. Here, the power of the PT was set at the same value as that of the QAM data per channel to detect the XPM components precisely. The remaining dummy channels were generated from 19 LDs. They were data-modulated altogether in a single IQ modulator. The IQ-baseband signal for 19 dummy channels is shifted by ∼5 symbols so that the data pattern is uncorrelated. These dummy channels were decorrelated by using a chirped-fiber Bragg grating (CFBG) with a group delay of −2580 ps/nm . This corresponds to a 70 ps (∼0.2 symbols for 3 Gbaud data) delay between adjacent WDM channels (3.33 GHz spacing). After polarization multiplexing, the test and dummy channels were combined with the PT.
In the loading dummy channel block, we used eight LDs to prepare a total of 40 dummy channels. Each LD was modulated by 5 ch, 3 Gbaud 256 QAM electrical signals. Then, we combined them with PTs. Finally, we coupled the main and dummy blocks with a wavelength selective switch. Figure 4 shows the optical spectrum of the 60 ch WDM signals obtained before transmission. It contains three blocks of data signals, where the spectral peaks are the PTs and the others are the QAM data. The generated WDM channels were then launched into a 160 km transmission line. The launch power was set at 4 dBm (−14 dBm/channel). This was experimentally optimized to obtain the best demodulation characteristics with compensation in ch#1. At launch powers below the optimum value, the demodulation performance was degraded because of OSNR degradation, and it was also degraded due to fiber nonlinearity at a higher launch power. We evaluated the characteristics without compensation by setting the launch power at the same value as that with compensation. The transmission line was composed of two spans of 80 km ultra-large-area fiber (ULAF) with a dispersion of 21 ps/nm/km and a loss of 0.18 dB/km at 1550 nm. The loss was compensated for with backward Raman amplifiers. The OSNR of the transmitted data signal measured with a 0.1 nm resolution bandwidth was ∼34 dB. The OSNR of the PT signal was also ∼34 dB after a 160 km transmission, the injection locking performance was not degraded even when the OSNR of PT decreased from 34 to 25 dB .
At the receiver, we demultiplexed the test channel with an optical tunable filter (OTF-1) and extracted the PT through OTF-2. The PT was injected into the tunable DFB-LD array used as an LO. The polarization state of the PT was manually controlled so that it was aligned with the polarization of the LO, which enabled the power of the seed signal to be kept constant after passing through a polarization sensitive circulator. This can be automated by employing an automatic polarization controller. The frequency of the LO was shifted to the carrier frequency of the test channel with OFS-2. We installed an optical delay line in the data signal path, which was controlled with an accuracy of a few cm for precise phase noise compensation . Finally, the homodyne-detected signal was A/D-converted and demodulated offline. The DSP incorporated polarization demultiplexing, chromatic dispersion compensation, and waveform equalization with a 99-tap finite impulse response filter, where we did not employ DBP. There was a slow phase fluctuation between the injection-locked LO and the transmitted data signal due to their different optical paths. However, we could easily compensate for such a slow phase fluctuation with DSP at receiver.
2.3 Experimental results
First, we compared the demodulation performance with and without XPM compensation in the following way. To evaluate the case without compensation, we installed an etalon with a pass bandwidth of 25 MHz as a narrowband optical filter after OTF-2, so that the XPM components imposed on the PT were removed. For the case with compensation, we removed the etalon and carried out wideband injection locking.
The constellation of ch. #5 (X polarization) after transmission is shown in Fig. 5, where (a) is the result without XPM compensation, and (b)–(d) are the results with XPM compensation with different polarization angles θ between the PT and the X polarization of the QAM data. In Fig. 5(a), phase rotation caused by XPM can be seen, where the error vector magnitude (EVM) was 2.54%. Figures 5(b)–5(d) correspond to θ = 0, 45, and 90 deg., respectively. Their EVMs were 2.21, 2.31, and 2.40%, respectively, and it can be seen that the phase rotation is reduced in the constellation. This indicates that the present scheme successfully reduced the XPM-induced phase noise, and higher compensation efficiency was achieved when the PT and data polarizations were parallel.
The XPM-compensated BERs for the three polarization relationships are shown in Fig. 6, where the horizontal axis represents the θ. The BERs were below the value without XPM compensation (5.1 × 10−3). The BER for X polarization increases as θ increases, whereas the BER for Y polarization decreases as θ increases. This indicates that the maximum compensation efficiency can be obtained when the polarizations of the PT and QAM data are parallel, but in order to obtain the identical compensation performance for both X and Y polarizations, the polarization angle of the PT should be set at 45 deg. with respect to the X and Y polarizations. We adopted this condition in the experiments described hereafter.
To clarify the polarization dependence on XPM detected by the PT, we measured the heterodyne-detected spectrum of an XPM-imposed PT signal. This signal was co-propagated with single-channel 3 Gbaud, 256 QAM data in a single polarization under different PT/QAM polarization angles using the setup shown in Fig. 3. The frequency spacing between the PT and QAM data was set at 10 GHz, and the transmission power was –2 dBm. The signal configuration is shown in Fig. 7(a). Figures 7(b)–7(d) shows the XPM-imposed spectrum of the heterodyne-detected PT signal under polarization angles of 0, 45, and 90 deg. In these spectra, XPM components can be seen around the PT carrier over a ± 3 GHz range. We evaluated the power of each XPM component by integrating the spectrum, and the ratio was 1 : 0.62 : 0.30 for a θ = 0, 45, and 90 deg. It can be said that the ratio is roughly the same as the ratio of the nonlinear coupling coefficients of the two orthogonal polarization components, namely 1 : 2/3 : 1/3, by noting that χ(3)xxyy/χ(3)xxxx = 1/3 .
The dependence of BER on PT polarization shown Fig. 6 can be explained as follows. The XPM imposed on the X-polarization data ϕsig, x, induced by the other channel Ex and Ey in the X and Y polarizations, is given by ϕsig, x = (2|Ex|2 + (2/3)|Ey|2)γz, where γ is the nonlinear coefficient and z is the fiber length. When θ = 0, namely PT is X-polarized, the XPM imposed on the PT is approximately the same as ϕsig, x assuming that the PT frequency is close to the data, namely ϕPT, x = (2|Ex|2 + (2/3)|Ey|2)γz. This indicates that, by cancelling the phase as ϕsig, x − ϕPT, x, the XPM can be fully compensated for thanks to the close correlation between ϕsig, x and ϕPT, x. On the other hand, when θ = 45 and 90 deg., the XPM imposed on the PT is given by ϕPT, y = ((4/3)|Ex|2 + (4/3)|Ey|2)γz and ((2/3)|Ex|2 + 2|Ey|2)γz, respectively. Therefore, after phase cancellation, we obtain ϕsig, x − ϕPT, y = ((2/3) |Ex|2 − (2/3)|Ey|2)γz for θ = 45 deg. and ((4/3) |Ex|2 − (4/3)|Ey|2)γz for θ = 90 deg., which indicate that the ϕsig, x values are partially reduced but residual components remain uncompensated for.
The polarization dependence of the compensation performance is caused by the polarization dependence of the XPM efficiency, as shown in Fig. 7. Polarization alignment of the PT is therefore needed to achieve comparable performance for the two polarizations. On the other hand, in longer reach scenarios where the Manakov model  can be applied, the asymmetry would disappear because the inter-polarization interaction is averaged out. In these situations, PT polarization control may be no longer necessary.
Finally, we evaluated the BER performance with and without XPM compensation as a function of channel location. θ was set at 45 deg. Figure 8 shows the BER characteristics of 20 channels in the center block. The BERs were 5∼6 × 10−3 without XPM compensation, but they were improved to less than 2 × 10−3 for all the channels with XPM compensation. The BERs of ch #−10, #−1, #1, and #10 were somewhat lower than those of other channels. This was because there was only one channel adjacent to these edge channels and they were less susceptible to XPM than the inner channels. The BERs for ch. #2 ∼ #9 and #−9 ∼ #−2 were almost uniform. Further analysis of the result, such as the dependence of the BER improvement on channel location and the influence of data correlation among different WDM channels, will be discussed in the next section. It should be note that this uniform dependence originates partly from the particular data pattern that we used in the experiment, namely it was undertaken in the presence of residual correlation among the channels. Such residual data correlation may result in higher XPM correlation even for a channel further from the PT, and this may lead to efficient XPM compensation. In the present transmission experiment, we realized a transmission capacity of 960 Gbit/s per block within an 86.7 GHz bandwidth, which corresponds to an SE of as high as 10.3 bits/s/Hz accounting for the 7% forward error correction (FEC) overhead.
If we assume that FEC provides a pre-FEC BER of 1.25 × 10−2 with a 15% overhead  applied when no nonlinear compensation is used, the SE is calculated to be 9.6 bit/s/Hz. By employing XPM compensation, we can obtain an 8% reduction in the coding overhead and a 6.8% improvement in SE. In addition, a lower FEC overhead reduces the DSP load and hence latency and power consumption are expected to be reduced.
3. Analysis of PT-based XPM compensation performance in the presence of GVD
3.1 Analysis of XPM phase noise
In the experimental results presented in the previous section, a single PT was capable of compensating for XPM over 20 WDM channels, namely over a ±36.67 GHz bandwidth. The coverage bandwidth of the PT was limited only by the tunability of the OFS (±40 GHz), and therefore it is important to evaluate in principle how far a single PT can deal with the XPM compensation. We expect the compensation range to be mainly determined by the fiber group delay due to chromatic dispersion as it causes walk-off between the PT and QAM data. Here we perform a theoretical and numerical analysis to clarify the fundamental limitation of the present scheme by taking the group delay into account.
The XPM-induced phase shift ϕ(t) imposed on the PT in the presence group velocity dispersion (GVD)-induced walk-off, where the loss was compensated for with an erbium-doped fiber amplifier (EDFA), was analyzed in  and is given by
We undertook the same experiment as in Fig. 7, while retaining the same PT/QAM polarization angle and varying the PT/QAM frequency spacing Δf. Figure 9 shows the measured XPM-imposed spectra of the PT [(a)∼(c)] and their numerical results [(d)∼(f)] for Δf = 10, 40, and 100 GHz. The spectra in Figs. 9(d)–9(f) were obtained by the Fourier transformation of a CW tone whose phase is modulated by ϕ(t). It can be seen both experimentally and analytically that the bandwidth and magnitude of the XPM components become smaller as Δf increases, which is a consequence of walk-off. From the numerical results, the ratio of the total power of the phase noise components of each Δf was 10 GHz : 40 GHz : 100 GHz = 1 : 0.44 : 0.22, which roughly agrees with the experimental data (1 : 0.32 : 0.14). We note that Figs. 9(d)–9(f) include interference patterns whose period is somewhat different from those in Figs. 9(a)–9(c). This is due to the difference in the amplifier model, where we assumed lumped amplification using only an EDFA when deriving Eqs. (1–3), while we employed distributed Raman amplification in the experiment. By incorporating backward Raman amplification in the analysis, Eq. (1) can be modified as follows.
Equation (4) consists of mA, mB, ϕA(t), ϕB(t), Leff,A, Leff,B, ηXPM,A(ω), ηXPM,B(ω), φA(ω), and φB(ω). Here, ϕA(t) and ϕB(t) correspond to the XPM contribution around the input and output of each span, respectively. We focus on the input and output portions of each span where the signal power is high. mA and mB are given in Eq. (5) where αA and αB are the loss coefficients around the input and output of each span given by Eq. (6). GR is the Raman gain, which is assumed to be GR =exp(αL), and this corresponds to all-Raman amplification as in the present experiment. Leffp = [(1−exp(−αpL)]/αp is the effective fiber length for a Raman pump where αp is the loss at the pump wavelength. LeffA,B, ηXPMA,B(ω), φA,B(ω) correspond to Leff, ηXPM(ω), φ(ω) given in Eqs. (2) and (3) with α replaced by αA and αB, respectively.
Figures 9(g)–9(i) are the spectra calculated with Eqs. (4) and (5). The ratio of the total power of the phase noise was 1 : 0.37 : 0.18, which was closer to the experimental data. By including the effect of the Raman amplifiers, the interference patterns in the spectrum become closer to the experimental results than in Figs. 9(d)–9(f). For example, when Δf = 40 GHz, the peak in the sidelobe was located at 1.5 GHz in Fig. 9(d) but shifted to 2 GHz in Fig. 9(h), showing better agreement with the experiment [Fig. 9(b)]. In the following analysis, we adopted Eqs. (4) and (5) to incorporate the Raman amplification.
3.2 PT-based compensation of two-channel XPM
Based on the model described above, we analyzed the PT-based phase noise compensation effect for a pair of WDM channels based on a numerical simulation to estimate the frequency range over which a single PT can detect XPM. The channel configuration model is shown in Fig. 10. The channel spacing of the two WDM channels is fixed at 3.3 GHz, and the frequency separation between the PT and one WDM channel, Δf, is varied to evaluate how far the correlation between XPM and the phase noise imposed on the PT can be maintained. Since it is difficult to extract the XPM component directly from the data, we replaced one of the data channels with an unmodulated CW carrier (labeled “signal” in Fig. 10), so that the phase noise equivalent to XPM can be easily detected. The detected phase noise provides an estimate of the XPM phase noise between two data channels. The degree of phase noise compensation can then be evaluated by subtracting the PT phase noise ϕPT from the detected phase noise ϕsig.
Figure 11 shows the profile of the phase noise imposed on the PT in the time and frequency domains for Δf = 10, 40, and 100 GHz, before and after the compensation (blue and yellow, respectively). For a lower Δf, it can be seen that the XPM phase noise is efficiently reduced in the time domain, and in the frequency domain the phase noise is successfully compensated for especially in lower frequency components as shown in Fig. 11(a), indicating a strong correlation between ϕPT and XPM. On the other hand, as Δf increases as in Figs. 11(b) and 11(c), it can be seen that the compensation becomes less efficient, which indicates that the correlation between ϕPT and XPM are reduced due to a larger group delay between the PT and the signal.
Figure 12 shows the relationship between Δf and the compensation factor F = Pw / Pw/o, which we defined as the ratio of the total power of the XPM phase noise components with (Pw) and without (Pw/o) compensation. On the vertical axis in Fig. 12, F = 0 corresponds to the case where XPM is completely compensated for, and F = 1 means that there is no compensation effect at all. As shown in Fig. 12, the compensation effect is gradually degraded as Δf increases. If we define F = 0.5 as a rough estimate for the compensation range, in which the XPM phase noise power is halved, it can be seen from Fig. 12 that a single PT can compensate for XPM at least over a 55 GHz range.
We discuss the relationship between F and Q improvement by combining Fig. 13 and Fig. 6. According to Fig. 13, F is approximately 0.5 when the PT polarization θ = 90 deg. As shown in Fig. 6, the BER was improved from 5.1 × 10−3 to 2.8 × 10−3 with compensation at θ = 90 deg., which corresponds to a Q improvement of 0.7 dB. This indicates that F = 0.5 corresponds to a Q improvement of 0.7 dB.
3.3 PT-based compensation of 60 channel XPM
Next, we evaluated the compensation factor for a 60 channel transmission analytically, where we assumed the same channel configuration and data pattern as in the experiment shown in Figs. 1 and 3. In the same way as the two channel case presented before, we replaced a test channel with an unmodulated CW carrier to estimate the XPM imposed on the test channel, and then we computed the compensation factor from the correlation with the PT phase noise. We first calculated the polarization dependence of the compensation factor to confirm the polarization-dependent XPM efficiency. As shown in Fig. 7, we have experimentally confirmed that the ratio of the nonlinear coupling coefficients of the two orthogonal polarization components is 1 : 1/3. This indicates that our configuration does not follow the Manakov model , and therefore we employed an analytical model based on the nonlinear Schrödinger equation. Figure 13 shows the compensation factor calculated at ch. #5 for polarization angles θ = 0, 45, and 90 deg. The same trend as in Fig. 6, namely the highest compensation factor at θ = 0 and lower efficiency for a larger θ, can be seen in Fig. 13. In the following, we set θ = 45 deg., namely the same condition as in the experiment.
To evaluate the dependence of the compensation factor on the channel location, we calculated the carrier spectrum at ch. 1, 5, and 10 in a 60 channel WDM transmission with and without XPM compensation, and the results are shown in Fig. 14. As shown by the yellow profiles, the XPM components are reduced after compensation. Figure 15(a) shows the compensation factor as a function of the channel location. The compensation performance was almost uniform for all the 10 channels in the main block, and ch. 1∼3 and 10 have a slightly better efficiency. These trends are in good agreement with the experimental result shown in Fig. 8. This uniform dependence originates partly from the particular data pattern that we used in the experiment, namely it was undertaken in the presence of residual correlation among the channels. Such residual data correlation may result in higher XPM correlation even for a channel further from the PT, and this may lead to efficient XPM compensation. For comparison, Fig. 15(b) shows the result we obtained when the data pattern of each WDM channel was completely random. In this case, unlike in Fig. 15(a), the compensation factor is gradually degraded for channels further from the PT. This is for the same reason as the result shown in Fig. 12, namely it is a consequence of the reduced correlation between the PT phase noise and XPM due to a larger group delay. In a totally uncorrelated data pattern among WDM channels, the compensation efficiency is somewhat reduced but F still remains below 0.5 up to ch. #10 or Δf = 36.7 GHz.
As we have seen, the compensation range covered by a single PT is determined by the group delay between the PT and the data, and thus it depends on the dispersion D of the fiber. We calculated the compensation range against the transmission distance by varying fiber D and compared the results on the assumption of totally uncorrelated data patterns, as shown in Fig. 16. Here the compensation coverage bandwidth is defined as the frequency range over which F < 0.5 is satisfied. The blue curve represents the characteristics for ULAF (D = 21 ps/nm/km). The orange and yellow curves correspond to D = 15 and 10 ps/nm/km, respectively. With ULAF, a compensation coverage bandwidth of 56.7 GHz was obtained at 160 km, and it can be extended to 320 and 560 km with D = 15 and 10 ps/nm/km fiber, respectively.
We proposed a wideband inter-channel XPM compensation method for short-reach, higher-order QAM transmission by using the injection locking of an XPM-imposed PT, in which a single PT can provide XPM compensation for multiple channels. We applied our proposed scheme to a 60 ch, 3 Gbaud PDM-256 QAM WDM transmission over 160 km with an SE of 10.3 bit/s/Hz, and successfully improved the BER from 5∼6 × 10−3 to 2 × 10−3. We also conducted experimental and analytical studies on the influences of the polarization relationship between PT and QAM data, the fiber group delay due to chromatic dispersion, and the QAM data pattern, on the compensation performance. The analysis clarified that the fiber group delay has the greatest influence on the compensation performance, which determines the frequency range for XPM compensation achievable with a single PT. This technique allows precise XPM compensation with the minimum sacrifice of SE and is expected to provide a simple method for performance improvement in a WDM transmission with a high QAM multiplicity.
Japan Society for the Promotion of Science (JP19J12822); Ministry of Internal Affairs and Communications, Research and Development of Innovative Optical Network Technology for a Novel Social Infrastructure (JPMI00316).
The authors declare no conflicts of interest.
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