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Abstract
We propose a novel reflection interference (RI) elimination method using a linear frequency modulated training sequence (LFMTS). Three LFMTSs and the signal are mixed in the electrical domain before being modulated onto an external cavity laser, and then utilized in reconstructing the RI. In the digital signal processing of the receiver, two LFMTSs identify the time mismatch between the signal and the RI, while the third is for carrier recovery of the RI. Simulations were carried out to investigate the impact of critical factors on the RI elimination, including the time mismatch, the bandwidth limitation, the laser linewidth and the frequency difference between lasers. Experiments were carried out on a 21-GBaud QPSK system to prove that the RI can be eliminated. Both simulations and experiments have proved the effectiveness of the proposed method in respect of RI elimination.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Since the first light transferred through the fiber, fiber communication has experienced rapid development, and numerous methods have been proposed to boost its capacity and spectral efficiency [1–3]. The same-wavelength bidirectional communication system is a very promising method to double the spectral efficiency [4–7]. The bidirectional system possesses several advantages, such as low cost, low complexity of implementation, and convenience of administration and maintenance [8,9]. Additionally, the bidirectional fiber-optic link can be utilized for both time as well as frequency transfer [10,11]. The bidirectional system is implemented via “interleaved” or “band-separated” wavelength arrangements [12], where the westbound and eastbound channels are allocated different wavelengths. This effectively suppresses the four-wave mixing, and negates the interference due to scattering and reflections in the fiber. Instead of different wavelength arrangements, same-wavelength bidirectional systems require both the westbound and eastbound channels to share the same wavelengths to obtain higher spectral efficiency. In the same-wavelength arrangement, the intrinsic Rayleigh scattering in the fiber and the reflections at the connectors back-scatter and reflect the forward signal, which generates moderate crosstalk on the opposite signal [13–16]. If we consider a practical example with the physical contact connectors along the fiber, being aged and having high reflection ratio, the reflection interference (RI) will be fatal and degrade the performance of the bidirectional system. With the connectors set away from the transceiver side, the RI remains a critical problem when the reflection takes place near the amplifiers, which counterbalances the fiber loss for RI.
This study focusses on eliminating the RI resulting from the Fresnel reflection of the connectors. It considers the phase noise and frequency offset of the lasers, along with the timing mismatch between the signal and RI. The data frame structures of each channel in both directions were rearranged. In the frequency domain, intervals are created between nearby channels incorporating the linear frequency modulated training sequence (LFMTS), for carrier recovery of the RI. Two LFMTSs are allocated in front of the payload for synchronization of the signal and the RI. In the digital signal processing (DSP) of the receiver, the RI will first be reconstructed from the carrier phase information obtained via the LFMTS and then subtracted from the received mixed sequence as per the time mismatch obtained from the synchronization. Simulations were carried out to investigate the impact of critical factors on the RI elimination, including the time mismatch, the bandwidth limitation, the laser linewidth and the frequency difference of lasers. Experiments were carried out on a 21-GBaud QPSK system to prove the effectiveness of our proposed RI elimination method. Both simulations and experiments have proved that our proposed method can effectively eliminate the RI.
2. Principle
Figure 1 shows the schematic of a same-wavelength bidirectional fiber communication system [16]. Henceforth, we consider the eastbound terminal will act as a receiver and the origin of the RI, while the westbound terminal launches the signal into the fiber. As shown in Fig. 1, the eastbound signal will be reflected back at the connectors due to Fresnel reflection, which will generate relatively severe interference at the receiver in the eastbound terminal. For expression convenience, we assume there is only one connector in the fiber link. Therefore, as shown in Fig. 2, the received mixed sequence can be written as
Fig. 1. Schematic of a same-wavelength bidirectional fiber communication system. Tx.: transmitter, Rx.: receiver.
Fig. 2. Schematic of the received mixed sequence. The red and blue lines represent the sample sequences of the received signal and RI respectively.
On obtaining the transmitted sequence $S_{Sig}^{Rx}(n )$, $S_{RI}^{Rx}(n )$ is reconstructed and subtracted from the received mixed sequence $S_{Mix}^{Rx}(n )$ in the DSP of the receiver. Assuming that $S_{Sig}^{Tx}(n )$ is obtainable in Rx.1, the necessary parameters required to reconstruct the received RI are the time mismatch parameters, the carrier phase information of the RI and the impact of transmission. In this paper, the transmission effect is treated as the combination of dispersion and bandwidth limitation, which can be measured in advance.
Among the time mismatch parameters, k can be derived from the transmission distance of RI obtained from the optical time domain reflectometry (OTDR). Therefore, as shown in Fig. 2, it can be identified which frame in Tx.1 is corresponding with the first received RI frame, referring to the first received signal frame. It is important to clarify that our proposed method is not a blind RI elimination method, which requires to utilize OTDR to identify the number, the locations and the reflection ratios of those reflection points along the fiber link.
Building upon a previous research [16], we propose to utilize three LFMTSs in the reconstruction process to overcome the time mismatch of the signal and the RI, as well as the phase and frequency offset uncertainty of the RI. Figure 3 shows the rearranged data frame structure as proposed. To synchronize, two LFMTSs ${\pm} \alpha $ are inserted in front of the payload, in the data frame of both directions. In the frequency domain, the spectra of LFMTSs ${\pm} \alpha $ overlap with that of the payload, but the spectra of LFMTSs ${\pm} \alpha $ in different directions remain separate. Furthermore, LFMTSs ${\pm} \beta $ inserted on both sides outside the payloads’ spectrum overlap with the LFMTSs ${\pm} \alpha $ and payloads in the time domain. The LFMTS $- \beta $ is for the carrier recovery of the eastbound channel X, which is received as the RI at the Rx.1 in the eastbound terminal.
Fig. 3. Modified data frame structure in the time and frequency domain. The Greek letter behind “LFMTS” represents the angle parameter of the corresponding LFMTS. (b) and (d) are the spectrums of the westbound channel X and eastbound channel X. The dashed lines represent the bandwidth of channels.
2.1 Time mismatch and LFMTSs ${\pm} \alpha $
The LFMTSs ${\pm} \alpha $ are two complex chirp sample sequences, which are responsible for identifying the unknown time mismatch parameter $\triangle m$. The LFMTSs ${\pm} \alpha $ of the signal frame and the RI frame can be written as
Figure 4 shows the received sample sequence with LFMTSs ${\pm} \alpha $. It can be deduced from Fig. 4 that $\triangle m = {N_\alpha } + \triangle n$, where $\triangle n$ needs to be identified through LFMTSs ${\pm} \alpha $. In the DSP of the receiver, dispersion compensation regarding RI shall first be implemented. Then, the component of the RI’s LFMTSs ${\pm} \alpha $, described by the blue rectangle in Fig. 4(b), is filtered out from the mixed sample sequence. Later, as shown in Fig. 4(a), the sequence after the filter is divided into several blocks of ${N_\alpha }$ samples, named as $S_{Mix}^{Bx}(n )$. Finally, we can obtain ${{\cal F}_{ + \alpha }}\{{S_{Mix}^{Bx}} \}(u )$ by transforming $S_{Mix}^{Bx}(n )$ into the fractional domain through the fractional Fourier transform (FRFT) with a transform angle of $+ \alpha $.
Fig. 4. The received mixed sequence with LFMTSs ${\pm} \alpha $ in the time domain and frequency domain, where the red color and blue color represent the signal and RI respectively.
Figure 5(a) shows the maximum modulus value of ${{\cal F}_{ + \alpha }}\{{S_{Mix}^{Bx}} \}(u )$. Considering that most of the samples of $S_{ + \alpha }^{RI}(n )$ is contained in the second sample block, marked as B2, therefore, the ${|{{{\cal F}_{ + \alpha }}\{{S_{Mix}^{B2}} \}(u )} |_{max}}$ shall be the largest among ${|{{{\cal F}_{ + \alpha }}\{{S_{Mix}^{Bx}} \}(u )} |_{max}}$. Figure 5(b) exhibits the distribution of $|{{{\cal F}_{ + \alpha }}\{{S_{Mix}^{B2}} \}(u )} |$, where the red dashed line is the FRFT result of $S_{ + \alpha }^{RI}(n )$, named as ${{\cal F}_{ + \alpha }}\{{S_{ + \alpha }^{RI}} \}(u )$. The peak shift $\triangle u_{ + \alpha }^{RI}$ satisfies the following equations
In this part, an impractical assumption has been made that the first received sample is exactly the first transmitted sample from Tx.2. However, this issue can be tackled with LFMTSs ${\pm} \alpha $ of the signal, through the same process of obtaining Eqs. (7)–(8). The mathematical process has been thoroughly studied in related papers and books, such as Ref. [17–19]. In the Appendix section of this paper, a brief review is provided for clarifying the synchronization process with LFMTSs ${\pm} \alpha $.
2.2 Carrier phase information and LFMTSs ${\pm} \beta $
Along with the synchronization problem, the phase and frequency offset uncertainty of the RI is overcome by the LFMTSs ${\pm} \beta $, which possess the similar mathematical form as LFMTSs ${\pm} \alpha $ with only the sample length, initial frequency, and chirp rate chosen differently. The LFMTSs ${\pm} \beta $ are written as
At the transmitter side, $S_{ - \beta }^{RI}(n )$ is generated and added to the data frame in the electrical domain. The electrical sample sequence $S_{RI}^{Tx}(n )$ in Eq. (3) shall be rewritten as
where $X_{RI}^{Tx}(n )$ consists of the payload and LFMTSs ${\pm} \alpha $, and $X_{RI}^{Tx}(n )$ is defined asFigure 6(a) shows the received mixed sequence with LFMTSs ${\pm} \beta $. In the DSP of the receiver, the received mix sequence $S_{Mix}^{Rx}(n )$ is first truncated for obtaining $U_{Mix}^{Rx}(n )$, which contains the entire M-th frame of RI. Next, the dispersion regarding the RI is compensated for, and the result can be written as
In Fig. 6(a), it can be found that the bandwidth of the LFMTS $- \beta $ is far less than that of the channel, which means $\frac{{f_{M, - \beta }^{RI}}}{2}{N_{Frm}}{T_s} \ll \frac{1}{{{T_s}}}$. Therefore, we can deduce $\beta \approx \frac{\pi }{2}$ according to $cot({ - \beta } )={-} f_{M, - \beta }^{RI}{N_{Frm}}{T_s}^2$. Further, the Eq. (15) can be rewritten as $\triangle f_{RI}^\ast{\approx} \frac{{\triangle u_{ - \beta }^{RI}}}{{{N_{Frm}}{T_s}}}$, which signifies that the estimated error of $\triangle {f_{RI}}$ is below $\frac{1}{{{N_{Frm}}{T_s}}}$.
Fig. 6. (a) is the received mixed sequence in the frequency domain. (b) is the distribution of $|{{{\cal F}_{ - \beta }}\{{{U_f}} \}(u )} |$.
On retrieving the phase noise sample sequence $\varphi _{RI}^{(M )}(n )$, ${U_f}(n )$ is filtered in the fractional domain, and the result can be described as
In Fig. 6(a), several frequency intervals are noticeable. The spectrum of the payload does not fully occupy the channel band; in these gaps, the LFMTSs ${\pm} \beta $ are inserted. In addition, there are guardian intervals, named as $\triangle f_{GI}^A$ and $\triangle f_{GI}^B$, between the LFMTSs ${\pm} \beta $, payload, and the edges of channel X. The $\triangle f_{GI}^A$ ensures that the spectrum of received signal payload will not overlay that of the received LFMTS $- \beta $. Meanwhile, the $\triangle f_{GI}^B$ is to avoid the LFMTS $- \beta $ exceeds the bandwidth limitation of the channel.
3. Simulation
As shown in Fig. 7(a), the simulation was carried out to investigate the impact of the critical factors on the proposed RI elimination method, such as the time mismatch, phase noise and frequency offset of lasers along with the bandwidth limitation. The transmitters were designed to generate 64-GBaud QPSK signals with a pulse shaped by a root raised cosine (RRC) filter with a roll-off coefficient of 0.01. The noise figure of the EDFA was 4.5. At the receiver end, the optical signal-to-noise ratio (OSNR) was adjusted by the amplified spontaneous emission (ASE) noise source. In the simulation, the sample rate was 128 GSa/s. The rest simulation parameters are listed in Table 1, where ${\alpha ^f}$, $\beta _2^f$ and ${\gamma ^f}$ are the coefficients of fiber loss, dispersion and nonlinearity, respectively.
Fig. 7. Simulation setup and the DSP procedure. (a) is the simulation setup. ECL: external cavity laser; Lo: local oscillator; IQ Mod: in-phase modulator; ICR: integrated coherent receiver; CP: coupler; VOA: variable optical attenuator.
Table 1. Simulation parameters
The DSP procedure of our proposed method and the regular DSP procedure are described in Figs. 7(b) and 7(c) respectively. In the regular DSP, the frequency offset is estimated through the power spectrum density of the sequence derived from taking the fourth power of the received sample sequence [20]. Meanwhile, the phase is corrected through the Viterbi-Viterbi phase estimation (VVPE) method [21]. As for the DSP of our proposed RI elimination method, the bandwidth limitation, dispersion, along with the carrier phase information are all included in the predistortion part, where the first two factors are measured in advance, and the last factor is retrieved from the mixed sample sequence by LFMTS $- \beta $. After the predistortion, the reconstructed RI is subtracted from the received mixed sequence as per the time mismatch obtained by the LFMTSs ${\pm} \alpha $. Finally, the signal without RI will be handled by the regular DSP, where the SNR shall be derived from the error vector amplitude (EVM) according to $EVM = \frac{1}{{\sqrt {SNR} }}$ [22] and the bit error ratio (BER) is the number of bit errors divided by the total number of transferred bits in a single frame.
In Fig. 8, $\triangle m = \triangle n = 20$, the phase noise and the frequency offset of lasers have been nullified, $L1$ and $L2$ are 10 km and 100 km respectively, the OSNR is 30 dB, and the received signal-to-RI power ratio (RSRIR) is 12 dB. Figures 8(b)–8(e) exhibit the process of identifying $\triangle {n^\ast }$, and the results are consistent with the analyses in section 2. In 8(c) and 8(e), the red lines denote the $|{{{\cal F}_{ + \alpha }}\{{S_{ + \alpha }^{RI}} \}(u )} |$ and $|{{{\cal F}_{ - \alpha }}\{{S_{ - \alpha }^{RI}} \}(u )} |$ respectively. As shown in Fig. 8(a), the RI elimination process is relatively sensitive to the time mismatch. However, according to the Eq. (7), we can obtain $\triangle u_{ {\pm} \alpha }^{RI} \approx 0.25\triangle n$, which indicates $|{\triangle {n^\ast } - \triangle n} |\le 2$ since a time shift of at least three samples shall induce one sample point shift of $\triangle u$. Therefore, we utilize the first 10 symbols of the payload as the training symbols for precisely identifying the time mismatch parameter.
Fig. 8. Simulation results. (a) is the simulated SNR against the time mismatch estimation error $\triangle {n^\ast } - \triangle n$. (b)-(e) are corresponding with Fig. 5.
The other critical factors have also been investigated, including the linewidth and frequency offset of lasers, along with the bandwidth limitation. In Figs. 9(a)–9(e), the 3-dB bandwidth of the system is approximately 26 GHz, and $L1$ and $L2$ are 10 km and 100 km respectively. It is believed that the phase shall vary stronger with linewidth growing higher, which will cause the peak of $|{{{\cal F}_{ - \beta }}\{{{U_f}} \}(u )} |$ to disperse. Thus, as shown in Fig. 9(c), when the linewidth of lasers is increased from 50 kHz to 500 kHz, a wider gate function $G(u )$ is required to retrieve the phase information from $|{{{\cal F}_{ - \beta }}\{{{U_f}} \}(u )} |$, with a price of more noise being included. Therefore, as shown in Fig. 9(a), the variance of the estimation error $var\{{\triangle \varphi (n )} \}$ grows with the increasing of the linewidth. However, as shown in Fig. 9(b), the retrieved carrier phase information is still in good consistence of the reference one when the linewidth is 500 kHz. Figure 9(d) shows the distribution of $var\{{\triangle \varphi (n )} \}$ against $|{\triangle {f_{Sig}}} |+ |{\triangle {f_{RI}}} |$, where the linewidth of lasers is fixed at 100 kHz and $\triangle {f_{Sig}} ={-} 10\triangle {f_{RI}}$. As shown in Fig. 9(d), $var\{{\triangle \varphi (n )} \}$ grows rapidly when $|{\triangle {f_{Sig}}} |+ |{\triangle {f_{RI}}} |$ exceeds 0.9 GHz, which is caused by the PSD overlapping of the payload and the received LFMTS $- \beta $, as shown in Fig. 9(e). The influence of the bandwidth limitation of the entire system is exhibited in Fig. 9(f), where the linewidth of lasers is 100 kHz, $\triangle {f_{Sig}}$ and $\triangle {f_{RI}}$ are set to zero. The estimation error increases with the 3-dB bandwidth decreasing, which is attributed to the power loss and distortion of the received LFMTS $- \beta $, caused by the filter.
Fig. 9. The impacts of the linewidth and frequency offset of the lasers along with the bandwidth limitation. In (a)-(c), $\triangle {f_{Sig}} = \triangle {f_{RI}} = 0$. In (e), $|{\triangle {f_{Sig}}} |+ |{\triangle {f_{RI}}} |= 0.88\textrm{ GHz}$, the red and blue lines represent the PSD component of $S_{ - \beta }^{RI}(n )$ and $S_{Mix}^{Rx}(n )$ respectively.
Figure 10 exhibits the overall performance of our proposed RI elimination method. In Fig. 10, the linewidth of the lasers, $\triangle {f_{Sig}}$, $\triangle {f_{RI}}$, $L1$ and $L2$ are 100 kHz, −800 MHz, 80 MHz, 10 km and 100 km, respectively. The 3-dB bandwidth in this simulation is approximately 26 GHz, which is about 0.8 times of the baud rate. As shown in Figs. 10(a) and 10(b), the performance of the regular DSP method is extremely restricted by the reflection interference. In contrast, our proposed method can effectively eliminate the RI regardless of the OSNR. Moreover, the proposed method is still functional even when the RSRIR approaches zero, where the power of the received RI is similar to that of the received signal. Figures 10(c) and 10(d) were derived with the OSNR set as 24 dB. Figure 10(c) is the SNR cost (△SNRC) of different RSRIR, where △SNRC is defined as the difference between the SNR derived from the proposed RI elimination method and the SNR obtained from the regular DSP with the RI nullified. The △SNRC is inversely proportional to the RSRIR, which is caused by the increasing difference between the reconstructed RI and the real RI. The SNR cost is controlled under 1 dB, when the RSRIR is above 8 dB, which is in accordance with the reflection ratio set below −24 dB. Figure 10(d) shows the SNR improvement (△SNRA) of our proposed method, compared with the regular DSP method. The improvement is quite noticeable with RSRIR approaching 4 dB, where the SNR derived from regular DSP method is approaching zero.
Fig. 10. The simulation results. In (a) and (b), the solid curves are the results of the proposed method, while the dashed lines represent those derived from the regular DSP. (c) and (d) are the SNR cost and SNR improvement regarding different RSRIR.
4. Experiment
The experimental setup is shown in Fig. 11. The RI originates from the signal generated at the eastbound terminal and is reflected back at the reflection point, which is emulated by the Cir.2 in Fig. 11(b) with the VOA.1 modifying the reflection ratio. Three PCs together with the PM.1 are utilized to control the polarization state to ensure that the received RI or signal is in the same polarization state of the local oscillator, which is divided from ECL.1 in Fig. 11(b). The power of the RI was controlled by VOA.1 and monitored by PM.2. The modulation format is 21 GBaud QPSK for transmitters on both sides, and an RRC filter with a roll-off factor of 0.01, is utilized for pulse shaping. As shown in Fig. 11(b), the total length of the fiber link is quite short to avoid interference derived from Rayleigh scattering. Considering that the RI is modulated and received through the same laser, the transmission fiber length must exceed the coherent length of ECL.1; otherwise, the phase noise and the frequency offset are negligible for RI. Therefore, a fiber with a length of 2 km is utilized here to ensure that the transmission distance of the RI traveling back and forth can exceed the coherent length of ECL.1, which is approximately 2 km, considering that the linewidth of ECL.1 is about 100 kHz.
Fig. 11. Experiment setups. (a) and (b) are the back-to-back (BTB) and the transmission setups respectively. PC: polarization controller; PBS: polarization beam splitter; OSA: optical spectrum analyzer; OSC: oscilloscope; PM: power meter. AWG: any waveform generator.
The DSP procedure of the experiment is similar with that provided in the simulation section, while the only difference is that the received mixed sample sequence should be resampled to 42 GSa/s before the operation of the DSP procedure in Fig. 7(b) or 7(c).
As shown in Fig. 12, the improvement obtained from our proposed method is noticeable from the experimental results, and the SNR cost is below 2 dB when the RSRIR is above 10 dB. Moreover, the BER is still below 3.8×10−3 even when the RSRIR is as high as 2 dB. In Fig. 12(a), the performance difference between back-to-back and transmission cases is believed to be resulted from the phase noise and frequency offset of the lasers. In the experiment, the 3-dB bandwidth is approximately 7 GHz and the SNR is limited below 18 dB by the imperfection of the transmitters and receiver. Therefore, the SNR cost and improvement are not satisfactory, compared with the simulation results.
Fig. 12. Experiment results. In (a) and (b), the red and black lines represent the results of the proposed and regular method respectively, while the dash dot lines represent the reference SNR without RI. (c) and (d) are the SNR cost and improvement of the proposed method under the transmission situation.
On verifying that the LFMTS ${\pm} \beta $ can effectively and correctly retrieve the carrier phase information, two special experiments are demonstrated with the ECL.2 and ECL.1 turned off, respectively, which are consistent with the cases of the RSRIR setting as $- \infty$ and $+ \infty$. In Figs. 13(a) and 13(c), the red lines are the phase sample sequences obtained from the regular DSP method, and the blue lines represent the results derived from the LFMTSs ${\pm} \beta $. Figures 13(b) and 13(d) exhibit the difference between the phase sample sequences retrieved from the two different methods. As shown in Figs. 13(b) and 13(d), $\triangle \varphi (n )$ is directly proportional to the sample number with a relatively small fluctuation. The direct proportion phenomenon is due to the difference between the frequency offsets retrieved from the LFMTSs ${\pm} \beta $ and the regular DSP method, while, the fluctuation represents the estimation error. Therefore, the carrier phase information can be effectively retrieved from the received mixed sequence through LFMTSs ${\pm} \beta $ before any other digital signal processing.
Fig. 13. (a) and (c) exhibit the phase sample sequences derived from different method. (b) and (d) represent the difference between the two curves in (a) and (c) respectively. The upper row shows the results of the RSRIR setting to $- \infty$, and the lower row is derived from the RSRIR setting to $+ \infty$.
5. Conclusion
In this paper, a novel reflection interference elimination method is proposed to handle the reflection problem in the same-wavelength bidirectional coherent fiber communication system. Three LFMTSs are utilized for the synchronization and carrier phase recovery, which are beneficial for reconstructing and subtracting the RI in the DSP of the receiver. Simulations were carried out to investigate the impact of the critical factors on the RI elimination, including the bandwidth limitation, time mismatch, along with the phase noise and frequency difference of lasers. Experiments were performed to verify the effectiveness of the proposed method. The results proved that the RI could be nearly eliminated when the RSRIR was above 12 dB, which is consistent with the case where the reflection ratio of the connector is 28 dB and the fiber loss per span is 16 dB. Moreover, the RI can be effectively removed even when the power of the received RI approaches that of the received signal. Additionally, according to our research, our proposed method is the first one to handle the phase noise and frequency offset uncertainty of the RI, which has been proved effective through simulations and experiments.
Appendix
Assume $x(n )$ is a linear frequency modulated sample sequence, which is written as
We define a function $y(n )$, described in Eq. (19), which is originated from $x(n )$ through a time shift $\triangle m{T_s}$ and a frequency shift $\triangle f$.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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