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Abstract
Non-orthogonal wavelength division multiplexing (WDM) channels are crucial in achieving significantly higher capacity and spectral efficiency than conventional schemes. Additionally, conventional schemes face challenges in electrical processing of wide-bandwidth signals. To suppress crosstalk in non-orthogonal WDM channels, the use of cascaded bandpass filters with suitable transmissivity and bandwidth is investigated for effective channel separation of large-capacity and multiplexed optical signals. This study employs the bandwidth ratio as a parameter, which is defined as the ratio of the channel spacing to the signal bandwidth, to quantify the extent of signal overlapping, and uses optical bandpass filters to filter non-orthogonal signals with a bandwidth ratio ranging from 1.0 to 0.75. The non-overlapping portion is set as the transmission bandwidth of the filter, and the crosstalk is maximally reduced with two-stage filters using Nyquist, super Gaussian, and Butterworth shaped filters. According to the analysis, the combination of Gaussian N = 1 and Gaussian N = 5 exhibits the lowest error vector magnitude (EVM) performance within a bandwidth ratio of 0.8 to 1.0. Simulations showed that a two-stage OBPF with a combination of Gaussian N = 1 and Gaussian N = 5 provides the best EVM performance at a bandwidth ratio between 0.85 to 1.0 within the combination of filter shapes and their orders we used. Additionally, the study includes an analytical investigation of the impact of amplified-spontaneous-emission noise associated with the Erbium-doped fiber amplifier (EDFA) and frequency resolution tolerance of the LCOS filter. The results demonstrate that cascaded EDFAs can be achieved down to OSNR of 10 dB at a minimum resolution of 4 GHz. Finally, the optimal filter shape is analyzed for different bandwidth ratios. The investigation shows that the optimal filter shape is independent of the function used and remains consistent across all bandwidth ratios. The tolerance of the filter is primarily affected by the −0.5 dB transmittance bandwidth between subchannels, which varies depending on the bandwidth ratio. Furthermore, a high tolerance is observed in the −20 dB transmittance bandwidth.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In metro/core networks, a reconfigurable optical add-drop multiplexer (ROADM) is a critical system that allows efficient connection between multiple points [1,2]. Within the ROADM, the wavelength selective switch (WSS) [3,4] is a key component to achieve add/drop required channels into/from the end users, not only in point-to-point, but also in point to multipoint, flexible channel bandwidth, and contentionless operation without converting optical signals into electrical signals. Additionally, higher spectral efficiency modulation methods are necessary to increase transmission capacity, and one of the potential candidates for integration into ROADM networks is optical orthogonal frequency division multiplexing (OFDM) [5,6]. However, the use of orthogonally related filters based on discrete Fourier transform (DFT) or fast Fourier transform (FFT) is necessary for subchannel separation. Consequently, handling wavelength division multiplexing (WDM) channels with mixed various bandwidths can be challenging [7–10]. Another potential candidate for increasing transmission capacity is the use of non-orthogonal WDM channels, where the symbol rate may exceed the wavelength channel spacing. The spacing between subchannels does not have to maintain the orthogonal relation, allowing for flexible channel spacing assignments. The signal quality of the demultiplexed non-orthogonal WDM channel, however, is affected by adjacent crosstalk, which results in degradation of spectral efficiency (SE). Furthermore, in anticipation of increased demand for autonomous driving and IoT in the future, situations such as mixed sensing signals and wide bandwidth should be considered. If the channel spacings of the added channel in ROADM systems could be as narrow as possible compared to the conventional guard-band and the channel spacings, keeping the quality of the received signal, total capacity of the system could increase. However, to achieve this type of multiplexing, simple scheme for separating each channel should be desirable, such that just extracting each channel with a bandpass filter and the complicated signal processing is not used. For instance, optical filters used in ROADM path switching, such as micro-electromechanical system (MEMS) mirror arrays, have a fixed bandwidth that covers the entire bandwidth of each channel, which can result in stronger crosstalk effect between adjacent signals [11]. Further, liquid crystal on silicon (LCOS)-based WSS exhibits several superior properties such as programmable and wavelength independent connection of arbitrary wavelength channels to arbitrary output ports [12]. Even in an LCOS bandpass filter (BPF), the conventional filtering scheme introduces strong crosstalk from adjacent signals in case of densely wavelength multiplexed channels. Moreover, complicated signal processing is required to mitigate such crosstalk using a digital signal processor, which inevitably increases power consumption and limits the bandwidth [13].
Previous studies have investigated channel separation and crosstalk reduction between densely-positioned channels with multiple-input multiple-output (MIMO) technology, maximum likelihood detection (MLD), or Faster than Nyquist technology (FTN) for optical multi-carrier signals like optical OFDM [14–16]. In case of MIMO, a local oscillator is used in digital coherent detection, where the wavelength is closely matched with the target subchannel. Other types of schemes called offset-QAM OFDM and spectrally efficient frequency division multiplexing (SEFDM) have been reported [17,18]. In these schemes, denser spectral assignment than the conventional OFDM were presented, and inter-symbol interference (ISI) was suppressed by using the waveform shaping. However, inter-channel interference (ICI) is one of the significant issues, and thus, cyclic prefix or MLD should be introduced to improve the performance.
Compared to multi-carrier signals with high spectral efficiency, non-orthogonal WDM or FTN WDM are other types of higher spectral efficiency than WDM with guard band [19–21]. In these multiplexing schemes, channels are closely assigned with overlapping, and ICI are compensated with MIMO detection.
However, in all electrical processing schemes, the device bandwidth should be sufficiently wide to recover the extracted signal; bandwidth limitations can reduce performance. Therefore, there is a need for a technique that provides sufficient bandwidth, excellent crosstalk suppression performance, and variable bandwidth for non-orthogonal WDM signals with flexible bandwidths.
This study proposes a technique to suppress crosstalk when separating high-capacity and multiplexed optical signals in non-orthogonal WDM using cascaded optical bandpass filters (OBPFs). The approach involves selecting appropriate filter shapes, determining the order of the transmissivity characteristics, and combining two OBPFs with different shapes. To evaluate the proposed method, simulations were conducted to measure the error vector magnitude (EVM) of the recovered signals with varying channel spacings. The transmissivity characteristics of the two-stage OBPFs were then obtained from the simulation results. This paper is organized as follows. In Section 2, the operating principle is briefly explained. Section 3 describes the simulation process and results, including the evaluation of filtering, considering practical environments. The tolerance of the filter shape is described in Section 4, and finally, we conclude in Section 5.
2. Analytical principle
The study assumed a rectangular shaped time waveform and utilized a sinc-function-shaped optical spectrum in each channel, with a frequency range from the first null point at the shorter-wavelength-side to that at the longer-wavelength-side. Figure 1 illustrates the analytical procedure of the proposed scheme [22], in which three-channel WDM signals (40 GBaud, single-polarized NRZ-16 QAM pseudo-random bit sequence (PRBS) with a word length of 217−1) were generated, and the coded data were shifted by 1-bit compared to other channels. Further, the center frequency of each channel was set to be narrower than the full bandwidth of each channel, which determines the bandwidth ratio between channels, which is defined as the ratio of the channel spacing to the signal bandwidth. For example, a channel spacing of double the Baud rate is expressed as bandwidth ratio of 1.0. This parameter is changed from 1.0 to 0.75 in the following simulation. In case of the bandwidth ratio of 1.0, two adjacent channels were connected at the null points for the first case (left in Fig. 1(a)). Further, in case of the bandwidth ratio of 0.75, they are overlapped, and the electric field amplitude of one channel coincides with the other at the frequency separated from the center by half the Baud rate (right in Fig. 1(a)). The generated three-channel WDM signals transmits through two-cascaded OBPFs using three types of filters, super Gaussian, Nyquist, and Butterworth (Fig. 1(b)). One-stage filter is simpler than the two-stage structure, however, the transmissivity characteristics of the filters in practical case is slightly different from the designed one and the desired transmissivity could not be covered by using the one-stage structure. Therefore, when we focus the optical approach, we utilized the two-stage structure to extend the selection of the transmissivity flexibly. In addition, transmissivity with the selected functions and the orders includes the characteristic similar to the root raised cosine function, and then, the waveform shaping at the transmitter could be emulated with two-stage structure when we select the suitable combination of the filter shape and orders.
Then, time waveform was obtained by executing inverse FFT of the frequency spectrum, and each symbol was downsampled to form a constellation map (Fig. 1(c)). A histogram was created from a time waveform, and a threshold level was derived between the most adjacent symbols, and accordingly, the position of each symbol was decided. However, the constellation of the recovered signal is misaligned from the ideal symbol positions (reference positions) in the constellation, and the misalignment was corrected. The constellation was divided into 16 groups using the threshold value of the hard decision. The difference between the individual mean value and reference value of the electric field amplitude was calculated, and the center of each symbol was corrected using the discrepancy between them. Then, the BER for the recovered signals and EVM was obtained [23]. In this paper, EVM is defined as a root mean square of error vector in each symbol for randomly transmitted data normalized by average electric field strength. On selecting the target quality of the recovered symbols as BER<${10^{ - 3}}$ before forward error correction, the target was an EVM of 18% or less. The accumulated amplified spontaneous emission (ASE) noise was considered by adding noise power with random phase in proportion to the number of Erbium-doped fiber amplifiers (EDFAs). The dispersion and nonlinear distortion were not taken into consideration. In addition, processing flow of the decode is not the same as that used in the conventional digital signal processing for digital coherent receiver. For example, linear equalization, linewidth of the transceiver and local oscillator, frequency offset, carrier phase recovery, and so on, were not taken into consideration in the simulation. However, our main purpose in this paper is to investigate the possibility of the suppression of the crosstalk with OBPFs in non-orthogonal WDM signals, and the results would be some information because the process in Fig. 1 can be merged in the conventional process.
We changed the filter shape, and three shapes, super Gaussian [24], Nyquist [25] and Butterworth [26], were created. The filter bandwidth was changed depending on the bandwidth ratio, as shown in Fig. 2.
Fig. 2. Transmissivity characteristics of three types of filters. Left figure: first-stage filter (Butterworth: $N = 1$, Super Gaussian: $N = 1$, Nyquist: $N = 1$) Right figure: second-stage filter (Butterworth: $N = 4$, Super Gaussian: $N = 5$, Nyquist: $N = 0.5$).
The Gaussian filter was used to produce a symmetrical output without overshoot in the time waveform because of its gradual slope feature as a function of the wavelength. The frequency characteristics of the super Gaussian filter is described below [24]:
The following equation is utilized as the Nyquist function [25].
The Nyquist filter is a frequency spectrum condition that mitigates symbol interference at a decision point when pulses are continuously transmitted at equal intervals. Here, T represents the time width of the −3 dB down, corresponding to the Baud rate. N represents the roll-off rate, which is a constant between 0 and 1. The closer it is to 1, the broader the tail becomes, and when $N = 0$, the filter becomes rectangle shaped.
The magnitude response of a low-pass Butterworth filter is given by [26]:
3. Simulation results
3.1 Optical filter selection
To select the filter shape, different filter combinations with several characteristics were tested, as shown in Fig. 3. Figure 3(a) indicates the one-stage Nyquist-shape for the $ N = 1$ case (single-lobe-shaped transmissivity), where a filter with a constant transmission bandwidth was used regardless of the bandwidth ratio. As the bandwidth ratio between non-orthogonal WDM channels is reduced, the crosstalk between channels increases, leading to a significant impact on the EVM of the recovered signal. Further, we selected another filter to form two-stage filters, where the first-stage filter was the same as that shown in Fig. 3(a). In Fig. 3(b), the selected rectangle filter is shown, where the bandwidth is changed according to the bandwidth ratio and does not overlap with adjacent signals in the second filter. As can be seen in Fig. 3(b), adjacent crosstalk can be suppressed at the bandwidth ratio of 1.0. However, when the bandwidth ratio decreases, EVM is deteriorated because the transmission bandwidth is limited to be narrower than that required to maintain the signal quality. To improve the performance, the second filter shape close to the rectangle shape with a small slope was selected. As indicated in Fig. 3(c), Nyquist $ N = 1$ was used as the first filter, and Nyquist $ N = 0.5$ was used as the second filter. Improvement in the EVM at the bandwidth ratio from 0.8 to 0.95 was achieved compared to that shown in Fig. 3(b). However, at the bandwidth ratio of 0.75, the required frequency bandwidth was not sufficiently maintained, resulting in a deterioration of the EVM.
To determine the suitable filter structure, the combination of two OBPFs in two-stage structures was changed. In the bandwidth ratio from 0.85 to 1.0, the second stage filter was fixed to Gaussian $\; N = 5$, and the EVM of the transmitted signals using Butterworth, Gaussian, and Nyquist $\; N = 1$ as the first stage filter were compared. As can be seen in Fig. 4(a), the combination of Gaussian $N = 1$ and Gaussian $ N = 5$ was suitable because the lowest value of the EVM at the bandwidth ratio from 0.85 to 1.0 was obtained. As shown in Fig. 4(b), when comparing the EVM using Butterworth $N = 4$, Gaussian $N = 5$, and Nyquist $ N = 0.5$ as the second-stage filters together with Gaussian $ N = 1$ as the fixed first stage filter, the Gaussian combination was also suitable, because the EVM is better at the bandwidth ratio from 0.9 to 1.0.
Fig. 4. Results of EVM as a function of the bandwidth ratio with the optimal combination of the two-stage structure.
Finally, Fig. 5 shows the results of the combination of Gaussian $ N = 1$ and Gaussian $N = 5$, and the constellation after symbol misalignment correction. The BER of the recovered signal was below ${10^{ - 6}}$ at the bandwidth ratio from 0.8 to 1.0, and the BER was ${10^{ - 3}}$ at the bandwidth ratio of 0.75 according to the calculated EVMs. It would be difficult to compare these results on the other reported ones, but the obtained EVM remains less than 10% up to the bandwidth ratio of 0.8, on the other hand, the non-orthogonal WDM in [20] reported the baud rate about 10% narrower than the channel spacing. Therefore, although the performance improvement depends on the spectrum shape, we consider that superior performance could be achieved in our scheme.
Fig. 5. EVM characteristics and constellation of transmitted signals through the combination of Gaussian $ N = 1$ and Gaussian $N = 5$.
3.2 Tolerance of the proposed scheme against filter resolution and ASE noise
In practical transmission conditions, ASE and frequency resolution of programmable LCOS filters should be included in simulation. We used Eqs. (4) and (5) for the spontaneous emission noise, signal power spectral density, and OSNR generated by $s$-stage connection of EDFAs [28], where $ s$ is the number of stages of EDFAs, $\; G$ is a gain coefficient, $Dim$ is the order of M-sequence (fixed as 17), and M is the order of multi-level modulation format (equal to 16). The parameters in the simulation are summarized in Table 1, and simulation flow of tolerance again OSNR and frequency resolution of the OBPFs are illustrated in Fig. 6.
Table 1. Parameters in ASE-added NRZ-16QAM signal generation.
Three-wavelength channel WDM signal was generated using a PRBS with a code length of ${2^{17}} - 1$. Then, after adding the ASE noise power and random phase to the 3-wavelength WDM signal, subsequent calculations were performed considering an output signal. A bandwidth-programmable LCOS-type bandpass filter was the main optical component, because the bandwidth ratio between signals was changed and suitable filter-shapes and bandwidths were investigated. However, due to the specification of the LCOS filter, it is necessary to consider the frequency resolution of the filter. Thus, we selected the frequency resolution of the LCOS-type OBPF as 6.25 GHz in the experiments (InLC Technology, OSG12), which is one of the center frequency spacing in ITU-grid. Additionally, insertion losses of 5.46 dB and 3.99 dB for filters with frequency resolutions of 2.61 GHz and 3.55 GHz have been reported in Ref. [29]. Therefore, frequency resolutions of 3, 4, and 6.25 GHz were assumed in calculation. If the curve of the filter transmissivity characteristics with frequency is discretized every frequency resolution interval, a zigzag-shaped wave is formed, discretized in the direction spreading wider-side of the transmissivity curve against the ideal curve of two-stage filters with Gaussian $N = 1$ and Gaussian $N = 5$ for each frequency resolution.
Figure 7 shows the results of EVM using the two-stage filter for 40 Gbaud 3-channel-single polarized NRZ-16QAM signals as a function of the bandwidth ratio. In case of 4.0-GHz resolution, the EVM was below 20% down to OSNR of 10 dB at the bandwidth ratio of 0.8 to 1.0. Further, as can be seen in Fig. 8, it was found that the EVM was degraded when the resolution was 6.25 GHz compared with that of less than 4 GHz at an OSNR of larger than 15 dB at a bandwidth ratio of 0.9. Therefore, it is reasonable to use a filter with a resolution of 4 GHz or less.
Fig. 7. EVM for 40 Gbaud 16QAM signal with ASE noise and minimum filter resolution of 4.0 GHz as a function of the bandwidth ratio.
4. Tolerance of the filter shape
4.1 Measurement of designed filter transmittance
As previously described, we utilized an LCOS filter in experiments as a programmable OBPF. The transmissivity characteristics were evaluated through simulations, and the results showed that the proposed scheme can effectively suppress crosstalk in non-orthogonal WDM systems with flexible bandwidths. These findings suggest that the proposed technology has the potential to be utilized in experimental settings.
The experimental setup for the transmission characteristics of the LCOS filter is shown in Fig. 9. Additionally, 12 types of LCOS filters for bandwidth ratios from 0.75 to 1.0 were tested including the discretized wider and narrower side of the transmissivity characteristics. Each blue rectangular shape shows the transmissivity characteristics after discretization every 6.25 GHz (lower left of Fig. 9), and the transmittance data for every 6.25 GHz interval was created using MATLAB. Then, the transmittance characteristics used in the measurement were imported to the LCOS-type OBPF as a CSV file. The output optical power of the white light source was set to +8 dBm, and the transmittance of the filter was observed with an optical spectrum analyzer. The transmissivity characteristics obtained are indicated in the lower right of Fig. 9. The black solid line shows the ideal transmission characteristics to achieve the best EVM at a bandwidth ratio of 1.0, and the orange solid line indicates the experimentally obtained characteristics. As can be seen in this figure, the insertion loss of the LCOS-type OBPF was 3.7 dB larger than the simulation result. Therefore, it is necessary to add the insertion loss in the simulation scheme shown in Fig. 1 when performing the EVM evaluation of the restored signal. Additionally, the transmissivity characteristics of the LCOS-type OBPF are different from those of the optimized one in simulation, and the effect of the discrepancy between the transmissivity used in the experimental and in ideal conditions should be investigated.
Fig. 9. Experimental setup of filter characteristics (upper), input file of discretization of the outer filter (lower left) and experimental output (black solid line) and simulation (orange solid line) results (lower right).
4.2 Tolerance results of optical filter characteristics for restored signal characteristics
4.2.1 EVM evaluation
Figure 10 shows the simulation diagram of the optical filter tolerance. Since the transmittance of the filter passband in the experiment was −3.7 dB lower than the ideal characteristic, the maximum transmittance was increased to 0 dB by normalization to match the simulation result, and bandwidths at −0.5 and −20 dB transmittance between the simulation and experimental results were calculated in each OBPF as described below. When the ideal filter has a wider (narrower) bandwidth than the experimental ones, the passband difference is expressed as a plus (minus) sign (right figure of Fig. 10). The filter shapes were varied, and the order of Nyquist N was changed from 0 to 1 in increments of 0.1; and those of the Gaussian and Butterworth $ N$ from 1 to 5 were changed in increments of 0.2. The transmitted signal through one of these filters, or combination of two of these filters were calculated, and the EVMs were plotted on figure with −0.5- and −20-dB transmissivity as the horizontal and vertical axes, respectively.
Fig. 10. Simulation procedure (left) and concept of filter shape comparison between simulation and experiments. Right figure: Single-stage Nyquist $N = 0.5$ shape created by simulation (orange solid line). Experimental results of transmittance (black dotted line)
4.2.2 Tolerance results for different bandwidth ratio conditions
The shape of the filter used in the first stage of the two-stage structure is represented by stars for Nyquist, circles for super Gaussian, triangles for Butterworth, and squares for one-stage structures. Additionally, red-colored symbols indicate an EVM difference, which is defined as the difference from EVM based on the experimental filter, of 1% or less (including the minus signed value), yellow-colored symbols for 1% to less than 2% difference, orange-colored symbols for 2% to less than 3% difference, green-colored symbols for 3% to less than 4% difference, and blue-colored symbols for 4% or more difference. The filter features of the red-colored symbols were defined as the shape tolerance. Figure 11 shows the results of shape tolerance of the optical filter. For all bandwidth ratios, the optimal filter shape does not depend on the function (super Gaussian, Nyquist, and Butterworth). Further, the red-colored range, indicating the results as good as or better than experimental filters, is limited within a narrow area as the bandwidth ratio becomes smaller. Similar to the results in Section 3, when the bandwidth ratio is large, a sharp-shaped filter at the first stage tends to suppress time fluctuations and improve the EVM. At the bandwidth ratio of 1.0 in Fig. 11(a), the transmittance of approximately −0.5 dB is on the minus side for red-colored symbols, i.e., the sharp-shaped filter improves EVM. Moreover, it was found that the tolerance is high against the change of bandwidth difference at a transmittance of −20 dB. Additionally, in case of the bandwidth ratio of 0.75, the change of bandwidth difference at a transmittance of −0.5 dB is tolerable on the plus side. This means that the EVM is better with a filter that can transmit the widest possible area as well as suppressing the crosstalk. It can be confirmed that the EVM is better in the plus side, and the −20 dB transmission bandwidth has a certain tolerance on the minus side.
Fig. 11. Results of optical filter shape tolerance for several bandwidth ratios. Color: Difference from EVM based on the experimental filter (red color is the same or better than the experimental filter). Symbol shape: The shape of the filter used in the first stage of the two-stage structure. Nyquist shape (star), super Gaussian (circle), Butterworth (triangle), single stage structure (square).
Figure 12 shows the signal transmission characteristics of the outer filter with a one-stage structure and the combination of the optical filters with the optimum bandwidth ratios. The blue solid lines indicate the results using transmission characteristics in experiments, and the best results in the simulation in this Section are indicated by asterisks. The combination of different filter shapes that achieve the lowest EVM may vary at each bandwidth ratio. However, optimal results with degradation within 2% are achieved at all bandwidth ratios, satisfying the target EVM of 18% or less.
Fig. 12. Comparison of optimal filter transmission results for each bandwidth ratio. Solid blue line: signal transmission characteristics of the experimental filter. Asterisk: optimal filter selection and combination shape at each bandwidth ratio.
5. Conclusion
We investigated a two-stage OBPF method for suppressing crosstalk of adjacent channels in non-orthogonal WDM systems. Simulations showed that a two-stage OBPF with a combination of Gaussian $\; N = 1$ and Gaussian $\; N = 5$ provides the best EVM performance at a bandwidth ratio between 0.85 to 1.0 within the combination of filter shapes and their orders we used. We also considered ASE noise and frequency resolution of the LCOS filter in the simulations to mimic a realistic measurement environment. The proposed method was found to effectively suppress crosstalk in the presence of cascaded EDFAs down to OSNR of 10 dB with a minimum resolution of 4 GHz or less. Additionally, we investigated the tolerance of the optical filter shape and found that a sharp-edged filter in the first stage suppresses time fluctuations while the second stage filter suppresses crosstalk to the maximum extent.
Acknowledgments
The authors would like to thank Honorary-Prof. K. Iga, Prof. Emeritus K. Kobayashi, Prof. Emeritus F. Koyama, and Assoc. Prof. T. Miyamoto of Tokyo Institute of Technology for helpful discussions.
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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