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Abstract
We propose a spectrally slicing-and-synthesizing coherent optical spectrum analyzer to measure complex field waveforms of quadrature amplitude modulation (QAM) optical signals with ultralong periods. The optical spectrum of a measured optical signal is divided into multiple narrowband spectral components, called slices. The slices are sequentially measured using low-speed coherent detection. After phase noise suppression and frequency fluctuation compensation on each slice, the measured slices are synthesized to recover the original signal spectrum. Our numerical and experimental results confirm that the proposed method can overcome the limitation of the measurement bandwidth because the signal spectrum can synthesize more than 100 slices. We experimentally demonstrate complex field measurements of 16QAM optical signals. Our method can measure high-speed optical complex field waveforms with no bandwidth limitation.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical coherent transmission systems with quadrature amplitude modulation (QAM) techniques [1,2] have been employed in practical optical fiber transmission systems. For optical performance monitoring in the coherent systems, it is necessary to observe waveforms of optical complex fields, i.e., amplitudes and phases, or to measure constellation diagrams of QAM optical signals. There have been reports on the technique using optical coherent receivers with sufficient bandwidth for the signal bandwidth [3]; however, high-cost broadband photodetectors and analog-to-digital converters (ADCs) are required. In addition, the signal distortion due to the imperfections in optical devices and electronics cannot be directly measured because digital signal processing (DSP) that follows coherent detection includes signal equalization. Simple and low-cost techniques, which do not use broadband receivers and signal equalization, are highly desired for measuring complex field waveforms. Although linear optical sampling based on coherent reception with a pulsed local oscillator (LO) is a promising technique [4,5], phase noise impairment becomes more serious at a slower sampling rate, and it is complex because ultrashort pulse sources are required.
Recently, we have proposed a frequency-domain approach for the complex field measurements [6,7]. The optical spectrum of a measured signal is divided into multiple narrowband components called slices, which are sequentially measured with narrow-band optical coherent receivers. We recover the broadband complex field spectrum of the signal by synthesizing the measured slices. This is called a spectrally slicing-and-synthesizing coherent optical spectrum analyzer (S3 coherent OSA). Although the phase and frequency of each slice fluctuate independently, they are compensated for by the offline DSP without signal equalization. Our proposed method is limited to monitoring waveforms of periodical signals. However, long periods are measurable; for example, a pseudo-random bit sequence (PRBS) with a bit length of 215–1. In this study, we investigate the performance of our proposed method for measuring complex field waveforms of QAM optical signals. We previously reported the proof-of-concept experiments [6,7]. This paper describes in detail the DSP to synthesize the measured slices, and includes the numerical and experimental investigation to identify the number of slices that the optical signal can synthesize.
2. Operation principle of spectrally slicing-and-synthesizing OSA
Figure 1 shows the configuration of our proposed method. We measure complex field waveforms of periodic optical signals. The repetition rate (or fundamental frequency) and period are f0 and 1/f0, respectively. The spectral waveforms of the periodical signals are comb-shaped with spacing of f0. The signal baudrate is B and measurement bandwidth of the signal spectrum is W. The optical signals are measured by an S3 coherent OSA, which consists of an optical 90° hybrid circuit, a tunable laser used as an LO, two balanced photodetectors (BPDs), and two ADCs followed by DSP. Although it is similar to a conventional coherent receiver used for single polarization, here, we can use low-speed BPDs and ADCs with bandwidths R that are much smaller than the measurement bandwidth W but more than the repetition rate f0, i.e., W >> R >> f0. Figure 2 shows the concept of our measurement method. An optical signal with a carrier frequency ν0 is measured using low-speed coherent detection, and a part of the signal spectrum with a narrow bandwidth of double-sideband 2R at the LO frequency is then downconverted to a baseband. From the received signal, a narrowband component “slice” with a bandwidth of double-sideband w is extracted, and it is digitized and stored through ADCs whose clock is synchronized with the repetition rate of the signal f0. The multiple slices are sequentially measured to wrap the entire measurement bandwidth W by tuning the LO frequency with even spacing ΔfLO. The neighborhood slices share overlapping components, which are used to synthesize the slices. In Fig. 2, the signal spectrum is divided into five slices.
The original signal spectrum cannot be precisely recovered by composing the slices because every slice is randomly and independently impaired with phase noise and frequency fluctuations, which are induced in intra-dyne coherent detection with a free-running LO. Before synthesizing the slices, it is necessary to suppress the phase noise and compensate for the frequency fluctuation. In our method, this is performed by the offline DSP, as shown in Fig. 3. First, the phase noise on the slice is suppressed. The spectral peak samples with even spacing f0 are extracted from the comb-shaped spectrum of the slice. The peak samples of the adjacent slices are synthesized upon compensating for the frequency fluctuation by detecting their overlapping components. This process is repeated for all slices, and thus, the signal spectrum can be precisely recovered. A detailed description of the process is presented in this section.
First, the phase noise on the slice is estimated and suppressed using signal periodicity. Because the signal is temporally periodic, the slice spectrum is comb-shaped. The comb components of the slice are spectrally broadened due to the phase noise. The phase noise can be estimated by extracting the broadened comb component. The procedure for the phase noise suppression is shown in Fig. 4. The measured slice data undergo the fast Fourier transformation (FFT), and a single comb is extracted by rectangular-shaped filtering with a bandwidth equal to f0. The temporal data with the phase noise is obtained after downconverting the extracted comb data to DC with the inverse FFT (IFFT). The phase noise is suppressed by multiplexing the original slice data with the conjugate of the processed data.
After the spectral peak samples are extracted from the comb-shaped spectrum of the slice, the frequency fluctuation between two adjacent slices is compensated using their overlapping components. The DSP for synthesizing k – 1-th and k-th slices is illustrated in Fig. 5. The phase components are extracted from the two adjacent slices, and their cross-correlation is calculated. Using the index of a peak in the correlation results, we can calculate the position and length of the overlapping component in the k-th slice. The amplitude and phase differences between the two adjacent slices are also compensated for using the overlapping components. They are calculated by averaging the spectral difference between adjacent overlapping components at every frequency. The two adjacent slices are composed after the overlapping component is removed from the k-th slice.
Thus, the measured slices are sequentially composed, and the original signal spectrum can be recovered. The spectral components with the measurement bandwidth W are extracted from the recovered spectrum. When a repetition signal with a symbol length of 215–1 is measured with the measurement bandwidth W of 2B, the samples with the size of 2 × (215–1) are extracted from the recovered spectrum. The temporal waveform of the optical signal is obtained by the IFFT of the spectrum. It is resampled to 1 sample/symbol while the temporal delay is optimized, and the constellation diagram is retrieved.
The number of measured slices K is determined by the desired measurement bandwidth W and frequency spacing of the LO tuning ΔfLO as described by
where ⌊·⌋ is the round function. Using bandwidths of the slices and the overlapping components, w and m, respectively, ΔfLO is given by ΔfLO = w – m. For example, assuming that the measurement bandwidth is twice the signal baudrate and the overlapping component bandwidth is half the slice bandwidth, i.e., W = 2B, m = w/2, and ΔfLO = w/2, it is required that the slice number K is larger than 4B/w + 1. For a baudrate of 12.5 Gbaud and slice bandwidth of 500 MHz, the signal spectrum should be divided into more than 100 slices.3. Evaluation of numerical performance
First, we numerically investigate the performance of our method. The aim of our simulation is to identify the number of slices that a measured signal can synthesize. In our method, the extraction of the spectral peak samples reduces additive white Gaussian noise such as amplified spontaneous emitted (ASE) noise. Although the intensity fluctuation between the measured slices can be caused by the power fluctuation of the signal and LO, it can be suppressed by the DSP, as mentioned in the previous section. The phase noise remains even after its suppression process because only the phase drift is compensated for in our method. In addition, the timing jitter of the ADC clock can induce independent and random temporal fluctuations of the slices. If the residual laser phase noise and ADC timing jitter are accumulated, the number of synthesized slices can be restricted. In this section, we identify the number of slices that can be synthesized in the presence of laser phase noise and ADC timing jitter.
The simulation model is shown in Fig. 6. Repetition PRBSs with lengths of 215–1 are mapped into gray-coded quadrature phase shift keying (QPSK) symbols. Rectangular Nyquist shaping is performed after upsampling the symbols to 2 sample/symbol. Using the I and Q samples of the QPSK samples, a CW light at a carrier frequency ν0 is modulated, and the QPSK optical signals are generated at the baudrate B. We assumed B = 10 Gbaud, and the repetition rate f0 is calculated to be approximately 300 kHz. They are received by a phase-diversity homodyne receiver with an LO. The received bandwidth is R, which is emulated by rectangular-shaped filtering of the received samples with a bandwidth of the single-sideband R. By tuning the LO frequency to ν0 – kΔfLO, where k is an integer and ΔfLO is tuning spacing, a part of the signal spectrum around ν0 – kΔfLO is measured, and a slice is extracted with a bandwidth (double-sideband) w that is equal to 2R. The measured slices independently suffer from timing jitter, which is assumed to be white Gaussian variables with zero mean and deviation τ. The spectral linewidths of the signal and LO are δf/2; hence, the total linewidth of the phase noise impairment on the slice is δf. By synthesizing the measured slices as mentioned in the previous section, the signal complex spectrum is recovered. The measurement bandwidth W is set to 2B = 20 GHz. The sample number of the optical signal is 1M and the DSP for the spectral synthesis is performed with the frequency resolution of 20 kHz.
In this simulation, the constellation diagrams of the QPSK signals are recovered. The symbol fluctuation on the constellation is evaluated with the timing jitter and laser phase noise. The slice number K and receiver bandwidth R are varied, while the bandwidth of the overlapping components m is kept as the receiver bandwidth, i.e., m = R. In the simulation with 1,000 iterations, we calculate the average variance values of the differences between the recovered symbols and ideal QPSK symbols. The variance values are normalized by the amplitude of the ideal QPSK symbols.
First, we calculate the symbol fluctuation of the recovered constellation with the timing jitter. The real and imaginary parts of the calculated symbol fluctuation were almost identical, and the variance values of the real parts are plotted in Fig. 7(a). The timing jitter deviation values τ are 1 ps, 2 ps, 5 ps, 10 ps, 20 ps, and 50 ps. We found that the symbol fluctuation increases as the magnitude of the timing jitter increases; however, the dependence on the slice number is negligible. Figure 7(b) shows the calculated dependence of the symbol fluctuation on the timing jitter, which is normalized by the symbol period 1/B. The horizontal axis represents τ·B. Closed dots, open dots, closed triangles, and open triangles indicate the results with the slice number K = 1, 10, 100, and 100, respectively. It is observed that the fluctuation variance is proportional to the timing jitter. Suppressing the fluctuation variance smaller than 10−2 requires τ·B smaller than 0.05. The requirement for the clock jitter can be addressed using conventional electronics.
Fig. 7. Calculated dependences of symbol fluctuation variance in the presence of timing jitter on (a) the slice number K and (b) variance of timing jitter normalized by the symbol period, τ·B.
Next, we calculate the recovered constellation with laser phase noise when the spectral linewidth values of the phase noise impairment are δf = 10 kHz, 20 kHz, 50 kHz, 100 kHz, and 200 kHz. The variance values of the real parts of the symbol fluctuation are plotted in Fig. 8(a). The imaginary parts were almost the same as the real parts. We found the same trend in the presence of the timing jitter. Although the variance values increase as increasing δf, they do not vary as increasing K. Figure 8(b) shows the calculated dependence of the symbol fluctuation on the spectral linewidth. The horizontal axis is normalized by f0 because the available bandwidth to suppress the phase noise is restricted by f0 in our method. Suppressing the fluctuation variance smaller than 10−2 requires reducing δf/f0 smaller than approximately 0.1. It is expected that lasers with 100-kHz linewidths are available for measuring a 32-Gbaud QAM optical signal with a symbol size of 215. By reducing the repetition length of the signal or increasing the signal baudrate, the lager linewidth becomes applicable.
Fig. 8. Calculated dependences of symbol fluctuation variance due to phase noise on (a) the slice number K and (b) the spectral linewidth δf.
These numerical results indicate that our method does not impose limitations on the slice number even in the presence of a timing jitter of the ADC clock and large phase noise.
4. Experimental demonstration of optical complex field measurement using spectrally slicing-and-synthesizing coherent OSA
We conducted an experimental demonstration of optical complex field measurements of QPSK/16QAM optical signals using our method. The aim is to perform proof-of-concept experiments and to identify the number of slices that the signal spectrum can synthesize. Figure 9 shows the configuration of the experimental setup. A CW light with a linewidth of 5 kHz at a wavelength of 1550 nm was generated from a tunable external cavity laser, and it was modulated by an optical IQ modulator (IQM), which was driven by two I and Q electrical streams of rectangular-shaped QPSK or 16QAM baseband signals generated from an arbitrary waveform generator (AWG) at a sampling rate of 25 GSample/sec. The signal baudrate, period, and repetition rate were 12.5 Gbaud, 2.62 µs, and 381 kHz, respectively. The spectra of the QAM optical signals were rectangular-shaped with the bandwidth of 12.5 GHz. After the optical signal-to-noise ratio (OSNR) was adjusted to 30 dB, the QAM optical signals were measured using our method. A tunable external cavity laser with a linewidth of 5 kHz was used as the LO. By tuning the LO frequency with even spacing, the slices were sequentially measured over the signal bandwidth, and they were stored by a high-speed oscilloscope with an analog bandwidth of 8 GHz at a sampling rate of 40 GSample/sec. The number of the stored samples was 2M. In the offline DSP, the frequency resolution was 20 kHz. Although the bandwidths of the receiver and oscilloscope used in our experiments were broader than the signal spectrum, the narrow receiver bandwidth was emulated by rectangular-shaped filtering of the stored data with a bandwidth of R. The bandwidth of the slice w was maintained to be 2R, and K and w were varied to satisfy Eq. (1). The measurement bandwidth W was set to B = 12.5 GHz ranging from −6.25 GHz to 6.25 GHz. The temporal and spectral complex field waveforms were recovered by the slice synthesis procedure, and the QAM constellation diagrams were retrieved. In our experiments, the normalized linewidth of laser phase noise impairment δf/f0 was calculated to be approximately 0.03, which satisfied the requirement of δf/f0 < 0.1, as mentioned in the previous section.
Fig. 9. Experimental setup for measuring complex field waveforms of QAM optical signals using our method.
First, we experimentally investigated the dependence on the number of slices, while we measured complex field waveforms of 12.5-Gbaud QPSK signals. The recovered constellation diagrams are shown in Fig. 10(a), when K was adjusted to 3, 6, 16, 32, 63, and 126. We found clear symbols on the recovered constellation diagrams, and the symbol fluctuation did not increase even with an increase in K. To explicit the dependence on the slice number, the variance values of the symbol fluctuation are plotted in Fig. 10(b). Open circles and closed circles indicate the real and imaginary parts of the variance values, respectively. We found a slight difference between the real and imaginary parts due to the imperfections in the IQ modulation. We did not observe any increase in the symbol fluctuation even with an increase in the slice number. These results confirm that it is possible to divide the signal spectrum into more than 100 slices without increasing the symbol fluctuation.
Fig. 10. (a) Recovered constellation diagrams of 12.5-Gbaud QPSK signals with the slice number K = 3, 6, 16, 32, 63, and 126. (b) Measured dependence of the symbol fluctuation variance on the slice number K.
Conventionally, the constellation diagrams of QAM optical signals are measured using broadband coherent receivers with sufficient bandwidths for the signal bandwidth. We compared our proposed method with the conventional method. Figure 11(a) shows a constellation diagram of the QPSK signals received using broadband coherent detection in which a laser was shared for the signal generation and LO, called “self-dye coherent detection” in this paper. The 12.5-Gbaud QPSK signals can be measured without any lack of spectral information even using the oscilloscope with the 8-GHz bandwidth (single-sideband) because the receiver bandwidth ranging from -8 GHz to +8 GHz covers the entire signal spectrum with the 12.5-GHz bandwidth (double-sideband). The measured data were processed with phase noise suppression and resampling in the same manner as our method. The results of our method are shown in Fig. 11(b), which is the same as that in Fig. 10(a) with K = 126. Compared with our method, we found a large fluctuation in the conventional method. This is due to the imperfection of the bandwidth flatness of the oscilloscope used in the experiments. Our method can overcome the imperfection of the bandwidth flatness and the bandwidth limitation because the narrowband slices are measured and synthesized. In addition, it is possible to directly measure the waveform distortion because signal equalization is not performed in our method. Figure 11(c) shows the retrieved constellation of the QPSK signals measured using our method when DC bias was not optimized in optical IQ modulation. A clear symbol skew caused by the DC drift was observed. The results confirm that our scheme is effective for monitoring optical IQ modulation.
Fig. 11. Measured constellation diagrams using (a) the broadband self-dye coherent receiver and (b) our method. (c) Our method when optical IQ modulation is not optimized.
We measured the complex field waveforms of 16QAM optical signals using our method. In this measurement, the LO frequency was tuned with spacing of 312.5 MHz, and the signal spectrum was measured by dividing it into 41 slices. The slice bandwidth (double-sideband) was 625 MHz, which corresponds to a receiver bandwidth (single-sideband) of approximately 350 MHz. Figure 12(a) shows the measured signal spectrum synthesized from 41 slices. For comparison, the spectral waveform measured using the broadband self-dyne coherent receiver is shown in Fig. 12(b). We found that their difference was negligible even on the linear scale of the vertical axis, confirming that the slices were precisely synthesized. The temporal waveforms can be recovered after the IFFT of the synthesized complex spectrum and upsampling them to 2 sample/symbol. Figure 12(c) shows the real and imaginary parts of the recovered temporal waveforms. Red lines and blue lines indicate the measured data and the AWG data used for the optical IQ modulation, respectively. Although their trends are almost identical, we observed a small discrepancy owing to the bandwidth limitation of the AWG and the IQ modulators. Figure 13(a) shows the constellation diagram retrieved from the temporal waveforms. We can see clear symbols in the constellation although the slight IQ skew was found. The measured result using the broadband self-dyne receiver is shown in Fig. 13(b), where the symbols are rather distorted owing to the imperfection of the bandwidth flatness and the bandwidth limitation in the receiver. Hence, these results indicate that our method is applicable to measure optical complex field waveforms of high-order QAM optical signals.
Fig. 12. Measured spectral waveforms of 16QAM optical signals using (a) our method with the slice number K = 41 and (b) the broadband self-dyne coherent receiver. (c) Real and imaginary parts of temporal waveforms of 16QAM optical signals. Red lines: measured data, Blue lines: AWG data for optical IQ modulation.
Fig. 13. Measured constellation diagrams using (a) our method and (b) broadband self-dyne coherent receiver.
In the current experiment, the measurement time is determined by the manual control of the LO laser and the data acquisition in the oscilloscope. By automatic control of the LO laser and real-time data acquisition, the measurement time can be drastically reduced. Although the DSP in our method needs FFT with several 10k samples approximately 100 times, the calculation delay is overestimated to be several 100 msec. Our method can sequentially display the measured waveforms with sub-second order time interval in principle.
5. Summary
We proposed a spectrally slicing-and-synthesizing coherent OSA for measuring complex field waveforms of QAM optical signals without bandwidth limitations. The signal spectrum is divided into narrowband slices, which are measured using low-speed coherent detection. The complex spectrum of the signal is recovered by synthesizing the measured slices after suppressing the laser phase noise and compensating for the frequency fluctuation on each slice. Our numerical and experimental results confirm that the signal spectrum can be divided into more than 100 slices even with independent laser phase noise and timing jitter of the ADC clock. Using our method, we experimentally demonstrated the measurements of complex field waveforms of 16QAM optical signals. These results confirm that our method can overcome the measurement bandwidth limitation.
Funding
Japan Society for the Promotion of Science (KAKENHI Grant Number 18H03231); Ministry of Internal Affairs and Communications (SCOPE 171507001).
Acknowledgments
The authors would like to express their gratitude to Professor K. Inoue of Osaka University and Professor F. Ito of Shimane University for the fruitful discussions.
Disclosures
The authors declare no conflicts of interest.
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