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Abstract
Linear optical sampling (LOS) is one of the most promising techniques for optical modulation analyzers. The LOS system generally adopts a mode-locked fiber laser (MFL) to generate an ultra-stable optical pulse to realize under-sampling for signal under test (SUT). However, it is challenging for MFL to produce a high-repetition-frequency pulse, making more measurement errors of conventional LOS technology, especially for high-speed signals. This paper proposes a dual-pulse mixing (DPM) based LOS system to increase the repetition frequency using fiber delay lines with the multiplied optical pulse. We propose the pulse location and peak extraction algorithms to compensate the time bias and amplitude bias in the DPM-based LOS system, which significantly improves the measurement speed and range. The experiment results show that the DPM-based LOS system can increase the number of sampling points twice compared with the conventional LOS within the same sampling time window. Furthermore, the proposed DPM-based LOS system can achieve less error vector magnitude with a reduction of 9.1% compared with the conventional LOS. Hence, the proposed DPM-based LOS system has great potential for high-speed signal processing.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the increasing data rate in long-haul optical transmission and data center interconnection, the efficient measurement of optical signals can facilitate the maintenance, management, and development of optical transport network [1,2]. However, the electrical oscilloscope with high-speed electrical devices, such as photo-detectors, analog-to-digital converters (ADCs) and sample-and-hold circuits, experiences bottlenecks in terms of measurement range, accuracy, and cost with the increasing of data rates. Given the above problems, optical sampling techniques (OSTs) have been proposed to perform time-domain measurements in a low-cost way without the high-speed devices [3]. In contrast to the high-speed sample-and-hold circuits in oscilloscopes, OST uses low-speed optical gates to realize an under-sampling for an optical modulation analyzer. Hence, OST is promising for high-speed optical signal measurement in the future. Generally, OST can be categorized into nonlinear optical sampling (NOS) [4] and linear optical sampling (LOS) [5]. NOS leverages the nonlinear effects of a short optical pulse to provide the gating function. However, NOS suffers from poor sensitivity because of the high pump power and inherent low energy efficiency of the nonlinear effect. Although the amplitude and phase can be characterized synchronously by nonlinear effect, such as the four-wave-mixing effect, the applied scope is limited due to the high-power pump [6]. The LOS is an alternative technique that realizes the linear optical process by coherent mixing of the short optical pulse of mode-locked fiber laser (MFL) and optical signal. After the linear mixing, LOS conducts a low-speed balanced photodetector (BPD) for the photoelectric conversion and sampling. Hence, LOS obtains high-speed signal characteristics via an under-sampling scheme, which adopts low-speed devices to reduce the hardware expenditure.
The measurement range of LOS is limited in both the time and frequency domains due to the characteristics of mode-locked fiber laser (MFL). Hence, many researchers have been attracted to expand the measurement range with extra hardware systems and digital signal processing (DSP) [5,7–9]. In terms of the hardware system of LOS, due to the coherent mixing process, the center wavelength of a MFL must be precisely tuned to match the signal under test (SUT), which limits the measurement range of the LOS system in the frequency domain. Focus on the problem, Wang in [10] has proposed an approach to simplify the WDM monitoring system, where an optical interferometer was used to evaluate 40-channel wavelength division multiplexing differential phase-shift keying (WDM-DPSK) signals over an 8-nm wavelength range. To enhance the measurement range in the time domain, Sunnerud proposed the time-resolved error vector magnitude (EVM) scheme to improve the characterizing ability of the LOS system and experimentally analyzed 66-Gbps PDM-QAM data by LOS [7]. Besides, lots of techniques have also been proposed to optimize hardware systems for LOS [11–13]. In terms of the DSP algorithm, due to hardware defects of the LOS system, the DSP algorithm is required to compensate signal impairments. The use of BPDs introduces time bias and amplitude bias for LOS system, which cannot be eliminated simultaneously. Hence, Liao revealed the relationship between the timing bias and the sampling accuracy [8]. He proposed a DSP scheme to mitigate the sampling error for the non-ideal response of multi-BPDs. To characterize the eye diagram accurately, Yu presented a bias balance detection (BBD) scheme and demonstrated a 32 GBaud PDM-QPSK experiment for a fiber-optics-frequency-comb (FOFC) based LOS system [14]. In addition, researchers have also studied advanced software synchronization algorithms to improve timing accuracy for DSP algorithm [15–17]. The above studies have greatly improved the measurement range and application scope of LOS.
However, the conventional LOS system contains many separated devices, such as an MFL pump source, wavelength hybrid, and oscillating ring including several meters of single-mode fiber (SMF). Hence, the repetition frequency of commercial passively MFL is limited to hundreds of megahertz [18]. Due to the non-ideal characteristics (frequency offset and linewidth) of the laser source of the SUT, the timing error of the signal accumulates between adjacent symbols. The repetition frequency decides the amount of timing error between the two samples. Hence, the MFL pump source with a fixed repetition frequency has a theoretical upper limit of the measurement range. The high-speed SUT is difficult to be characterized through the LOS system with a low-repetition-frequency MFL [19]. In addition, the low repetition frequency increases the sampling period, which increases the constructing time of the eye diagram. Therefore, it is necessary to increase the repetition frequency in a low-cost way to extend the measurement range of the LOS system.
In this work, we propose an optical sampling technique based on dual-pulse mixing (DPM) to improve the repetition frequency. First, the pulsed laser is divided into multiple parts through a power splitter and then combined after passing through the fiber delay lines (FDLs). A series of DSP algorithms with the pulse location and peak extraction is introduced to compensate the time and amplitude error. The repetition frequency of the proposed DPM-based LOS can be increased significantly, which extends the measurement range and reduces EVM bias by 9.1%. Hence, the eye diagram can be constructed fast using high repetition frequency. The rest of the paper is organized as follows. In Section II, we introduce a DPM-based LOS scheme and theoretically investigate the digital signal processing after sampling the SUT. A collaborative peak extraction (CPE) algorithm is proposed to obtain the real-time eye diagram with the DPM-based LOS system. In Section III, numerical simulations were carried out to compare the performance of conventional LOS and the proposed DPM-based LOS. In Section IV, we demonstrate an experimental for the DPM-based LOS system. Finally, we draw our conclusions.
2. Operation principle
2.1 DPM-based LOS system
The DPM-based LOS system consists of a DPM module, a receiving module, and a SUT module, as shown in Fig. 1. In the DPM module, a FOFC is used as the local oscillator (LO) source to generate the optical pulse, separated into multi-paths by a 1:n optical splitter. Each path is connected to an FDL to separate the different pulses in the time domain without overlapping. Note that the length difference of each FDL should be larger than the pulse width of the pulses. Hence, the aggregated pulses are separated in the time domain without overlapping. The SUT is a modulated optical signal whose center frequency is within the spectrum range of the MFL. The receiving module consists of a $90^{\circ }$ wavelength hybrid, four BPDs, a four-channel ADC, and a DSP module. The wavelength hybrid coheres to the SUT and the DPM-based pulses and then outputs eight signals to four BPDs. The four BPDs extract four electrical signals, $Ix$. $Iy$, $Qx$ and $Qy$ for ADCs. In terms of the DSP module, the DSP algorithms include peak location, peak extraction, normalization-orthogonalization, polarization division demultiplexing, frequency offset estimation, and carrier phase recovery. Then, software synchronization is carried out to achieve high fidelity of period estimation. Both EVM and eye diagrams can be obtained based on the corresponding DSP algorithm.
Fig. 1. Schematic configuration of the DPM-based LOS system (FOFC: fiber optics frequency comb; T-BPF: tunable band-pass filter; EDFA: erbium doped fiber amplifier).
2.2 Coherent detection process
The section first elaborates on the hybrid process between pulse LO and SUT. Theoretical analysis reveals that the DPM-based LOS can increase the sampling rate. As described in [14], the electric field of the SUT can be expressed as
where $E_S$ is the electric-field intensity of signal, $w_s$ is the carrier frequency, and $\varphi _S$ is the phase. For a high-order modulation format, such as $n^{2}$QAM, both $E_S$ and $\varphi _S$ are encoded. Hence, it is essential for LOS system to extract both amplitude and phase information.The FOFC of the DPM module can be described as
where $E_L$ represents the electric-field intensity of each tone at a frequency of $w_0+n\cdot w_d$, $w_0$ is the carrier envelope-offset frequency, $n$ is the index of the FOFC tone, $w_d$ represents the frequency spacing between two adjacent tones, $\varphi _L$ is a constant phase item between adjacent frequency tones, and $N$ is the number of comb tones. In addition, $w_d/2 \pi$ also represents the repetition frequency of the FOFC source. Because the FOFC source is the superposition of multiple tones, the tone intensities ($E_L$) of the broadband FOFC are same to each other. Here, we illustrate the principle by analyzing a scenario including two FDLs. At the same time, the scenarios with more than two FDLs can be analyzed via the same principle. Considering a scenario that pulse is divided into two parts, the output of DPM module can be shown asHence, we can obtain the optical intensity of one BPD channel by
The $I_1(t)$ is consisted of pulse-related terms and SUT-related terms. The pulse-related terms ($I_N(t)+I_N(t+\Delta t$)) can be eliminated using BPDs. Another input of BPD is denoted by
Considering the different BPD responses of BPD between the two channels (e,g, $R_1$ and $R_2$ in the example), the output of the BPD is
The first term of this equation refers to the residual component of optical pulses and the second term represents the SUT-related term. In general, it is a trade-off between the time delay and amplitude response for the forward and the reverse signals using BPDs, such as Ix+ and Ix- in Fig. 1. The time delay is set to very short in DPM-based LOS, where the difference in amplitude response between BPDs is significant [14]. As a result, the DSP algorithm is updated to compensate for the amplitude differential. Assuming that the sampling gate samples the electrical signal with a fixed period ($t'$), the SUT-related term is converted into a discrete numerical sequence, which is given by
Hence, combining two SUT-related terms, $D(m)$ can be given by
Equation (18) shows that we can increase the repetition frequency through a DPM-based system, and the two sequences of optical pulses can be analyzed at the receiver. Theoretically, we can achieve more multiple pulses by FDLs based on the same principle. However, since the lengths of FDLs are hard to configure accurately, it is difficult to predict the location relationship of multi pluses. Hence, it is necessary to obtain $\Delta t$ and then realize the DSP to recover the signal and eye diagram.
2.3 Digital signal processing
The schematic of DSP is shown in Fig. 2, which is consisted of pulse location, peak extraction, normalization-orthogonalization, polarization demultiplexing, frequency estimation, phase recovery, period estimation and SUT analysis. First, pulse location measures the time interval between two adjacent pulses before the peak extraction, representing two pulse sequences’ time bias.
Then DSP algorithm searches the pulse peaks for each pulse sequence. Compared with the single pulse sequence, DPM introduces time bias $\Delta t$ and amplitude bias $\Delta A$ between two pulse sequences due to the different FDLs and inserting loss of fiber components. Hence, we propose a CPE algorithm, including two steps. Firstly, given that the period of one pulse sequence is $T$. The CPE finds the maximum value of two pulses in the first period $T$, as shown in Fig. 3(a). Then, CPE records the corresponding position, $X$, in the time domain. To eliminate the impact of this pulse on another peak searching, CPE deletes the points between the interval $[X-W/2, X+W/2]$, as shown in Fig. 3(b). CPE then finds another peak and position in the remaining points, denoted by $Y$. After locating the $X$ and $Y$, CPE identifies the order of two sequences.
Fig. 3. Process of pulse location and peak extraction (a) collaborative peak extraction (b) peak location.
After the peak extraction of the pulse, the peak sequences should be normalized and orthogonalized. However, the time and amplitude biases between two pulse sequences introduce timing and amplitude errors in the eye diagram. The two sequences are denoted by $D_{L1}(N)$ and $D_{L2}(N)$. Hence, two sequences should be normalized separately, which can be expressed as Eqs. (19) (20), as shown in Fig. 3(a). The normalization is carried out for $D_{L1}(N)$ and $D_{L2}(N)$ as the following equations,
where $D^{\prime}_{L1}(N)$ and $D^{\prime}_{L2}(N)$ represent the normalized peak sequences. Then the normalized location sequences are orthogonalied using the GSOP algorithm in [21,22].After normalization and orthogonalization, a constant modulus algorithm (CMA) is used to demultiplex the polarization mode of the digital signals [23]. The process is shown as the following equations,
In (23), the elements in $\boldsymbol {p}$ contain the condition requirement of the CMA algorithm [21].
After the polarization demultiplexing, we take the M th-power phase estimation and the Viterbi-Viterbi algorithm for the carrier and phase recovery [24–26]. A chirp-z-transform-based (CZT) software synchronization algorithm is used to precisely estimate the signal period for peak value sequences to eliminate the timing error caused by LOS system [16]. Then, the $D^{\prime\prime}_{L1}(N_X)$, $D^{\prime\prime}_{L1}(N_Y)$, $D^{\prime\prime}_{L2}(N_X)$ and $D^{\prime\prime}_{L2}(N_Y)$ are ready for portraying an eye diagram and calculating the EVMs.
3. Experiment and results
3.1 Experiment setup
We conducted a preliminary experiment to validate the DPM-based LOS system described in Section II. A customized MFL pump source that works at 99.945 MHz (gain spectrum width 20 nm) served as a seed source. We then used a T-BPF with a 6-nm passband and 1560 nm center frequency to obtain a 6 nm pulse. Figure 4(b) illustrates the measured waveform and pulse frequency of the MFL pump source. Then, a 1.5 m SMF acts as FDL in the DPM-based module. According to the DPM process, the repetition frequency of the sampling pulses is 199.89 MHz, as shown in Fig. 4(c). For the SUT, a 100 kHz linewidth fiber laser (EXFO IQS-636) outputs a continuous wavelength laser with a center frequency of 1560 nm. The optical carrier was modulated via an IQ Mach-Zehnder modulator (IQ-MZM) driven by a trace of PRBS signal from an arbitrary waveform generator (Keysight M8192). A $2\times 8$ wavelength hybrid (Kylia, COH24-X) realizes the mixing of the SUT and the optical pulse. The signal trace after the wavelength hybrid is shown in Fig. 4(d). After receiving four BPDs (Thorlabs, BPD470C), the temporal waveform was collected by a 12-bit oscilloscope analyzer (OSA) (Tektronics, DPO72004C) at a sampling rate of 12.5 GSamples/s. After obtaining the samples, we take the DSP in Section II to characterize the SUT.
Fig. 4. (a) Experimental setup for DPM-based LOS system. (b) Optical signal trace of the MFL pump source after T-BPF. (c) Optical signal trace after FDLs. (d) Signal trace after mixing with SUT.
3.2 Results and discussion
In this section, we present and analyze the data obtained from experiments. After the OSA collects the samples with 12.5 GHz, pulse peaks of two sequences are located through the proposed CPE algorithm. Figure 5(a) shows the extracted peaks for two pulse sequences of the 16G-PMD QPSK SUT. Although there is an amplitude bias between two pulse sequences, the proposed CPE algorithm could simultaneously search the two sequences of pulse peaks accurately. Then the two peak sequences can be separated according to the location of the peaks for further processing.
Fig. 5. Experimental results of DSP for DPM-based LOS and conventional LOS. For DPM-LOS system, (a) the results of peak extraction, (b) coarse eye-diagram after FFT-based period estimation and (c) precise eye-diagram after CZT estimation. As a comparison, (d) peak extraction, (e) coarse eye-diagram and (f) precise eye-diagram of conventional LOS system.
After the pulse demultiplexing, we estimate the signal period and portray the eye diagram by FFT-based frequency estimation, as shown in Figs. 5(b),(e). For the DPM-based scheme, after the DSP of two peak sequences, the LOS system calculates the phase relationship of the two sets according to the positions of the two peak sequences. Then, the LOS system aggregates the two pulse sequences into an eye diagram. Timing error is introduced in the FFT-based algorithm of the LOS system due to the interval period of under-sampling frequency, resulting in a blurring of the eye diagram. Hence, a CZT software synchronization algorithm is used to estimate precise frequency before the frequency estimation, as shown in Figs. 5(c),(f) [16]. We can obtain a clear eye diagram with the aid of software synchronization. More importantly, the sample number of the DPM-based LOS is increased twice as much as that of the conventional LOS, reducing the sampling period significantly.
After the DSP, we recover the eye diagram and collect the samples in the eye’s middle to build a constellation. The constellation and eye diagrams of the 16 Gbps PDM-QPSK signal are characterized by the conventional LOS and the DPM-based LOS, respectively, as shown in Figs. 6(a),(b). The EVM of the DPM-based LOS system and conventional LOS system is 0.1362 and 0.1436, respectively. In addition, it is clearly shown that the DPM-based LOS system collects more peaks than conventional LOS, indicating a fast manner to extract the EVM precisely. Besides, we statistic the peak numbers within same samples of the OSA. For data rates from 4 to 64 Gbps, we obtain 500K samples through the OSA with a sampling rate of 12.5 GHz. Then the effective points are obtained by the peak extraction algorithm. Due to the stability of the pulse period, the number of peaks in 500K samples is fixed. As shown in Table 1, DPM-based LOS collects twice the peak numbers compared with conventional LOS. Then we statistics the average point number per signal period in each eye, which illustrates that DPM-based LOS can increase the sampling speed under a fixed time window.
Table 1. The collected peak numbers for 40 $\mu$s time window.
To compare the EVM estimations among different data rates, we carry out an experimental demonstration with data rates from 4 Gbps to 64 Gbps. Figure 7(a) shows the EVM of X-polarization SUT concerning different LOS schemes. Besides conventional LOS and DPM-based LOS, we measure the OSNR with a commercial spectrometer (Yokogawa, AQ6370D) and calculate the EVM with the following equation [27],
where $R_s$ is the symbol rate of SUT and $B_{ref}$ is the reference bandwidth of 12.5 GHz. The EVM of a commercial spectrometer can be used as a reference value, Ref-value. It is observed that a DPM-based LOS system can obtain a smaller EVM value compared with the conventional LOS system. As we know, the interference caused by signal linewidth and frequency offset will accumulate in the time domain of the SUT, which means that a shorter sampling window in the time domain introduces less noise. Hence, the noise of the proposed DPM-based LOS can be reduced significantly because the sampling window of DPM-based LOS is half compared with the conventional LOS. In the experiment, the sampling window is $4 \ \mu s$ with a sampling rate of 12.5 GHz. In a real-time acquisition module with a typical sampling rate of 1.25 GHz, the sampling period is beyond $40 \ \mu s$. Hence, the linewidth of the SUT impacts the coherence between adjacent symbols for a considerable sampling period. The DPM-based LOS scheme improves the repetition frequency of the pulse source. In Fig. 7, the $Ref_{value}$ is only a reference EVM obtained from the OSNR of the OSA. By comparing the values in Figs. 7(a),(b), we can observe that DPM-based LOS can achieve better performance than the conventional LOS for both the X/Y- polarization. At the data rate of 8 Gbps, the DPM-based LOS can achieve an EVM reduction of 9.1% compared with the conventional LOS, while the EVM of DPM-based LOS and conventional LOS are 0.1464 and 0.1586, respectively.Fig. 7. EVM performance versus data rate for different LOS schemes (a) X polarization (b) Y polarization.
In order to investigate the improvement of the DPM scheme under different receiving powers, we demonstrate the performance of both schemes under different receiving SUT power from -6 dBm to 6 dBm. Figures 8(a) and (b) show the relationship between SUT power and the EVM of LOS techniques (the power of the MFL pump source is 2 dBm). To get a precise EVM evaluation, we adapt a BBD scheme in our experiments [14]. Regarding X-polarization, the minimum EVM (0.1368) can be achieved at the SUT power of 2.58 dBm. Besides, the EVM performance is improved significantly compared with conventional LOS. The EVM benefit can be achieved at 0.0199, 0.016, 0.0008, 0.0114, and 0.0031 with the transmission speed of 4,8,16,32, and 64 Gbps, indicating the proposed DPM can increase the accuracy of EVM evaluation. As same as the X-polarization, the Y-polarization also expresses an excellent performance in terms of EVM evaluation, as shown in Fig. 8(b). In addition, the minimum EVM (0.1385) of 4 Gbps SUT is achieved at the power of 2.58 dBm. The BBD scheme has a pulse amplitude limitation for SUT power. Hence, excessive power of SUT will cause peak extraction error. Hence, the EVM becomes worse when the SUT power is 5.26 dBm. From Fig. 8(b), the EVM benefit for 4, 8, 16, 32, and 64 Gbps at 2.58 dBm is 0.0212, 0.007, 0.0124, 0.007, and 0.0017, respectively. The tested EVM of the DPM scheme is decreased by 6% in average compared with the conventional LOS scheme at the power of 2.58 dBm.
Fig. 8. EVM performance versus SUT power for different LOS schemes (a) X polarization (b) Y polarization.
To compare the construction time of the eye diagram for different LOS techniques, we recorded the time consumption during sampling and eye-diagram construction for the same sampling numbers. We design a sampling system based on MATLAB, which can record the generation time of sampling commands and the time to complete the construction of the eye diagram. Therefore, by changing the number of sampling points, we can record the construction time of the eye diagram for different sampling scenarios. The box diagram of the time consumption is shown in Fig. 9, which records the time consumption for sampling numbers of 200, 400, 600 and 800 points. We collect the construction time for 20 times for both LOS techniques. The asterisk of each box shows the maximum/minimum of the data set. Each box’s top and bottom line means the quarter line of 25% and 75%, where the box’s middle line means the average value of the data set. For all scenarios, the construction time of the eye diagram for the DPM-based LOS is lower than that of the conventional LOS due to the short sampling window. The maximum reduction of the construction time of the DPM-based LOS is at the sampling number of 800, where the average time consuming is reduced by 5.29% compared with the conventional LOS. Hence, the DPM-based LOS can realize real-time sampling and analysis for the high-speed signal.
4. Conclusion
We propose a dual-pulse-mixing-based linear optical sampling (DPM-based LOS) technique to improve the repetition frequency and a series of digital signal processing (DSP) algorithms to characterize the high-speed optical signal. The optical pulse of the mode-locked fiber laser is divided into multi-part in the time domain with the aid of the fiber delay line to increase the sample rate of the LOS. Then, the DSP algorithm of pulse location and peak extraction is studied to compensate for the time and amplitude bias. The experiment results show that a repetition frequency of 199.89 MHz can be generated by an optical pulse source with 99.945 MHz, which can afford a 64 Gbps data rate measurement. Besides, the error vector magnitude evaluation of the proposed DPM-based LOS is more precise than the conventional LOS. The construction time is also reduced by 5.29% compared with the traditional LOS system.
Funding
National Key Research and Development Program of China (2021YFB2900604); National Natural Science Foundation of China (61727817, 61835002, 61935005, 62021005, 62022016); China Postdoctoral Science Foundation (2021M690411); Beijing Municipal Natural Science Foundation (4222075); Open Fund of IPOC (BUPT) (IPOC2020A006).
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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