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Abstract
A low-disturbance automatic bias point control (ABC) method for optical in-phase and quadrature modulators (IQM) is proposed using digital chaotic waveform as dither signals. Two distinct chaotic signals, each with unique initial values, are introduced to the direct current (DC) port of IQM in conjunction with a DC voltage. Due to the robust autocorrelation performance and exceptionally low cross-correlation of chaotic signals, the proposed scheme is capable of mitigating the impact of low-frequency interference, signal-signal beat interference, and high-power RF-induced noise on transmitted signals. In addition, due to the broadwidth of chaotic signals, their power is distributed across a broad frequency range, resulting in a significant reduction in power spectral density (PSD). Compared to the conventional single-tone dither-based ABC method, the proposed scheme exhibits a reduction in peak power of the output chaotic signal by over 24.1 dB, thereby minimizing disturbance to the transmitted signal while maintaining superior accuracy and stability for ABC. The performance of ABC methods, based on single-tone and chaotic signal dithering, are experimentally evaluated in both 40Gbaud 16QAM and 20Gbaud 64QAM transmission systems. The results indicate that the utilization of chaotic dither signals leads to a reduction in measured bit error rate (BER) for 40Gbaud 16QAM and 20Gbaud 64QAM signals, with respective decreases from 2.48% to 1.26% and from 5.31% to 3.35% when the received optical power is −27dBm.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In the fifth generation (5 G) of mobile communication systems, a high-capacity network is essential for augmented reality (AR), virtual reality (VR), and unmanned driving. Due to its broadwidth and high spectrum efficiency, the coherent optical transmission scheme utilizing advanced high-order modulation techniques has emerged as a promising solution for satisfying the ever-increasing demand for high-capacity communication. The optical in-phase and quadrature modulator (IQM) is a crucial component in coherent optical transmission systems. [1]. However, ambient temperature changes and mechanical vibrations, and aging of IQM [2,3] could cause the IQM to deviate from its optimal bias point, leading to a decline in performance. Therefore, an ABC module is essential for achieving long-term stabilization of IQM bias states.
Nowadays, several ABC schemes have been reported, mainly including optical power monitoring technologies (OPM) [4–6] and dither signal monitoring technologies (DSM) [7–9]. The fundamental principle of the OPM is to monitor either the power value of the optical carrier or the power ratio between the input and output optical carriers of the IQM. Thanks to the characteristic of being “dither-free”, OPM technologies have little effect on the spurious free dynamic range of the system [10]. However, it is vulnerable to fluctuations in optical power and variations in insertion loss [11]. Due to its limited control accuracy, only a few manufacturers currently employ OPMs in practical applications. As the mainstream ABC scheme in practical applications, the DSM scheme is the “dither-added” scheme, and a dither signal is required (which generally is a single-tone dither signal (STDS)) to drive the DC port of IQM. By monitoring the 1st and the 2nd harmonic frequency signals of dither signals using fast Fourier transform (FFT) [12] or by detecting the correlation integral degree (CI) of the dither signals and the received electrical signal [13], the IQM can be kept at the linear bias point. The DSM methods exhibit high robustness and stability, but to achieve precise bias control, the amplitude of the dither signal (typically ranging from 1% to 10% of the half-wave voltage of IQM) must be sufficiently large. This may result in second-order distortions being induced into the transmitted signal [10,14], thereby further degrading transmission performance. Reducing the amplitude of the dither signal is a straightforward approach to enhance the purity of the transmitted signal. However, this may lead to a decline in control accuracy due to the decreased signal-to-noise ratio (SNR) of the dither signal [15]. Therefore, under the premise of ensuring the accuracy of ABC, it is very important to reduce the disturbance caused by the dither signal to the transmitted signal.
Another problem is that if the low-frequency band of the transmitted signal is in close proximity to or overlaps with the dither signal, it will interfere with the normal running of the ABC module. Even if a frequency gap is reserved for the dither signal, the monitoring photodetector (MPD) in the ABC module will beat out the signal-signal beat interference (SSBI) noise [16,17], and the low-frequency band of this SSBI noise may still affect the normal operation of the ABC. To attain more precise bias control for higher modulation formats and baud rates, the aforementioned issues are inevitable. Besides, for microwave photonic applications such as using IQM to generate optical frequency comb [18,19], etc., high-power RF signals are needed to make the modulation depth generally 2∼4 times the half-wave voltage of IQM. In this case, the RF signal has much higher power than the dither signal. As the power of the RF signal escalates, so does that of the noise floor (NF) due to amplification by the amplifier [20], which means that the SNR of the dither signal relative to the NF diminishes. This will also have a significant impact on the normal running of the ABC module. As far as our knowledge goes, the conventional single-tone dither methods pose difficulties in addressing the aforementioned situations. Therefore, the ABC scheme based on “dither-added” need to be optimized, so that it could not only reduce the impact on the transmitted signals but also avoid it being interfered with by the transmitted signal.
In this paper, an ultra-stable and low-disturbance ABC scheme is proposed and demonstrated, which utilizes chaotic signals (CS) as dither signals to lock the IQM at its optimal bias point. Due to the strong autocorrelation performance and extremely low cross-correlation of CS [21–23], our scheme is capable of mitigating the impact of the transmitted signal’s low-frequency interference and the noise induced by high-power RF signals. Compared to STDS, CS is a broadband signal, which means it has lower PSD and peak power of the chaotic signal at the same power level. Therefore, using CS as the dither signal will cause less nonlinear distortion of the transmitted signal than using the single-tone signal while maintaining higher accuracy and stability of the bias control. The performance using single-tone dither-based ABC and chaotic signal dither-based ABC is experimentally evaluated in both 40Gbaud 16QAM and 20Gbaud 64QAM transmission systems. When the received optical power is −27 dB, the BER of the 40Gbaud 16QAM and 20Gbaud 64QAM signals are reduced from 2.48% to 1.26% and from 5.31% to 3.35% with the help of the proposed ABC scheme, respectively. The stable performance of systems using the proposed chaotic signal dither-based ABC methods is evaluated at various temperatures. The error vector magnitude (EVM) fluctuation remains below 0.258 even with a temperature change from 25.6$\mathrm{\circ{C}}$ to 40.2$\mathrm{\circ{C}}$. To the best of our knowledge, this is the first paper, which pays attention to the interaction of the ABC system and the transmitted signals.
2. Principle of proposed ABC scheme
The proposed ABC scheme is configured with CS as a dither signal, as illustrated in Fig. 1(a). To streamline the analysis process, we will only consider the scenario of a single-polarization IQM situation. However, our approach is also applicable to dual-polarization IQM. To monitor chaotic dither signals (CDS), a low-bandwidth (<2 GHz) MPD is utilized to detect a small fraction (<10%) of the output optical power $I(t)$. Two distinct chaotic signals are utilized to dither the bias signal of two child Mach-Zehnder modulators ($MZM\_I$ and $MZM\_Q$) via a digital-to-analog converter (DAC). CS can be generated with digital chaotic signal generators (DCSG), and CS can be expressed as $f = A \cdot {f_{cs}}(t)$. Here A (about 0.26%${V_\pi }$) is the amplitude of CDS and ${f_{cs}}(t)$ is normalized digital CDS. Meanwhile, a low-speed (500kHz) analog-to-digital converter (ADC) is employed to sample the output of MPD for subsequent signal processing. The correlation integral module (CIM) is subsequently employed to calculate the degree of correlation integral ($CIk,k = I,Q,P$) between the CDS and the output optical signal of IQM. A fuzzy proportional-integral-differential (FPID) module is utilized to calculate and output the low-speed bias signals to DAC based on the $CIk$ calculated by the CIM. The output optical power $I(t)$ of IQM can be expressed as
Fig. 1. (a) The proposed ABC scheme using chaotic signal, (b) the time domain waveforms of ${f_{CS\_I}}(t )$ and ${f_{CS\_Q}}(t )$ under short time scales, (c) the correlation function of ${f_{CS\_I}}(t )$ and ${f_{CS\_Q}}(t )$.
For the DSM methods, there are two mainstream ABC schemes. One is the FFT-based spectrum analysis scheme, and the other is the dither-correlation monitoring scheme. However, monitoring dither harmonic signal power of broadband signals is more complicated for FFT. If the frequency spectrum resolution is insufficient, only leakage frequency components may be detected due to the picket-fence effect [2], which could result in reduced detection sensitivity and failure to detect the desired dither signal. Therefore, our work monitors the bias points by detecting the correlation degree of the CDS and the output optical signal of IQM. The operations of correlation integration could be expressed as
As shown in Fig. 1(c), the autocorrelation function (ACF) exhibits a $\delta$-like shape, indicating that each segment of CDS is dissimilar to other parts in the time domain and possesses strong randomness. In addition, from the cross-correlation function (CCF) of the ${f_{cs\_I}}(t)$ and ${f_{cs\_Q}}(t)$, it can be concluded that CDS does not correlate with other signals. Since the CS exhibits strong autocorrelation performance and extremely low cross-correlation characteristics, its correlation function will only be non-zero when correlated with itself [23]. Therefore, Eq. (2) can be expressed as
The constant values ${C_n}(n = 1,2,3)$ are influenced by the parameters of the CDS and the input optical electrical field of IQM, such as A of the dither signal and NF of the ABC module.
The optimum bias point of the optical IQM is $(\pi ,\pi ,{{ \pm \pi } / 2})$. As shown in Eq. (3), it could be observed clearly that when the phase bias of parent MZM is at its optimum point, the value of $CIP$ will approach zero. The relationship between $CIP$ and bias phase of parent MZM is illustrated in Fig. 2(a), which is easy to achieve ${\varphi _P} = {{ \pm \pi } / 2}$ by scanning the bias voltage of parent MZM. Assuming the parent MZM bias is set to approximately the optimal bias point, Eq. (3) can be reformulated as
The relationship between $CII$ and the bias phase of MZM_I is shown in Fig. 2(b). When the value of $CII$ is around zero and the slope of $CII$ is positive, the bias phase of MZM_I will be set at the optimum bias point $({{\varphi_I} = \pi } )$. MZM_I and MZM_Q are symmetrical in the optical IQM, thus the process of tracking the optimal bias phase for MZM_Q is identical to that of MZM_I.
Fig. 2. (a) the simulated $CIP$ as a function of ${\varphi _P}$, (b) the simulated $CII$ as a function of bias phase of MZM_I.
3. Experimental setup and results
The influence of the dither tone on the transmitted signal is investigated. The single-tone RF signal is added onto the RF port of MZM_I, with a frequency of 20 GHz and power of 25 dBm. The CDS and STDS are added onto the bias port of MZM_I, respectively. To ensure the detection accuracy of the dither signal is not impacted by device resolution, the CDS bandwidth is set to 125 MHz and STDS frequency to 5 MHz. The amplitude of CDS and STDS is the same. The single-tone RF and dither signals modulated onto the optical carrier are detected by a 40 GHz bandwidth photodetector, converting them back to the electrical domain. The output electrical signal of PD is detected by an electrical spectrum analyzer and Fig. 3(a) shows the resulting electrical spectra. It can be observed that, compared with the STDS component, the peak power of the CDS component drops by more than 24.1 dB. The ABC system based on CDS is indicated to introduce less signal degradation during transmission compared to the conventional ABC system based on STDS.
Fig. 3. (a) The output signal's electrical spectrum at the optimum bias point of IQM, where the dither signals are STDS and CDS, respectively, (b) the real-time optical power variations of IQM at the Null points, without control, with STDS, and with CDS.
The performance comparison of bias control between CDS-based and STDS-based is evaluated by measuring the optical power drift. The optical powers of the output signal from the IQM with CDS-ABC, STDS-ABC, and without bias control at the null point were measured over a period of 60 minutes and the results are shown in Fig. 3(b). The amplitude of CDS and STDS is the same. The optical power is measured and monitored using an optical power meter. The green-dashed curve shows the output powers in the absence of bias control, and a discernible optical power variation is observed due to the offset of the bias point. This means that ABC is essential for the stability of the IQM bias point. The blue-cross curves demonstrate the output powers achieved through CDS-based bias control, with optical power fluctuations limited to less than 0.1 dB. The red-star curves indicate the presence of optical power fluctuations in the IQM when subjected to STDS-based bias control, with a fluctuation range of 0.7 dB. Compared to the bias-uncontrolled system, regardless of whether the dither signal is CDS or STDS, the optical power exhibits minimal drift. As the null point of IQM corresponds to carrier suppression, the output optical power of IQM is extremely low in the absence of signals applied to RF ports. Therefore, the fluctuation of optical power at the carrier suppression point serves as another indicator for evaluating the performance of the bias control system. By comparing the power fluctuation range of CDS and STDS, it can be concluded that due to the lower PSD and power spectrum peak of CDS, a smaller power fluctuation range and a larger carrier suppression ratio can be exhibited from IQM controlled by CDS-ABC. Therefore, it can be inferred that CDS-ABC exhibits superior stability performance, which further suggests that the impact of chaos dither on IQM carrier is relatively minimal.
For microwave photonics [18–20] based on IQM, typically larger RF signals are used and the modulation depth is generally 2 to 4 times the half-wave voltage of IQM at this time. In this case, the ABC utilized for stabilizing the IQM bias point will face a significant challenge. Therefore, it is imperative to analyze the stability and accuracy performance of ABC under high-power RF signals. In our test, a 20 GHz single-tone signal with an output power of 7dBm is generated by the signal source and then amplified by an electric amplifier with a gain factor of approximately 30 dB. The output signal of the electric amplifier is about 15 V, which is about 4.28 times the ${V_\pi }$ of the IQM. To compare the performance of both STDS-based ABC and CDS-based ABC schemes, we have obtained curves of CI value versus bias voltages under high-power RF signals. As shown in Fig. 4(a) and 4(b), an increase in RF power results in a corresponding increase in noise power. The CI curve of the STDS-based ABC system is evidently affected by noise, whereas the correlation curve of the CDS-based ABC system remains consistently smooth. Additionally, there exists an overall offset in the correlation curve based on STDS-based ABC due to the limited ability of bias control schemes based on single-tone signals to resist noise. Although the trend of the STDS curve is consistent with that of CDS, the accuracy and stability of STDS have been compromised. The ABC scheme utilizing CDS exhibits superior noise resistance compared to STDS, owing to the robust autocorrelation performance and exceptionally low cross-correlation of CDS.
Fig. 4. (a) $CII$ as a function of the bias voltage of MZM_I under high-power (about four times the half-wave voltage of IQM) RF signals, (b) $CIP$ as a function of the bias voltage of parent MZM under high-power RF signals.
The setup for a coherent optical back-to-back (B2B) transmission system is shown in Fig. 5(a), which aims to further investigate and compare the performance of the proposed CDS-based ABC scheme with that of the conventional ABC method. For the purpose of simplification in discourse, only the scenario with a single polarization is considered. A laser is utilized as the optical source, while the laser's linewidth is 100kHz, respectively. Additionally, an external cavity laser operating at a linewidth of 100kHz serves as the local oscillator (LO) optical source. An arbitrary waveform generator (AWG, Keysight M8195A) is utilized to generate the transmitted electrical signals that drives an optical dual-polarization IQM (Fujitsu FTM7977, ${V_\pi }$=3.5 V). The optical signals of IQM and LO are captured by an integrated coherent receiver (ICR) and demodulated to electrical signals. Polarization controllers (PC) are utilized to align the polarization states of both ICR and LO and the polarization states of both laser source and IQM. The electrical signals detected by ICR are acquired by a digital sampling oscilloscope (DSO, Tektronix DPO 73304D). The modulation depth of dither signals is 2%${V_\pi }$. The bandwidth of the CDS is limited to 125kHz primarily due to the constraints imposed by the utilized DAC.
The impact of RF signals with varying modulation depths (MD) on the real-time correlation coefficient, as calculated by ABC modules utilizing distinct dither signals, is illustrated in Fig. 6. The MD of the transmitted RF signal is defined as $MD = A/{V_\pi }$, where A represents the amplitude of the transmitted signal. When QPSK signals with a bandwidth of 10 GHz are added, the real-time CII has a significant jumping change. The reason is that the DC bias change is attributed to the QPSK signal itself and additional noise introduced by the low-frequency interference of the transmitted signal and SSBI. The larger the modulation depth of the transmitted signal makes the jump change of the correlation coefficient larger. In addition, the larger the MD of the transmitted signal makes the larger the fluctuation range of CII, even after the jump change of CII is offset by the ABC adjustment. The fluctuation of the correlation coefficient reflects the impact of the transmitted signal on the dither harmonic, which serves as a basis for ABC to maintain stable control over IQM's bias point. As a result, significant fluctuations in correlation coefficients can cause instability in the IQM bias voltage, leading to degradation of transmission performance. By comparing Figs. 6(a) and 6(b), it can be observed that the CDS-based ABC exhibits a real-time correlation curve with smaller jumps and fluctuations due to its superior autocorrelation characteristics and noise resistance. This means that CDS could effectively improve the transmission performance compared to STDS.
Fig. 6. The CII versus time curves with different MD: (a) STDS-based ABC scheme, and (b) CDS-based ABC scheme.
The BER performance of 40/20Gbaud 16/64QAM signals is presented in Fig. 7 as a function of received optical power (ROP), utilizing various dither signals. The MD of 40Gbaud 16QAM and 20Gbaud 64QAM signals is 80%${V_\pi }$. The BER values in these two cases are observed to fall below the 7% overhead hard-decision forward error correction (HD-FEC) threshold of 3.8e−3. Under the same ROP, the CSD-based transmission link has better performance than the STDS-based one. The curves shown in Fig. 7 demonstrate that the CDS-based ABC technology outperforms conventional STDS-based ABC technologies, and the larger the modulation format is, the more effective the CDS bias point control is for transmission performance improvement.
To demonstrate the stable and long-term performance of the proposed CDS-based ABC method, Fig. 8 shows both the EVM performance of the 40Gbaud 16QAM signal and the corresponding environmental temperature of IQM. The ROP is maintained at −14dBm during the test, and a heat gun indirectly adjusts the environmental temperature of IQM. During the experiment, fluctuations in EVM performance were observed due to both temperature variations and induced mechanical vibrations caused by the hot wind. Therefore, it can be observed that the utilization of a heat gun to apply heat to the IQM for a duration ranging from 5 to 14 minutes leads to inferior measured EVM performance with ABC-Off in comparison with ABC-On. After the heat gun is powered off and allowed to cool completely (between 15 to 30 minutes), the measured EVM performance of ABC-Off gradually improves until it reaches parity with that of ABC-On. Therefore, it can be concluded that the proposed CDS-based ABC scheme is capable of maintaining transmission system stability in the face of significant environmental changes over an extended period, thus ensuring reliable operation.
4. Conclusion
We have experimentally demonstrated a novel ABC technique for optical in-phase and quadrature-phase modulators using CDS. Compared with the traditional STDS-based ABC schemes, utilizing a chaotic signal as a dither signal exhibits a stronger ability to resist interference by transmitted signals and noise by transmission link. Due to the broadwidth of a chaotic signal, its power is spread across a broad frequency range, resulting in a significant reduction in PSD. Compared to the conventional single-tone dither-based ABC technique, the peak power of the chaotic signal in the output electrical signal is reduced by more than 24.1 dB. Under the same power, our scheme will cause less disturbance to the transmitted signal than the STDS-based ABC system, while maintaining higher accuracy and stability of the bias control. The performance using single-tone dither-based ABC and chaotic signal dither-based ABC is experimentally evaluated in both 40/20Gbaud 16/64QAM transmission systems. The results indicate that the utilization of chaotic dither signals leads to a reduction in measured BER. Specifically, for 40Gbaud 16QAM, the measured BER decreased from 2.48% to 1.26%, and for 20Gbaud 64QAM, it decreased from 5.31% to 3.35%, when the received optical power is −27dBm. The results demonstrate that CDS-based ABC represents an efficacious approach to enhancing the performance of coherent communication links, and our scheme is eminently suited for high-speed coherent optical communication systems.
Funding
National Key Research and Development Program of China (2018YFB1800903); National Natural Science Foundation of China (62171190); Science and Technology Planning Project of Shenzhen Municipality (JCYJ20220818103214029).
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.
References
1. Y. Wang, K. Kasai, M. Yoshida, and M. Nakazawa, “320 Gbit/s, 20 Gsymbol/s 256 QAM coherent transmission over 160 km by using injection-locked local oscillator,” Opt. Express 24(19), 22088–22096 (2016). [CrossRef]
2. X. Li, L. Deng, X. Chen, M. Cheng, S. Fu, M. Tang, and D. Liu, “Modulation-format-free and automatic bias control for optical IQ modulators based on dither-correlation detection,” Opt. Express 25(8), 9333–9345 (2017). [CrossRef]
3. H. Li, C. Huang, Y. Wang, R. Deng, M. Cheng, Q. Yang, D. Liu, M. Tang, and L. Deng, “Simple and ultrafast automatic bias control for optical IQ modulators enabled by dither vector mapping monitoring,” in Optical Fiber Communication Conference (OSA, 2022), paper Th1C.7. [CrossRef]
4. Y. Li, Y. Zhang, Y. Huang, Y. Hao, and J. Tao, “A modulation-format free ditherless bias control technique for MZ modulator with monitoring the slope value of average output optical power,” in Proc. Asia Commun. Photon. Conf., pp. 18–20(2013).
5. H. G. Choi, Y. Takushima, H. Y. Choi, J. H. Chang, and Y. C. Chung, “Modulation-format-free bias control technique for MZ modulator based on differential phasor monitor,” in Proc. Opt. Fiber Commun. Conf./Nat. Fiber Optic Eng. Conf., pp. 1–3 (2011).
6. P. S. Cho, J. B. Khurgin, and I. Shpantzer, “Closed-loop bias control of optical quadrature modulator,” IEEE Photonics Technol. Lett. 18(21), 2209–2211 (2006). [CrossRef]
7. T. Yoshida, T. Sugihara, K. Uto, H. Bessho, K. Sawada, K. Ishida, K. Shimizu, and T. Mizuochi, “A study on automatic bias control for arbitrary optical signal generation by dual-parallel Mach–Zehnder modulator,” in Proc. 36th Eur. Conf. Exhib. Opt. Commun., Sep. 2010, pp. 1–3.
8. H. Kawakami, E. Yoshida, and Y. Miyamoto, “Auto bias control technique based on asymmetric bias dithering for optical QPSK modulation,” J. Lightwave Technol. 30(7), 962–968 (2012). [CrossRef]
9. E. Kawakami, T. Kobayashi, E. Yoshida, and Y. Miyamoto, “Auto bias control technique for optical 16-QAM transmitter with asymmetric bias dithering,” in Proc. Eur. Conf. Exhib. Opt. Commun., pp. 18–23(2011).
10. E. I. Ackerman and C. H. Cox, “Effect of pilot tone-based modulator bias control on external modulation link performance,” in Proc. Int. Top. Meeting Microw. Photon. (MWP), Sep. 2000, pp. 121–124.
11. L. Wang and T. Kowalcyzk, “A versatile bias control technique for any point locking in lithium niobate Mach–Zehnder modulators,” J. Lightwave Technol. 28(11), 1703–1706 (2010). [CrossRef]
12. T. Gui, C. Li, Q. Yang, X. Xiao, L. Meng, C. Li, X. Yi, C. Jin, and Z. Li, “Auto bias control technique for optical OFDM transmitter with bias dithering,” Opt. Express 21(5), 5833–5841 (2013). [CrossRef]
13. X. Li, L. Deng, X. Chen, H. Song, Y. Liu, M. Cheng, S. Fu, M. Tang, M. Zhang, and D. Liu, “Arbitrary Bias Point Control Technique for Optical IQ Modulator Based on Dither-Correlation Detection,” J. Lightwave Technol. 36(18), 3824–3836 (2018). [CrossRef]
14. Y. Fu, X. Zhang, B. Hraimel, T. Liu, and D. Shen, “Mach-Zehnder: A review of bias control techniques for Mach-Zehnder modulators in photonic analog links,” IEEE Microwave Magazine , vol. 14, no. 7, pp. 102–107(2013). [CrossRef]
15. Z. Pan, S. Liu, N. Zhu, P. Li, M. Liu, L. Yang, C. Du, Y. Zhang, and S. Pan, “Arbitrary Bias Point Control for Mach-Zehnder Modulator Using a Linear-Frequency Modulated Signal,” IEEE Photonics Technol. Lett. 33(11), 577–580 (2021). [CrossRef]
16. D. Li, Q. Yu, L. Deng, L. Huo, S. Fu, M. Tang, M. Cheng, M. Zhang, and D. Liu, “Bidirectional long-reach PON using Kramers-Kronig-based receiver for Rayleigh Backscattering noise and SSBI interference elimination,” Opt. Express 26(15), 19020–19036 (2018). [CrossRef]
17. T. Bo and H. Kim, “Kramers-Kronig receiver operable without digital upsampling,” Opt. Express 26(11), 13810–13818 (2018). [CrossRef]
18. L. Sun, J. Li, J. Lin, L. Xi, X. Tang, and X. Zhang, “Performance analysis on quality of optical frequency comb generated by the recirculating frequency shifter based on linear IQ modulator,” Opt. Eng. 54(11), 116106 (2015). [CrossRef]
19. J. Li, H. Ma, Z. Li, and X. Zhang, “Optical frequency comb generation based on dual-polarization IQ modulator shared by two polarization-orthogonal recirculating frequency shifting loops,” IEEE Photonics Journal 9(6), 1–7(2017). [CrossRef]
20. I. Badillo and J. Portilla, “Experimental Study of AM and PM Noise in Cascaded Amplifiers,” Electronics 11(3), 470 (2022). [CrossRef]
21. X. Jiang, M. Cheng, C. Luo, F. Luo, L. Deng, S. Fu, C. Ke, M. Zhang, M. Tang, P. Shum, and D. Liu, “Reproducible optical noise-like signal generation subjected by digital sequences,” Opt. Express 25(23), 29189–29198 (2017). [CrossRef]
22. S. Li, M. Cheng, L. Deng, S. Fu, M. Zhang, M. Tang, P. Shum, and D. Liu, “Secure Strategy for OFDM-PON Using Digital Chaos Algorithm with Fixed-Point Implementation,” J. Lightwave Technol. 36(20), 4826–4833 (2018). [CrossRef]
23. C. Macovei, A. Vaduva, A. Vlad, and B. Badea, “The autocorrelation function of the logistic map chaotic signal in relation with the statistical independence issue,” 13th International Conference on Communications (COMM), pp. 25–30(2020).
