A frequency-domain approach for phase noise analysis of integer-N multiplier-type phase-locked loops (PLLs), based on the conversion matrix approach, is introduced that can take all non-linearities ...in the loop into account. It can also characterise all kinds of power spectral densities and correlation between variables and all aspects of phase noise-to-phase noise or amplitude noise-to-phase noise (AN–PN) conversions. The noise transfer between various sidebands is also taken into account. This is especially important for characterising the folding of the voltage-controlled oscillator's phase noise which results in the phase noise augmentation at small frequency offsets. Unlike the linear phase-domain models, the stochastic phase noise local maxima at large offset frequencies are also accurately characterised. Giving the phase/amplitude noise spectra of various PLL blocks, this approach computes the resulting output phase noise spectrum. The validity of the new approach is verified by comparing its results with those of a numerical time-domain stochastic simulation. The proposed method has far much faster runtimes, independent of the time constants in the system, compared to the corresponding time-domain methods that allow a convenient simulation-based design of PLLs especially at radio frequencies.
Equalization enhanced phase noise (EEPN) occurs due to the interplay between laser phase noise and electronic dispersion compensation (EDC) module. It degrades significantly the performance of ...uncompensated long-haul coherent optical fiber communication systems. In this work, a general expression accounting for EEPN is presented based on Gaussian noise model to evaluate the performance of multi-channel optical communication systems using EDC and digital nonlinearity compensation (NLC). The nonlinear interaction between the signal and the EEPN is analyzed. Numerical simulations are carried out in nonlinear Nyquist-spaced wavelength division multiplexing (WDM) coherent transmission systems. Significant performance degradation due to EEPN in the cases of EDC and NLC are observed, with and without the consideration of transceiver (TRx) noise. The validation of the analytical approach has been done via split-step Fourier simulations. The maximum transmission distance and the laser linewidth tolerance are also estimated to provide important insights into the impact of EEPN.
This Letter presents a method of predicting the phase noise limits of static frequency dividers. The proposed phase noise model for free-running and injection-locked modes is based on the circuit ...parameters only. The model provides an intuitive comprehension of the phase noise behaviour of static frequency dividers and is proved to be useful in primary hand calculations. The method was verified against measurement results of a static frequency divider-by-two, operated at 77 GHz and fabricated in a SiGe $0.13 {\rm\mu} {\rm m}$0.13μm process.
This study addresses the problem of estimating the parameters of a single chirp signal affected by Wiener phase noise with an unknown variance and observed in an additive white Gaussian noise (AWGN) ...environment. We derive the time-domain joint maximum likelihood (ML) estimators for the three phase coefficients (initial phase, initial frequency, frequency rate), along with the maximum a posteriori probability (MAP) estimator for the phase noise. As a critical input for the joint ML and MAP estimators, we further derive the ML estimation of the unknown phase noise variance. All derived estimators are closed-form expressions based on the phases and magnitudes of the received signal samples. To establish benchmarks for comparison in scenarios with phase noise, we concurrently derive the Cramer-Rao lower bounds (CRLBs) for the ML estimators of the phase coefficients and the phase noise variance, along with the Bayesian CRLB (BCRLB) for the MAP estimator. The joint ML estimators for the phase coefficients and the MAP estimator for the phase noise are unbiased, and their mean-square errors (MSEs) asymptotically achieve the CRLBs and BCRLB at high signal-to-noise ratio (SNR). The MSE performance of the joint ML and MAP estimators is validated using Monte Carlo simulations considering both exact and estimated phase noise variances. In scenarios with large phase noise variance, the MSE performance of the ML estimators for the phase coefficients demonstrates a significant improvement compared with the most current estimators.
Carrier phase recovery (CPR) is a key digital signal processing (DSP) subsystem in optical fiber communications. In this paper, we review recent advances in CPR algorithms and analyze their ...performance under the impact of different system impairments in a long-haul 256 GBaud setting. We study both single- and dual-stage CPR configurations, in the linear and nonlinear regimes, and at different system baud rates. By exploiting CPR algorithms tailored for digital subcarrier multiplexing (DSCM) systems, we are able to reap the benefits of their intrinsic resilience to the two main performance-limiting effects of optical fiber systems: equalization enhanced phase noise (EEPN) and nonlinear interference (NLI). Overall, the paper sheds light on the potential benefits of DSCM and highlights the need for further research into CPR algorithms that specifically target the effect of nonlinear phase noise (NLPN).
High-capacity wireless links at millimeter-Waves are candidate for backhaul infrastructure to small-cell mobile networks. However, the use of high-order modulation schemes sets challenging ...phase-noise specifications for integrated frequency synthesizers. Moreover, the use of adaptive modulation suggests local oscillators exploiting noise scaling, up to several decibel depending on channel conditions. In this paper, multi-core switch-coupled LC voltage-controlled oscillators are proposed to achieve ultra-low phase noise and scalable noise performance according to system requirements in a power-efficient way. A theoretical model investigating the effect of LC core component mismatches shows very good agreement with experiments. Design insights are provided, key in order to take effective advantage from the proposed low-noise technique. A quad-core ~20 GHz oscillator prototype, followed by a frequency quadrupler, has been realized in 55-nm BiCMOS technology. Measured performances are ~70-to-81 GHz frequency range with -106.5-dBc/Hz minimum phase noise at 1-MHz offset from an 80-GHz carrier with 50-mW power consumption and 1.2-V supply. To authors' knowledge, this is the lowest phase noise measured in the E-Band using integrated technologies and CMOS-compatible supplies. When noise requirements are relaxed, auxiliary cores are turned off rising phase noise by 6 dB but with power consumption reduced down to 18 mW only.
An approach to transmitting two independent microwave vector signals on a single optical carrier with one polarization state based on coherent detection and digital phase noise cancellation is ...proposed and experimentally demonstrated. At the transmitter, two independent microwave vector signals are modulated on an optical carrier via a dual-drive Mach-Zehnder modulator (DD-MZM). The modulated optical signals are transmitted over a single-mode fiber (SMF) and sent to a coherent receiver. At the receiver, the optical signals are detected where a local oscillator (LO) optical wave generated by a second free-running laser source is also applied. To recover the two microwave vector signals, a novel digital signal processing (DSP) algorithm is developed and applied to eliminate the joint phase noise terms from the transmitter and the LO laser sources as well as the unstable offset frequency between the two laser sources. An experiment is performed. The transmission of two independent 16 quadrature amplitude modulation (16-QAM) microwave vector signals at 4 GHz with a symbol rate of 1 GSymb/s over a 9-km SMF is demonstrated. The transmission performance in terms of error vector magnitudes (EVMs) and bit error rates (BERs) is also evaluated.
A microwave photonic link (MPL) with quadrupled capacity based on coherent detection and digital phase noise cancellation is proposed and experimentally demonstrated. At the transmitter, a ...continuous-wave (CW) light wave is intensity modulated by four independent microwave vector signals with two having an identical center microwave frequency at a dual-parallel Mach-Zehnder modulator (DPMZM) consisting of two dual-drive MZMs (DEMZMs) with the sub-DEMEMs biased at the quadrature transmission point. Four intensity-modulated optical signals are generated and transmitted over a single-mode fiber (SMF) to a coherent receiver. To perform coherent detection, a second CW laser source as a local oscillator (LO) is also applied to the coherent receiver. To recover the microwave vector signals, a novel digital phase noise cancellation algorithm is developed and applied to eliminate the joint phase noise from the transmitter laser source and the LO laser source as well as the unstable offset frequency between the two laser sources. A theoretical analysis is performed to show the recovery of the microwave vector signals which is verified by an experiment. For four independent 16 quadrature amplitude modulation (16-QAM) microwave vector signals with a symbol rate of 0.5 GSymbol/s, error-free transmission over a 9-km SMF is achieved when the received optical power at the coherent receiver is higher than −18 dBm with forward error correction (FEC).
A method to reduce the spectral linewidth of a laser source by direct phase noise compensation is proposed and demonstrated experimentally. To extract the phase noise information, the laser output is ...phase modulated and the in- and quadrature-phases are detected by homodyne mixing. Phase noise compensation is achieved by simply applying an error signal to an external phase modulator, where the error signal is generated to keep the same power level for the detected in- and quadrature-signals. The spectral linewidth of the laser is reduced significantly from 450 to 60 kHz.
A computationally efficient framework is presented for calculating features used to train machine learning (ML) models for estimating the nonlinear signal-to-noise ratio (<inline-formula><tex-math ...notation="LaTeX">S\!N\!R_{N\!L}</tex-math></inline-formula>) in heterogeneous optical networks. Data used for training and testing is obtained from a first-order perturbation analytical model, which is calculated for over 500,000 distinct system configurations, covering a wide range of system and channel compositions. System configurations vary based on span lengths, number of spans, number of wavelength division multiplexed (WDM) channels, channel spacings, modulation formats, shaping rates, and symbol rates. Five ML models have been trained using features extracted from the nonlinear phase noise generated by signal-signal interaction between WDM channels. Model comparison suggests that ensembles of regression trees produce highest estimation accuracy. A robust model building method is presented that aggregates important features from three ensemble models with boosting and shows universal application to all considered training cases. The impact from the extent of heterogeneity and training diversity in terms of number of WDM channels, symbol rate, and total distance covered in training is explored. Estimation results demonstrate the benefit of considering heterogeneous system configurations in training and indicate high accuracy and generalization potential to arbitrary system configurations.
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