Phase Noise Model Research Articles

Phase-reference-intensity attack on continuous-variable quantum key distribution with a local local oscillator

In practical continuous-variable quantum key distribution system using local local oscillator (LLO CV-QKD), the phase noise related to coherent detection and phase-reference pulse intensity can be locally calibrated at the receiver side. Therefore, it can be regarded as trusted noise in order to obtain a higher secret key rate and transmission distance. However, security loopholes will be opened for the eavesdropper to launch attacks without appropriate countermeasures. To this end, we propose two practical phase-reference pulse intensity attack strategies, where Eve can reduce the trusted phase noise by manipulating the intensity of the phase-reference pulse, thereby hiding her attack on the signal pulse. The performance of the LLO CV-QKD system under these attacks has been analyzed. We show that precisely monitoring the intensity of the phase-reference pulse in real time is an essential countermeasure to prevent the proposed attacks. Moreover, an intensity-monitoring scheme for the phase-reference pulse is proposed to strengthen the security of the practical LLO CV-QKD system and make the trusted phase noise model more robust.

Accurate Performance Evaluation of Jitter-Power FOM for Multiplying Delay-Locked Loop

An accurate performance evaluation of jitter-power figure-of-merit (FOM) for multiplying delay-locked loop (MDLL) is presented. For a typical MDLL employing a single-ended multiplying-delay ring voltage-controlled oscillator (MDVCO), it can be tuned via the capacitive loads to uphold a constant normalized phase noise (PN) across different frequencies for better jitter-power performance. Linear approximation and z-domain PN model are utilized to simplify the analysis with excellent agreement between the time-domain simulation and z-domain approximation. The influences of the asymmetric waveform, flicker noise corner, frequency error and reference noise are also discussed and then ignored based on the reasonable approximation. Under a given process, reference clock frequency and supply voltage, the ideal FOM can be derived theoretically. Based on these insights, the predicted FOM can be the benchmark metric in the design of MDLL for the possible best jitter-power performance.

Analysis and Simulation of the Impact of Gamma parameter and Phase Noise on Phase-Locked Loop with PID Controller

In this work, detailed simulation and analysis of impact of gamma parameter and phase noise on the proportional-integral-derivative controlled phase-locked loop is carried out. The linear mathematical model for gamma parameter along with the phase noise model of the proposed system is developed. To improve the loop dynamics, a new type of loop filter is designed by considering a parallel combination of second order passive low pass filter and a proportional-integral-derivative controller in place of the traditional loop filter. The transfer function of gamma parameter as well as noise sources of each component of the phase-locked loop is derived from the proposed model in s-domain. Simulation is carried out on MATLAB to study how gamma parameter impacts on system response as well as on the phase noise contribution to the proposed system. The impact of gamma parameter on lock time, phase margin and loop bandwidth is also studied for gamma parameter less than one and greater than one. Finally, a comparison is done between second order low pass filter, proportional-integral-derivative controller and the newly designed loop filter. Simulation results shows that the proposed system with newly designed loop filter improves the system stability with fast switching speed and reduced the phase noise with gamma greater than one.

Joint ML/MAP Estimation of the Frequency and Phase of a Single Sinusoid With Wiener Carrier Phase Noise

We address here the issue of jointly estimating the angle parameters of a single sinusoid with Wiener carrier phase noise and observed in additive, white, Gaussian noise (AWGN). We develop the theoretical foundation for time-domain, phase-based, joint maximum likelihood (ML) estimation of the unknown carrier frequency and the initial carrier phase, with simultaneous maximum a posteriori probability (MAP) estimation of the time-varying carrier phase noise. The derivation is based on the amplitude and phase-form of the noisy received signal model together with the use of the best, linearized, additive observation phase noise model due to AWGN. Our newly derived estimators are closed-form expressions, consisting of both the phase and the magnitude of all the received signal samples. More importantly, they all have a low-complexity, sample-by-sample iterative processing structure, which can be implemented iteratively in real-time. As a basis for comparison, the Cramer-Rao lower bound (CRLB) for the ML estimators and the Bayesian CRLB (BCRLB) for the MAP estimator are derived in the presence of carrier phase noise, and the results simply depend on the signal-to-noise ratio (SNR), the observation length and the phase noise variance. It is theoretically shown that the estimates obtained are unbiased, and the mean-square error (MSE) of the estimators attain the CRLB/BCRLB at high SNR. The MSE performance as a function of the SNR, the observation length and the phase noise variance is verified using Monte Carlo simulation, which shows a remarkable improvement in estimation accuracy in large phase noise.

Phase noise model for continuous-variable quantum key distribution using a local local oscillator

The value of residual phase noise, after phase compensation, is one of the key limitations of performance improvement for continuous-variable quantum key distribution using a local local oscillator (LLO CV-QKD) system, since it is the major excess noise. However, due to the nonideality of the realistic devices implemented in practice, for example, imperfect lasers, detectors, and unbalanced interferometers, the value of residual phase noise in the current system is still relatively large. Here, we develop a phase noise model to improve the phase noise tolerance of the LLO CV-QKD schemes. In our model, part of the phase-reference measurement noise associated with detection efficiency and electronic noise of Bob's detector as well as a real-time monitored phase-reference intensity at Bob's side is considered trusted because it can be locally calibrated by Bob. We show that using our phase noise model can significantly improve the secure key rate and transmission distance of the LLO CV-QKD system. We further conduct an experiment to substantiate the superiority of the phase noise model. Based on experimental data of a LLO CV-QKD system in the 25-km optical fiber channel, we demonstrate that the secure key rate under our phase noise model is approximately 40% higher than that under the conventional phase noise model.

A System Phase Noise Model for Frequency-Modulated MEMS Gyroscopes

A system phase noise model is proposed in this paper for frequency-modulated (FM) gyroscopes, which gives us a clearly guidance for different noise and how to improve the final performance. The author here introduces a mathematical calculation method to deal with the time domain noise and transforms the time-varying noise into phase modulation paths to analyze the frequency noise effect. Meanwhile, the proposed model reveals the relationships about mechanical vibration noise mechanical additional loop noise and performance indicators. In this way, combing frequency spectrum and Allan variance curves, the weight of each noise can be determined. Here, we get different physical noise sources from actual circuit chip by the proposed phase noise decomposition method and analyze the whole noise contribution. After that, we can clearly understand the performance indicators required to design the circuit. Finally, this work offers a whole theory instructions to quantitate different frequency noise for FM gyroscopes.

Phase noise suppression in LC oscillators: Tutorial

AbstractThis paper presents a comprehensive study of phase noise (PN) suppression in LC‐tank oscillators. The goal of this study is to provide designers with the latest techniques for reducing PN in cross‐coupled oscillators. To this end, we begin with a discussion of two prevalent PN models in oscillators: Hajimiri and Demir. We prefer the Hajimiri model because it does not involve very complicated math, and it offers engineers better insight into designing low‐PN oscillators in the two‐PN close‐in regions in an oscillator spectrum (1/f2 and 1/f3). In 1/f2 region, we show that a need for a large output‐voltage swing leads to Class D and B oscillators, and a large output‐current swing results in Class C oscillators. Also, reduction of the impulse sensitivity functions (ISFs) of an oscillator core can happen in Class F oscillators. A few solutions are presented for mitigating flicker noise up‐conversion, such as adding resistances, controlling the oscillation amplitude, decreasing the conduction angle, guiding the high‐frequency harmonics of current, and shifting the phase of VGS against VDS. We also provide a comparison of recent state‐of‐the‐art literature to show what constitutes a good PN in both 1/f2 and 1/f3 regions in cross‐coupled oscillators. We conclude that a cross‐coupled oscillator can reach the best performances in 1/f3 and 1/f2 PN regions if the oscillator is designed in Class C with the K block and uses the techniques of narrowing the conduction angle, the tail inductor, and the modified tank simultaneously.

Phase noise modeling and characterization of a self-started VCSEL-based harmonic frequency generator (SVHFG)

This article presents the experimental characterization of the first self-started closed-loop system for the generation of microwave harmonics using a long-wavelength VCSEL modulated in a gain-switched regime. A 15-GHz microwave signal is generated with a phase noise of −104 dBc/Hz at 10 kHz from the carrier when the fundamental frequency is f0=2.5 GHz. The side-mode suppression ratio (SMSR) for all the microwave frequencies generated is higher than 30 dB. We propose a predictive model to estimate the phase noise of the fundamental oscillating frequency, considering the noise contributions of each loop component. Several simulation scenarios are included to demonstrate the significant influence of the electrical power, the laser frequency noise, and the optical fiber dispersion over the phase noise performance. We also present the carrier-to-noise ratio deterioration of the microwave harmonics distributed through an optical fiber link.

Improvement of the phase noise model based on an optoelectronic oscillator using a directly modulated distributed feedback laser

A scheme of dual-loop optoelectronic oscillator (OEO) based on a directly modulated distributed feedback (DFB) laser is proposed and experimentally demonstrated. In the proposed scheme, thanks to the DFB laser with enough output optical power utilized as an optical source and a modulator at the same time, high-performance microwave signals are generated without external modulator and erbium-doped fiber amplifier (EDFA). A theoretical model based on the control theory is detailed to assess the single sideband (SSB) phase noise performance of the dual-loop OEO. The laser frequency noise under small-signal direct modulation is proposed and introduced to make the phase noise model more complete for the first time. According to the theoretical analysis, the close-in (<1 MHz) SSB phase noise floor of the dual-loop OEO is dominated by the flicker noise when the offset frequency is below 10 kHz, and determined by the laser’s relative intensity noise (RIN) when the offset frequency is beyond 10 kHz. Microwave signals with the frequency tuned from 8 to 12 GHz and 3-dB linewidth less than 100 Hz are realized. The side mode suppression ratio (SMSR) of the generated microwave signals are measured to be 55 dB based on the dual-loop configuration. Meanwhile, within the whole frequency tuning range, the SSB phase noises of about −125 dBc/Hz at 10 kHz offset frequency are obtained. The experimental results of the SSB phase noise agree very well with the simulation results based on the theoretical model.

Studies on Phase Noise Profiles of Proportional-Integral-Derivative Controlled PLL

Phase noise in a phase-locked loop is originated from reference oscillator, phase detector, loop filter, voltage controlled oscillator and frequency divider which make the system unstable by generating high phase noise at the output spectrum. In this work, a mathematical linear phase noise model is therefore developed to investigate the effect of reference noise, phase detector noise, voltage controlled oscillator noise, frequency divider noise and specifically the loop filter noise. For this purpose, the conventional active or passive low pass filter of the phase locked loop is replaced by a proportional-integral-derivative controller during acquisition. The noise problem of each component is formulated as a transfer function derived from linear analysis of the proposed mathematical noise model. The simulation results show that the effect of noise attenuation of voltage controlled oscillator is -40dB/decade while the noise attenuation of the reference noise, phase detector noise, proportional integral derivative controller noise and frequency divider noise are approximately -20dB/decade each. The 6.21GHz proposed proportional-integral-derivative controlled phase-locked loop is also highly stable with fast switching speed of 0.238nS at damping factor of 0.625 and phase margin of 92° for minimum phase noise.

Adaptive leakage signal cancellation algorithm in heterodyne FMCW system

To mitigate the leakage signal that obstructs the target information extraction in miniatured frequency modulated continuous wave (FMCW) radar system, an adaptive leakage signal cancellation algorithm is proposed in this paper. Without any help of the additional auxiliary path, all the processing for the intermediate frequency (IF) signal can be conducted in the digital domain. The basic principle to cancel leakage signal is to produce a cancelling signal, which has the same amplitude and anti-phase with the leakage signal. Differently, in this paper, the input phase parameter of the proposed method can be arbitrary and it can be modified by the corresponding corrected function. Besides, to acquire the phase noise in the leakage signal conveniently when generating cancelling signal, the information geometry theory is applied to transform the complex phase noise model into statistical characteristics calculation of the input signal. The effectiveness of the model and the proposed algorithm is verified by simulated results. Furthermore, a real FMCW system is designed to collect the practice echo signals. The resulting data denotes that the leakage signal in the received signal is greatly suppressed and the leakage signal power drops by −15.92 dB.

Joint MAP channel estimation and data detection for OFDM in presence of phase noise from free running and phase locked loop oscillator

This paper addresses a computationally compact and statistically optimal joint Maximum a Posteriori (MAP) algorithm for channel estimation and data detection in the presence of Phase Noise (PHN) in iterative Orthogonal Frequency Division Multiplexing (OFDM) receivers used for high speed and high spectral efficient wireless communication systems. The MAP cost function for joint estimation and detection is derived and optimized further with the proposed cyclic gradient descent optimization algorithm. The proposed joint estimation and detection algorithm relaxes the restriction of small PHN assumptions and utilizes the prior statistical knowledge of PHN spectral components to produce a statistically optimal solution. The frequency-domain estimation of Channel Transfer Function (CTF) in frequency selective fading makes the method simpler, compared with the estimation of Channel Impulse Response (CIR) in the time domain. Two different time-varying PHN models, produced by Free Running Oscillator (FRO) and Phase-Locked Loop (PLL) oscillator, are presented and compared for performance difference with proposed OFDM receiver. Simulation results for joint MAP channel estimation are compared with Cramer-Rao Lower Bound (CRLB), and the simulation results for joint MAP data detection are compared with “NO PHN” performance to demonstrate that the proposed joint MAP estimation and detection algorithm achieve near-optimum performance even under multipath channel fading.

Study of the Influence of Phase Noise on the MEMS Disk Resonator Gyroscope Interface Circuit.

In this paper, a detailed analysis of the influence of phase noise on the micro-electro-mechanical system (MEMS) disk resonator gyroscope (DRG) is presented. Firstly, a new time-varying phase noise model for the gyroscope is established, which explains how the drive loop circuit noise converts into phase noise. Different from previous works, the time-varying phase noise model in this paper is established in mechanical domain, which gain more physical insight into the origin of the phase noise in gyroscope. Furthermore, the impact of phase noise on DRG is derived, which shows how the phase noise affects angular velocity measurement. The analysis shows that, in MEMS DRG, the phase noise, together with other non-ideal factors such as direct excitation of secondary resonator, may cause a low frequency noise in the output of the gyroscope system and affect the bias stability of the gyroscope. Finally, numerical simulations and experiment tests are designed to prove the theories above.

A 32-GHz Nested-PLL-Based FMCW Modulator With 2.16-GHz Bandwidth in a 65-nm CMOS Process

This article presents a 32-GHz frequency modulated continuous wave (FMCW) modulator based on the phase-locked loop (PLL) with nested sub-PLL structure in a 65-nm CMOS process. With the sub-PLL, the low-pass effect in phase domain is realized, reducing the noise folding effect, quantization noise, and spurs due to the delta sigma modulator (DSM). To achieve good stability and phase noise performance, both the phase-domain model and the phase noise model are analyzed and simulated. Based on these models, the chirp linearity is discussed and simulated, which helps to determine the design parameters and verifies the linearity improvement. The measurement results illustrate that in fractional-N mode, the nested-PLL achieves the phase noise of -91 dBc/Hz at 1-MHz offset frequency and the fractional spurs of less than -54 dBc at 30.78-GHz output frequency. In FMCW mode, the proposed modulator achieves a triangular chirp with 1.08-2.16-GHz bandwidth at about 32-GHz center frequency. In addition, the measured root mean square (rms) frequency errors of 400 and 770 kHz are achieved with the ramp slopes of 1.08 GHz/93 μs and 2.16 GHz/93 μs, respectively. Measurement results prove the improvements of the phase noise and chirp linearity with the sub-PLL. Including all pads, the chip occupies a silicon area of 1.5 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , and consumes 62-mW dc power.

Low Phase Noise RF Oscillators Based on Thin-Film Lithium Niobate Acoustic Delay Lines

An RF oscillator has been demonstrated using a wideband SH0 mode lithium niobate acoustic delay line (ADL). The design space of the ADL-based oscillators is theoretically investigated using the classical linear time-invariant (LTI) phase noise model. The analysis reveals that the key to low phase noise is low insertion loss (IL), large delay ( ${\tau }_{\mathbf {G}}$ ), and high carrier frequency ( $\mathbf {f}_{\mathbf {o}}$ ). Two SH0 ADL oscillators based on a single SH0 ADL ( $\mathbf {f}_{\mathbf {o}}= 157$ MHz, IL = 3.2 dB, ${\tau }_{\mathbf {G}} = 270$ ns) but with different loop amplifiers have been measured, showing low phase noise of −114 dBc/Hz and −127 dBc/Hz at 10-kHz offset with a carrier power level of −8 dBm and 0.5 dBm, respectively. These oscillators not only have surpassed other Lamb wave delay oscillators but also compete favorably with surface acoustic wave (SAW) delay line oscillators in performance. [2019-0223]

Adaptive EKF Based Estimation Method for Phase Noise in CO-OFDM/OQAM System

Recently, dynamic optical network has attracted wide concern for its high efficiency and flexible configurations. Known for high spectral efficiency and flexible allocations of frequency resources orthogonal frequency-division multiplexing offset-quadrature amplitude modulation (OFDM/OQAM) is a promising scheme for future dynamic networks. Phase noise estimation (PNE) and compensation are key technologies for maintaining the performance of coherent optical OFDM/OQAM system. In this paper, a simplified phase noise (PN) model for OFDM/OQAM under channel effect is deduced according to distribution feature of intrinsic interference. Some blind PNE methods are studied and their specific implementation process for OFDM/OQAM are presented. Based on PN model and Kalman filter theory, we propose a new adaptive extended Kalman filter (AEKF) blind scheme to meet the demand of flexibility in dynamic networks. Numerical results show that AEKF can adjust the implementation complexity of PNE according to the varying laser linewidth. When the commercial laser linewidth is 200 kHz, its time complexity is only 1/3 of that of modified blind phase search with feedback loop. Besides, AEKF can achieve a stable and reliable PNE performance under varying subcarrier allocation. AEKF can achieve a stable normalized linewidth tolerance over $1.5\times 10^{-3}$ under different subcarrier allocations.

Performance of Analog Beamforming Systems With Optimized Phase Noise Compensation

Millimeter-wave and Terahertz frequencies, while promising high throughput and abundant spectrum, are highly susceptible to hardware non-idealities like phase-noise, which degrade the system performance and make transceiver implementation difficult. While several phase-noise compensation techniques have been proposed, there are limited results on the post-compensation system performance. Consequently, in this paper, a generalized reference-signal (RS) aided low-complexity phase-noise compensation technique is proposed for high-frequency, multi-carrier systems. The technique generalizes several existing solutions and involves an RS that is transmitted in each symbol, occupies adjacent sub-carriers, and is separated from the data by null sub-carriers. A detailed theoretical analysis of the post-phase-noise compensation performance is presented for an analog beamforming receiver under an arbitrary phase-noise model. Using this analysis, the performance-impact of several system parameters is examined and the throughput-optimal designs for the RS sequence, RS bandwidth, power allocation, number of null sub-carriers, and the number of estimated phase-noise spectral components are also derived. Simulations performed under 3GPP compliant settings suggest that the proposed scheme is robust to phase-noise modeling errors and can, with the optimized parameters, achieve better performance than several existing solutions.

A Phase compensation method for MEMS quadruple mass gyroscope in zero bias drift

This paper proposes a system phase analysis for MEMS quadruple mass gyroscope (QMG) and improves the stability by 20 times. The improvement factors come from the phase noise model analysis and front-end amplifier design. To make sure which factor is dominant in zero bias and improve the stability, a series of experiments are carried out here to discuss their drift contribution, including environmental change. Meanwhile, a new systematic phase noise method is applied for stability analysis, which helps find the dominant physics sources to improve the zero bias. Combing the experimental results and the theoretical noise model, we establish the actual noise model. By analysis, the dominant noise sources mainly come from the demodulation reference signal and the sense signal, both influenced by the front-end amplifier. In this paper, we design a two-stage capacitive amplifier instead of the trans-impedance amplifier, in which, the noise of input current introduced by cross-resistance (signal noise) and the overall phase shift of the loop (demodulation noise) are greatly reduced. Finally, the stability is improved by an order of magnitude after relative compensation circuit design.

Phase Noise Effect on Millimeter-Wave Pre-5G Systems

The introduction of millimeter waves for 5G wireless communication systems enables the use of more bandwidth and higher carrier frequency, surpassing the capacity of current systems by more than one order of magnitude. The leap of millimeter band results from the development of analog frontends that unfortunately induce relatively large phase noise in phase-locked loop synthesizers. Large phase noise may generate considerable random phase error and residual frequency offset, which in turn produces additional phase error. We evaluate phase error from phase noise on an implemented pre-5G system operating in the millimeter band and through a simulation by modeling the characteristics of a radio frequency integrated circuit. We measure and then compare the residual frequency offset, phase error, and error vector magnitude between the experimental and simulation results. We verify that the phase noise model suitably approximates to the real conditions. Moreover, we show that phase error remains at approximately 4° in the implemented system. By exploiting the implemented phase error compensation, our pre-5G system can overcome a degradation of 1.5 dB in error vector magnitude and achieve an approximate transmission rate of 4 Gbps at gain of 1.49.

Emitter Individual Identification Based on Nonlinearity Analysis of Oscillators

Background: According to the characteristics of phase noise, phase noise power spectrum feature was used for emitter individual identification. Methods: For different emitter individuals, we established a phase noise model with the influence of both transmitter and receiver based on the research of its characteristics. Using power spectrum of phase noise, the corresponding scattered information entropy was proposed. The same type of communication equipments can be identified by Minimum Error Minimax Probability Machine (MEMPM) classifier through extracting this feature at a different frequency offset. Results: Simulation results show that the new features can be effectively used to classify emitter individuals with stable classification performance. Conclusion: According to the simulation, when the SNR was higher than 10dB, the accuracy rate was higher than 90%. It proved that the method is useful and effective. In addition, the recognition performance of the proposed method is very stable, showing the stability of the device phase noise. Therefore, it can be used in practice.