Phase Synchronization Research Articles

Enhanced network synchronization connectivity following transcranial direct current stimulation (tDCS) in bipolar depression: Effects on EEG oscillations and deep learning-based predictors of clinical remission

AimTo investigate oscillatory networks in bipolar depression, effects of a home-based tDCS treatment protocol, and potential predictors of clinical response. Methods20 participants (14 women) with bipolar disorder, mean age 50.75 ± 10.46 years, in a depressive episode of severe severity (mean Montgomery-Åsberg Rating Scale (MADRS) score 24.60 ± 2.87) received home-based transcranial direct current stimulation (tDCS) treatment for 6 weeks. Clinical remission defined as MADRS score < 10. Resting-state EEG data were acquired at baseline, prior to the start of treatment, and at the end of treatment, using a portable 4-channel EEG device (electrode positions: AF7, AF8, TP9, TP10). EEG band power was extracted for each electrode and phase locking value (PLV) was computed as a functional connectivity measure of phase synchronization. Deep learning was applied to pre-treatment PLV features to examine potential predictors of clinical remission. ResultsFollowing treatment, 11 participants (9 women) attained clinical remission. A significant positive correlation was observed with improvements in depressive symptoms and delta band PLV in frontal and temporoparietal regional channel pairs. An interaction effect in network synchronization was observed in beta band PLV in temporoparietal regions, in which participants who attained clinical remission showed increased synchronization following tDCS treatment, which was decreased in participants who did not achieve clinical remission. Main effects of clinical remission status were observed in several PLV bands: clinical remission following tDCS treatment was associated with increased PLV in frontal and temporal regions and in several frequency bands, including delta, theta, alpha and beta, as compared to participants who did not achieve clinical remission. The highest deep learning prediction accuracy 69.45 % (sensitivity 71.68 %, specificity 66.72 %) was obtained from PLV features combined from theta, beta, and gamma bands. ConclusionstDCS treatment enhances network synchronization, potentially increasing inhibitory control, which underscores improvement in depressive symptoms. Baseline EEG-based measures might aid predicting clinical response.

Cortical oscillations are modified by expertise in dance and music: Evidence from live dance audience.

Over the past decades, the focus of brain research has expanded from using strictly controlled stimuli towards understanding brain functioning in complex naturalistic contexts. Interest has increased in measuring brain processes in natural interaction, including classrooms, theatres, concerts and museums to understand the brain functions in the real world. Here, we examined how watching a live dance performance with music in a real-world dance performance setting engages the brains of the spectators. Expertise in dance or music has been shown to modify brain functions, including when watching dance or listening to music. Therefore, we recorded electroencephalography (EEG) from an audience of dancers, musicians and novices as they watched the live dance performance and analysed their cortical oscillations. We compared intrabrain oscillations when participants watched the performance (with music) or listened to the music alone without the dance. We found that dancers have stronger fronto-central and parieto-occipital theta phase synchrony (4-8Hz) than novices when watching dance, likely reflecting the effects of dance experience on motor imagery, multisensory and social interaction processes. Also, compared with novices, dancers had stronger delta phase synchrony (0.5-4Hz) when listening to music, and musicians had stronger delta phase synchrony when watching dance, suggesting expertise in music and dance enhances sensitivity or attention to temporal regularities in movement and sound.

Synchronization in Coupled Laser Arrays with Correlated and Uncorrelated Disorder.

The effect of quenched disorder in a many-body system is experimentally investigated in a controlled fashion. It is done by measuring the phase synchronization (i.e., mutual coherence) of 400 coupled lasers as a function of tunable disorder and coupling strengths. The results reveal that correlated disorder has a nontrivial effect on the decrease of phase synchronization, which depends on the ratio of the disorder correlation length over the average number of synchronized lasers. The experimental results are supported by numerical simulations and analytic derivations.

Neuron configuration enhances the synchronization dynamics in ring networks with heterogeneous firing patterns

Neuron synchronization is fundamental for brain dynamics. While several efforts have been made to understand neuron coupling between tonic and bursting neurons, the position of neurons in a neural network and its relationship with synchronization is not fully understood. This work investigates the impact of neuronal heterogeneity on firing pattern transitions and synchronization in networks comprising tonic and bursting neurons. Using the Huber-Braun model, we explore two configurations: one with neurons grouped closely and another with maximal separation. Our findings reveal that while increased coupling strength generally promotes synchronization, the specific mix of neuron types and their spatial configuration crucially modulate both synchronization and firing pattern transitions, leading to phenomena such as cluster synchronization and global phase synchrony. The results indicate that the configuration with maximal separation and with mostly bursting neurons synchronizes more quickly. Firing pattern transitions are also configuration-dependent. For example, in the network with half tonic and half bursting, the configuration grouped closely undergoes diverse complex dynamics transition in the synchronized state, while the other configuration synchronize with chaotic bursting dynamics. Behaviors like cluster synchronization are observed in this network. The study underscores the significance of considering neuronal heterogeneity in understanding network dynamics.

The phase coherence of cortical oscillations predicts dynamic changes in perceived visibility.

The phase synchronization of brain oscillations plays an important role in visual processing, perceptual awareness, and performance. Yet, the cortical mechanisms underlying modulatory effects of post-stimulus phase coherence and frequency-specific oscillations associated with different aspects of vision are still subject to debate. In this study, we aimed to identify the post-stimulus phase coherence of cortical oscillations associated with perceived visibility and contour discrimination. We analyzed electroencephalogram data from two masking experiments where target visibility was manipulated by the contrast ratio or polarity of the mask under various onset timing conditions (stimulus onset asynchronies, SOAs). The behavioral results indicated an SOA-dependent suppression of target visibility due to masking. The time-frequency analyses revealed significant modulations of phase coherence over occipital and parieto-occipital regions. We particularly identified modulations of phase coherence in the (i) 2-5Hz frequency range, which may reflect feedforward-mediated contour detection and sustained visibility; and (ii) 10-25Hz frequency range, which may be associated with suppressed visibility through inhibitory interactions between and within synchronized neural pathways. Taken together, our findings provide evidence that oscillatory phase alignments, not only in the pre-stimulus but also in the post-stimulus window, play a crucial role in shaping perceived visibility and dynamic vision.

Assessing the impact of climate change and reservoir operation on the thermal and ice regime of mountain rivers using the XGBoost model and wavelet analysis

AbstractThis study presents an analysis of the influence of climatic conditions and the operation of a dam reservoir on the occurrence of ice cover and water temperature in two rivers (natural and transformed by reservoir operations) located in the Carpathian Mountains (central Europe). The analyses are based on data obtained from four hydrological and two climatological stations. The Extreme Gradient Boosting (XGBoost) machine learning model was used to quantitatively separate the effects of climate change from the effects arising from the operation of the dam reservoir. An analysis of the effects of reservoir operation on the phase synchronization between air and river water temperatures based on a continuous wavelet transform was also conducted. The analyses showed that there has been an increase in the average air temperature of the study area in November by 1.2 °C per decade (over the period 1984–2016), accompanied by an increase in winter water temperature of 0.3 °C per decade over the same period. As water and air temperatures associated with the river not influenced by the reservoir increased, there was a simultaneous reduction in the duration of ice cover, reaching nine days per decade. The river influenced by the dam reservoir showed a 1.05 °C increase in winter water temperature from the period 1994–2007 to the period 1981–1994, for which the operation of the reservoir was 65% responsible and climatic conditions were 35% responsible. As a result of the reservoir operation, the synchronization of air and water temperatures was disrupted. Increasing water temperatures resulted in a reduction in the average annual number of days with ice cover (by 27.3 days), for which the operation of the dam reservoir was 77.5% responsible, while climatic conditions were 22.5% responsible.

Beta bursts in the parkinsonian cortico-basal ganglia network form spatially discrete ensembles

Defining spatial synchronisation of pathological beta oscillations is important, given that many theories linking them to parkinsonian symptoms propose a reduction in the dimensionality of the coding space within and/or across cortico-basal ganglia structures. Such spatial synchronisation could arise from a single process, with widespread entrainment of neurons to the same oscillation. Alternatively, the partially segregated structure of cortico-basal ganglia loops could provide a substrate for multiple ensembles that are independently synchronized at beta frequencies. Addressing this question requires an analytical approach that identifies groups of signals with a statistical tendency for beta synchronisation, which is unachievable using standard pairwise measures. Here, we utilized such an approach on multichannel recordings of background unit activity (BUA) in the external globus pallidus (GP) and subthalamic nucleus (STN) in parkinsonian rats. We employed an adapted version of a principle and independent component analysis-based method commonly used to define assemblies of single neurons (i.e., neurons that are synchronized over short timescales). This analysis enabled us to define whether changes in the power of beta oscillations in local ensembles of neurons (i.e., the BUA recorded from single contacts) consistently covaried over time, forming a “beta ensemble”. Multiple beta ensembles were often present in single recordings and could span brain structures. Membership of a beta ensemble predicted significantly higher levels of short latency (<5 ms) synchrony in the raw BUA signal and phase synchronisation with cortical beta oscillations, suggesting that they comprised clusters of neurons that are functionally connected at multiple levels, despite sometimes being non-contiguous in space. Overall, these findings suggest that beta oscillations do not comprise of a single synchronisation process, but rather multiple independent activities that can bind both spatially contiguous and non-contiguous pools of neurons within and across structures. As previously proposed, such ensembles provide a substrate for beta oscillations to constrain the coding space of cortico-basal ganglia circuits.

Functional Network Connectivity for Components of Depression-Related Psychological Fragility.

Psychological resilience (PR) is known to be inversely associated with depression. While there is a growing body of research examining how depression alters activity across multiple functional neural networks, how differences in PR affect these networks is largely unexplored. This study examines the relationship between PR and functional connectivity in the alpha and beta bands within (and between) eighteen established cortical nodes in the default mode network, the central executive network, and the salience network. Resting-state EEG data from 99 adult participants (32 depressed, 67 non-depressed) were used to measure the correlation between the five factors of PR sourced from the Connor-Davidson Resilience Scale and eLORETA-based measures of coherence and phase synchronisation. Distinct functional connectivity patterns were seen across each resilience factor, with a notable absence of overlapping positive results across the depressed and non-depressed samples. These results indicate that depression may modulate how resilience is expressed in terms of fundamental neural activity.

On mathematical analysis of synchronization of bidirectionally coupled Kuramoto oscillators under inertia effect

In this article, we analyze the phase synchronization and frequency synchronization for the bidirectionally coupled Kuramoto model under the effect of inertia. Unlike the classical Kuramoto model equipped with all-to-all coupled interaction, in the setting of this model, each oscillator θi only interacts directly with θi+1 and θi−1. The bidirectional interaction is a typical setting of the concatenation in power systems. Additionally, it is necessary to impose the effect of inertia in the Kuramoto model in the applications such as power systems and Josephson junction array. In this article, we first present a theory of the global convergence for frequency synchronization for the identical case. For the non-identical case, we prove that the second-order bidirectionally coupled Kuramoto model exhibits a frequency synchronization if the coupling strength is large, inertia is small, and all oscillators are initially confined to a sector. We emphasize that the arc length of this sector possesses a positive lower bound which is independent of the number of oscillators. If, in addition, all natural frequencies are identical, we further show that the phase synchronization emerges. Moreover, we demonstrate the numerical simulations to support the main results. On the other hand, we observe that the model equipped with large inertia can exhibit the synchronization. Exploring the synchronization theory for large inertia case is left as the future work.

Energy Efficiency for Faster-than-Nyquist Data Transmission Using Processing Algorithms with Decision Feedback

One of the ways to increase the volume of transmitted information is to increase the bit rate above the Nyquist barrier. However, an increase in bit rate in the case of FTN (Faster-Than-Nyquist) signals leads to an increase in energy costs for receiving information on channels with limited bandwidth, for example, in Digital Video Broadcasting satellite systems like DVB-S2/S2X. It is possible to minimize energy losses by using the processing algorithm “maximum likelihood sequence estimation”. However, the computational complexity of this algorithm is extremely high, which limits its use, especially in terrestrial mobile satellite terminals. We propose a new bit-by-bit decision feedback algorithm with maximum likelihood ratio estimation of subsequent symbols in the observation interval. This algorithm provides minimal energy costs comparable to the method “maximum likelihood sequence estimation” at speeds 2–3 times higher than the Nyquist barrier. At the same time, the complexity is two orders of magnitude less. It is shown by simulation for a channel with additive noise that energy losses in relation to the potential bit error rate (BER) are less than 4.5 dB. In the presence of Rayleigh fading, the application of the proposed algorithm makes it possible to provide the processing of FTN signals for double bit rates in urban areas with energy costs equal to 12 dB when using an equalizer. We give numerical estimations of the increase in computational complexity for the proposed processing algorithm. It is shown that an increase in the bit rate by 1.5 times leads to an increase in the computational complexity by more than an order of magnitude. The same conclusion can be reformulated in another form: for the proposed algorithm, each decibel of energy gain is achieved by increasing the number of computational operations by 1.5×105. It is experimentally shown that additional energy losses due to non-ideal phase and timing synchronization are no more than 1 dB when the proposed algorithm is applied in a fading channel. The energy costs in fading channels relative to a stationary channel for twice the Nyquist rate are equal to 13.8 dB when using an equalizer.

Cortical beta oscillations help synchronise muscles during static posture holding in healthy motor control

How cortical oscillations are involved in the coordination of functionally coupled muscles and how this is modulated by different movement contexts (static vs dynamic) remains unclear. Here, this is investigated by recording high-density electroencephalography (EEG) and electromyography (EMG) from different forearm muscles while healthy participants (n = 20) performed movement tasks (static and dynamic posture holding, and reaching) with their dominant hand. When dynamic perturbation was applied, beta band (15–35 Hz) activities in the motor cortex contralateral to the performing hand reduced during the holding phase, comparative to when there was no perturbation. During static posture holding, transient periods of increased cortical beta oscillations (beta bursts) were associated with greater corticomuscular coherence and increased phase synchrony between muscles (intermuscular coherence) in the beta frequency band compared to the no-burst period. This effect was not present when resisting dynamic perturbation. The results suggest that cortical beta bursts assist synchronisation of different muscles during static posture holding in healthy motor control, contributing to the maintenance and stabilisation of functional muscle groups. Theoretically, increased cortical beta oscillations could lead to exaggerated synchronisation in different muscles making the initialisation of movements more difficult, as observed in Parkinson's disease.

The brain’s duck test in phantom percepts: Multisensory congruence in neuropathic pain and tinnitus

Chronic neuropathic pain and chronic tinnitus have been likened to phantom percepts, in which a complete or partial sensory deafferentation results in a filling in of the missing information derived from memory. 150 participants, 50 with tinnitus, 50 with chronic pain and 50 healthy controls underwent a resting state EEG. Source localized current density is recorded from all the sensory cortices (olfactory, gustatory, somatosensory, auditory, vestibular, visual) as well as the parahippocampal area. Functional connectivity by means of lagged phase synchronization is also computed between these regions of interest. Pain and tinnitus are associated with gamma band activity, reflecting prediction errors, in all sensory cortices except the olfactory and gustatory cortex. Functional connectivity identifies theta frequency connectivity between each of the sensory cortices except the chemical senses to the parahippocampus, but not between the individual sensory cortices. When one sensory domain is deprived, the other senses may provide the parahippocampal ‘contextual’ area with the most likely sound or somatosensory sensation to fill in the gap, applying an abductive ‘duck test’ approach, i.e., based on stored multisensory congruence. This novel concept paves the way to develop novel treatments for pain and tinnitus, using multisensory (i.e. visual, vestibular, somatosensory, auditory) modulation with or without associated parahippocampal targeting.

Longitudinal variability of complexities associated with equatorial electrojet and its coupling with Solar Quiet Daily variation Sq field

The large-scale solar quiet (Sq) current and the Equatorial Electrojet (EEJ) current are two structures produced by electric current in the Earth’s ionosphere. For a long time, the characteristics of these two currents, particularly whether the EEJ is an extended portion of the Sq current has been a hot topic within the community. This study examined magnetic data obtained from ground-based magnetometers at 6 representative stations for the year 2009 and for geomagnetically quiet days (Ap⩽3). The selected stations are along the magnetic equator in the South America (Huancayo), Africa (Ilorin; Addis Ababa), and the Philippines (Langkawi, dip latitude -2.32°; Davao, dip latitude -1.02°; Yap, dip latitude -1.49°). Results showed that both current systems are complex, and this complexity varies significantly from one longitudinal station to another. The strongest and weakest complexity were found in Huancayo and Ilorin, respectively. Afterwards, using four entropy quantifiers (Phase synchronization, Mutual Information, Ensemble Symbolic Coupling Traces, and S-independence), this study examined the relationship between the EEJ and Sq currents. Results revealed clearly a significant information exchange between both currents; that is, the Sq and EEJ currents are indeed coupled. As a step further, using the transfer entropy approach, a directional investigation was carried out to ascertain the direction of information flow between the Sq and EEJ stations. Observations revealed that due to the weak coupling obtained over the African sectors, only the currents over these stations exchanged information. This study further discussed the possible physical mechanisms responsible for the identified variabilities.

The Difference Between Expert Dancers' and Non-Dancers Tapping Timing With and Without an Auditory Stimulus at a Slow Tempo.

Our primary purpose in this study was to determine whether trained dancers differed from untrained non-dancers in their ability to accurately control motor timing during finger and heel tapping tasks, both with and without slow isochronous auditory stimuli. Dancers and non-dancers were instructed to synchronize their taps with isochronous auditory stimuli under three conditions: 30, 40, and 50BPM. After the synchronization phase, participants were asked to continue tapping without the auditory sequences. On the synchronization task, the tapping onset of both groups lagged behind the stimulus onset in all tempo conditions. In all conditions, dancers showed more accurate and stable beat synchronization and continuation than non-dancers. As the tempo condition slowed down (from 50 to 30BPM), synchronization accuracy decreased while synchronization and continuation variability increased. Unlike for novices, dancers showed no difference between the finger and heel tapping synchronization tasks. During the continuous tasks, their timing accuracy was higher for heel than for finger tapping. Collectively, these findings suggest that dance training, which involves synchronizing bodily movements based on rhythm, may lead to an accumulation of experience that enhances specific sensorimotor skills related to synchronizing movements with external stimuli or continuing rhythmic movements temporally.

Sleep stages and brain oscillations: An in-depth analysis using quantitative and mathematical models

This study explores the intricate relationship between sleep stages and brain oscillations, utilizing quantitative EEG analysis and mathematical models. We examine the distinct EEG characteristics of light sleep, deep sleep, and REM sleep, focusing on power spectral density (PSD), coherence, and phase synchronization analyses. The Ising model and Kuramoto model provide frameworks for understanding the synchronization dynamics and phase relationships of neuronal populations across sleep stages. Our findings highlight significant variations in oscillatory activity, coherence, and phase synchronization, offering insights into the neural mechanisms underlying sleep regulation. Additionally, we discuss the implications of these findings for sleep disorders such as insomnia, sleep apnea, and narcolepsy, demonstrating how mathematical models can predict therapeutic outcomes and guide targeted interventions. This comprehensive analysis contributes to the understanding of sleep architecture and the development of novel treatments for sleep disorders.

Beat frequency induced transitions in synchronization dynamics

In neurosciences, the brain processes information via the firing patterns of connected neurons operating across a spectrum of frequencies. To better understand the effects of these frequencies in the neuron dynamics, we have simulated a neuronal network of Izhikevich neurons to examine the interaction between frequency allocation and intermittent phase synchronization dynamics. As the synchronized population of neurons passes through a bifurcation, an additional frequency mode emerges, enabling a match in the mean frequency while retaining distinct most probable frequencies among neurons. Subsequently, the network intermittently transits between two patterns, one partially synchronized and the other unsynchronized. Through our analysis, we demonstrate that the frequency changes on the network lead to characteristic transition times between synchronization states. Moreover, these transitions adhere to beat frequency statistics when the neurons’ frequencies differ by multiples of a frequency gap. Finally, our results can improve the performance in predicting transitions on problems where the beat frequency strongly influences the dynamics.

A modified dispersed frequency and phase consensus algorithm based on differential evolution and credibility weighting matrix

In distributed antenna array systems, accurate synchronization of the frequency and phase of the transmission signals among subarrays is a premise for beamforming. To solve this problem, a modified dispersed frequency and phase consensus (MDFPC) algorithm, which is based on differential evolution (DE) and the credibility weighting matrix, is proposed in this paper. DE algorithm is adopted to optimize the mixing matrix of MDFPC algorithm, and the convergence speed of consensus algorithm can be improved. Moreover, Lanczos method is adopted to calculate the fitness of individuals during optimization, thus the computation amount of the eigenvalue decomposition of the large-scale, sparse and symmetric mixing matrix can be effectively reduced. In addition, the influence of the transmission distance between subarrays on the received Signal-to-Noise Ratio (SNR) is considered, and the credibility weighting matrix can be obtained. Then the contribution of low-credible frequency and phase messages to the iterative updated values can be decreased by the credibility weighting matrix, thus more accurate frequency and phase updated values can be obtained in each iteration. It is shown from simulation results that the proposed algorithm can further reduce the phase synchronization error by at least 8% and achieve at least 18% convergence speed improvement compared to dispersed frequency and phase consensus (DFPC) algorithm.

Sex Differences in the Effect of Brain-derived Neurotrophic Factor (BDNF) Val66Met Polymorphism on Baseline EEG Connectivity

Dependent on Val66Met polymorphism in BDNF gene secretion of neurotrophin affects morphological and functional changes in the developing and mature nervous system, in particular, may contribute to associated with white matter degradation changes in connectivity observed with aging. It was also shown that the associated with Val66Met polymorphism differences in connectivity between cortical structures are moderated by the sex of the subjects. However, there are no studies examining the effect of polymorphism on connectivity, taking into account age and gender differences. In this regard, the present study examined the associations of the Val66Met polymorphism of the BDNF gene with the characteristics of delayed phase synchronization based on EEG data in 223 younger (from 18 to 35 years old) and 134 older (over 55 years old) men and women. The analysis included connections between 84 cortical areas, identified on the basis of 42 Brodmann areas located in the left and right hemispheres. A statistically significant effect, including the factor of polymorphism, was the SEX × GENOTYPE interaction when considering associations at the frequency of the α1-rhythm: in Val/Met men, the strength of thirty-three connections was higher compared to Val/Val. Strengthening of connections was observed mainly between the parahippocampal regions of different hemispheres. At the frequency of the gamma rhythm, associated with the genotype differences in connectivity depended on gender and age. In young subjects, the scores of connectivity in Val/Val women were lower in comparison with men, however, no differences between Val/Val and Met carriers were found in any age group. The combined effect of sex and BDNF genotype on the baseline EEG parameters of brain connectivity may be a background for further study of the role of these factors in the formation of basic characteristics of brain activity.

Adaptation to photoperiod via dynamic neurotransmitter segregation.

Changes in the amount of daylight (photoperiod) alter physiology and behaviour1,2. Adaptive responses to seasonal photoperiods are vital to all organisms-dysregulation associates with disease, including affective disorders3 and metabolic syndromes4. The circadian rhythm circuitry is implicated in such responses5,6, yet little is known about the precise cellular substrates that underlie phase synchronization to photoperiod change. Here we identifya brain circuit and system of axon branch-specific and reversible neurotransmitter deployment that are critical for behavioural and sleep adaptation to photoperiod. A type of neuron called mrEn1-Pet17 in the mouse brainstem median raphe nucleus segregates serotonin from VGLUT3 (also known as SLC17A8,a proxy for glutamate) to different axonal branches that innervate specific brain regions involved in circadian rhythm and sleep-wake timing8,9. This branch-specific neurotransmitter deployment did not distinguish between daylight and dark phase; however, it reorganized with change in photoperiod. Axonal boutons, but not cell soma, changed neurochemical phenotype upon a shift away from equinox light/dark conditions, and these changes were reversed upon return to equinox conditions. When we genetically disabled Vglut3 in mrEn1-Pet1 neurons, sleep-wake periods, voluntary activity and clock gene expression did not synchronize to the new photoperiod or were delayed. Combining intersectional rabies virus tracing and projection-specific neuronal silencing, we delineated a preoptic area-to-mrEn1Pet1 connection that was responsible for decoding the photoperiodic inputs, driving the neurotransmitter reorganization and promoting behavioural synchronization. Our results reveal a brain circuit and periodic, branch-specific neurotransmitter deployment that regulates organismal adaptation to photoperiod change.

High-Accuracy Phase Frequency Detection Technology Based on BDS Time and Frequency Signals.

For the time and frequency signals of Beidou satellites, a high-accuracy phase frequency detection technology based on phase group synchronization is proposed. Using the Beidou receiver and satellite signals as the frequency standard and the measured signals, respectively. The Beidou receiver and the satellite signals are sent to the phase coincidence detector of the different frequencies to generate a phase coincidence point pulse, which is sent to the different frequency phase detector as a control signal to generate the phase differences between the Beidou receiver and satellite signals, and then complete the high-accuracy phase synchronization between the Beidou receiver and satellite signals. Experimental results show that when the delay resolution reaches ps level, the phase synchronization accuracy of the system can reach 10 ps, which has the characteristics of small phase noise, low development cost, simple circuit structure, and high synchronization accuracy compared with the traditional phase synchronization technologies. Therefore, it would be widely used in satellite positioning, astrometry, precision navigation, aerospace, satellite launch, power transmission, communications, radar, and other high-tech fields.