Phase synchronization and synchronization frequency of two-coupled van der Pol oscillators with delayed coupling

In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and the necessary conditions for phase synchronization are also achieved. Finding the vicinity of the synchronization frequency is the major advantage of the describing function method over other traditional methods. The equations obtained based on this method justify the phenomenon of the synchronization of coupled oscillators on a frequency either higher, between, or lower than the highest, in between, or lowest natural frequency of the aggregate oscillators. Several numerical examples simulate the different cases versus the various synchronization frequency delays.

Precise time frequency synchronization technology for bistatic radar

A complete method of synchronization technology of bistatic radar using global position system （GPS） is presented. The pulse per second signal （1PPS） is elaborately modified to increase the time synchronization precision and keep loop locking. A very high time synchronization precision is achieved. Using the modified 1PPS to discipline the local OCXO, the reference frequency signal achieves both high long term stability （LTS） and short term stability （STS） properties. An algorithm, named phase abrupt change CFAR is presented to restrain the 1PPS phase abrupt change and keep loop locking. The experimental results indicate that this time and frequency synchronization method is effective and the time synchronization precision of the synchronization system can be improved from ±100 ns to ±25 ns. In addition, the phase noise is improved to 20 dB.

Joint timing synchronization and frequency offset acquisition algorithm for MIMO OFDM systems

For multiple-input multiple-output （MIMO） orthogonal frequency division multiplexing （OFDM） systems, a joint timing synchronization and frequency offset acquisition algorithm based on fractional Fourier transform （FRFT） is proposed. The linear frequency modulation signals superimposed on the data signals are used as the training signals. By performing FRFT on the received signals and searching the peak value of the FRFT results, the receiver can realize timing synchronization and frequency offset acquisition simultaneously. Compared with the existing methods, the proposed algorithm can provide better timing synchronization performance and larger frequency offset acquisition range even under multi-path channels with low signal to noise ratio. Theoretical analysis and simulation results prove this point.

Different Frequency Synchronization Theory and Its Frequency Measurement Practice Teaching Innovation Based on Lissajous Figure Method

According to the requirement of multi-parameter time and frequency measurement without frequency normalization,a different frequency synchronization theory is proposed based on Lissajous figure method and the variation lawof Lissajous figure which are used in practice teaching of frequency measurement. The theory can achieve high-precision transmission and comparison of time and frequency and precise locking and tracking of phase and frequency,improve the level of scientific research on time and frequency for postgraduate,and promote practice teaching innovation of time frequency measurement for undergraduate. Utilizing the ratio of horizontal and vertical inflection point of the Lissajous figure,the nominal frequency of the measured signal is precisely calculated.The frequency deviation between the measured frequency and its nominal frequency can be obtained by combining the turning cycle of the Lissajous figure. By observing the phase relationship between the frequency standard signal and the measured signal,the accurate measurement of the frequency is implemented. Experimental results showthat the direct measurement and comparison better than the 10-11 order of magnitude with common frequency source can be finished between any signal frequencies.The frequency measurement method based on the theory has the advantage of simple operation,quick measurement speed,small error,lownoise and high measurement precision. It plays an important role in time synchronization,communications,metrology,scientific research,educational technology practice and equipment and other fields.

Effects of Reduced Frequency on Network Configuration and Synchronization Transition

Synchronization of networked phase oscillators depends essentially on the correlation between the topological structure of the graph and the dynamical property of the elements. We propose the concept of ＇reduced frequency＇, a measure which can quantify natural frequencies of each pair of oscillators. Then we introduce an evolving network whose linking rules are controlled by its own dynamical property. The simulation results indicate that when the linking probability positively correlates with the reduced frequency, the network undergoes a first-order phase transition. Meanwhile, we discuss the circumstance under which an explosive synchronization can be ignited. The numerical results show that the peculiar butterfly shape correlation between frequencies and degrees of the nodes contributes to an explosive synchronization transition.

Modeling of cascaded high isolation bidirectional amplification in long-distance fiber-optic time and frequency synchronization system

We propose a physical model of estimating noise and asymmetry brought by high isolation Bi-directional erbiumdoped fiber amplifiers(Bi-EDFAs),no spontaneous lasing even with high gain,in longdistance fiber-optic time and frequency(T/F)synchronization system.It is found that the Rayleigh scattering noise can be suppressed due to the high isolation design,but the amplified spontaneous emission(ASE)noise generated by the high isolation Bi-EDFA and the bidirectional asymmetry of the transmission link caused by the high isolation Bi-EDFA will deteriorate the stability of the system.The calculated results show that under the influence of ASE noise,the frequency instability of a 1200 km system composed of 15 high isolation Bi-EDFAs is 1.773×10^(-13)/1 s.And the instability caused by asymmetry is 2.6064×10^(-16)/30000–35000 s if the total asymmetric length of the bidirectional link length is 30 m.The intensity noises originating from the laser and detector,the transfer delay fluctuations caused by the variation in ambient temperature and the jitter in laser output wavelength are also studied.The experiment composed of three high isolation Bi-EDFAs is done to confirm the theoretical analysis.In summary,the paper shows that the short-term instability of the T/F synchronization system composed of high isolation Bi-EDFAs is limited by the accumulation of ASE noise of amplifiers and the laser frequency drift,while the long-term instability is limited by the periodic variation in ambient temperature and the asymmetry of the amplifiers.The research results are useful for pointing out the direction to improve the stability of the fiber-optic T/F synchronization system.

Pseudo-noise preamble based joint frame and frequency synchronization algorithm in OFDM communication systems

Frame and frequency synchronization are essential for orthogonal frequency division multiplexing （OFDM） systems. The frame offset owing to incorrect start point position of the fast Fourier transform （FFT） window, and the carrier frequency offset （CFO） due to Doppler frequency shift or the frequency mismatch between the transmitter and receiver oscil ators, can bring severe inter-symbol interference （ISI） and inter-carrier interference （ICI） for the OFDM system. Relying on the relatively good correlation charac-teristic of the pseudo-noise （PN） sequence, a joint frame offset and normalized CFO estimation algorithm based on PN preamble in time domain is developed to realize the frame and frequency synchronization in the OFDM system. By comparison, the perfor-mances of the traditional algorithm and the improved algorithm are simulated under different conditions. The results indicate that the PN preamble based algorithm both in frame offset estimation and CFO estimation is more accurate, resource-saving and robust even under poor channel condition, such as low signal-to-noise ratio （SNR） and large normalized CFO.

A novel frequency synchronization scheme for OFDM systems

A novel frequency synchronization scheme for orthogonal frequency division multiplexing (OFDM) systems is proposed, including a novel frequency offset estimation algorithm and a novel frequency offset compensation algorithm. The frequency offset estimation includes both the fractional frequency offset (FFO) estimation and the integral frequency offset (IFO) estimation. Firstly, the FFO was obtained by the conventional ML algorithm in time domain. After the FFO was compensated in time domain, the IFO was obtained by the proposed algorithm based on the energy of virtual carriers. This algorithm needs only simple calculations and has a large frequency offset estimation range. Furthermore, it is insensitive to symbol synchronization errors and channel changing. Finally, the IFO was compensated based on the carrier-positions offset, which can be completed through carrier-positions cyclic shifts in frequency domain. This proposed frequency synchronization scheme can decrease the system redundancy without any need of assistant data, and can be applied to the fast synchronization with the only need of one OFDM symbol. The analyses and simulations show the improved performance of the proposed frequency synchronization scheme.

STATISTICAL APPROXIMATION BASED FINE FREQUENCY SYNCHRONIZATION FOR OFDM SYSTEMS

The paper proposes a novel approach for fine frequency synchronization of OFDM syn- chronization systems in multi-path channels. Maximum Likelihood (ML) function of frequency offsets including integral and decimal parts in frequency domain is developed according to the law of great number to eliminate the noise impact of the signal. When the timing delay close to the actual time, the proposed function produces a deep valley indicating frequency offset when large Valley-Square- Error (VSE) appears. Coarse timing offset can also be detected when function’s Valley-Square-Error (VSE) is maximized. Simulation results shows that the proposed algorithm gives very robust estimation of frequency offset, and a coarse timing offset estimation.

Fiber-based multiple-access frequency synchronization via 1f–2f dissemination

Considering the reference frequency dissemination requirements of the Square Kilometre Array telescope（SKA）project,on the basis of the 1f–2f precision frequency synchronization scheme,we propose and demonstrate a fiber-based multiple-access frequency synchronization scheme.The dissemination reference frequency can be recovered at arbitrary nodes along the entire fiber link.It can be applied to antennas close proximity to the SKA central station,and will lead to a better SKA frequency synchronization network.As a performance test,we recover the disseminated 100-MHz reference frequency at an arbitrary node chosen as being 5 km away from the transmitting site.Relative frequency stabilities of2.0×10^（-14）/s and 1.6×10^（-16）/10~4 s are obtained.We also experimentally verify the feasibility of a frequency dissemination link with three access points.

A step to the decentralized real-time timekeeping network

The composite time scale(CTS) provides an accurate and stable time-frequency reference for modern science and technology. Conventional CTS always features a centralized network topology, which means that the CTS is accompanied by a local master clock. This largely restricts the stability and reliability of the CTS. We simulate the restriction and analyze the influence of the master clock on the CTS. It proves that the CTS's long-term stability is also positively related to that of the master clock, until the region dominated by the frequency drift of the H-maser(averaging time longer than ~10~5s).Aiming at this restriction, a real-time clock network is utilized. Based on the network, a real-time CTS referenced by a stable remote master clock is achieved. The experiment comparing two real-time CTSs referenced by a local and a remote master clock respectively reveals that under open-loop steering, the stability of the CTS is improved by referencing to a remote and more stable master clock instead of a local and less stable master clock. In this way, with the help of the proposed scheme, the CTS can be referenced to the most stable master clock within the network in real time, no matter whether it is local or remote, making democratic polycentric timekeeping possible.

Fast synchronization scheme for SMCC+system with lower SNR

Synchronization with lower SNR hadn't been considered by the conventional publications. Based on the Synchronized multi-carrier CDMA plus (SMCC+) system, which is one of the candidate schemes of digital terrestrial TV broadcasting (DTTB) standard in China, a scheme under lower SNR with one short training sequence and one Barker code group, which were constructed in time domain. Computer simulation results show that the timing estimator here is designed to avoid the ambiguity which occured in Tufvesson's timing synchronization method. The 99.9% correct timing synchronization probability and lower false probability are got in AWGN and Rayleigh fading channels with SNR under -20 dB, and the optimum properties of frequency synchronization are obtained at the same time. It is shown that the proposed scheme is much better than the conventional synchronization methods.

Real-Time Upstream Services Demonstration in Orthogonal Frequency Division Multiplexing- Passive Optical Network System

Abstract： Real-time digital service and mul- timedia service upstream transmission in Dig- ital Signal Processing （DSP）-based Orthogo- nal Frequency Division Multiplexing-Passive Optical Network （OFDM-PON） is experimen- tally demonstrated with Centralised Light Sou- rce （CLS） configuration in this paper. After transmitted over 25 km Standard Single Mode Fibre （SSMF） with -16.5 dBm optical power at receiver, the Bit Error Rate （BER） is 9.5 ×10^-11. The implementations of digital domain up-conversion and down-conversion based on Field Programmable Gate Array （FPGA） are int- roduced, which can reduce the cost of In-ph- ase and Quadrature （IQ） radio frequency mix- ers utilised at transmitter and receiver. A car- rier synchronization algorithm is implemented for compensating carrier offset. A channel eq- ualization algorithm is adopted for compen- sating the damage of channel. A new structure of Frequency Synchronization Unit （FSU） des- igned in FPGA is also proposed to cope with the frequency shifting at receiver.

Efficient Timing and Frequency Offset Estimation Scheme for OFDM Systems

A new training symbol weighted by pseudo-noise(PN) sequence is designed and an efficient timing and fre-quency offset estimation scheme for orthogonal frequency division multiplexing(OFDM) systems is proposed. The timing synchronization is accomplished by using the piecewise symmetric conjugate of the primitive training symbol and the good autocorrelation of PN weighted factor. The frequency synchronization is finished by utilizing the training symbol whose PN weighted factor is removed after the timing synchronization. Compared with conventional schemes, the pro-posed scheme can achieve a smaller mean square error and provide a wider frequency acquisition range.

Carrier frequency offset estimation for a generalized OFDMA uplink

A residual carrier frequency offset （CFO） estimation scheme is proposed for the uplink of orthogonal frequency division multiple access （OFDMA） systems. Multiple access interference caused by CFOs in the uplink is investigated, as it severely affects the performance of a classical maximum likelihood （ML） frequency estimator. By the use of the estimated CFOs of the active users, the linear maximum mean square error （LMMSE） equalization is performed before the ML frequency estimator for the interference cancellation, which can help to sufficiently improve the estimation accuracy for the residual CFO of the incoming user. Analysis and simulations show that the modified ML estimator provides a tradeoff between estimation accuracy and computational complexity caused by the LMMSE interference cancellation, and the proposed method allows OFDMA systems flexibly allocating subcarriers to users.

Analysis of time and frequency synchronization error for wireless systems using OFDM

Due to frequency-selective and time-variant property of wireless channel together with additive noise and mismatch of oscillators between transmitter and receiver, there are always time and frequency synchronization errors in a practical OFDM system. To investigate the effect of the two kinds of errors on system performance, the average normalized interference power (NIP) is defined. A simple supper bound for NIP caused by time synchronization error (TSE) and the tighter upper bound for NIP resulting from frequency synchronization error (FSE) are derived independently. Simulations in typical short wave (SW) and medium wave (MW) channels further verify the correctness and tightness of these upper bounds. They actually provide good approximations to NIPs. Moreover, the upper bound for NIP resulting from FSE is tighter than traditional upper bound. Additionally, a new solution is proposed to relax the precision requirement for time synchronization algorithm, which can achieve a better tradeoff between time synchronization precision and bandwidth efficiency. These upper bounds will be useful in developing and choosing time and frequency synchronization algorithms in OFDM system to achieve a specific NIP value for a given channel condition.

Joint optimization of time and frequency synchronization based on polynomial sequences for OFDM systems

In orthogonal frequency division multiplexing （OFDM） systems, time and frequency synchronization are two critical elements for guaranteeing the orthogonality of OFDM subcarriers. Conventionally, with the employment of pseudo-noise （PN） sequences in preamble design, the preamble information is not fully utilized in both symbol timing offset acquisition and carrier frequency offset estimation. In this article, a new synchronization algorithm is proposed for jointly optimizing the time and frequency synchronization. This algorithm uses polynomial sequences as synchronization preamble instead of PN sequences. Theoretical analysis and simulation results indicate that the proposed algorithm is much more accurate and reliable than other existing methods.

Frequency synchronization for TD-LTE-A downlink receiver

A high accuracy frequency synchronization method is proposed for the 3rd generation partnership project （3GPP） long term evolution advanced （LTE-A） downlink receiver in time division duplexing （TDD） mode. In general, cyclic prefix （CP） correlation based fractional frequency offset （FFO） estimation method and primary synchronization signal （PSS） differential correlation based integer frequency offset （IFO） estimation method are applied for LTE-A frequency synchronization. However, the polarity of CP based FFO estimation result may get reversed when system FFO is closer to the edge of frequency estimation range on account of noise interference; PSS based IFO estimation has performance degradation in low signal noise ratio （SNR）. We propose polarity detection aided CP based FFO estimation and frequency domain enhanced differential correlation based IFO estimation to obtain higher accuracy of frequency synchronization. Computer simulation shows that the proposed method greatly outperforms the conventional methods, especially in low SNR scenario.

Asynchronism-synchronism of regional precipitation in South-to-North Water Transfer planned areas

This paper proposes a method on analyzing the asynchronism-synchronism of precipitation of different hydrological regions regarding the S-to-N water transfer areas of eastern China. The general process of the analysis includes three steps. Firstly, we created the rainfall series of the region concerned by calculating the regional average rainfall of the stations in the area with the help of the classical Thiessen Polygon method. Secondly, the standards of assessment indices for wetness or dryness are set according to Gamma distribution function with a certain probability P 37.5% or 62.5% given respectively. Finally, the frequency of nine combinations are counted as the quantitative feature of asynchronism and synchronism in three time scales, that is the yearly, seasonal and monthly scales. The asynchronism-synchronism of two region pairs has been estimated. The results show that the frequency of precipitation asynchronism in 1957–1998 is larger than the synchronism frequency for both the North China-middle and lower Yangtze River pair and for the North China-upper Hanjiang River pair. As for the synchronism phenomena, the frequency of Nd?Sd is rather low. As the combinations that are suitable for water transfers are Nd?Sw, Nn?Sw, Nd?Sn and Nn?Sn, the total frequency of these combinations for North China-middle and lower Yangtze River is 40% on an annual basis, but only 28% in spring when water shortages are most likely to occur. The total frequency of these combinations for North China-upper Hanjiang River is about 24% on an annual basis, but 35% in spring and winter. It should be noted that if future precipitation patterns are similar to that of the period 1957–1998, it is very important to change the natural character of asynchronism-synchronism by enhancing the capability of hydro-projects regulation and improving management of the water transfer project.

Performance analysis of frequency synchronization in MIMO-OFDM systems with ST/MRC scheme

In this paper, the performance of frequency synchronization in a multiple-input multiple-output orthogonal frequency division multiplexing （MIMO-OFDM） system is analyzed for the purpose of carrier frequency offset （CFO） estimation and compensation. Specifically, a joint transmit antenna selection （ST） and receive maximum ratio combining （MRC） （ST/MRC） method is adopted, that is, only one transmit antenna with the highest channel power is selected while MRC is used at the receiver to maximize the sum of frequency synchronization metric of CFO estimation are derived for several antenna configurations validate the theoretical analysis. The mean square error （MSE） closed-form expressions Simulations in both flat and multipath fading channels