Integer Frequency Research Articles

Design and Implementation of Digital Integrated Circuit Based Frequency Dividers

This research aims to research the basic fractional frequency division. This article first introduces the theory of the dualmode prescaler method, and then use this method to calculate the number of integer frequency divisions and show that how to achieve the target fractional division ratio. after that, Verilog code is used to implement fractional frequency division, and using simulation to show the operation of the divider. The simulation shows that the designed fractional frequency divider can be implemented by evenly inserting different values of integer frequency dividers. However, the experiment in this article may has time error in the output signal, because the accurate 50% duty cycle cannot be achieved. In addition, the frequency division period is not completely uniform. Finally, the challenges and limitations of fractional frequency division technology in theory and practice will be summarized.

W-band photonic-aided mm-wave ISAC system enabled by a shared OFDM signal waveform and a two-stage carrier frequency recovery algorithm.

Integrated sensing and communication (ISAC) systems will play a potential role in the upcoming six-generation (6G) networks. The reason is that ISAC systems can effectively solve the spectrum resource shortage problem and decrease the cost of deploying hardware equipment for simultaneously realizing communication and sensing. In this Letter, we successfully realize a W-band photonic-aided millimeter-wave (mm-wave) ISAC system enabled by a shared orthogonal-frequency-division-multiplexing (OFDM) signal waveform and two-stage carrier frequency recovery (CFR) algorithm. The digital-signal-processing (DSP)-based two-stage CFR algorithm includes the first-stage fractional frequency offset (FFO) estimation and compensation as well as the second-stage integer frequency offset (IFO) estimation and compensation. We experimentally analyze and verify that, with the introduction of the two-stage CFR algorithm, the system robustness to carrier frequency offset can be significantly enhanced. We also experimentally demonstrate, based on the ISAC system and our receiver DSP, a net data rate of up to 47.54 Gbit/s with a total signal bandwidth of 16 GHz over a 5.2 m wireless link at 94.5 GHz. Moreover, the sensing results indicate that the ISAC system can realize the detection of one target 2 m away from the transmitter with a ranging resolution of 0.98 cm and a ranging error of 4 mm. The system is anticipated to facilitate diverse potential applications in future 6G networks.

Simulation Study on Mechanical Vibration Characteristics of GIS Bus Misalignment

Abstract Gas-insulated switchgear (GIS) has been widely used in power grid systems. The busbar is a crucial element within a GIS system, responsible for facilitating electrical connections between different GIS components. Any defects during manufacturing or improper installation procedures can lead to busbar misalignment, resulting in abnormal vibrations within the GIS. This study focuses on analyzing the mechanical vibration characteristics of GIS bus misalignment using a simulation model based on the finite element method for a 252kV GIS. When the busbar is misaligned and the conductor experiences an unbalanced force, it undergoes Coulomb forces at double the voltage frequency. Under normal or misaligned conditions, the conductor exhibits forced vibrations at the power frequency of 100Hz. However, when misalignment occurs, there is a coupling effect between electrodynamics and vibrations, causing the shell to display integer frequency vibration components.

A 0.59 nW/kHz Clock Circuit with High-Precision Clock Calibration for Passive Internet of Things Chips

The high precision and low power consumption of the clock generator are critical in passive RFID transponders and passive IoT chips, but fluctuations in PVT can cause considerable degradation in the precision of the chip’s internal clocks. This paper proposes a high-precision clock circuit with a single-shot calibration method to addresses this issue in a low-power clock solution. Based on the reference timespan in the preamble of the down-link RF envelope, a TDIF (Time-digital to current-frequency) calibration method was implemented with both a streamlined procedure and customized circuits. By computing the difference between the time counts and applying it to an ultra-low-power, current-starved oscillator, the current change ratio can be linearly controlled. Compared to the traditional integer frequency division scheme used by passive tags for a 160 k bits up-link data rate, the required frequency for the clock generator was reduced from 960 kHz to 320 kHz, the calibration error was reduced from ±10% to ±3% for ±25% frequency deviation, the calibration time was 133.3 μs for a single shot in this work, and the power consumption was 158 nW after the calibration was completed. This leads to an excellent power efficiency of 0.59 nW/kHz and meets the requirements of low power, low cost, and PVT robustness in the RF-powered passive IoT chips. By appropriately increasing the number of calibration digits and the duration, this calibration approach could also be used for other ultra-low-power passive IoT chips that require higher-precision clocking without the use of off-chip crystals.

Improved Sliding DFT Filter With Fractional and Integer Frequency Bin-Index

Improved Sliding DFT Filter With Fractional and Integer Frequency Bin-Index

Complexity-Effective Joint Detection of Physical Cell Identity and Integer Frequency Offset in 5G New Radio Communication Systems

This paper presents a simplified joint synchronization scheme for the integer carrier frequency offset and physical cell identity using a primary synchronization signal (PSS) in 5G new radio (NR) communication systems. We demonstrate the efficiency of our proposed NR-PSS synchronization scheme by deriving its simplified implementation, which exploits the near-zero autocorrelation feature between cyclically shifted NR-PSS symbols. As a figure of merit, we compute the probability of detection failure of the proposed NR-PSS synchronization scheme and validate its accuracy via simulations. To illustrate the benefits and limitations of the proposed NR-PSS synchronization scheme, we compare it with the conventional NR-PSS synchronization scheme, considering factors such as detection performance and computation complexity. Numerical results indicate that, regardless of the channel environment, the proposed NR-PSS synchronization scheme achieves a significant reduction in arithmetic complexity while maintaining the same detection capability as existing NR-PSS synchronization schemes.

Complex bursting oscillations induced by pulse-shaped explosion and integer frequency ratios in a Rayleigh–van der Pol system

Complex bursting oscillations induced by pulse-shaped explosion and integer frequency ratios in a Rayleigh–van der Pol system

Microwave Frequency Dividers With Reconfigurable Fractional 2/N and 3/N Division Ratios

Two microwave photonic signal processing structures, which are capable to realise microwave frequency division with a tunable integer or non-integer division ratio, are presented. They are based on applying an input RF signal to a Mach Zehnder modulator, which is biased to generate a carrier-suppressed double sideband (DSB) or single sideband (SSB) optical signal. The carrier-suppressed DSB optical signal consists of the upper and lower 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> order sidebands with a separation of two times the input RF signal frequency. The carrier of the SSB optical signal is suppressed by a fibre Bragg grating (FBG) connected to the modulator output. Hence the FBG output consists of the upper 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> order and lower 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order sidebands with a separation of three times the input RF signal frequency. The carrier-suppressed DSB or SSB optical signal is injected into a semiconductor laser. The semiconductor laser is oscillated in the period-one state that generates a number of equally spaced frequency components, which are frequency locked by the injection light wave. Beating of these optical frequency components at the photodetector produces an RF signal with a frequency of 2/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> or 3/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> times the input RF signal frequency where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> can be between 3 and 6. Hence the 2/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> frequency divider can realise 2/3, 1/2, 2/5 and 1/3 frequency division operation, and the 3/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> frequency divider can realise 3/4, 3/5 and 1/2 frequency division operation. The proposed 2/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> and 3/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> frequency dividers have a very simple structure compared to the reported photonics-based microwave frequency divider that can realise both integer and non-integer frequency divisions. The frequency division ratio can be tuned by simply adjusting the forward bias current of the semiconductor laser subject to optical injection. Experimental results demonstrate the two proposed structures can realise microwave frequency division with a tunable integer and non-integer division ratio for different input RF signal frequencies of 10 to 18 GHz, and over 60 dB output signal-to-noise ratio performance. More than 27 dB suppression in the unwanted frequency components around the frequency divided signal is also demonstrated.

Further Research on Frequency Allocation (19-Cell System) Method based on IFR and FFR

Many of the most advanced technology has a basic need for efficient telecommunication. In order to achieve this goal, the team should allocate those frequency channels in an intelligent way so that the interference can be reduced to the maximum extent. Here the team introduced a new method based on IFR3&amp;IFR1 (Integer frequency reuse) in a 19-cell network, but also apply the FFR (fractional frequency reuse) method to reduce the interference ulteriorly. In the pure IFR situation, the integer frequency reuse factor and the cellular network specification collectively decide the network capacity. While in FFR only a fraction of the whole bandwidth is used by the users in the edge. By contrast, the users near the BS can make use of the total bandwidth. The cell is divided into an outer and an inner part in this effective way. Fractional Frequency Reuse (FFR) and its derivative method are accepted widely in the downlink (DL) inter-cell interference coordination(ICIC) schemes. The team also optimized the FFR method by measuring the distance in a more precise way. The team utilized Matlab to make a simulation of the system applying the new method and come to a couple of reasonable conclusions by comparing the FFR+IFR3 with FFR+IFR3. FFR+IFR3 has a better performance against FFR+IFR1 in a system whose distance between each cell is with more accuracy. While the average number of users per cell and transmission power for cell edge have little impact on average capacity. When the SNR increases, the network capacity starts steep but later flattens. Our method is more intelligent and can minish interference efficiently.

Comparison of Different Frequency Channel Allocation Methods in ultra-dense networks

The impact of information transmission on production and life under dense networking is self-evident. Dense networking application scenarios include airports, dense residential buildings, dense business districts and blocks, campuses, large gatherings, stadiums, subways, etc. However, with the increase of 5G frequency band, the 5G macro base station signal attenuates more when it penetrates the wall than 4G, which makes it difficult to cover indoor signals. The outdoor 5G macro base station signal can only provide shallow indoor coverage after penetrating obstacles such as brick walls, glass and cement, which cannot guarantee the good experience required for indoor deep coverage. This paper compares and discusses various channel allocation algorithms based on user scenarios in ultra-dense networks. By adjusting some parameters of 19 units, the integer frequency reuse (IFR) method (N=1,3), fractional frequency reuse (FFR) method, simultaneous water injection (SWF) method, and transmission interference temperature limit (TX-ITL) method are compared. In order to increase the capacity, a combination of several algorithms will also be used.

Comparison of FFR+IFR and IFR Models with Different Frequency Reuse Factors in Cellular Networks

With the development of information network transmission, how to efficiently complete frequency reuse has been studied by many scholars. Frequency reuse refers to reusing the same frequency in a digital cellular system. Generally, limited frequencies are divided into several groups. As we all know, fractional frequency reuse (FFR) and integer frequency reuse (IFR) are classical frequency reuse methods in cellular networks. The combination of FFR method and IFR method to find the best model has attracted the attention of researchers at home and abroad. Therefore, through the fusion and combination of the four models, this paper will first introduce two frequency reuse methods, IFR and FFR, as well as the combination of these two methods and the calculation methods of these two methods. Through Matlab software modeling and simulation, according to the average capacity results, study the impact of different user numbers on the average capacity of the central area and the edge area. The experimental results provide a new idea for future practical applications.

Understanding Harmonic Structures Through Instantaneous Frequency.

The analysis of harmonics and non-sinusoidal waveform shape in time-series data is growing in importance. However, a precise definition of what constitutes a harmonic is lacking. In this paper, we propose a rigorous definition of when to consider signals to be in a harmonic relationship based on an integer frequency ratio, constant phase, and a well-defined joint instantaneous frequency. We show this definition is linked to extrema counting and Empirical Mode Decomposition (EMD). We explore the mathematics of our definition and link it to results from analytic number theory. This naturally leads to us to define two classes of harmonic structures, termed strong and weak, with different extrema behaviour. We validate our framework using both simulations and real data. Specifically, we look at the harmonic structures in shallow water waves, the FitzHugh-Nagumo neuronal model, and the non-sinusoidal theta oscillation in rat hippocampus local field potential data. We further discuss how our definition helps to address mode splitting in nonlinear time-series decomposition methods. A clear understanding of when harmonics are present in signals will enable a deeper understanding of the functional roles of non-sinusoidal oscillations.

A Neural Network based Integer Frequency Offset Estimation and PSS Detection in 5G NR Systems

A Neural Network based Integer Frequency Offset Estimation and PSS Detection in 5G NR Systems

A smarter algorithm-IFR3+FFR in wireless network to optimize frequency allocation

All latest technologies require frequency channels to be allocated intelligently so that interference can be avoided. Nowadays, it is still quite challenging for people to propose an effective method to enhance the frequency allocation system, which reduces interference further and allows more users to utilize the base station at the same time. Here we describe the method of improving the frequency allocation system-IFR3 (Integer frequency reuse) plus FFR (fractional frequency reuse) in a nineteen-cell network. We simulate the system based on MATLAB, comparing capacity results against different parameters. We draw some useful conclusions after the simulation. When the number of frequencies increases, average network capacity also increases. When SNR increases, average network capacity increases at the beginning, and then at a certain critical point, it starts to decrease. Thereby, it is required to find the best system with both the appropriate number of frequencies and SNR to maximize the network capacity. As for users who are in the distance, the interference will be large when using IFR1 but small if using IFR3. Therefore, finding the best reuse factor when using FFR is indispensable. Smaller transmit power should be allocated to users in the cell’s inner area, and larger transmit power allocated to users in the outer area of the cell. This system is more advanced and capable of reducing interference efficiently.

The impact of PSS autocorrelation on cell search based on robust maximum likelihood scheme in LTE system

Robust Maximum Likelihood scheme for primary synchronization signal (PSS) detection and integer frequency offset (IFO) in Long Term Evolution (LTE) system has the best performance of cell search [5]. This scheme provides good synchronization performance based on correlation properties of Zadoff-Chu (ZC) sequences and reduced-rank representation of channel frequency response in multi-path propagation fading environment. The three ZC sequences used for PSS in LTE system cannot be said to have sufficient correlation properties in considering impact of symbol timing error. In this paper, we evaluate impact of the autocorrelation of PSS on PSS detection and IFO estimation and raise an issue of using other ZC sequence with better correlation properties. The simulation results show that PSS detection and IFO estimation performances are improved by using proposed ZC sequence.

A novel timing and frequency offset estimation algorithm for filtered OFDM system

As a critical technology of 5G air interface waveform, filtered orthogonal frequency division multiplexing (F-OFDM) not only inherits the technical advantages of OFDM, but also has outstanding advantages in system flexibility and spectrum efficiency. However, as a multi-carrier technology, it is still extremely sensitive to sample timing offset (STO) and carrier frequency offset (CFO). In this letter, an improved Park frequency domain training sequence (FS-Park) is proposed to complete STO and CFO estimation of F-OFDM system. Firstly, a real-value pseudorandom number (PN) sequence is sent to each subcarrier as training sequence in frequency domain, the corresponding time domain training symbol has a conjugate symmetry structure. Secondly, the training symbol is utilized for timing synchronization, then the fractional frequency offset is estimated based on the cyclic prefix in time domain. Finally, the integer frequency offset is estimated in frequency domain based on the auto-correlation of PN sequence. The simulation results illustrate that the FS-Park algorithm not only has a single pulse timing metric curve and great STO estimation accuracy, but also has better performance of CFO estimation than classical Park algorithm and Liang Xiao’s method.

A Low Complexity joint synchronization algorithm based on CAZAC sequence for OFDM system

To solve the problem of timing ambiguity and reduce the complexity of integer frequency offsets (IFO) estimation for OFDM system, this paper proposes a novel synchronization algorithm based on CAZAC sequence in time domain. The algorithm constructs a training sequence with conjugate and symmetry properties. Firstly, timing synchronization and IFO estimation are completed simultaneously by utilizing the cross-correlating of the training sequence and local signal based on the analysis of the impact of IFO on the timing of meric peak positions. Then the fractional frequency offsets (FFO) estimation is done using the repeatability of the symmetrical training sequence. Compared with the existing representative algorithms, the proposed algorithm achieves better synchronous performances with lower computational complexity and acceptable transmission efficiency.

Accurate frequency estimation for removal of orbital fringes in SAR interferograms

ABSTRACT Differential interferogram of space-borne SAR data may be affected by residual orbital fringes resulting from errors in the orbit (i.e. baseline) determination that hinder subsequent InSAR applications (deformation or elevation measurements). In this paper, an easy-to-use method was developed to remove the orbit errors in complex SAR interferogram in the radar coordinate system by accurately estimating the frequencies of the orbital ramp phase. The method first finds an approximate integer frequency by searching for the peak of the sum of the Fourier spectra of all the rows of the interferogram. It then uses the 100-order Burg spectral estimation algorithm to estimate the power spectrum for each row of the interferogram, and calculates the high-resolution power spectrum over the frequency range Hz. Finally, the method obtains the exact frequency of the orbital ramp phase in the row direction by searching for the peak of the sum of the high-resolution power spectra of all rows. By performing the same operations on all columns of the interferogram, the exact frequency in the column direction can be obtained. The orbital ramp phase can be calculated using these exact frequencies and be removed from the interferogram. Validation tests demonstrate that our method can accurately estimate the frequencies of the orbital ramp phase in the row and column directions, and eliminate the orbital ramp fringes from the simulated and actual interferograms. The proposed method only needs to calculate the high-resolution spectrum in a small frequency range, so the burden of calculation is light. The proposed method is easy to use since phase unwrapping or a priori satellite orbit information is not required.

Time-Delay-Estimation-Liked Detection Algorithm for LoRa Signals Over Multipath Channels

LoRa promises long range reliable communication for the Internet of Things (IoT). However, multipath fading severely affects LoRa’s BER performance. In this letter, we propose a simple detection algorithm for the frame-based LoRa PHY signals mainly composed of a preamble and a variable-length PHY-payload. We first prove that detecting the frame-based LoRa signals over multipath fading channels can be formulated as a Time-delay-estimation (TDE)-liked problem. Based on this, a cyclic cross-correlation implemented by a matched filter is utilized to detect the LoRa signals. Additionally, the proposed TDE-liked detection algorithm is insensitive to the integer frequency offset due to the nature of implying a differential operation. The simulation results indicate that, the proposed algorithm significantly outperforms the existing detection algorithms for the LoRa signals over multipath fading channels. Under the multipath fading channel, the BER performance of the proposed algorithm is slightly inferior to that in the AWGN channel while the existing scheme fails to work.

A 65 nm CMOS Statistical Frequency Ratio Calculator for Frequency Measurement

The frequency ratio calculator (FRC) based on the statistical algorithm is proposed to obtain the integer and fractional frequency ratios of an input signal and a reference signal. The function of FRC can be used for fast frequency measurement of an unknown signal. Thanks to the proposed statistical algorithm, the circuit implementation of the FRC can be realized by synthesis of CMOS standard cell library and its performance is resistant to the variation of process, voltage, and temperature. The FRC is developed in a commercial 65 nm CMOS technology and its input signal frequency range is from 300 MHz to 1.5 GHz. The ratio calculation time takes only two reference cycles and the ratio accuracy is better than 0.003. The FRC consumes 12-42 mW of power from a 1.2 V supply voltage for different input frequency.