Enhanced Wideband Frequency Estimation via FFT: Leveraging Polynomial Interpolation and Array Indexing

Accurate frequency estimation in a wideband digital receiver using the FFT algorithm encounters challenges, such as spectral leakage resulting from the FFT’s assumption of signal periodicity. High-resolution FFTs pose computational demands, and estimating non-integer multiples of frequency resolution proves exceptionally challenging. This paper introduces two novel methods for enhanced frequency precision: polynomial interpolation and array indexing, comparing their results with super-resolution and scalloping loss. Simulation results demonstrate the effectiveness of the proposed methods in contemporary radar systems, with array indexing providing the best frequency estimation despite utilizing maximum hardware resources. The paper demonstrates a trade-off between accurate frequency estimation and hardware resources when comparing polynomial interpolation and array indexing.

Robust Frequency Estimation Under Additive Symmetric α-Stable Gaussian Mixture Noise

Here the estimating problem of a single sinusoidal signal in the additive symmetricα-stable Gaussian(ASαSG)noise is investigated.The ASαSG noise here is expressed as the additive of a Gaussian noise and a symmetricα-stable distributed variable.As the probability density function(PDF)of the ASαSG is complicated,traditional estimators cannot provide optimum estimates.Based on the Metropolis-Hastings(M-H)sampling scheme,a robust frequency estimator is proposed for ASαSG noise.Moreover,to accelerate the convergence rate of the developed algorithm,a new criterion of reconstructing the proposal covar-iance is derived,whose main idea is updating the proposal variance using several previous samples drawn in each iteration.The approximation PDF of the ASαSG noise,which is referred to the weighted sum of a Voigt function and a Gaussian PDF,is also employed to reduce the computational complexity.The computer simulations show that the performance of our method is better than the maximum likelihood and the lp-norm estimators.

Robust Frequency Estimation Under Additive Mixture Noise

In many applications such as multiuser radar communications and astrophysical imaging processing,the encountered noise is usually described by the finite sum ofα-stable(1≤α<2)variables.In this paper,a new parameter estimator is developed,in the presence of this new heavy-tailed noise.Since the closed-formPDF of theα-stable variable does not exist exceptα=1 andα=2,we take the sum of the Cauchy(α=1)and Gaussian(α=2)noise as an example,namely,additive Cauchy-Gaussian(ACG)noise.The probability density function(PDF)of the mixed random variable,can be calculated by the convolution of the Cauchy’s PDF and Gaussian’s PDF.Because of the complicated integral in the PDF expression of the ACG noise,traditional estimators,e.g.,maximum likelihood,are analytically not tractable.To obtain the optimal estimates,a new robust frequency estimator is devised by employing the Metropolis-Hastings(M-H)algorithm.Meanwhile,to guarantee the fast convergence of the M-H chain,a new proposal covariance criterion is also devised,where the batch of previous samples are utilized to iteratively update the proposal covariance in each sampling process.Computer simulations are carried out to indicate the superiority of the developed scheme,when compared with several conventional estimators and the Cramér-Rao lower bound.

STUDY ON FREQUENCY ESTIMATION BASED ON WEIGHTED LEAST SQUARE METHOD WITH THREE FOURIER COEFFICIENTS

In this paper,a sinusoidal signal frequency estimation algorithm is proposed by weighted least square method.Based on the idea of Provencher,three biggest Fourier coefficients in the maximum periodogram are considered,the Fourier coefficients can be written as three equations about the amplitude,phase,and frequency,and the frequency is estimated by solving equations.Because of the error of measurement,weighted least square method is used to solve the frequency equation and get the signal frequency.It is shown that the proposed estimator can approach the Cramer-Rao Bound(CRB)with a low Signal-to-Noise Ratio(SNR)threshold and has a higher accuracy.

l_(1)-norm Based GWLP for Robust Frequency Estimation

In this work,we address the frequency estimation problem of a complex single-tone embedded in the heavy-tailed noise.With the use of the linear prediction(LP)property and l_(1)-norm minimization,a robust frequency estimator is developed.Since the proposed method employs the weighted l_(1)-norm on the LP errors,it can be regarded as an extension of the l_(1)-generalized weighted linear predictor.Computer simulations are conducted in the environment of α-stable noise,indicating the superiority of the proposed algorithm,in terms of its robust to outliers and nearly optimal estimation performance.

Sarve:synthetic data and local differential privacy for private frequency estimation

The collection of user attributes by service providers is a double-edged sword.They are instrumental in driving statistical analysis to train more accurate predictive models like recommenders.The analysis of the collected user data includes frequency estimation for categorical attributes.Nonetheless,the users deserve privacy guarantees against inadvertent identity disclosures.Therefore algorithms called frequency oracles were developed to randomize or perturb user attributes and estimate the frequencies of their values.We propose Sarve,a frequency oracle that used Randomized Aggregatable Privacy-Preserving Ordinal Response(RAPPOR)and Hadamard Response(HR)for randomization in combination with fake data.The design of a service-oriented architecture must consider two types of complexities,namely computational and communication.The functions of such systems aim to minimize the two complexities and therefore,the choice of privacy-enhancing methods must be a calculated decision.The variant of RAPPOR we had used was realized through bloom flters.A bloom filter is a memory-efficient data structure that offers time complexity of O(1).On the other hand,HR has been proven to give the best communication costs of the order of log(b)for b-bits communication.Therefore,Sarve is a step towards frequency oracles that exhibit how privacy provisions of existing methods can be combined with those of fake data to achieve statistical results comparable to the original data.Sarve also implemented an adaptive solution enhanced from the work of Arcolezi et al.The use of RAPPOR was found to provide better privacy-utility tradeoffs for specific privacy budgets in both high and general privacyregimes.

The frequency estimation of harmonic signals embedded in multiplicative and additive noise

A method to separate a harmonic signal from multiplicative and additive noises is proposed. The method is to square the signal x(t), which consists of a harmonic signal embedded in multiplicative and additive noises, to form another signal y(t) = x2(t)-E[x2(t)]. After y(t) having been gotten, the Fourier transform is imposed on it. Because the information of x(t) (especially about frequency) is included in y(t), the frequency of x(t) can be estimated from the power spectrum of y(t). According to the simulation, under the condition where frequencies divided by resolution dω are integer, the maximum relative error of estimated frequencies is less than 0.4% when the signal-to-noise ratio (SNR) is greater than -23 dB. If frequencies divided by resolution dω are not integer, the maximum relative error will be less than 2.9%. But it is still small in terms of engineering.

Two-step compressed acquisition method for Doppler frequency and Doppler rate estimation in high-dynamic and weak signal environments

To acquire global navigation satellite system(GNSS)signals means four-dimension acquisition of bit transition,Doppler frequency,Doppler rate,and code phase in high-dynamic and weak signal environments,which needs a high computational cost.To reduce the computations,this paper proposes a twostep compressed acquisition method(TCAM)for the post-correlation signal parameters estimation.Compared with the fast Fourier transform(FFT)based methods,TCAM uses fewer frequency search points.In this way,the proposed method reduces complex multiplications,and uses real multiplications instead of improving the accuracy of the Doppler frequency and the Doppler rate.Furthermore,the differential process between two adjacent milliseconds is used for avoiding the impact of bit transition and the Doppler frequency on the integration peak.The results demonstrate that due to the reduction of complex multiplications,the computational cost of TCAM is lower than that of the FFT based method under the same signal to noise ratio(SNR).

Data-Aided Frequency Offset Estimation with Narrowband Interference

An algorithm for carrier frequency offset estimation with narrowband interference in burstmode transmissions is proposed.The algorithm is data-aided and has a feedforward structure that can be easily implemented digitally.The principle of the algorithm is based on a properly designed training sequence and an interpolation technique.Simulation results indicate that the estimation range is about ±20% of the symbol rate.The performance is satisfactory for a signal-to-noise ratio(SNR)as low as -13 dB and the mean square error(MSE)is approximately irrelevant to signal-to-interference ratio(SIR)values over -20 dB.

Deep learning based Doppler frequency offset estimation for 5G-NR downlink in HSR scenario

In the fifth-generation new radio(5G-NR) high-speed railway(HSR) downlink,a deep learning(DL) based Doppler frequency offset(DFO) estimation scheme is proposed by using the back propagation neural network(BPNN).The proposed method mainly includes pre-training,training,and estimation phases,where the pre-training and training belong to the off-line stage,and the estimation is the online stage.To reduce the performance loss caused by the random initialization,the pre-training method is employed to acquire a desirable initialization,which is used as the initial parameters of the training phase.Moreover,the initial DFO estimation is used as input along with the received pilots to further improve the estimation accuracy.Different from the training phase,the initial DFO estimation in pre-training phase is obtained by the data and pilot symbols.Simulation results show that the mean squared error(MSE) performance of the proposed method is better than those of the available algorithms,and it has acceptable computational complexity.

KSKV:Key-Strategy for Key-Value Data Collection with Local Differential Privacy

In recent years,the research field of data collection under local differential privacy(LDP)has expanded its focus fromelementary data types to includemore complex structural data,such as set-value and graph data.However,our comprehensive review of existing literature reveals that there needs to be more studies that engage with key-value data collection.Such studies would simultaneously collect the frequencies of keys and the mean of values associated with each key.Additionally,the allocation of the privacy budget between the frequencies of keys and the means of values for each key does not yield an optimal utility tradeoff.Recognizing the importance of obtaining accurate key frequencies and mean estimations for key-value data collection,this paper presents a novel framework:the Key-Strategy Framework forKey-ValueDataCollection under LDP.Initially,theKey-StrategyUnary Encoding(KS-UE)strategy is proposed within non-interactive frameworks for the purpose of privacy budget allocation to achieve precise key frequencies;subsequently,the Key-Strategy Generalized Randomized Response(KS-GRR)strategy is introduced for interactive frameworks to enhance the efficiency of collecting frequent keys through group-anditeration methods.Both strategies are adapted for scenarios in which users possess either a single or multiple key-value pairs.Theoretically,we demonstrate that the variance of KS-UE is lower than that of existing methods.These claims are substantiated through extensive experimental evaluation on real-world datasets,confirming the effectiveness and efficiency of the KS-UE and KS-GRR strategies.

Synchronous Vibration Suppression of Magnetic Bearing Systems without Angular Sensors

Active Magnetic Bearing(AMB)levitates rotor by magnetic force without friction,and it can provide active control force to suppress vibration while rotating.Most of vibration suppressing methods need angular speed sensors to obtain rotating speed,but in many occasions,angular speed sensor is difficult to install or is difficult to guarantee reliability.This paper proposed a vibration suppressing strategy without angular speed sensor based on generalized integrator and frequency locked loop(GI-FLL)and phase shift generalized integrator(PSGI).GI-FLL and high-pass filter estimate frequency from control current,PSGI is applied to generate compensating signal.Firstly,model of AMB system expressed by transfer function is established and effect of centrifugal force is analyzed.Then,principle and process of vibration suppressing strategy is introduced.Influence of parameters are analyzed by root locus and bode diagram.Simulation results display the process of frequency estimation and performance of displacement.Experiments are carried on a test rig,results of simulations and experiments demonstrate the effectiveness of proposed vibration suppressing strategy.

基于卡尔曼滤波的水声信号线谱增强

To detect weak underwater acoustic signals radiated by submarines and other underwater equipment,an effective line spectrum enhancement algorithm based on Kalman filter and FFT processing is proposed.The proposed algorithm first determines the frequency components of the weak underwater signal and then filters the signal to enhance the line spectrum,thereby improving the signal-to-noise ratio(SNR).This paper discussed two cases:one is a simulated signal consisting of a dual-frequency sinusoidal periodic signal and Gaussian white noise,and the signal is received after passing through a Rayleigh fading channel;the other is a ship signal recorded from the South China Sea.The results show that the line spectrum of the underwater acoustic signal could be effectively enhanced in both cases,and the filtered waveform is smoother.The analysis of simulated signals and ship signal reflects the effectiveness of the proposed algorithm.

Two-Dimensional Interpolation Criterion Using DFT Coefficients

In this paper,we address the frequency estimator for 2-dimensional(2-D)complex sinusoids in the presence of white Gaussian noise.With the use of the sinc function model of the discrete Fourier transform(DFT)coefficients on the input data,a fast and accurate frequency estimator is devised,where only the DFT coefficient with the highest magnitude and its four neighbors are required.Variance analysis is also included to investigate the accuracy of the proposed algorithm.Simulation results are conducted to demonstrate the superiority of the developed scheme,in terms of the estimation performance and computational complexity.

High-Precision Vital Signs Detection Method Based on Spectrum Refinement and Extended DCMA

In this paper,the spectral estimation algorithm is extended to the detection of human vi-tal signs by mm-wave frequency modulated continuous wave(FMCW)radar,and a comprehensive algorithm based on spectrum refinement and the extended differentiate and cross multiply al-gorithm(DCMA)has been proposed.Firstly,the improved DFT algorithm is used to accurately obtain the distance window of human body.Secondly,phase ambiguity in phase extraction is avoided based on extended DCMA algorithm.Then,the spectrum range of refinement is determ-ined according to the peak position of the spectrum,and the respiratory and heartbeat frequency information is obtained by using chirp z-transform(CZT)algorithm to perform local spectrum re-finement.For verification,this paper has simulated the radar echo signal modulated by the simu-lated cardiopulmonary signal according to the proposed algorithm.By recovering the simulated car-diopulmonary signal,the high-precision respiratory and heartbeat frequency have been obtained.The results show that the proposed algorithm can effectively restore human breathing and heart-beat signals,and the relative error of frequency estimation is basically kept below 1.5%.

An Efficient Topography Adaptive Filter for Insar Processing

An efficient implementation of the topography adaptive filter based on local frequency estimation is proposed, where chirp z transform is applied to enhance the accuracy of the frequency estimation. As a by product of this adaptive filter, the linear approximated phase model of the interferogram is employed to improve the coherence estimation. The impacts of the adaptive filter on global and local phase unwrapping algorithms are discussed. Finally, aiming at the negative effect that the adaptive filter can bring to local phase unwrapping algorithms, a fusion scheme that takes advantage of least square and several local phase unwrapping algorithms is presented.

Adaptive Observer for Dynamic Voltage Restorer with Optimized Proportional Integral Gains

An algorithm based on a sliding-mode adaptive observer is proposed for the effective control of dynamic voltage restorers(DVRs).Three single-phase voltage source converter-based topologies are implemented for the DVR.In this control,frequency adaption is considered for estimating the phase angle,system frequency,and fundamental component of the disturbed input voltage signals.The estimated fundamental component of the supply voltage is used to generate the DVR reference load voltage.The phase jump in the supply voltage is also considered for DVR compensation studies along with voltage sag,swell,and voltage distortions.For this purpose,the gains of the proportional integral(PI)controllers used in this control algorithm are estimated using a nature-inspired optimization approach for the desired response.A moth flame optimization algorithm is implemented for PI controller gain tuning owing to the advantage of finding the best solution by each moth’s search and updating it.Through Matlab simulation and hardware testing,the performance of the DVR with an adaptive observer is found to be satisfactory for supply voltage sag,swell,phase jump,and voltage distortions.

Link level performance comparison between LTE V2X and DSRC

Applications of VANETs(Vehicular Ad hoc Networks)have their own requirements and challenges in wireless communication technology.Although regarded as the rst standard for VANETs,IEEE 802.11p is still in the eld-trial stage.Recently,LTE V2X(Long-Term Evolution Vehicular to X)appeared as a systematic V2X solution based on TD-LTE(Time Division Long-Term Evolution)4G.It is regarded as the most powerful competitor to 802.11p.We conduct link level simulations of LTE V2X and DSRC(Dedicated Short-Range Communication)for several di erent types of scenarios.Simulation results show that LTE V2X can achieve the same BLER(Block Error Ratio)with a lower SNR(Signal Noise Ratio)than DSRC.A more reliable link can be guaranteed by LTE V2X,which can achieve the same BLER with lower receiving power than DSRC.The coverage area of LTE V2X is larger than that of DSRC.

Conjugate Decomposition and Its Applications

The conjugate decomposition(CD),which was given for symmetric and positive definite matrices implicitly based on the conjugate gradient method,is gen-eralized to every m×n matrix.The conjugate decomposition keeps some S VD prop-erties,but loses uniqueness and part of orthogonal projection property.From the com-putational point of view,the conjugate decomposition is much cheaper than the SVD.To illustrate the feasibility of the CD,some application examples are given.Finally,the application of the conjugate decomposition in frequency estimate is given with comparison of the SVD and FFT.The numerical results are promising.