Improving the utility of locally differentially private protocols for longitudinal and multidimensional frequency estimates

This paper investigates the problem of collecting multidimensional data throughout time(i.e.,longitudinal studies)for the fundamental task of frequency estimation under Local Differential Privacy(LDP)guarantees.Contrary to frequency estimation of a single attribute,the multidimensional aspect demands particular attention to the privacy budget.Besides,when collecting user statistics longitudinally,privacy progressively degrades.Indeed,the“multiple”settings in combination(i.e.,many attributes and several collections throughout time)impose several challenges,for which this paper proposes the first solution for frequency estimates under LDP.To tackle these issues,we extend the analysis of three state-of-the-art LDP protocols(Generalized Randomized Response–GRR,Optimized Unary Encoding–OUE,and Symmetric Unary Encoding–SUE)for both longitudinal and multidimensional data collections.While the known literature uses OUE and SUE for two rounds of sanitization(a.k.a.memoization),i.e.,L-OUE and L-SUE,respectively,we analytically and experimentally show that starting with OUE and then with SUE provides higher data utility(i.e.,L-OSUE).Also,for attributes with small domain sizes,we propose Longitudinal GRR(L-GRR),which provides higher utility than the other protocols based on unary encoding.Last,we also propose a new solution named Adaptive LDP for LOngitudinal and Multidimensional FREquency Estimates(ALLOMFREE),which randomly samples a single attribute to be sent with the whole privacy budget and adaptively selects the optimal protocol,i.e.,either L-GRR or L-OSUE.As shown in the results,ALLOMFREE consistently and considerably outperforms the state-of-the-art L-SUE and L-OUE protocols in the quality of the frequency estimates.

High-Precision Doppler Frequency Estimation Based Positioning Using OTFS Modulations by Red and Blue Frequency Shift Discriminator

Orthogonal Time Frequency and Space(OTFS) modulation is expected to provide high-speed and ultra-reliable communications for emerging mobile applications, including low-orbit satellite communications. Using the Doppler frequency for positioning is a promising research direction on communication and navigation integration. To tackle the high Doppler frequency and low signal-to-noise ratio(SNR) in satellite communication, this paper proposes a Red and Blue Frequency Shift Discriminator(RBFSD) based on the pseudo-noise(PN) sequence.The paper derives that the cross-correlation function on the Doppler domain exhibits the characteristic of a Sinc function. Therefore, it applies modulation onto the Delay-Doppler domain using PN sequence and adjusts Doppler frequency estimation by red-shifting or blue-shifting. Simulation results show that the performance of Doppler frequency estimation is close to the Cramér-Rao Lower Bound when the SNR is greater than -15dB. The proposed algorithm is about 1/D times less complex than the existing PN pilot sequence algorithm, where D is the resolution of the fractional Doppler.

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.

A NEW ESPRIT METHOD FOR BLIND ESTIMATES OF DOA-DOPPLER FREQUENCY WITH UNKNOWN ARRAY MANIFOLD

A novel rotational invariance technique for blind estimates of direction of arrival (I)OA) and Doppler frequency with unknown array manifold due to array sensor uncertainties is proposed, taking Doppler frequency difference between a successive pulses as rotational parameter. The effectiveness of the new method is confirmed by computer simulation. Compared with the existing 2-D DOA-frequeucy estimate techniques, the computation load of the proposed method can be saved greatly.

Frame Length Dependency for Fundamental Frequency Extraction in Noisy Speech

The fundamental frequency plays a significant part in understanding and perceiving the pitch of a sound. The pitch is a fundamental attribute employed in numerous speech-related works. For fundamental frequency extraction, several algorithms have been developed which one to use relies on the signal’s characteristics and the surrounding noise. Thus, the algorithm’s noise resistance becomes more critical than ever for precise fundamental frequency estimation. Nonetheless, numerous state-of-the-art algorithms face struggles in achieving satisfying outcomes when confronted with speech recordings that are noisy with low signal-to-noise ratio (SNR) values. Also, most of the recent techniques utilize different frame lengths for pitch extraction. From this point of view, This research considers different frame lengths on male and female speech signals for fundamental frequency extraction. Also, analyze the frame length dependency on the speech signal analytically to understand which frame length is more suitable and effective for male and female speech signals specifically. For the validation of our idea, we have utilized the conventional autocorrelation function (ACF), and state-of-the-art method BaNa. This study puts out a potent idea that will work better for speech processing applications in noisy speech. From experimental results, the proposed idea represents which frame length is more appropriate for male and female speech signals in noisy environments.

Parameter estimation method for a linear frequency modulation signal with a Duffing oscillator based on frequency periodicity

In view of the complexity of existing linear frequency modulation(LFM)signal parameter estimation methods and the poor antinoise performance and estimation accuracy under a low signal-to-noise ratio(SNR),a parameter estimation method for LFM signals with a Duffing oscillator based on frequency periodicity is proposed in this paper.This method utilizes the characteristic that the output signal of the Duffing oscillator excited by the LFM signal changes periodically with frequency,and the modulation period of the LFM signal is estimated by autocorrelation processing of the output signal of the Duffing oscillator.On this basis,the corresponding relationship between the reference frequency of the frequencyaligned Duffing oscillator and the frequency range of the LFM signal is analyzed by the periodic power spectrum method,and the frequency information of the LFM signal is determined.Simulation results show that this method can achieve high-accuracy parameter estimation for LFM signals at an SNR of-25 dB.

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.

A High Spectral Efficient Frequency-Domain Channel-Estimation Method for the Polarization-Division-Multiplexed CO-OFDM-OQAM System

Contrary to the other multi-carrier modulation systems, the coherent optical orthogonal frequency division multiplexing communication system with an offset quadrature amplitude modulation (CO-OFDM-OQAM) possesses inherent imaginary interference (IMI). This has an important impact on the channel estimation process. Currently, a variety of frequency-domain channel estimation methods have been proposed. However, there are various problems that still exist. For instance, in order to reduce the influence of IMI, it is necessary to insert more guard intervals between the training sequence and the payload, leading to the occupation of excessive spectrum resources. In order to address this problem, this work designs a high spectral efficient frequency-domain channel estimation method for the polarization-division-multiplexing CO-OFDM-OQAM systems. First, the working principle of the proposed method is described in detail. Then, its spectral efficiency, power peak-to-average ratio, and channel estimation performance are studied based on simulations. The simulation results show that the proposed method improves the spectral efficiency without worsening the power peak-to-average ratio. The channel estimation capability of this method is verified in three scenarios of long-distance transmissions, including back-to-back, 100 km, and 200 km transmissions. .

Rainfall Infiltration Return Frequency Estimates

Depth-duration analysis, such as accomplished for rainfall, can be useful in the analysis of infiltration of rainfall. The assessment of infiltration depth-duration in terms of return frequency is of interest. In this paper, depth-duration values of daily rainfall infiltration are estimated using the National Resources Conservation Service (NRCS) Curve Number (CN) approach for estimating daily runoff. The CN methods may be generally applicable to soils that are free draining. From the estimated history of daily infiltration, a depth-duration analysis is accomplished for all duration sizes from 1 day to 365 days. These annual outcomes are then analyzed as to a possible underlying probability distribution. For the rain gages considered, the depth-duration infiltration estimates (using the CN approach) appear to be normally distributed. From the fitted distribution, estimates of rare events of rainfall infiltration may be made, and possible linkage to earth movement events accomplished with respect to return frequency of infiltration, which in turn can aid in the design and risk assessment of fixed works involving soil water accumulation.

Architecture design of GPS software receiver and implementation of its acquisition algorithm with fine frequency estimation

The design of a global positioning system （GPS） software receiver is introduced. This design uses the concept of software radio, and it consists of the following parts： front-end, acquisition, tracking, synchronization, navigation solution and some assisting modules. In the acquisition module, the acquisition algorithm based on circular correlation is utilized. The input data and the local code are converted into the frequency domain by means of the fast Fourier transform （FFT）. After performing circular correlation, the initial phase of the C/A code can be obtained and the cartier frequency can be found in 1 kHz frequency resolution, which is too coarse to use for the tracking loop. In order to improve the frequency resolution, the fine frequency estimation through a phase relationship is then achieved, by which, the frequency resolution is improved dramatically. Experiments show that the inaccuracy of the carrier frequency can be estimated within a few hertz by the fine frequency estimation method, and the fine frequency attained can be directly used for the tracking loop.

Polynomial rooting based frequency offset estimation for MIMO OFDM systems

Based on the frequency domain training sequences, the polynomial-based carrier frequency offset （CFO） estimation in multiple-input multiple-output （ MIMO ） orthogonal frequency division multiplexing （ OFDM ） systems is extensively investigated. By designing the training sequences to meet certain conditions and exploiting the Hermitian and real symmetric properties of the corresponding matrices, it is found that the roots of the polynomials corresponding to the cost functions are pairwise and that both meger CFO and fractional CFO can be estimated by the direct polynomial rooting approach. By analyzing the polynomials corresponding to the cost functions and their derivatives, it is shown that they have a common polynomial factor and the former can be expressed in a quadratic form of the common polynomial factor. Analytical results further reveal that the derivative polynomial rooting approach is equivalent to the direct one in estimation at the same signal-to-noise ratio（SNR） value and that the latter is superior to the former in complexity. Simulation results agree well with analytical results.

Research on Estimation of Frequency Response Function

Based on an investigation of existing methods for estimating fre- quency response functions(FRF)at home and abroad,two methods are ad- vanced.The one,denoted as H_(12),avoids underestimates at resonances and overestimates at antiresonances,while the other,denoted as H_F,regards the noise ratio of output to input as varying with the frequency.Finally,a soft- ware for estimating frequency response functions is introduced.A modal test for a steel plate excited with a random signal is made,and frequency response function estimates are made,making use of the above software.The test re- sults conform well with the theoretical analysis.

Adaptive compensating method for Doppler frequency shift using LMS and phase estimation

The novel compensating method directly demodulates the signals without the carrier recovery processes, in which the carrier with original modulation frequency is used as the local coherent carrier. In this way, the phase offsets due to frequency shift are linear. Based on this premise, the compensation processes are： firstly, the phase offsets between the baseband neighbor-symbols after clock recovery is unbiasedly estimated among the reference symbols; then, the receiving signals symbols are adjusted by the phase estimation value; finally, the phase offsets after adjusting are compensated by the least mean squares （LMS） algorithm. In order to express the compensation processes and ability clearly, the quadrature phase shift keying （QPSK） modulation signals are regarded as examples for Matlab simulation. BER simulations are carried out using the Monte-Carlo method. The learning curves are obtained to study the algorithm＇s convergence ability. The constellation figures are also simulated to observe the compensation results directly.

A comparative study of data-driven battery capacity estimation based on partial charging curves

With its generality and practicality, the combination of partial charging curves and machine learning(ML) for battery capacity estimation has attracted widespread attention. However, a clear classification,fair comparison, and performance rationalization of these methods are lacking, due to the scattered existing studies. To address these issues, we develop 20 capacity estimation methods from three perspectives:charging sequence construction, input forms, and ML models. 22,582 charging curves are generated from 44 cells with different battery chemistry and operating conditions to validate the performance. Through comprehensive and unbiased comparison, the long short-term memory(LSTM) based neural network exhibits the best accuracy and robustness. Across all 6503 tested samples, the mean absolute percentage error(MAPE) for capacity estimation using LSTM is 0.61%, with a maximum error of only 3.94%. Even with the addition of 3 m V voltage noise or the extension of sampling intervals to 60 s, the average MAPE remains below 2%. Furthermore, the charging sequences are provided with physical explanations related to battery degradation to enhance confidence in their application. Recommendations for using other competitive methods are also presented. This work provides valuable insights and guidance for estimating battery capacity based on partial charging curves.

Blind channel estimation for multiple antenna OFDM system subject to unknown carrier frequency offset

The problem of channel estimation for multiple an- tenna orthogonal frequency division multiplexing （OFDM） systems subject to unknown carrier frequency offset （CFO） is addressed. Multiple signal classification （MUSIC）-Iike algorithm, which generally has been used for direction estimation or frequency estimation, is used for channel estimation in multiple antenna OFDM systems. A reduced dimensional （RD）-MUSIC based algorithm for channel estimation is proposed in multiple antenna OFDM systems with unknown CFO. The Cramer-Rao bound （CRB） of channel estimation in multiple antenna OFDM systems with unknown CFO is derived. The proposed algorithm has a superior performance of channel estimation compared with the Capon method and the least squares method.

Estimation of DOA and Doppler Frequency on Nonideal UCA

The problem of estimating direction of arrivals (DOA) and Doppler frequency for many sources is considered in the presence of general array errors (such as amplitude and phase error of sensors, setting position error of sensors). Adopting direct array manifold in a uniform circular array (UCA), the estimation of Doppler frequency can be obtained by DOA matrix. Based on analyzing the statistic characters of general array errors, the estimation of DOA can be obtained by Weight Total Least Squares. Numerical results illustrate that the estimator is robust to general array errors and show the capabilities of the estimator.

Velocity estimation of moving targets with stepped-frequency radar based on Doppler frequency difference

By analyzing the signal model of stepped-frequency waveform, a novel method for velocity measurement is proposed. The method is based on Doppler frequency difference which is achieved by using Hough transform. As the estimated velocity is inversely proportional to the frequency step size instead of the carrier frequency of the transmitted signal as the pulse-Doppler （PD） processing, the new algorithm can achieve much wider unambiguous velocity range. Furthermore, non-coherent integration of the sub-pulses with different carrier frequencies can be implemented by Hough trans- form to improve the anti-noise performance. Besides, field experimental results show that the high range resolution profile （HRRP） of a bullet with high speed can be reconstructed correctly without distortion.

Decoupled estimation of frequency-dependent IQI and channel for OFDM systems with direct-conversion transceivers

The in-phase and quadrature-phase imbalance (IQI) is one of the major radio frequency impairments existing in orthogonal frequency division multiplexing (OFDM) systems with direct-conversion transceivers. During the transmission of the communication signal, the impact of IQI is coupled with channel impulse responses (CIR), which makes the traditional channel estimation schemes ineffective. A decoupled estimation scheme is proposed to separately estimate the frequency-dependent IQI and wireless channel. Firstly, the generalized channel model is built to separate the parameters of IQI and wireless channel. Then an iterative estimation scheme of frequency-dependent IQI is designed at the initial stage of communication. Finally, based on the estimation result of IQI, the least square algorithm is utilized to estimate the channel-related parameters at each time of channel variation. Compared with the joint estimation schemes of IQI and channel, the proposed decoupled estimation scheme requires much lower training overhead at each time of channel variation. Simulation results demonstrate the good estimation performance of the proposed scheme.

Efficient integer frequency offset estimation for OFDM systems

An efficient scheme of integer frequency offset estimate for orthogonal frequency division multiplexing （OFDM） systems is proposed based on a training symbol with several identicalparts. In this scheme, the received training symbol is first reshaped into several sub-symbols.It shows that the reshaping process in-troduees time diversity multiplexing.After a special fast Fourier transform （FFT） algorithm is applied to the sub-symbol,the integer frequency is estimated by finding the maximum magnitude of the resulting fre-quency domain signal.To improve the estimate performance,diversity combining methods are presented to makefull use of the multiple frequency domain sub-symbols.Compared to the traditional scheme, theproposed one has an improved estimate performance demonstrated by the computation simulation, while maintaining a very low complexity.

Blind carrier frequency estimation for phase shift keying signals in low signal to noise ratio

In order to solve the problem of carrier frequency blind estimation of PSK signals in electronic reconnaissance, a new estimation method was proposed. The phase shift keying（PSK） signal was divided into several overlapping intervals which had equal length, and the spectrum concentration measures of every interval were extracted by the FFT. And then, using the grid-density clustering, the spectrum concentration measures were classified into two categories, the narrowband spectrum interval and the wideband spectrum interval. The narrowband spectrum interval was regarded as the characteristic class. The spectrums of the characteristic class were accumulated to estimate the carrier frequency of PSK signal. The proposed method had avoided the non linear operation in the traditional PSK signal carrier frequency estimation algorithm. Thus, the signal to noise ratio （SNR） threshold was remarkably decreased. Moreover, the proposed method did not need the prior knowledge of the signal, which was suitable to the electronic reconnaissance occasion. Experimental results had verified the validity of the proposed estimation method in low SNR.