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.

Fuzzy-Model-Based Finite Frequency Fault Detection Filtering Design for Two-Dimensional Nonlinear Systems

This article studies the fault detection filtering design problem for Roesser type two-dimensional(2-D)nonlinear systems described by uncertain 2-D Takagi-Sugeno(T-S)fuzzy models.Firstly,fuzzy Lyapunov functions are constructed and the 2-D Fourier transform is exploited,based on which a finite frequency fault detection filtering design method is proposed such that a residual signal is generated with robustness to external disturbances and sensitivity to faults.It has been shown that the utilization of available frequency spectrum information of faults and disturbances makes the proposed filtering design method more general and less conservative compared with a conventional nonfrequency based filtering design approach.Then,with the proposed evaluation function and its threshold,a novel mixed finite frequency H_(∞)/H_(-)fault detection algorithm is developed,based on which the fault can be immediately detected once the evaluation function exceeds the threshold.Finally,it is verified with simulation studies that the proposed method is effective and less conservative than conventional non-frequency and/or common Lyapunov function based filtering design methods.

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.

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.

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.

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.

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.

Computationally Efficient MUSIC-Based Algorithm for Joint Direction of Arrival (DOA) and Doppler Frequency Estimation in Monostatic MIMO Radar

The problem of joint direction of arrival (DOA) and Doppler frequency estimation in monostatic multiple-input multiple-output (MIMO) radar is studied and a computationally efficient multiple signal classification (CE-MUSIC) algorithm is proposed.Conventional MUSIC algorithm for joint DOA and Doppler frequency estimation requires a large computational cost due to the two dimensional (2D) spectral peak searching.Aiming at this shortcoming,the proposed CE-MUSIC algorithm firstly uses a reduced-dimension transformation to reduce the subspace dimension and then obtains the estimates of DOA and Doppler frequency with only one-dimensional (1D) search.The proposed CE-MUSIC algorithm has much lower computational complexity and very close estimation performance when compared to conventional 2D-MUSIC algorithm.Furthermore,it outperforms estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm.Meanwhile,the mean squared error (MSE) and Cramer-Rao bound (CRB) of joint DOA and Doppler frequency estimation are derived.Detailed simulation results illustrate the validity and improvement of the proposed algorithm.

Fractional Frequency Offset Estimation for OFDM Systems in Non-Cooperative Communication

The traditional fractional frequency offset(FFO) estimation schemes for orthogonal frequency division multiplexing(OFDM) in non-cooperative communication have the problems of susceptible performance with the frequency offset values and the number of OFDM symbols,a novel fractional frequency offset blind estimation scheme based on EKF for OFDM systems is conceived.The nonlinear function of the frequency offset is calculated by employing the correlation.And then the frequency offset is estimated by means of the iterative algorithm of EKF.The finally fractional frequency offset is estimated by adopting repeated the above process.Simulation results demonstrate that the proposed scheme is robust to the frequency offset values without any requirements of a prior knowledge.

Modified OMP method for multi-target parameter estimation in frequency-agile distributed MIMO radar

Introducing frequency agility into a distributed multipleinput multiple-output(MIMO)radar can significantly enhance its anti-jamming ability.However,it would cause the sidelobe pedestal problem in multi-target parameter estimation.Sparse recovery is an effective way to address this problem,but it cannot be directly utilized for multi-target parameter estimation in frequency-agile distributed MIMO radars due to spatial diversity.In this paper,we propose an algorithm for multi-target parameter estimation according to the signal model of frequency-agile distributed MIMO radars,by modifying the orthogonal matching pursuit(OMP)algorithm.The effectiveness of the proposed method is then verified by simulation results.

ESTIMATION OF DOPPLER CENTROID FREQUENCY IN SPACEBORNE SCANSAR

Doppler centroid frequency is an essential parameter in the imaging processing of the Scanning mode Synthetic Aperture Radar (ScanSAR). Inaccurate Doppler centroid frequency will result in ghost images in imaging result. In this letter, the principle and algorithms of Doppler centroid frequency estimation are introduced. Then the echo data of ScanSAR system is analyzed. Based on the algorithms of energy balancing and correlation Doppler estimator in the estimation of Doppler centroid frequency in strip mode SAR, an improved method for Doppler centroid frequency estimation in ScanSAR is proposed. The method has improved the accuracy of Doppler centroid frequency estimation in ScanSAR by zero padding between burst data. Finally, the proposed method is validated with the processing of ENVIronment SATellite Advanced Synthetic Aperture Radar (ENVISAT ASAR) wide swath raw data.

Nonparametric Spectral Estimation Technique to Estimate Dominant Frequency for Atrial Fibrillation Detection

Atrial fibrillation (Afib) is related with heart failure, stroke, and high mortality rates. In frequency domain analysis, pre-requisite for Afib detection has been the estimation of reliable dominant frequency (DF) of atrial signals via different spectral estimation techniques. DF further characterizes Afib, and helps in its treatment. This paper aims at finding the most appropriate nonparametric FFT-based spectral estimation technique to estimate reliable DF for Afib detection. In this work, real-time intra-atrial electrograms have been acquired and pre-processed for frequency analysis. DF is estimated via Bartlett using Hanning window, and Welch methods. Regularity index (RI), a parameter to ensure reliability of DF, is calculated using Simpson 3/8 and Trapezoidal rules. The best method is declared based upon high accuracy of Afib detection using reliable DF. On comparison, Welch method is found to be more appropriate to estimate reliable DF for Afib detection with 98% accuracy.

Application of frequency estimation algorithm based on a single vector sensor in underwater acoustic communication

A method of high resolution frequency estimation based on a single vector sensor using ESPRIT （Estimating Signal Parameters via Rotational Invariance Techniques） algorithm is proposed and applied to the underwater acoustic （UWA） communication system of frequency modulation. Higher resolution frequency estimation can be obtained by this algorithm using fewer snapshots comparing with the sound intensity frequency estimation. Results of simulation and lake experiment show that the proposed algorithm can improve the communication data rate and reduce the bandwidth of the system. Because higher signal-to-noise ratio （SNR） is demanded, range UWA communication at oresent. this algorithm can be used in high speed short