Coarse Frequency Estimation Research Articles

Design and Implementation of a Low-Complexity and Reconfigurable Carrier Frequency Synchronizer for Satellite Communications

In this letter, we propose a novel frequency offset estimation algorithm based on the redefined auto-correlation (AC) operator. The proposed algorithm comprises two supporting algorithms: 1) coarse frequency estimation (CFE) based on the M&M algorithm to exploit the estimation range; 2) fine frequency estimation (FFE) based on the Fitz algorithm to improve the estimation accuracy. Significantly, the M&M algorithm and Fitz algorithm are implemented as a reconfigurable structure due to their similarities, which means that the FFE only occupies a few additional multiplexers and registers. Simulation results demonstrate that the proposed algorithm can estimate the full normalized frequency offset (NFO) in the range of [−0.5, +0.5]; moreover, the bit error rate (BER) performance of the proposed algorithm is almost consistent with the ideal synchronization under various modulation schemes. The comparison of implementation complexity shows that the multiplication resource consumption can be reduced by at least 74.31%.

Predicting impact of Hitchhike on coexisted heterogeneous IoT networks

In Internet of Things (IoT), plenty of heterogeneous nodes coexist and contend for wireless channel for data transmission. Therefore, improving the channel utilization is of great importance. Hitchhike is a promising mechanism of improving the channel utilization. With Hitchhike, a node can carry control signals on the preamble field of another transmitting packet, thereby eliminating the extra time of transmitting the control signals and improving the channel utilization. However, this control signals may seriously interfere with the packet transmission of coexisted heterogeneous networks. In this paper, considering that an 802.15.4 network with Hitchhike enabled and an 802.11 network coexist, we develop theoretical models to predict the impact of Hitchhike on the time and frequency synchronizations, the packet error rate, as well as the system throughput of the 802.11 network. Extensive experiments verify that the proposed prediction models are very accurate and effective. Experimental results show that when control signals are superposed on the 802.11 Preamble, they can hurt the 802.11 performance (specifically, frame synchronization, coarse frequency estimation, and system throughput). However, they have little effect on symbol timing synchronization. This study is very helpful for providing parameter optimization and protocol-design guidance for the coexistence of heterogeneous IoT networks. When multiple heterogeneous networks coexist, we may apply machine learning algorithms to help design better Hitchhike protocols. The insights from our theoretical model (say, the frequency spectrum of the Hitchhike control message is a good design parameter for minimizing the interference with coexisted heterogeneous networks) can be used to choose appropriate machine learning algorithms and construct appropriate algorithm modules, for improving the performance of Hitchhike protocols in complex IoT scenarios.

Space-Ground Coherent Optical Links: Ground Receiver Performance With Adaptive Optics and Digital Phase-Locked Loop

In the framework of optical high data rate satellite-to-ground links, we investigate the performance of a coherent receiver which combines an adaptive optics system and a digital carrier synchronization technique. We propose a digital carrier synchronization system based on a phase-locked loop and use end-to-end simulations to characterize the impact of the atmospheric turbulence in the case of a representative low Earth orbit satellite-to-ground transmission link. The results show that classical digital phase-locked loop techniques can be a reliable solution to accurately compensate for the Doppler frequency shift between the incoming signal and the local oscillator at the ground station, in the presence of a preliminary coarse frequency estimation. Adaptive optics compensation enables the loop to lock after a few milliseconds and to accurately track the phase fluctuations. The bit-error-rate performance is not degraded by the digital loop but suffers from the residual signal amplitude fluctuations.

Efficient and Accurate Detection and Frequency Estimation of Multiple Sinusoids

The method for detection of complex sinusoids in additive white Gaussian noise and estimation of their frequencies is proposed. It contains two stages: 1) sinusoid detection (model order estimation) and coarse frequency estimation, and 2) fine frequency estimation. The proposed method operates in the frequency domain, i.e., it uses the discrete Fourier transform (DFT) as the main tool. Sinusoid detection is performed so that a fixed probability of false alarm is provided (Neymann–Pearson criterion). For both coarse and fine frequency estimations, the three-point periodogram maximization approach is used. Simulations are carried out for variable signal-to-noise ratio, variable frequency displacement between the sinusoids and variable offset from the frequency grid. The proposed method meets the Cramer-Rao lower bound in frequency estimation and practically does not depend on the frequency displacement except for very small displacement values. In terms of model order estimation accuracy, it outperforms the state-of-the-art approaches. The most expensive operation in the method is the calculation of the DFT. Therefore, in terms of calculation complexity, the proposed method is on par with the most efficient algorithms for multiple frequency estimations.

Flexible and Accurate Frequency Estimation for Complex Sinusoid Signal by Interpolation Using DFT Samples

A flexible and accurate frequency estimator is first proposed for frequency estimation of a complex sinusoid weighted with a rectangular window function in additive white Gaussian noise. This proposed frequency estimator can be operated in the application of an arbitrary length discrete Fourier transform where the original input data is padded with any zeroes, which makes it more flexible in practice. The proposed frequency estimator utilizes the maximum sample value and its two adjacent samples in the frequency domain to perform the fine frequency estimation with unbiased results obtained. Then a modified frequency estimator is proposed to estimate the frequency when the complex sinusoid signal is weighted with different nonrectangular window functions. Although the modified frequency estimator is nonanalytic and biased, it can still improve the estimation performance for certain applications. Simulation results demonstrate that both of the proposed frequency estimators are effective to achieve the high frequency estimation accuracy. And the root mean square errors of the proposed frequency estimators approach the Cramer-Rao bound when the signal-to-noise ratio is large enough to make the coarse frequency estimation work effectively.

Frequency estimator of sinusoid based on interpolation of three DFT spectral lines

A frequency estimator of sinusoid based on interpolation of three discrete Fourier transform (DFT) spectral lines is proposed. The FFT is performed first on the sampled sinusoid signal and the coarse frequency estimation is made by searching the location of the discrete spectral line with maximum amplitude (the primary spectral line). Fine frequency estimation is made by the interpolation using the primary spectral line and two auxiliary spectral lines located at arbitrary position within the main lobe or the first sidelobe of the frequency spectrum. The formula for calculating the MSE of the proposed estimator in additive white noise is derived. The influence of the interval between the primary spectral line and the auxiliary spectral lines on the MSE is analyzed through theoretical analysis and simulation experiments. To further improve the estimation performance, iterative procedures are used. Simulation results show that the RMSE of the proposed estimator is closer to CRLB than the competing estimators especially at high SNR.

A fast and accurate frequency estimation algorithm for sinusoidal signal with harmonic components.

Frequency estimation is a fundamental problem in many applications, such as traditional vibration measurement, power system supervision, and microelectromechanical system sensors control. In this paper, a fast and accurate frequency estimation algorithm is proposed to deal with low efficiency problem in traditional methods. The proposed algorithm consists of coarse and fine frequency estimation steps, and we demonstrate that it is more efficient than conventional searching methods to achieve coarse frequency estimation (location peak of FFT amplitude) by applying modified zero-crossing technique. Thus, the proposed estimation algorithm requires less hardware and software sources and can achieve even higher efficiency when the experimental data increase. Experimental results with modulated magnetic signal show that the root mean square error of frequency estimation is below 0.032 Hz with the proposed algorithm, which has lower computational complexity and better global performance than conventional frequency estimation methods.

An Accurate Method for Frequency Estimation of a Real Sinusoid

It is well known that the positive- and negative-frequency components of a real sinusoid spectrally interact with each other; thus, introducing bias in frequency estimation based on the periodogram maximization. We propose to filter out the negative-frequency component. To that end, a coarse frequency estimation is obtained using the windowing approach, known to reduce the estimation bias, and then used to filter out the negative-frequency component via modulation and discrete Fourier transform bin excision approach. Fine estimation is performed using accurate frequency estimators, developed for complex sinusoids, on the filtered signal. The proposed method is characterized by the $ O(N\log _2N)$ complexity in terms of additions/multiplications and the $ O(N)$ complexity in terms of sine/cosine operations and comparisons. Moreover, it achieves the Cramer–Rao lower bound and is not sensitive to sinusoid frequency and initial phase, thus, outperforming the state-of-the-art methods.

从傅里叶望远镜接收信号中获取目标速度的方法

The signals received by Fourier telescopy are analyzed and demonstrated to contain not only image information but also two-dimensional velocity information of the measured target. The velocities on each component can be calculated by the periodic signal frequencies that can be extracted from received signals. Then the two-dimension velocity is composited. The frequency of the signal is extracted by fast Fourier transform analysis for coarse frequency estimate, and by ratio frequency correction algorithms using Hanning window for precise frequency correction. Simulation is made to measure the flight velocity of the missile by Fourier telescopy. The result shows that the target velocity acquired by this method has almost no error without noise, while it has relatively high precision with noise when SNR is higher than 5 dB. The velocity acquisition method from receiving signal of Fourier telescopy is demonstrated to have high precision, a good anti-noise property and to be theoretically feasible.

Initial-Estimation-Based Adaptive Carrier Recovery Scheme for DVB-S2 System

A data-aided (DA) carrier recovery (CR) method, which can select different coarse frequency estimation (CFE) paths adaptively according to the initial-estimation of frequency offset, is proposed for the 2nd Generation Digital Video Broadcasting Satellite (DVB-S2) system to accomplish the convergence within at most 400 pilot blocks. The well-known two-step CR scheme is used for the consideration of precision and speed, whereas both the CFE and the fine frequency estimation (FFE) adopt L&R algorithm as their basic frequency estimator so that the same correlation operation can be used by both of them to decrease the realization complexity. Optimum threshold values for different CFE paths are determined by analyzing the ill-selection probability and robust Root Mean Square Error (RMSE) performance has been confirmed by our simulations.

Closed-Form Real Single-Tone Frequency Estimator Based on Phase Compensation of Multiple Correlation Lags

A new frequency estimator for a single real-valued sinusoid signal in white noise is proposed. The new estimator uses the Pisarenko Harmonic Decomposer (PHD) estimator to get a coarse frequency estimate and then makes use of multiple correlation lags to obtain an adjustment term. For the limited-length single sinusoid, its correlation has the same frequency as itself but with a non-zero phase. We propose to use Taylor series to expand the correlation at the PHD coarse estimated frequency with amplitude and phase of the correlation into consideration. Simulation results show that this new method improves the estimation performance of the PHD estimator. Moreover, when compared with other existing estimator, the mean square frequency error of the proposed method is closer to the Cramer-Rao Lower Bound (CRLB) for certain SNR range.

A closed-form expanded autocorrelation method for frequency estimation of a sinusoid

A closed-form expanded autocorrelation method for real single-tone frequency estimation is proposed. Firstly, the modified covariance (MC) method based on multiple autocorrelation lags is applied to provide a coarse frequency estimate. Then, a closed-form adjustment term based on a least square cost function is derived to get the fine frequency estimate. Simulation results show that the performance of the proposed algorithm, when compared with several existing closed-form time-domain estimators, is closer to the Cramer–Rao bound (CRB). Moreover, the proposed method has lower computation complexity than other autocorrelation-based approaches, which also use multiple autocorrelation lags.

A Method For Fine Resolution Frequency Estimation From Three DFT Samples

The parameter estimation of a complex exponential waveform observed under white noise is typically tackled in two stages. In the first stage, a coarse frequency estimate is found by the application of an N-point DFT to the input of length <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> . In the second stage, a fine search around the peak determined in the first stage is conducted. The method proposed in this paper presents a simpler alternative. The method suggests a nonlinear relation involving three DFT samples already calculated in the first stage to produce a real valued, fine resolution frequency estimate. The estimator approaches Jacobsen's estimator for large <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> and presents a bias correction which is especially important for small and medium values of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> .

Robust M-periodogram with dichotomous search

The problem of sinusoidal frequency estimation in heavy-tailed noise environment is addressed. A method based on the robust M-periodogram is proposed. Specifically, a suboptimal coarse frequency estimate provided by the robust M-periodogram is improved using the modified dichotomous search. Simulations that consider most common heavy-tailed noise models demonstrate that the proposed method outperforms several recently proposed methods. The method can be readily extended to deal with multiple sinusoids.

A frequency offset estimation algorithm for OFDM systems

A new fine carrier frequency offset estimation algorithm in Orthogonal Frequency Division Multiplexing (OFDM) system is proposed. The correlation item is the training sequence instead of the received signal in the new algorithm. Simulation results show that the performance of the new algorithm is 4dB–9dB better than that of Schmidl’s algorithm. Coarse frequency offset estimation is also discussed in this paper, which is the improvement of Zhang’s method. The estimation range using the improvement method is twice as that using the Zhang’s method. Based on the hardware of the receiver and the improved algorithm, a method using Fast Fourier Transform (FFT) is proposed to implement the coarse frequency estimation. The chip area of OFDM system can be reduced by using the proposed method.

Robust Timing and Frequency Synchronization Scheme for DTMB System

In this paper a robust timing and frequency synchronization algorithm for DTMB system is developed. A two-step frequency offset estimation and compensation process is proposed to perform carrier recovery. Firstly coarse frequency estimation is achieved by utilizing the shift-and-add property of m-sequence. The second step finds the frame start position and the remaining frequency offset simultaneously. Meanwhile a timing tracking strategy is proposed to effectively track the dynamic changes in mobile environment. Thus the proposed scheme can resist large frequency offset and achieve accurate timing and frequency estimation. Simulation results under different channel situations verify the performance of the proposed scheme.

Estimation of single-tone signal frequency by using the L-DFT

Frequency estimation of complex sinusoidal signal parameters for mixed Gaussian and impulse noise environment is considered. We assume that the sinusoid has constant amplitude. The first stage in the proposed algorithm is calculation of the L-DFT forms for various parameters. Then, an optimal value of the L-DFT parameter is estimated as a value minimizing the L-DFT energy. Position of the L-DFT maximum calculated for the optimal parameter is used as a coarse frequency estimate. Fine estimation is performed by a recently proposed iterative procedure. Numerical analysis confirms accuracy of the proposed technique.