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The use in radio communication systems of phase modulation of a signal intended for the transmission of useful information in a continuous mode creates the problem of frequency uncertainty of the received signal by frequency.In practice, it is not possible to implement frequency estimation in the conditions of chat uncertainty of the signal in the channel with low energy of the signal received in the continuous mode. Therefore, the estimation of the carrier frequency offset of the signal received relative to the nominal value is carried out before other synchronization procedures are included, namely: phase synchronization and clock synchronization. The paper generalizes the procedure and forms a two-step procedure for calculating the carrier frequency of the phase-modulated signal of a radio communication system for data transmission in a continuous mode, taking into account the condition of uncertainty of all signal parameters. Achieving the minimum observation interval in the given order of calculation of the carrier frequency is ensured by the use of the fast Fourier transform function. In order to analyze the effectiveness of this procedure, the process of estimating the carrier frequency of the phase-modulated signal of the radio communication system during data transmission in continuous mode and functional dependences of the maximum frequency in the signal spectrum and the minimum variance of carrier frequency estimation. This procedure allows a two-stage assessment of the carrier frequency according to the rule of maximum likelihood, taking into account the condition of uncertainty of all parameters of the signal received by the satellite communication system in a continuous mode with a minimum observation interval. Achieving the minimum observation interval in the given order of carrier frequency estimation is ensured by using the fast Fourier transform function and two estimation steps. The analysis of the efficiency of the estimation of the specified order was carried out on the basis of comparison of a ratio of the received minimum variance of an estimation of a carrier frequency and theoretically possible border of the minimum variance.

The use in radio communication systems of phase modulation of a signal intended for the transmission of useful information in a continuous mode creates the problem of frequency uncertainty of the received signal by frequency.In practice, it is not possible to implement frequency estimation in the conditions of chat uncertainty of the signal in the channel with low energy of the signal received in the continuous mode. Therefore, the estimation of the carrier frequency offset of the signal received relative to the nominal value is carried out before other synchronization procedures are included, namely: phase synchronization and clock synchronization. The paper generalizes the procedure and forms a two-step procedure for calculating the carrier frequency of the phase-modulated signal of a radio communication system for data transmission in a continuous mode, taking into account the condition of uncertainty of all signal parameters. Achieving the minimum observation interval in the given order of calculation of the carrier frequency is ensured by the use of the fast Fourier transform function. In order to analyze the effectiveness of this procedure, the process of estimating the carrier frequency of the phase-modulated signal of the radio communication system during data transmission in continuous mode and functional dependences of the maximum frequency in the signal spectrum and the minimum variance of carrier frequency estimation. This procedure allows a two-stage assessment of the carrier frequency according to the rule of maximum likelihood, taking into account the condition of uncertainty of all parameters of the signal received by the satellite communication system in a continuous mode with a minimum observation interval. Achieving the minimum observation interval in the given order of carrier frequency estimation is ensured by using the fast Fourier transform function and two estimation steps. The analysis of the efficiency of the estimation of the specified order was carried out on the basis of comparison of a ratio of the received minimum variance of an estimation of a carrier frequency and theoretically possible border of the minimum variance.

A line spectrum presents the form of a narrow-band time-varying signal due to Doppler effect when the single hydrophone node observes flight-radiated noise. The modulation law of the time-varying signal contains a large number of feature information of moving targets, which can be used for detection and classification. This paper studies the possibility of using instantaneous frequency measurements from the hydrophone node to improve the precision of the flight parameter estimates when the source spectrum contains a harmonic line of constant frequency. First of all, we build up and analyze the underwater sound field excited by the aircraft using the ray theory model; then the Doppler shift in the two isospeed media, which is caused by the aircraft, is established; finally, a robust time–frequency transform describes the time–frequency distribution of the received signal, and a geometric approach solves the flying parameters.

Time-frequency distributions (TFDs) allow direction of arrival (DOA) estimation algorithms to be used in scenarios when the total number of sources are more than the number of sensors. The performance of such time–frequency (t–f) based DOA estimation algorithms depends on the resolution of the underlying TFD as a higher resolution TFD leads to better separation of sources in the t–f domain. This paper presents a novel DOA estimation algorithm that uses the adaptive directional t–f distribution (ADTFD) for the analysis of close signal components. The ADTFD optimizes the direction of kernel at each point in the t–f domain to obtain a clear t–f representation, which is then exploited for DOA estimation. Moreover, the proposed methodology can also be applied for DOA estimation of sparse signals. Experimental results indicate that the proposed DOA algorithm based on the ADTFD outperforms other fixed and adaptive kernel based DOA algorithms.

Frequency-Modulated Continuous Wave (FMCW) lidar for long-distance measurements face challenges in signal acquisition and frequency estimation due to the high sampling rates required, leading to increased processing load, cost, and power consumption. Although sub-Nyquist sampling can alleviate the burden of high sampling rates, it requires a complex reconstruction process that degrades real-time performance. In this study, we propose a frequency estimation algorithm based on multi-coset sampling (MCS) that not only reduces the sampling rate but also avoids reconstructing the original signal. This algorithm performs a preliminary frequency estimation by exploiting the relationship among the signal support set, the measured sequences by sampling spectrum, and the original signal spectrum, and then refines the spectrum to obtain an accurate frequency estimate. Since the algorithm relies solely on the sampled sequences for estimation, frequency ambiguity may occur during the calculation. We analyze the causes of ambiguity and propose a support set determination method to eliminate this issue. Simulation results demonstrate that the proposed algorithm attains the Cramér–Rao lower bound (CRLB) at low signal-to-noise ratios. It achieves a 10-fold improvement over Nyquist method and a 35 dB SNR reduction compared with the original MCS, while maintaining stable performance down to −20 dB.

In this study, the authors discuss the topic of joint angle and Doppler frequency estimation in a monostatic multiple-input–multiple-output radar and a compressed sensing parallel factor (CS-PARAFAC) analysis-based algorithm is proposed. In this algorithm, the joint estimation problem is firstly linked to the compressed sensing trilinear model, then the estimated compressed matrix can be derived through trilinear alternating least square method and the angle and Doppler frequency are jointly estimated with sparsity from the compressed matrices. The proposed CS-PARAFAC algorithm, which can obtain automatically paired angle and Doppler frequency estimation, has very close estimation performance to the conventional parallel factor analysis algorithm. When compared to the conventional subspace-based algorithm, such as estimation of signal parameters via rotational invariance techniques, it can achieve much better joint angle and Doppler frequency estimation performance. As the compression, the proposed algorithm has much lower computational complexity and smaller memory capacity meanwhile. Numerical simulations verify the efficiency and illustrate performance improvement of the proposed algorithm.

Maximum likelihood (ML) carrier-frequency offset estimation for orthogonal frequency-division multiple access uplink is a complex multi-parameter estimation problem. The ML approach is a global optima search problem, which is prohibitive for practical applications because of the requirement of multidimensional exhaustive search for a large number of users. There are a few attempts to reduce the complexity of ML search by applying evolutionary optimisation algorithms. In this study, the authors propose a novel canonical particle swarm optimisation (CPSO)-based scheme, to reduce the computational complexity without compromising the performance and premature convergence. The proposed technique is a two-step process, where, in the first step, low resolution alternating projection frequency estimation (APFE) is used to generate a single better positioned particle for CPSO, followed by an actual CPSO procedure in second step. The mean square error performance of the proposed scheme is compared with existing low complexity algorithms namely APFE and linear particle swarm optimisation with mutation. Simulation results presented in this study show that the new scheme completely avoids premature convergence for a large number of users as high as 32.

This study proposes a robust estimation technique for the single-phase grid voltage fundamental frequency under grid disturbances. The technique relies on a demodulation method and a finite-impulse-response-based differentiation filter (DF). A frequency domain analysis for designing the DF is presented and is used to estimate the time-varying fundamental frequency from the instantaneous phase angle obtained by the demodulation method. The technique can reject the negative effects caused by the presence of DC offset and harmonics. The proposed DF shows less sensitivity to the presence of oscillations caused by the demodulation method when compared to a similar finite-impulse-response-based DF. Simulation and experimental results are provided to verify the performance of the proposed technique.

There are two important factors which impact the performance of phase-based frequency estimation algorithms remarkably: the approximations of noise phase model and imperfections in phase unwrapping process. Support vector regression (SVR) exits excellent capabilities for learning unknown data and forecasting the future ones, especially under the small sample condition. Therefore, the authors introduce it to predict the variation trend of instantaneous phase and unwrap phases efficiently. Even though with that being the case, errors still exist in phase unwrapping process because of its ambiguous phase characteristic. Furthermore, a SVR-based frequency estimation algorithm is proposed and makes it immune to these error phases by means of setting the SVR's parameters properly. The results show that, compared with other phased-based algorithms, not only does the proposed one maintain a wide estimation range and quality capabilities at low frequencies, but also improves accuracy at high frequencies and decreases the impact with the initial phase. The proposed algorithm is fit for not only linear phase signal but also polynomial phase signal, under both the Gaussian and non-Gaussian condition.

Calibration is an essential step for improving the accuracy of simulations generated using hydrologic models. A key modeling decision is selecting the performance metric to be optimized. It has been common to use squared error performance metrics, or normalized variants such as Nash–Sutcliffe efficiency (NSE), based on the idea that their squared-error nature will emphasize the estimates of high flows. However, we conclude that NSE-based model calibrations actually result in poor reproduction of high-flow events, such as the annual peak flows that are used for flood frequency estimation. Using three different types of performance metrics, we calibrate two hydrological models at a daily step, the Variable Infiltration Capacity (VIC) model and the mesoscale Hydrologic Model (mHM), and evaluate their ability to simulate high-flow events for 492 basins throughout the contiguous United States. The metrics investigated are (1) NSE, (2) Kling–Gupta efficiency (KGE) and its variants, and (3) annual peak flow bias (APFB), where the latter is an application-specific metric that focuses on annual peak flows. As expected, the APFB metric produces the best annual peak flow estimates; however, performance on other high-flow-related metrics is poor. In contrast, the use of NSE results in annual peak flow estimates that are more than 20 % worse, primarily due to the tendency of NSE to underestimate observed flow variability. On the other hand, the use of KGE results in annual peak flow estimates that are better than from NSE, owing to improved flow time series metrics (mean and variance), with only a slight degradation in performance with respect to other related metrics, particularly when a non-standard weighting of the components of KGE is used. Stochastically generated ensemble simulations based on model residuals show the ability to improve the high-flow metrics, regardless of the deterministic performances. However, we emphasize that improving the fidelity of streamflow dynamics from deterministically calibrated models is still important, as it may improve high-flow metrics (for the right reasons). Overall, this work highlights the need for a deeper understanding of performance metric behavior and design in relation to the desired goals of model calibration.