Parameter Estimation of Multicomponent Polynomial Phase Signals

This paper considers the parameter estimation of multicomponent polynomial-phase signals (mc-PPSs) with orders greater than two. The proposed method combines the product cubic phase function (PCPF) and high-order ambiguity function (HAF) when the mc-PPS orders exceed three. In the proposed method, the HAF is first applied to the observed mc-PPS to produce a cubic phase signal. Second, the algorithm is modified to estimate the parameters of mc-PPS using the CPF. To obtain accurate estimates of the two highest-order parameters (i.e., $$ a_{P} $$ and $$ a_{P - 1} $$ of each component), all possible $$ a_{P} $$ and $$ a_{P - 1} $$ must be obtained in this step in all combinations of the instantaneous frequencies; then, the maximum absolute value of all sum values must be identified by dechirping with all possible $$ a_{P} $$ and $$ a_{P - 1} $$ . In addition, non-uniformly-spaced signal sample methods are used to employ fast Fourier transformation in the CPF. The proposed method is different from the PCPF–HAF method proposed by other researchers; it is referred to as the improved PCPF–HAF method and can remedy the shortcomings of the traditional method when estimating mc-PPS parameters. Additionally, the PCPF–HAF method cannot be used to treat multicomponent third-order polynomial-phase signals, but the proposed method can treat them using non-uniformly-spaced signal sample methods. The cross-terms can also be restrained more effectively than with the CPF, resulting in higher accuracy of the estimated parameters and a lower signal-to noise ratio threshold. Theoretical analysis and simulations are presented to support these claims.

This paper addresses the issue of interference suppression in noise radars. The proposed methods can be divided into non-parametric and parametric ones. The considered non-parametric methods are based on linear time-frequency (TF) tools, namely the short-time Fourier transform (STFT) and local polynomial Fourier transform (LPFT). The STFT is the simplest TF method, but, due to the resolution problem, it performs poorly with highly nonstationary interferences. The LPFT resolves the resolution problem, however at the cost of increased complexity. In parametric methods, the phase of interference is locally approximated by a polynomial, which is motivated by the Weierstrass's theorem. Using the phase approximation, the corrupted received signal is demodulated and successively filtered. Two methods for polynomial phase approximation are considered, the high-order ambiguity function (HAF) and product high-order ambiguity function (PHAF). The method based on the HAF is computationally efficient; however, it suffers from the identifiability problem when multicomponent signals are considered. The identifiability problem can be resolved using the PHAF.

An efficient method for parameter estimation and separation of multi-component LFM signals

Parameter estimation of chirp signals based on fractional Fourier transform

This letter introduces a new approach for the demodulation of fringe patterns recorded in holographic interferometry using high-order ambiguity function (HAF). The proposed approach is capable of retrieving the phase from a single fringe pattern. The main advantage of this approach is that it directly provides an estimation of the continuous phase distribution and thereby avoids the necessity of using a cumbersome 2D phase unwrapping procedure. This method first computes the discrete-time analytic signal of the recorded fringe pattern. Then, by modelling this analytic signal as a polynomial phase signal embedded in additive complex white Gaussian noise, a parametric estimation procedure based on HAF is employed to directly estimate the unwrapped phase distribution. Numerical simulations and experimental results demonstrate the potential of the proposed approach.

LFM signals are widely used in the fields of radar and communication etc., which make signals detection and parameters estimation a very important technology in multicomponent LFM signals. To solve the problems of error detection caused by the cross-terms in WVD-Hough methods and other modified WVD distribution methods, and low parameter estimation precision due to poor timefrequency concentration in S-Hough transform, this paper proposed a detection and parameter estimation algorithm of multicomponent LFM signals based on reassigned generalized S-transform and Hough transform. Firstly calculate the time-frequency distribution of multicomponent LFM signals by generalized S-transform. Secondly reassign the S-transform time-frequency distribution to improve the time-frequency concentration property. Finally implement signal detection and parameter estimation by Hough transform to the reassigned S-transform TFD. The simulation results show that this algorithm has good performance in detecting multicomponent LFM signals and estimating the parameters in low SNR case.

The detection and parameter estimation of spread spectrum signals under non-cooperative conditions are key problems to which more attentions are paid in the field of signal processing. A cyclic-cumulant based DS-SS (direct sequence spread spectrum) signal detection scheme is developed in this paper by extending the asymptotically optimal chi-squared test for the presence of cyclostationarity to DS-SS signal detection. The explicit formula of the second-order cyclic-cumulant is derived, and the influence of time interval on the cycle-frequency estimation from the cyclic-cumulant is analyzed in detail. On the base of this, a new cyclic-cumulant based DS-SS signal parameter estimation method is proposed, which can perform blind detection and blind parameter estimation without a priori knowledge of the signal such as pseudorandom sequence and frequencies. Moreover, the method also avoids multi-dimensional searching in parameter estimation. Simulation results have proved the validity of the method.

In an ultra-wideband (UWB) system, the two-dimensional (2D) multiple signal classification (MUSIC) algorithms based on high-precision 2D spectral peak search can jointly estimate the time of arrival (TOA) and angle of arrival (AOA). However, the computational complexity of 2D-MUSIC is very high, and the corresponding data model is only based on the dual antennas. To solve these problems, a low-complexity algorithm for joint AOA and TOA estimation of the multipath ultra-wideband signal is proposed. Firstly, the dual antenna sensing data model is extended to the antenna array case. Then, based on the array-sensing data model, the proposed algorithm transforms the 2D spectral peak search of 2D-MUSIC into a secondary optimization problem to extract the estimation of AOA via only 1D search. Finally, the acquired AOA estimations are brought back, and the TOA estimations are also obtained through a 1D search. Moreover, in the case of an unknown transmitted signal waveform, the proposed method can still distinguish the main path signal based on the time difference of arrival of different paths, which shows wider applications. The simulation results show that the proposed algorithm outperforms the Root-MUSIC algorithm and the estimation of signal parameters using the rotational invariance techniques (ESPRIT) algorithm, and keeps the same estimation accuracy but with greatly reduced computational complexity compared to the 2D-MUSIC algorithm.

Multi-buoy sonar systems achieve target localization by receiving broadband Linear Frequency Modulation signals emitted from the transmitter. Accurate estimations of the parameters of Linear Frequency Modulation signals significantly enhance the localization accuracy. Linear Frequency Modulation signals can be focused into the fractional domain through Fractional Fourier Transform, but this increases the computational complexity. In marine environments, the low signal-to-noise ratio and multipath effects degrade the parameter estimation accuracy further. To address these issues, this paper proposes a fast estimation algorithm based on the Fractional Fourier Transform and a Gradient Subtraction-Average-Based Optimizer. This algorithm leverages the impulsive characteristics of Linear Frequency Modulation signals after Fractional Fourier Transform transformation, using the Fractional Fourier Transform as the fitness function. The Gradient Subtraction-Average-Based Optimizer algorithm includes three enhancement strategies: chaotic mapping initialization, a Golden Sine Algorithm, and an adaptive t-distribution variational operator. The simulation results demonstrate that the Gradient Subtraction-Average-Based Optimizer algorithm improves the issues of low diversity in the search agents, imbalanced global and local search capabilities, and susceptibility to local optima. A comparative analysis and statistical testing confirm that under a low signal-to-noise ratio and multipath effect conditions, the Gradient Subtraction-Average-Based Optimizer algorithm not only ensures real-time parameter estimation but also improves the estimation accuracy. The results of the parameter estimation provide reliable data support for subsequent target localization.

Investigation on drought characteristics such as severity, duration, and frequency is crucial for water resources planning and management in a river basin. While the methodology for multivariate drought frequency analysis is well established by applying the copulas, the estimation on the associated parameters by various parameter estimation methods and the effects on the obtained results have not yet been investigated. This research aims at conducting a comparative analysis between the maximum likelihood parametric and non-parametric method of the Kendall \(\tau \) estimation method for copulas parameter estimation. The methods were employed to study joint severity–duration probability and recurrence intervals in Karkheh River basin (southwest Iran) which is facing severe water-deficit problems. Daily streamflow data at three hydrological gauging stations (Tang Sazbon, Huleilan and Polchehr) near the Karkheh dam were used to draw flow duration curves (FDC) of these three stations. The \(Q_{75}\) index extracted from the FDC were set as threshold level to abstract drought characteristics such as drought duration and severity on the basis of the run theory. Drought duration and severity were separately modeled using the univariate probabilistic distributions and gamma–GEV, LN2–exponential, and LN2–gamma were selected as the best paired drought severity–duration inputs for copulas according to the Akaike Information Criteria (AIC), Kolmogorov–Smirnov and chi-square tests. Archimedean Clayton, Frank, and extreme value Gumbel copulas were employed to construct joint cumulative distribution functions (JCDF) of droughts for each station. Frank copula at Tang Sazbon and Gumbel at Huleilan and Polchehr stations were identified as the best copulas based on the performance evaluation criteria including AIC, BIC, log-likelihood and root mean square error (RMSE) values. Based on the RMSE values, nonparametric Kendall-\(\tau \) is preferred to the parametric maximum likelihood estimation method. The results showed greater drought return periods by the parametric ML method in comparison to the nonparametric Kendall \(\tau \) estimation method. The results also showed that stations located in tributaries (Huleilan and Polchehr) have close return periods, while the station along the main river (Tang Sazbon) has the smaller return periods for the drought events with identical drought duration and severity.

The aim is to propose a method for detection and parameter estimation of nonlinear FM signals, mono- or multicomponent, embedded in white Gaussian noise. The proposed approach consists in mapping the signal into the time-frequency plane by a time-frequency distribution with reassignment, and then in applying a pattern recognition technique, like the Hough transform, to the time-frequency representation to recognize specific shapes. The advantages of this method over the conventional maximum likelihood estimator are (1) a simpler implementation, because it reduces the dimension of the search space and (2) a consistent attenuation of the interference terms between different components of a signal or between signal and noise.

The frequency space of modern radar system has been extended to a wide range. To intercept the modern radar signals with high interception probability, the wideband receiving is of significance to the radar reconnaissance receiver. The Nyquist folding receiver (NYFR) is a novel ultra-wideband receiving architecture, which requires a small amount of equipment. Because the mono-pulse radar signal is widely used in radar systems, the multiple mono-pulse radar signals will be intercepted by the NYFR. The parameter estimation of multiple simultaneous arrival mono-pulse radar signals intercepted by the NYFR using periodic chirp local oscillator is considered. The definition of Periodic fractional autocorrelation (PFA) is proposed. Based on the PFA, a novel fast parameter estimation method is given. The proposed estimation approach can estimate the multiple NYFR outputs under frequency aliasing condition and the computational complexity of the proposed method is low. Simulation results show the effectiveness of the proposed method.

This paper presents focus on physical feature extraction and parameter estimation for satellites in space. In the context of increasingly prominent space security issues, it is necessary to improve the security and protection capabilities of the space system, especially the refined feature extraction and recognition technology of space targets. However, the feature extraction methods based on optical or radar imagery are limited by resolution and observation conditions, making it difficult to extract refined features. This paper is based on the attribute scattering center theory, using high-frequency electromagnetic wave detection method. Through the attribute parameter estimation result of the scattering center, the scattering structure on the space target can be identified and its distribution position can be analyzed, and the structure and size of the typical parts in the space target can be extracted. Aiming at the problem of high parameter dimension and large amount of calculation, an attributed scattering centers parameter estimation method with amplitude and phase separation is proposed, which reduces the time complexity of parameter estimation by an order of magnitude, saves system resources and increases the parameter estimation rate, and the estimation accuracy is better than 90%. In terms of the efficiency and accuracy of parameter estimation from simulation and experimental data, the effectiveness of the proposed method in this paper is verified.

This study proposes a novel integrated polarisation and diversity smoothing (IPDS) algorithm to solve the direction estimation problem of coherent targets in bistatic multiple‐input multiple‐output (MIMO) radar with electromagnetic vector sensors (EVSs). The IPDS algorithm partitions the transmit and receive arrays into multiple subarrays based on the sensor elements and the spatial phase shift factors. Then the covariance matrices of the received signals from coherent targets associated with these subarrays are smoothened to restore the rank inadequacy of the reflection coefficient covariance matrix. After applying the IPDS algorithm, the direction of departure (DOD) and the direction of arrival (DOA) are estimated using the estimation of signal parameters via rotational invariance technique and the multiple signal classification methods. The effectiveness of the proposed algorithm in terms of decorrelation factor, estimation accuracy, precision and the spatial spectrum is evaluated through computer simulations. Cramér–Rao lower bound is derived for the bistatic MIMO radar with EVSs to substantiate the proposed algorithm. The simulation results are compared with the diversity smoothing and the polarisation smoothing algorithms available in literature. The results obtained by using the proposed algorithm were found to be impressive.

This paper proposed an improved method based on fractional Fourier transform (FRFT) for multicarrier LFM signals of MIMO radar (MIMO-LFM) by analyzing its characteristics. First, the intercepted signal model and FRFT are analyzed. Then the signal detection and parameter estimation of MIMO-LFM signals based on FRFT autocorrelation envelope is derived after analyzing the superiority and shortage of conventional FRFT. After that, the detection performance of the proposed method is deduced, and the theoretical results show that this method outperformance the conventional time-frequency method for MIMO-LFM signals processing. Finally, the simulation results demonstrate the validity of the proposed method.