Polynomial Phase Signals Research Articles

Multiple signal classification technique for phase estimation from a fringe pattern

The paper introduces a multiple signal classification technique based method for fringe analysis. In the proposed method, the phase of a fringe pattern is locally approximated as a polynomial. The polynomial phase signal is then transformed to obtain signals comprising of only even- or odd-order polynomial coefficients. Subsequently, covariance matrix formulation is applied, and the two sets of coefficients are jointly estimated from the noise subspace of the covariance matrix using the multiple signal classification technique. The method allows simultaneous estimation of multiple coefficients and provides phase without the requirement of complex unwrapping algorithms. The effectiveness of the proposed method is validated through numerical simulation.

Cramér–Rao bounds of direction-of-arrival and distance estimation of a near-field incident source for an acoustic vector sensor: Gaussian source and polynomial-phase source

The near-field array manifold of the acoustic vector sensor was recently derived by Wu et al [see `the acoustic vector sensor`s near-field array manifold` in IEEE Trans. Signal Process. ]. The CramerRao bounds (CRBs) of direction-of-arrival and distance estimation with a single pure tone were also derived therein. This study aims to investigate the estimation accuracy of the acoustic vector sensor in the near-field, through the CRBs analysis, by modelling the incident source as: (i) a Gaussian distributed random sequence, and (ii) a polynomial-phase signal. All the four different compositions of the acoustic vector sensor in the near-field are considered, and their closed-form CRBs are derived.

Improving Polynomial Phase Parameter Estimation by Using Nonuniformly Spaced Signal Sample Methods

This paper investigates the computationally efficient parameter estimation of polynomial phase signals embedded in noise. Many authors have previously proposed multilinear analysis methods which operate on uniformly spaced samples of the signal. Such methods include the higher-order ambiguity functions (HAFs), the Polynomial Wigner-Ville distributions (PWVDs) and the higher-order phase (HP) functions. This paper investigates the use of multilinear methods which operate on nonuniformly spaced signal samples. It is seen that the relaxation of the requirement to use uniformly spaced samples in the analysis can lead to significant performance improvements. A theoretical analysis and simulations are presented in support of these claims.

The higher-order reassigned local polynomial periodogram and its properties

Recently the second order reassigned local polynomial periodogram (LPP) has been reported to show some desirable properties for signal representation in the time–frequency domain. In this paper, the higher-order reassigned LPPs and their properties are discussed. With the definition of the modified Wigner–Ville distribution, the reassignment operators of the third, fourth and the arbitrary higher-order reassigned LPP are defined and derived. It is shown that the higher-order reassigned LPPs share the properties with the second order reassigned LPP, such as the non-negativity, non-bilinearity, time and frequency shifts invariance, time-scaling property and energy conservation. The property of the higher-order reassigned LPP to perfectly localize the corresponding order polynomial phase signals is also investigated to obtain improved signal concentration in the time–frequency domain.

Are genetic algorithms useful for the parameter estimation of FM signals?

The estimation of polynomial-phase signals (PPSs) is a multiparameter problem, and the maximum likelihood (ML) optimization functions have numerous local optima, making the application of gradient techniques impossible. The common solution to this problem is based on the phase differentiation (PD) techniques that reduce the number of dimensions but, at the same time, reduce the accuracy and generate additional difficulties such as spurious components and error propagation. Here we show that genetic algorithms (GAs) can serve as a powerful alternative to the PD techniques. We investigate the limits of accuracy of the ML technique, and of some alternatives such as the high-order cubic phase function (HO-CPF) and high-order Wigner distribution (HO-WD). The ML approach combined with the proposed GA setup is limited up to the fifth-order PPS, which is not sufficient in many applications. However, the HO-CPF and HO-WD techniques coupled with the GA are able to accurately estimate phase parameters up to the tenth-order PPS. They significantly improve the accuracy with respect to the high-order ambiguity function (HAF) and product HAF (PHAF) and, for higher-order PPSs, they are much simpler and more efficient than the integrated generalized ambiguity function (IGAF).

STFT-based estimator of polynomial phase signals

The short-time Fourier transform (STFT) based instantaneous frequency (IF) estimator has been used for polynomial phase signal (PPS) parameters estimation. This estimator is biased but it is less sensitive to the noise influence than the higher-order techniques such as the high-order ambiguity function (HAF). Here, we have developed a method for estimation of the optimal window width in the STFT for the PPS estimation. Obtained results are then refined with the strategy proposed recently by O'Shea. In this way the resulting estimates of parameters outperform the HAF based ones.

Estimating the DOA and the Polarization of a Polynomial-Phase Signal Using a Single Polarized Vector-Sensor

This paper introduces a novel algorithm to estimate the direction-of-arrival (DOA) and the polarization of a completely-polarized polynomial-phase signal of an arbitrary degree. The algorithm utilizes a polarized vector-sensor, comprising a spatially collocated six-component electromagnetic vector-sensor, a dipole triad, or a loop triad. This ESPRIT-based algorithm is based on a time-invariant matrix-pencil pair, derived from the time-delayed data-sets collected by a single polarized vector-sensor. The high-order difference-function of the signal's phase constructs the invariant-factor used in the ESPRIT algorithm. The steering vector is estimated from the signal-subspace eigenvector of the data-correlation matrix, following which the closed-form DOA and polarization can be obtained. Given the degree of the polynomial-phase signal, this approach resolves the two-dimensional azimuth-elevation angle and the polarization of the source, and requires neither a priori knowledge of the polynomial-phase signal's coefficients nor a priori knowledge of the polynomial-phase signal's frequency-spectrum. The efficacy of the proposed algorithm is verified by Monte Carlo simulations. Estimation accuracies of the DOA and the polarization parameters are evaluated by the closed-form Cramer-Rao bounds, which are independent of the polynomial coefficients, the degree of the polynomial-phase signal, and the azimuth-angle of the source.

An efficient joint estimation of wideband polynomial-phase signal parameters and direction-of-arrival in sensor array

Abstract We consider the joint estimation of the direction-of-arrival (DOA) and parameters of wideband polynomial-phase signals (PPSs) in sensor array. Unlike concurrent methods that require multidimensional searches, the proposed method requires 1D searches for all the parameters of interest. In this way, we can efficiently estimate the considered parameters in applications where large antenna arrays, containing tens or hundreds of sensors, are used. As special cases, we consider in detail the estimation of the second- and third-order PPSs. The former are estimated using the high-order ambiguity function (HAF), while the latter are estimated using the cubic phase function (CPF), known to outperform the HAF in terms of both accuracy and signal-to-noise ratio (SNR) threshold. In both cases, the estimation of the highest order parameter reaches the Cramér-Rao lower bound (CRLB), while the DOA estimation is above the CRLB for around 1 dB (second-order PPS) and around 6 dB (third-order PPS).

Estimation of multiple phases from a single fringe pattern in digital holographic interferometry

Simultaneous measurement of multidimensional displacements using digital holographic interferometry involves multi-directional illumination of the deformed object and requires the reliable estimation of the resulting multiple interference phase distributions. The paper introduces an elegant method to simultaneously estimate the desired multiple phases from a single fringe pattern. The proposed method relies on modeling the reconstructed interference field as a piecewise multicomponent polynomial phase signal. Effectively, in a given region or segment, the reconstructed interference field is represented as the sum of different components i.e. complex signals with polynomial phases. The corresponding polynomial coefficients are estimated using the product high-order ambiguity function. To ensure proper matching of the estimated coefficients with the corresponding components, an amplitude based discrimination criterion is used. The main advantage of the proposed method is direct retrieval of multiple phases without the application of spatial carrier based filtering operations.

CPF-HAF estimator of polynomial-phase signals

A simple and effective modification of the high-order ambiguity function (HAF) is introduced. The number of phase differentiations is decreased to two with respect to the HAF. The obtained signal has a cubic phase, the parameters of which can be estimated using the cubic phase function (CPF) in the final stage. The SNR threshold of the proposed modification is reduced for 9 dB with respect to the HAF, while the MSE is about 2 dB less.

Aliasing detection and resolving in the estimation of polynomial-phase signal parameters

A novel method for aliasing detection and resolving in the estimation of polynomial-phase signal (PPS) parameters is presented. Aliasing is detected using two high-order ambiguity functions (HAFs) of a uniformly sampled PPS embedded in noise. If aliasing occurred, we propose a way of recovering the true parameters from their aliased positions. To that end, a closed-form expression for the true parameter value is derived. As opposed to the concurrent methods, the proposed method provides much more robust results with higher order PPSs and does not require nonuniform sampling. In addition, it can be readily extended to the multicomponent PPS case. Simulations support the theoretical results.

Quasi-Orthogonal Space-Time Block Coding Using Polynomial Phase Modulation

Recently, polynomial phase modulation (PPM) was shown to be a power- and bandwidth-efficient modulation format. These two characteristics are in high demand nowadays specially in mobile applications, where devices with size, weight, and power (SWaP) constraints are common. In this paper, we propose implementing a full-diversity quasiorthogonal space-time block code (QOSTBC) using polynomial phase signals as modulation format. QOSTBCs along with PPM are used in order to improve the power efficiency of communication systems with four transmit antennas. We obtain the optimal PPM constellations that ensure full diversity and maximize the QOSTBC's minimum coding gain distance. Simulation results show that by using QOSTBCs along with a properly selected PPM constellation, full diversity in flat fading channels and thus low BER at high signal-to-noise ratios (SNR) can be ensured. More importantly, it is also shown that QOSTBCs using PPM achieve a better error performance than those using conventional modulation formats.

A New Estimation Method of Instantaneous Frequency Rate for Multicomponent Polynomial Phase Signal

该文在分数阶傅里叶(FRFT)计算分解的基础上，讨论了其某些步骤在信号检测中的冗余，提出了一种简化的分数阶傅里叶算法(RFRFT)，详细讨论了它的几种重要性质，并结合一次相位差分法提出了乘积性RFRFT(PRFRFT)算法，实现了mc-PPS的瞬时频率变化率(IFR)估计。同时借助角度变换提高了RFRFT识别参数的分辨率。该方法运算量小，易于实现。仿真结果证实了该方法能够有效地抑制噪声和交叉项，可以适应低信噪比环境。

ISAR Imaging of Ship Target with Complex Motion Based on New Approach of Parameters Estimation for Polynomial Phase Signal

ISAR imaging of ships at sea with significant motion results in the Doppler frequency shift for the received signal is time-varying, which will deteriorate the ISAR image quality for the Range-Doppler (RD) algorithm. In this paper, the received signal is modeled as a multicomponent cubic phase signal (CPS), and a new method for estimating the parameters of CPS based on the integrated high-order matched phase transform (IHMPT) is proposed. This algorithm is simpler and more computational efficient than some of other parameters estimation algorithms proposed previously. Then, combined with the Range-Instantaneous-Doppler (RID) technique, the high quality instantaneous ISAR images can be obtained. The results of simulated and measured data are provided to demonstrate the effectiveness of the new method proposed.

New method for parameter estimation of polynomial phase signals

In this correspondence, a linear transform called polynomial to Hermite polynomial transform (PHPT) is proposed, and the PHPT-based method for parameter estimation of polynomial phase signals (PPS) embedded in additive white Gaussian noise is addressed. The first advantage is the low computational complexity. If the number of samples is N, the computational complexity is O(3N log2N) regardless of the order or the component number of PPS. The second advantage is that there is no non-linear operation in PHPT algorithm; therefore there is no cross-term interference in between the various components. In addition, the proposed method can well process the PPS with unknown order phase. Simulations illustrate that the proposed algorithm is more effective as compared with the existing ones.

Instantaneous Frequency Calculation for Intrinsic Mode Functions Based on High-order Ambiguity Function

Instantaneous frequency(IF) calculation is a key step for empirical mode decomposition(EMD).But signal analysis accuracy is not very well for practical condition signal analysis based on traditional IF calculation method.Although non-stationary signals can be modeled as polynomial phase signals(PPS),traditional phase model estimation methods are not very suitable for practical application,such as maximum likelihood estimation and the least squares method.In most circumstances,a lot of calculations are needed.Thus,several problems need to be solved during IF calculation for intrinsic mode function obtained from EMD.The boundary effect for signal analysis is very obvious.High-order ambiguity function(HAF) is put forward for IF calculation.Then,Hilbert time-frequency spectrum can be constructed for signal analysis.HAF can reduce computation and improve IF estimation accuracy.Simulation signal and practical monitored signal are used to testify the effectiveness of this method for IF calculation.The research shows that this method can effectively eliminate the influence of boundary effect and improve the reliability of Hilbert time-frequency spectrum.

MAXIMUM LIKELIHOOD ESTIMATION OF CO-CHANNEL MULTICOMPONENT POLYNOMIAL PHASE SIGNALS USING IMPORTANCE SAMPLING

Unlike some traditional polynomial phase signal (PPS) parameter estimation methods restricted to monocomponent case, this paper focuses on the parameter estimation of multicomponent PPSs mixed in a single channel, which is more sophisticated and always involves the cross-term issue. In this investigation, based on the model of multicomponent PPSs in additional white Gaussian noise, we partition the maximum likelihood estimation into two consecutive steps. The flrst one involving estimation of polynomial coe-cients is intensively studied using importance sampling, while the second one involving the estimation of amplitude and initial phase is trivial. Numerical experiments show satisfactory estimation performance even if the parameters are closely spaced.

DETECTION AND ESTIMATION OF MULTI-COMPONENT POLYNOMIAL PHASE SIGNALS BY CONSTRUCTING REGULAR CROSS TERMS

A regular cross terms algorithm is derived for the parameter estimation of the multi-component polynomial phase signals in additive white Gaussian noise. The basic idea is flrst to separate its phase parameters into two sets by nonlinear proceduresand then each set has half of the parameters in its auto-terms. Furthermore, using two linear transforms to deal with the two signals respectively, the phase coe-cients of cross terms can be regulated for the identiflcation and elimination of false peaks caused by the cross terms. Simulations are presented to illustrate the performance of the proposed algorithm.

Double-characters detection of nonlinear frequency modulated signals based on FRFT

In many practical applications, signals to be detected are unknown nonlinear frequency modulated (FM) and are corrupted by strong noise. The phase histories of the nonlinear FM signals are assumed to be unknown smooth functions of time, which are usually poorly modeled or cannot be modeled at all by a small number of parameters. Because of the lack of phase model, a nonparametric detection method is proposed based on successive fractional Fourier transform and double-characters detection. The detection process goes in three steps. First, an image is constructed by the fractional Fourier transforms of successive angles in one period. Then, the threshold procedure is utilized to transform the image into a binary image. After the multiple median filtering, the binary image is refined where the isolated noise pixels are removed. Finally, two complementary features are extracted from the refined image, and a double-characters detector is proposed to decide whether the target is present or not. The simulation experiments to three polynomial phase signals with different orders and a sinusoidal phase signal show that the proposed detection method is effective and robust.

A parametric method for non-stationary interference suppression in direct sequence spread-spectrum systems

The problem of non-stationary interference suppression in direct sequence spread-spectrum (DS-SS) systems is considered. The phase of interference is approximated by a polynomial within the considered interval. According to the local polynomial Fourier transform (LPFT) principle, the received signal is dechirped by using the obtained phase approximation and the interference is, in turn, suppressed by excising the corrupted low-pass frequency band. For the estimation of polynomial coefficients, we use the product high-order ambiguity function (PHAF), known for its capability to successfully resolve components of a multicomponent polynomial-phase signal (PPS). The proposed method can suppress interferences with both polynomial and non-polynomial phase. In addition, it can suppress both monocomponent and multicomponent interferences. The simulations show that the proposed method outperforms time-frequency (TF) methods, that successfully deal with multicomponent interferences, in terms of the error probability and computational complexity.