High-order Polynomial Phase Signals Research Articles

Imaging and Relocation for Extended Ground Moving Targets in Multichannel SAR-GMTI Systems

In a multichannel synthetic aperture radar (SAR) system, because of the target uncooperative motion, a ground moving target (GMT) is usually smeared, distorted, and shifted in an SAR image. In this article, a novel approach for multichannel SAR-GMT indication (GMTI) processing is proposed. The main innovations of this method are that a GMT can be well refocused and relocated since the target high-order Doppler parameters can be precisely estimated based on a high-order polynomial phase signal (PPS) model, and the target statistical amplitude and phase information is jointly applied to improve the radial velocity estimation robustness. Compared with the current SAR-GMTI algorithms, the improvements of this method over the existing methods are: 1) the topography interferometric phase can be effectively compensated by applying an adaptive 2-D spectrum filtering technique via iterative processing; 2) a GMT can be well imaged since the target Doppler chirp rate and the quadratic chirp rate can be well estimated via the 2-D coherent integration in the time–frequency plane; and 3) a GMT can be precisely relocated into its original position by applying the generalized amplitude and phase weighting technique. Real-measured SAR data processing results are presented to validate the effectiveness and feasibility of the proposed method.

Estimation of Higher Order Polynomial Phase Signals in an Impulsive Noise

Parametric estimation of polynomial phase signals (PPSs) corrupted by an impulsive noise has been considered. The interpolation in joint-variable domain has been combined with the hybrid cubic phase function—high-order ambiguity function-based estimator to address this issue. Technique for estimating the percentage of impulses and threshold selection is also proposed. In addition, we propose the refinement procedure to further decrease the mean squared error of PPS parameters estimates.

A new method for parameter estimation of high-order polynomial-phase signals

Parameter estimation of a high-order polynomial phase signal (PPS) is considered in this paper. We propose a method to estimate phase parameters more efficiently and accurately. In the proposed method, we define an operator referred to as non-uniform sampled reducing-order operator (NURO) to reduce the order of a polynomial phase by half, when the order of PPS is even. By combined using NURO and phase differentiation (PD) operators, the PPS order is reduced to one, i.e., the PPS degenerates into a complex sinusoid. Then, the parameter estimation can be done by jointly using fast Fourier transform (FFT) and one-dimensional search. Compared with the traditional methods, the reducing-order procedure in the proposed method has lower-order nonlinearities. Simulation results show that the proposed method outperforms the hybrid CPF-HAF and HAF in both mean square error (MSE) and the threshold when the PPS order is higher than 5.

High precision technique for PPS estimation in impulsive noise environment

A technique for high precision parametric estimation of high-order polynomial phase signals (PPS) is introduced that can be used in impulsive noise environments. It is inspired by the recently proposed quasi maximum likelihood (QML) estimator with several modifications in coarse and fine estimation stages as well as in the optimization criterion. The developed technique achieves improvement in the mean squared error (MSE) for more than 20dB with respect to the standard QML for high-order PPSs of short length and up to 20% of impulses.

Parameter estimation of underwater moving sources by using matched Wigner transform

According to the acoustical Doppler effect, an improved narrow-band technique is proposed to estimate underwater source’s motion parameters including speed, closest distance, rest frequency, and closest point of approach (CPA) time, by using a single receiving sensor. First, the matched Wigner transform (MWT), which produces a time–frequency distribution (TFD) with optimal energy concentration and without inner artifacts for a high-order polynomial phase signal, is defined. On the basis of the MWT, a method is developed for the accurate instantaneous frequency (IF) estimation of Doppler signal. Moreover, we deduce that the Wigner–Ville distribution of the Doppler signal has a peak at the center of the TFD. Thereafter, the CPA time is directly estimated. When the CPA time is obtained, the other motion parameters can be easily estimated by using a simplified amplitude weighted nonlinear least-squares method, which fits the IF estimates to the predicted Doppler shift. Finally, the effectiveness of the proposed scheme is validated by using underwater acoustic data.

Quasi maximum likelihood estimator of polynomial phase signals for compressed sensed data

Several papers in the literature cover parameter estimation of frequency modulated (FM) signals under reduced number of signal samples with respect to the Nyquist/Shannon criterion, i.e., within the compressive sensing (CS) framework. However, scope of these papers is mainly limited to sinusoids or sum of sinusoids. In this paper, the CS framework is extended to parameter estimation of higher order polynomial phase signals (PPSs) using the quasi-maximum likelihood (QML) estimator and robust short-time Fourier transform (STFT). The considered signal is assumed to be non-uniformly sampled PPS with smaller number of samples with respect to the Nyquist/Shannon criterion. However, the proposed technique can also be generalized to uniformly sampled signals with missing or unreliable samples.

Instantaneous Frequency Rate Estimation for High-Order Polynomial-Phase Signals

Instantaneous frequency rate (IFR) estimation for high-order polynomial phase signals (PPSs) is considered. Specifically, an IFR estimator with only a second-order nonlinearity is proposed. The asymptotic mean-squared error (MSE) of the proposed IFR estimator is obtained via a multivariate first-order perturbation analysis. Our results show that the proposed estimator yields a smaller MSE and a lower signal-to-noise ratio (SNR) threshold than a popular IFR estimator involving higher nonlinearity. The proposed IFR estimator is also extended to estimate the phase parameters of a PPS. Numerical studies are presented to illustrate the performance of the proposed estimator.

Radix-3 fast algorithms for polynomial time frequency transforms

The polynomial time frequency transforms have been used as an effective tool to reveal the polynomial-phase information by converting a one-dimensional polynomial-phase signal in the time domain into a multi-dimensional output array in the frequency domain. To significantly reduce the prohibitive computational complexity for dealing with high order polynomial-phase signals, efficient fast algorithms are extremely important for any practical applications. Based on radix-3 decomposition techniques, this paper presents fast algorithms for any order of the polynomial-phase signals. It shows that the computational complexity, except that for twiddle factors, of the radix-3 algorithm is independent of the order of the polynomial time frequency transform. The proposed algorithms are simple in concept and achieve significant savings on computational complexity.

A New Flexible Approach to Estimate the IA and IF of Nonstationary Signals of Long-Time Duration

In this paper, we propose an original strategy for estimating and reconstructing monocomponent signals having a high nonstationarity and long-time duration. We locally apply to short-time duration intervals the strategy developed in our previous work about nonstationary short-time signals. This paper describes a nonsequential time segmentation that provides segments whose lengths are suitable for modeling both the instantaneous amplitude and frequency locally with low-order polynomials. Parameter estimation is done independently for each segment by maximizing the likelihood function by means of the simulated annealing technique. The signal is then reconstructed by merging the estimated segments. The strategy proposed is sufficiently flexible for estimating a large variety of nonstationarity and specifically applicable to high-order polynomial phase signals. The estimation of a high-order model is not necessary. The error propagation phenomenon occurring with the known approach, the higher ambiguity function (HAF)-based method, is avoided. The proposed strategy is evaluated using Monte Carlo noise simulations and compared with the Cramer-Rao bounds (CRBs). The signal of a songbird is used as a real example of its applicability.

Split-Radix Algorithms for Arbitrary Order of Polynomial Time Frequency Transforms

The polynomial time frequency transform is one of important tools for estimating the coefficients of the polynomial-phase signals (PPSs) with the maximum likelihood method. The transform converts a one-dimensional (1-D) data sequence into a multidimensional output array from which the phase coefficients of the data sequence are estimated. A prohibitive computational load is generally needed for high-order polynomial-phase signals although the 1-D fast Fourier transform (FFT) algorithm can be used. Based on the split-radix concept, this paper derives a fast algorithm for arbitrary order of polynomial time frequency transforms to significantly reduce the computational complexity. Comparisons on the computational complexity needed by various algorithms are also made to show the merits of the proposed algorithm

Radix-2 DIF fast algorithms for polynomial time-frequency transforms

The polynomial time-frequency transform (PTFT) converts a one-dimensional polynomial-phase signal (PPS) into a multi-dimensional (MD) output array in the frequency domain from which the phase coefficients are estimated. To significantly reduce the prohibitive computational complexity to deal with high order PPSs, effective decomposition of the overall computational task is important for any practical applications. This paper derives a radix-2 decimation-in-frequency (DIF) fast algorithms for any order of the PPSs by using the periodic and symmetric properties of the PTFT. Compared with other reported fast algorithms, the proposed one is simple in concept and achieves a significant reduction of the required computational complexity.

Detection of phase modulated signals in additive noise

We consider detection of constant amplitude phase modulated signals in noise. A simple detector based on second- and fourth-order moments is proposed. The detector has several good properties including independence of the signal phase, consistency, and computational efficiency. Numerical simulations are used to compare the detector to a bootstrap-based one. The moment-based detector is shown to have better performance for higher-order polynomial phase signals.