Marko Simeunović

A Hybrid CPF-HAF Estimation of Polynomial-Phase Signals: Detailed Statistical Analysis

In this paper, we consider parameter estimation of high-order polynomial-phase signals (PPSs). We propose an approach that combines the cubic phase function (CPF) and the high-order ambiguity function (HAF), and is referred to as the hybrid CPF-HAF method. In the proposed method, the phase differentiation is first applied on the observed PPS to produce a cubic phase signal, whose parameters are, in turn, estimated by the CPF. The performance analysis, carried out in the paper, considers up to the tenth-order PPSs, and is supported by numerical examples revealing that the proposed approach outperforms the HAF in terms of the accuracy and signal-to-noise-ratio threshold. Extensions to multicomponent and multidimensional PPSs are also considered, all supported by numerical examples. Specifically, when multicomponent PPSs are considered, the product version of the CPF-HAF outperforms the product HAF (PHAF) that fails to estimate parameters of components whose PPS order exceeds three.

Instantaneous frequency in time-frequency analysis: Enhanced concepts and performance of estimation algorithms

Abstract The instantaneous frequency (IF) is a very important feature of nonstationary signals in numerous applications. The first overview of the concept and application of the IF estimators is presented in seminal papers by Boashash. Since then, a significant knowledge has been gained about the performance of the IF estimators. This knowledge has been used not only for development of various IF estimators but also for introduction of novel time–frequency (TF) representations. The IF estimation in environments characterized by low signal-to-noise (SNR) has achieved significant benefits from these theoretical developments. In this paper, we review some of the most important developments in the last two decades related to the concept of the IF, performance analysis of IF estimators, and development of IF estimators for low SNR environments.

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).

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

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).

Combined HO-CPF and HO-WD PPS estimator

Recently, the high-order cubic phase function (HO-CPF) and high-order Wigner distribution (HO-WD) have been proposed for parameter estimation of polynomial-phase signals (PPSs). To estimate PPS parameters, both the HO-CPF and HO-WD are evaluated at two points. One point is usually the center of the considered time interval, whereas the other one is shifted from the center. Shifting shortens the signal sequence and reduces the performance of the considered technique. In this paper, we propose an estimation procedure that combines the HO-CPF and HO-WD. The procedure evaluates both functions at the origin only, implying no signal shortening. Simulation results and statistical study have shown a significant performance improvement over the HO-CPF- and the HO-WD- based estimators.

Non-uniform sampled cubic phase function

Parameter estimation of polynomial phase signals (PPSs) based on the cubic phase function (CPF) and its extensions cannot be performed by using the fast Fourier transform (FT) algorithm. Therefore, in order to express the CPF by means of the FT, in this paper we propose a scheme for the CPF evaluation based on non-uniform sampling. Calculation complexity of the estimation procedure is significantly reduced, whereas the accuracy is the same or better compared to the original algorithm.

Resolving aliasing effect in the QML estimation of PPSs

The quasimaximum likelihood (QML) estimator of polynomial-phase signals (PPSs) is based on the maximization of the short-time Fourier transform and suffers from aliasing when signals are sampled below the Nyquist sampling rate. In this paper, a phase unwrapping procedure has been proposed as an additional step in the QML to estimate parameters of such signals. Statistical study has shown excellent performance of the proposed approach.

Robust time-frequency representation based on the signal normalization and concentration measures

An efficient procedure for obtaining time-frequency representations under high influence of impulsive noise is proposed in this paper. The procedure uses the fast Fourier transform based algorithm instead of sorting procedures common in the case of various robust time-frequency representations proposed recently. Concentration measure is used to select a free parameter of the transform.

The STFT-Based Estimator of Micro-Doppler Parameters

A two-stage technique for estimating micro-Doppler signal parameters has been proposed. In the first stage, rough parameter estimations are performed by regression of instantaneous frequency estimate obtained from the short-time Fourier transform. Afterwards, rough estimates are refined in the second stage. The proposed technique has better performance with respect to current state-of-the-art algorithms, and it reaches the Cramer–Rao lower bound for sinusoidal frequency-modulated signal parameters.

Parameter Estimation of Multicomponent 2D Polynomial-Phase Signals Using the 2D PHAF-Based Approach

This paper considers parameter estimation of multicomponent 2D polynomial-phase signals (mc-2D PPSs). The main contributions included are: Derivation of the Cramer-Rao lower bound (CRLB) for mc-2D PPSs; Two dimensional product high-order ambiguity function (2D PHAF) based estimation procedure, recently proposed by Barbarossa, for the estimation of third-order mc-2D PPSs is extended to signals of arbitrary orders; Procedure for optimal lag set selection in the proposed 2D PHAF has been proposed; Since the 2D PHAF is characterized by large mean squared error (MSE) for higher-order signals, refinement procedure is introduced that is able to improve the estimation accuracy and to reduce MSE up to the CRLB. The proposed estimator has been used for target focusing in radar images.