Slobodan Djukanovic

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.

Local Polynomial Fourier Transform Receiver for Nonstationary Interference Excision in DSSS Communications

The problem treated in this paper is monocomponent nonstationary interference excision in direct sequence spread spectrum (DSSS) communication systems by means of the local polynomial Fourier transform (LPFT). First, the interference is optimally concentrated in the time-frequency (t-f) plane and then its t-f signature is removed via a binary mask. The LPFT receiver is derived in matrix form and its optimization is performed, having in mind an influence of the binary mask on the received signal. The conventional (suboptimal) and the optimal LPFT receiver performances are compared by means of simulations carried out on the received signal corrupted by different FM types of interferences. The short-time Fourier transform (STFT) receiver is considered as a special case of the LPFT receiver and its performance is assessed simultaneously with the LPFT receiver, both in conventional and optimal case.

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).

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.

High-resolution time-frequency representations based on the local polynomial Fourier transform for over-the-horizon radars

In this paper, we consider resolving over-the-horizon radar (OTHR) Doppler returns. A high-resolution time-frequency (TF) representation of the received signal is obtained by using the local polynomial Fourier transform (LPFT). From the optimally concentrated LPFT, multicomponent Doppler signatures, which are only several frequency bins apart, are extracted using an instantaneous frequency estimation method based on the Viterbi algorithm. The performance of the proposed method is validated using real data.

Fast communication: Robust M-periodogram with dichotomous search

The problem of sinusoidal frequency estimation in heavy-tailed noise environment is addressed. A method based on the robust M-periodogram is proposed. Specifically, a suboptimal coarse frequency estimate provided by the robust M-periodogram is improved using the modified dichotomous search. Simulations that consider most common heavy-tailed noise models demonstrate that the proposed method outperforms several recently proposed methods. The method can be readily extended to deal with multiple sinusoids.

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.

Order adaptive local polynomial FT based interference rejection in spread spectrum communication systems

Methods for jammer rejection in spread spectrum communications, based on time-frequency representations, have been proposed in order to improve desired signal receiving performances. We also consider nonstationary jammer. The local polynomial Fourier transform (LPFT) is used to represent received corrupted signal. Time-varying filtering is implemented in this domain, having in mind that the LPFT is linear with respect to the signal. An order adaptive algorithm of the LPFT calculation is presented. Performance of the proposed nonparametric method is tested in the presence of linear and sinusoidal FM interferences in the noisy signal, without any a priori assumption about the jammer form. Results in terms of the bit error rate (BER) values are calculated, showing the achieved improvements. Since the first order LPFT is closely related to windowed modified fractional Fourier transform, procedure for an efficient optimization is presented.

An Accurate Method for Frequency Estimation of a Real Sinusoid

It is well known that the positive- and negative-frequency components of a real sinusoid spectrally interact with each other; thus, introducing bias in frequency estimation based on the periodogram maximization. We propose to filter out the negative-frequency component. To that end, a coarse frequency estimation is obtained using the windowing approach, known to reduce the estimation bias, and then used to filter out the negative-frequency component via modulation and discrete Fourier transform bin excision approach. Fine estimation is performed using accurate frequency estimators, developed for complex sinusoids, on the filtered signal. The proposed method is characterized by the O(N log2 N) complexity in terms of additions/multiplications and the O(N) complexity in terms of sine/cosine operations and comparisons. Moreover, it achieves the Cramer-Rao lower bound and is not sensitive to sinusoid frequency and initial phase, thus, outperforming the state-of-the-art methods.