Abstract—Parameter estimation and performance analysis issues are studied for multicomponent polynomial-phase signals (PPS’s) embedded in white Gaussian noise. Identifiability issues arising with existing approaches are described first when dealing with multicomponent PPS having the same highest order phase coefficients. This situation is encountered in applications such as synthetic aperture radar imaging or propagation of polynomialphase signals through channels affected by multipath and is thus worthy of a careful analysis. A new approach is proposed based on a transformation called product high-order ambiguity function (PHAF). The use of the PHAF offers a number of advantages with respect to the high-order ambiguity function (HAF). More specifically, it removes the identifiability problem and improves noise rejection capabilities. Performance analysis is carried out using the perturbation method and verified by simulation results. I.

Abstract—The discrete Fourier transform (DFT) has found tremendous applications in almost all fields, mainly because it can be used to match the multiple frequencies of a stationary signal with multiple harmonics. In many applications, wideband and nonstationary signals, however, often occur. One of the typical examples of such signals is chirp-type signals that are usually encountered in radar signal processing, such as synthetic aperture radar (SAR) and inverse SAR imaging. Due to the motion of a target, the radar return signals are usually chirps, and their chirp rates include the information about the target, such as the location and the velocity. In this paper, we study discrete chirp-Fourier transform (DCFT), which is analogous to the DFT. Besides the multiple frequency matching similar to the DFT, the DCFT can be used to match the multiple chirp rates in a chirp-type signal with multiple chirp components. We show that when the signal length is prime, the magnitudes of all the sidelobes of the DCFT of a quadratic chirp signal are 1, whereas the magnitude of the mainlobe of the DCFT is. With this result, an upper bound for the number of the detectable chirp components using the DCFT is provided in terms of signal length and signal and noise powers. We also show that the-point DCFT performs optimally when is a prime. Index Terms—Chirp-Fourier transform, chirp rate estimation, chirps. I.

The aim of this paper is to propose an adaptive method for suppressing wideband interferences in spread spectrum (SS) communications. The proposed method is based on the time--frequency representation of the received signal from which the parameters of an adaptive time-varying interference excision filter are estimated. The approach is based on the generalized Wigner--Hough transform as an effective way to estimate the instantaneous frequency of parametric signals embedded in noise. The performance of the proposed approach is evaluated in the presence of linear and sinusoidal FM interferences plus white Gaussian noise in terms of SNR improvement factor and bit error rate (BER).

Incoherent detection based on differential encoding has been successfully applied to phase-shift-keying (PSK) signals because it eliminates the need for carrier phase acquisition and tracking at the receiver. This paper generalizes the idea of differential encoding by using a nonlinear transformation called multilag high-order instantaneous moment (ml-HIM). The ml-HIM decoder is capable of removing the effects of phase ambiguity, Doppler frequency, Doppler rate, and even higher order phase distortions. The degrees of freedom offered by the different lags is exploited to optimize system performance. In addition to the classical M-ary PSK, the generalized differential encoding idea is also applied to nonconstant modulus constellations, such as M-ary QAM and AM-PM. I. INTRODUCTION I N DIGITAL communication systems, phase ambiguity and/or frequency errors are likely to be present in the received signal due to imperfect knowledge of the carrier's phase and frequency, fading effects, ...

Parameter estimation for a combination of a polynomial phase signal (PPS) and a frequency modulated (FM) sig- nal is addressed. A novel approach is proposed that allows one to alecouple estimation of the FM parameters from that of the PP$ parameters, exploiting the properties of the multi-lag High-order Ambiguity Function (ml-HAF). Per- formante analysis is carried out and Cramer-Rao bounds are compared with simulation results.

nals (PPS) has been extensively studied in the recent literature in view of possible important applications in remote sensing as well as in telecommunications. How- ever, the detection of PP$ has not received similar attention. In this paper we propose and analyze an adap- tive method for the detection of PPS embedded in white Caussian noise based on the use of the so called product high order ambiguity function.

INTRODUCTION Synthetic Aperture Radar (SAR) produces high resolution microwave images: the range resolution is c/2B, where c is the speed of light and B is the bandwidth of the transmitted signal (typically a chirp signal); the cross-range resolution is approximately A/2A0, where A is the transmission wavelength and A0 is the angle under which each point on the scene is observed from the radar [4]. The high cross-range resolution is obtained by coherently integrating the echoes received from each point of the observed scene during the observation interval. The coherent integration allows synthesis of an aperture much greater than the real aperture. A correct coherent integration however requires an accurate knowledge of the relative motion between the radar and the observed scene. On-board instrumentation provides the data relative to the position of the aircraft carrying the radar, but the accuracy with which these data are delivered by the instrumentation is much lower than that nec

some paradigms of signal processing via concrete examples