| Estimation of signal parameters via higher-order statistics and cyclostationarity is a rapidly evolving area of statistical signal processing with growing applications in engineering and intensive research in theory.When signals are non-Gaussian, higher order statistics (HOS) can reveal more information about them than second order statistics can. Ideally the entire probability density function is needed to charactertenze a non-Gaussian signal while a Gaussian density function is completely characterized by its first two moments. In practice the entire probability density ftrnction is not available, but the probability density function can be characterized by its moments (if they exist, and there may be an infinite number of them). It is logical therefore to use more than just the lirst two moments to extract information about non-Gaussian signals. That is what is now being done in the signal processing community within the framework of ?applications of HOS(or spectra)? Although the phrase æ…¼igher order statistics?sounds quite mathematical, it is the myraid of applications of HOS that is driving this field. It is no exaggcration to claim that every application which makes use of second order statictics should be reexamined using HOS if signals are non-Gaussian.Many conventional statistical signal processing methods treat random signals as if they were statistically stationary, in which case the parameters of the underlying physical mechanism that generates the signal would not vary with time. But for most manmade signals encountered in communication, telemetry, radar, and sonar systems, some parameters do vary periodically with time. In some cases even multiple incommensurate (not harmonically related) periodicities are involved. Examples include sinusoidal carriers in amplitude, phase and frequency modulation systems, periodic keying of the amplitude, phase, or frequency in digital modulation systems, and periodic scanning in television, facsimile, and some radar systems. Although in some cases these periodicities can be ignored by signal processors, such as receivers which must detect the presence of signals of interest, estimate their parameters, and/or extract their messages, in many cases there can be much to gain in terms of improvements in performance of these signal processors by recognizing and exploiting underlying periodicity. This typical requires that the random signal be modeled as cycIostationa~y, in Which case the statistical parameters vary in time with single or multiple periodicities.This dissertation aims at the development of parametric estimation techniques of polynomial phase signal with random or time-varying amplitude based on HOS orcyclostationarity, and the performance analysis of several HOS-based or cyclostationaritybased algorithms. The main work can be summarized as follows.In chapter 1, we first provide a background of this work and give a brief overview about the development of the cumulant and cyclostationarity. We highlight the key points of this dissertation at the end of this Chapter.In chapter 2, we investigate multiplicative models of the fcmn z(t) = p(t)s(t), where :Q) is the observed process, the complex stationary signal process sQ), the complex stationary multiplicative noise process pQ) are mutually independent . by using of cumulants, some statistical properties of the complex signal process s(l) are estimated from observations of zQ).Chapter 3 deals with the finite data estimates of the higher-order moments of a complex signal consisting of random harmonics. Conditions for the higher-order stationarity and ergodicity are obtained. Explicit formulas for the estimation error and its variance, as well as their limiting large sample value are also derived.Periodogram is an useful tool to reveal hidden periodicities in a given time series. In chapter 4, smoothed periodograms are proposed for cyclic spectral estimation of complex signal and are shown to be consistent. Asymptotic covariance expressions are der...
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