Generalizations of Cyclostationary Signal Processing, 2012

The relative motion between the transmitter and the receiver modifies the nonstationarity properties of the transmitted signal. In particular, the almost-cyclostationarity property exhibited by almost all modulated signals adopted in communications, radar, sonar, and telemetry can be transformed into more general kinds of nonstationarity. A proper statistical characterization of the received signal allows for the design of signal processing algorithms for detection, estimation, and classification that significantly outperform algorithms based on classical descriptions of signals. Generalizations of Cyclostationary Signal Processing addresses these issues and includes the following key features:

• Presents the underlying theoretical framework, accompanied by details of their practical application, for the mathematical models of generalized almost-cyclostationary processes and spectrally correlated processes; two classes of signals finding growing importance in areas such as mobile communications, radar and sonar.
• Explains second- and higher-order characterization of nonstationary stochastic processes in time and frequency domains.
• Discusses continuous- and discrete-time estimators of statistical functions of generalized almost-cyclostationary processes and spectrally correlated processes.
• Provides analysis of mean-square consistency and asymptotic Normality of statistical function estimators.
• Offers extensive analysis of Doppler channels owing to the relative motion between transmitter and receiver and/or surrounding scatterers.
• Performs signal analysis using both the classical stochastic-process approach and the functional approach, where statistical functions are built starting from a single function of time.

Front Matter (pages i–xxi) [pdf free access]

Chapter 1

Background (pages 1–43)

In Chapter 1, background material that will be referenced in the subsequent chapters is reviewed. The statistical characterization of persistent (finite-power) nonstationary stochastic processes is presented. Both strict-sense and wide-sense characterization are considered. Harmonizability, and time-frequency representations are treated. A survey of definition and properties of almost-periodic functions is provided. A brief review on almost-cyclostationary processes is also presented. The chapter ends with some properties of cumulants.

Chapter 2

Generalized Almost-Cyclostationary Processes (pages 45–121)

In Chapter 2, the class of the generalized almost-cyclostationary (GACS) processes is presented and characterized. GACS processes have multivariate statistical functions that are almost-periodic function of time. The (generalized) Fourier series of these functions have both coefficients and frequencies, named lag-dependent cycle frequencies, that depend on the lag shifts of the processes. Almost-cyclostationary processes are obtained as special case when the frequencies do not depend on the lag parameters. The problems of linear filtering and sampling of GACS processes are addressed. The cyclic correlogram is shown to be, under mild conditions, a mean-square consistent and asymptotically Normal estimator of the cyclic autocorrelation function. Such a function allows a complete second-order characterization in the wide-sense of GACS processes.

Numerical examples of communications through Doppler channels due to relative motion between transmitter and receiver with constant relative radial acceleration are considered.

Simulation results on statistical function estimation are carried out to illustrate the theoretical results. Proofs of the results in Chapter 2 are reported in Chapter 3.

Chapter 3

Complements and Proofs on Generalized Almost-Cyclostationary Processes (pages 123–179)

In Chapter 3, complements and proofs for the results presented in Chapter 2 are reported.

Each proof is constituted of two parts. The first part contains formal manipulations that lead to the result. The second part contains the justifications of mathematical manipulations of the first part. Thus, proofs can be followed with two different levels of rigor, depending on the background and interest of the reader.

Chapter 4

Spectrally Correlated Processes (pages 181–290)

In Chapter 4, the class of the spectrally correlated (SC) processes is presented and characterized. SC processes have Loève bifrequency spectrum with spectral masses concentrated on a countable set of support curves in the bifrequency plane. Almost-cyclostationary processes are obtained a special case when the curves are lines with unit slope. The problems of linear filtering and sampling of SC processes are addressed. The time-smoothed and the frequency-smoothed cross-periodogram are considered as estimators of the spectral correlation density. Consistency and asymptotic Normality properties are analyzed. Illustrative examples and simulation results are presented. Proofs of the results in Chapter 4 are reported in Chapter 5.

Chapter 5

Complements and Proofs on Spectrally Correlated Processes (pages 291–354)

In Chapter 5, complements and proofs for the results presented in Chapter 4 are reported. The scheme is the same of Chapter 3.

Chapter 6

Functional Approach for Signal Analysis (pages 355–379)

In Chapter 6, the problem of signal modeling and statistical function estimation is addressed in the functional or fraction-of-time (FOT) approach. Such an approach is alternative to the classical one where signals are modeled as sample paths or realizations of a stochastic process. In the FOT approach, a signal is modeled as a single function of time and a probabilistic model is constructed by this only function of time starting from the concepts of relative measure of sets and functions. Nonstationary models that can be treated in this approach are discussed.

Chapter 7

Applications to Mobile Communications and Radar/Sonar (pages 381–464)

In Chapter 7, applications in mobile communications and radar/sonar systems are presented. A model for the wireless channel is developed. It is shown how, in the case of relative motion between transmitter and receiver or between radar and target, the almost-cyclostationary transmitted signal is modified into a received signal with a different kind of nonstationarity. Conditions under which the generalized almost-cyclostationary or spectrally correlated model are appropriate for the received signal are derived.

Chapter 8

Bibliographic Notes (pages 465–468)

In Chapter 8, citations are classified into categories and listed in chronological order.

References (pages 469–477) [pdf free access]

Index (pages 479–480) [pdf free access]