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Generalizations of Cyclostationary Signal Processing
Spectral Analysis and Applications1145
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.
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This book is written both for advanced readers with the background of graduate students in engineering and for specialists (e.g., mathematicians). (Zentralblatt MATH, 1 May 2013)
Antonio Napolitano, University of Napoli "Parthenope", Italy Dr. Napolitano is currently Professor of Telecommunications at the University of Napoli "Parthenope". He is a Senior Member of IEEE. He has been a member of various journal editorial boards such as Signal Processing (Elsevier) and Journal of Electrical and Computer Engineering (Hindawi). He is the principal investigator of a NATO Grant on Communications Security. Recent awards include 2008 Most Cited Paper Award from Elsevier for a paper co-authored with W. A. Gardner and L. Paura entitled "Cyclostationarity: Half a century of research" (Signal Processing, vol. 86, April 2006), the most cited article in the last 5 years on Signal Processing (Elsevier); and in the 10 top most downloaded articles in the journal. Dr. Napolitano has held visiting appointments including: University Jeann Monnet, France; University of South Australia and Centro de Investigacion en Matematicas (CIMAT), Mexico. His research interests include statistical signal processing, system identification, the theory of higher order statistics of nonstationary signals and wireless systems.
Dedication iii Acknowledgements xiii Introduction xv 1 Background 1 1.1 Second-Order Characterization of Stochastic Processes 1 1.1.1 Time-Domain Characterization 1 1.1.2 Spectral-Domain Characterization 2 1.1.3 Time-Frequency Characterization 4 1.1.4 Wide-Sense Stationary Processes 5 1.1.5 Evolutionary Spectral Analysis 5 1.1.6 Discrete-Time Processes 7 1.1.7 Linear Time-Variant Transformations 8 1.2 Almost-Periodic Functions 10 1.2.1 Uniformly Almost-Periodic Functions 11 1.2.2 AP Functions in the Sense of Stepanov,Weyl, and Besicovitch 12 1.2.3 Weakly AP Functions in the Sense of Eberlein 13 1.2.4 Pseudo AP Functions 14 1.2.5 AP Functions in the Sense of Hartman and Ryll-Nardzewski 15 1.2.6 AP Functions Defined on Groups and with Values in Banach and Hilbert Spaces 16 1.2.7 AP Functions in Probability 16 1.2.8 AP Sequences 17 1.2.9 AP Sequences in Probability 18 1.3 Almost-Cyclostationary Processes 18 1.3.1 Second-OrderWide-Sense Statistical Characterization 18 1.3.2 Jointly ACS Signals 20 1.3.3 LAPTV Systems 24 1.3.4 Products of ACS Signals 27 1.3.5 Cyclic Statistics of Communications Signals 29 1.3.6 Higher-Order Statistics 30 1.3.7 Cyclic Statistic Estimators 32 1.3.8 Discrete-Time ACS Signals 32 1.3.9 Sampling of ACS Signals 33 1.3.10 Multirate Processing of Discrete-Time ACS Signals 37 1.3.11 Applications 37 1.4 Some Properties of Cumulants 38 1.4.1 Cumulants and Statistical Independence 38 1.4.2 Cumulants of Complex Random Variables and Joint Complex Normality 392 Generalized Almost-Cyclostationary Processes 43 2.1 Introduction 43 2.2 Characterization of GACS Stochastic Processes 47 2.2.1 Strict-Sense Statistical Characterization 48 2.2.2 Second-OrderWide-Sense Statistical Characterization 49 2.2.3 Second-Order Spectral Characterization 59 2.2.4 Higher-Order Statistics 61 2.2.5 Processes with Almost-Periodic Covariance 65 2.2.6 Motivations and Examples 66 2.3 Linear Time-Variant Filtering of GACS Processes 70 2.4 Estimation of the Cyclic Cross-Correlation Function 72 2.4.1 The Cyclic Cross-Correlogram 72 2.4.2 Mean-Square Consistency of the Cyclic Cross-Correlogram 76 2.4.3 Asymptotic Normality of the Cyclic Cross-Correlogram 80 2.5 Sampling of GACS Processes 84 2.6 Discrete-Time Estimator of the Cyclic Cross-Correlation Function 87 2.6.1 Discrete-Time Cyclic Cross-Correlogram 87 2.6.2 Asymptotic Results 91 2.6.3 Asymptotic Results 95 2.6.4 Concluding Remarks 102 2.7 Numerical Results 104 2.7.1 Aliasing in Cycle-Frequency Domain 105 2.7.2 Simulation Setup 105 2.7.3 Cyclic Correlogram Analysis with Varying N 105 2.7.4 Cyclic Correlogram Analysis with Varying N and T 106 2.7.5 Discussion 111 2.7.6 Conjecturing the Nonstationarity Type of the Continuous-Time Signal 114 2.7.7 LTI Filtering of GACS Signals 116 2.8 Summary 116 3 Complements and Proofs on Generalized Almost-Cyclostationary Processes 123 3.1 Proofs for Section 2.2.2 Second-OrderWide-Sense Statistical Characterization 123 3.2 Proofs for Section 2.2.3 Second-Order Spectral Characterization 125 3.3 Proofs for Section 2.3 Linear Time-Variant Filtering of GACS Processes 129 3.4 Proofs for Section 2.4.1 The Cyclic Cross-Correlogram 131 3.5 Proofs for Section 2.4.2 Mean-Square Consistency of the Cyclic Cross-Correlogram 136 3.6 Proofs for Section 2.4.3 Asymptotic Normality of the Cyclic Cross-Correlogram 147 3.7 Conjugate Covariance 150 3.8 Proofs for Section 2.5 Sampling of GACS Processes 151 3.9 Proofs for Section 2.6.1 Discrete-Time Cyclic Cross-Correlogram 152 3.10 Proofs for Section 2.6.2 Asymptotic Results as 158 3.11 Proofs for Section 2.6.3 Asymptotic Results as 168 3.12 Proofs for Section 2.6.4 Co