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.

Dedication iiiAcknowledgements xiiiIntroduction xv1 Background 11.1 Second-Order Characterization of Stochastic Processes 11.2 Almost-Periodic Functions 101.3 Almost-Cyclostationary Processes 181.4 Some Properties of Cumulants 382.1 Introduction 432.2 Characterization of GACS Stochastic Processes 472.3 Linear Time-Variant Filtering of GACS Processes 702.4 Estimation of the Cyclic Cross-Correlation Function 722.5 Sampling of GACS Processes 842.6 Discrete-Time Estimator of the Cyclic Cross-Correlation Function 872.7 Numerical Results 1042.8 Summary 1163 Complements and Proofs on Generalized Almost-Cyclostationary Processes 1233.1 Proofs for Section 2.2.2 "Second-OrderWide-Sense Statistical Characterization" 1233.2 Proofs for Section 2.2.3 "Second-Order Spectral Characterization" 1253.3 Proofs for Section 2.3 "Linear Time-Variant Filtering of GACS Processes" 1293.4 Proofs for Section 2.4.1 "The Cyclic Cross-Correlogram" 1313.5 Proofs for Section 2.4.2 "Mean-Square Consistency of the Cyclic Cross-Correlogram" 1363.6 Proofs for Section 2.4.3 "Asymptotic Normality of the Cyclic Cross-Correlogram" 1473.7 Conjugate Covariance 1503.8 Proofs for Section 2.5 "Sampling of GACS Processes" 1513.9 Proofs for Section 2.6.1 "Discrete-Time Cyclic Cross-Correlogram" 1523.10 Proofs for Section 2.6.2 "Asymptotic Results as 1583.11 Proofs for Section 2.6.3 "Asymptotic Results as 1683.12 Proofs for Section 2.6.4 "Concluding Remarks" 1763.13 Discrete-Time and Hybrid Conjugate Covariance 1774 Spectrally Correlated Processes 1814.1 Introduction 1824.2 Characterization of SC Stochastic Processes 1864.3 Linear Time-Variant Filtering of SC Processes 2054.4 The Bifrequency Cross-Periodogram 2084.5 Measurement of Spectral Correlation - Unknown Support Curves 2154.6 The Frequency-Smoothed Cross-Periodogram 2224.7 Measurement of Spectral Correlation - Known Support Curves 2254.8 Discrete-Time SC Processes 2334.9 Sampling of SC Processes 2364.10 Multirate Processing of Discrete-Time Jointly SC Processes 2564.11 Discrete-Time Estimators of the Spectral Cross-Correlation Density 2724.12 Numerical Results 2734.13 Spectral Analysis with Nonuniform Frequency Resolution 2814.14 Summary 2865 Complements and Proofs on Spectrally Correlated Processes 2915.1 Proofs for Section 4.2 "Spectrally Correlated Stochastic Processes" 2915.2 Proofs for Section 4.4 "The Bifrequency Cross-Periodogram" 2925.3 Proofs for Section 4.5 "Measurement of Spectral Correlation - Unknown Support Curves" 2985.4 Proofs for Section 4.6 "The Frequency-Smoothed Cross-Periodogram" 3065.5 Proofs for Section 4.7.1 "Mean-Square Consistency of the Frequency-Smoothed Cross-Periodogram" 3095.6 Proofs for Section 4.7.2 "Asymptotic Normality of the Frequency-Smoothed Cross-Periodogram" 3255.7 Alternative Bounds 3335.8 Conjugate Covariance 3345.9 Proofs for Section 4.8 "Discrete-Time SC Processes" 3375.10 Proofs for Section 4.9 "Sampling of SC Processes" 3395.11 Proofs for Section 4.10 "Multirate Processing of Discrete-Time Jointly SC Processes" 3426 Functional Approach for Signal Analysis 3556.1 Introduction 3556.2 Relative Measurability 3566.3 Almost-Periodically Time-Variant Model 3616.4 Nonstationarity Classification in the Functional Approach 3746.5 Proofs of FOT Counterparts of Some Results on ACS and GACS Signals 3757 Applications to Mobile Communications and Radar/Sonar 3817.1 Physical Model for the Wireless Channel 3817.2 Constant Velocity Vector 3937.3 Constant Relative Radial Speed 3957.4 Constant Relative Radial Acceleration 4077.5 Transmitted Signal: Narrow-Band Condition 4097.6 Multipath Doppler Channel 4167.7 Spectral Analysis of Doppler-Stretched Signals - Constant Radial Speed 4177.8 Spectral Analysis of Doppler-Stretched Signals - Constant Relative Radial Acceleration 4487.9 Other Models of Time-Varying Delays 4527.10 Proofs 4558 Bibliographic Notes 4638.1 Almost-Periodic Functions 4638.2 Cyclostationary Signals 4638.3 Generalizations of Cyclostationarity 4648.4 Other Nonstationary Signals 4648.5 Functional Approach and Generalized Harmonic Analysis 4648.6 Linear Time-Variant Processing 4658.7 Sampling 4658.8 Complex Random Variables, Signals, and Systems 4658.9 Stochastic Processes 4658.10 Mathematics 4668.11 Signal Processing and Communications 466References 467List of Abbreviations 475