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Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications

Book Description

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.

  • Table of Contents

    1. Cover
    2. Title Page
    3. Copyright
    4. Dedication
    5. About the Author
    6. Acknowledgements
    7. Preface
    8. List of Abbreviations
    9. Chapter 1: Background
      1. 1.1 Second-Order Characterization of Stochastic Processes
      2. 1.2 Almost-Periodic Functions
      3. 1.3 Almost-Cyclostationary Processes
      4. 1.4 Some Properties of Cumulants
    10. Chapter 2: Generalized Almost-Cyclostationary Processes
      1. 2.1 Introduction
      2. 2.2 Characterization of GACS Stochastic Processes
      3. 2.3 Linear Time-Variant Filtering of GACS Processes
      4. 2.4 Estimation of the Cyclic Cross-Correlation Function
      5. 2.5 Sampling of GACS Processes
      6. 2.6 Discrete-Time Estimator of the Cyclic Cross-Correlation Function
      7. 2.7 Numerical Results
      8. 2.8 Summary
    11. Chapter 3: Complements and Proofs on Generalized Almost-Cyclostationary Processes
      1. 3.1 Proofs for Section 2.2.2 “Second-Order Wide-Sense Statistical Characterization”
      2. 3.2 Proofs for Section 2.2.3 “Second-Order Spectral Characterization”
      3. 3.3 Proofs for Section 2.3 “Linear Time-Variant Filtering of GACS Processes”
      4. 3.4 Proofs for Section 2.4.1 “The Cyclic Cross-Correlogram”
      5. 3.5 Proofs for Section 2.4.2 “Mean-Square Consistency of the Cyclic Cross-Correlogram”
      6. 3.6 Proofs for Section 2.4.3 “Asymptotic Normality of the Cyclic Cross-Correlogram”
      7. 3.7 Conjugate Covariance
      8. 3.8 Proofs for Section 2.5 “Sampling of GACS Processes”
      9. 3.9 Proofs for Section 2.6.1 “Discrete-Time Cyclic Cross-Correlogram”
      10. 3.10 Proofs for Section 2.6.2 “Asymptotic Results as N→ ∞”
      11. 3.11 Proofs for Section 2.6.3 “Asymptotic Results as N→ ∞ and Ts → 0′′
      12. 3.12 Proofs for Section 2.6.4 “Concluding Remarks”
      13. 3.13 Discrete-Time and Hybrid Conjugate Covariance
    12. Chapter 4: Spectrally Correlated Processes
      1. 4.1 Introduction
      2. 4.2 Characterization of SC Stochastic Processes
      3. 4.3 Linear Time-Variant Filtering of SC Processes
      4. 4.4 The Bifrequency Cross-Periodogram
      5. 4.5 Measurement of Spectral Correlation –Unknown Support Curves
      6. 4.6 The Frequency-Smoothed Cross-Periodogram
      7. 4.7 Measurement of Spectral Correlation –Known Support Curves
      8. 4.8 Discrete-Time SC Processes
      9. 4.9 Sampling of SC Processes
      10. 4.10 Multirate Processing of Discrete-Time Jointly SC Processes
      11. 4.11 Discrete-Time Estimators of the Spectral Cross-Correlation Density
      12. 4.12 Numerical Results
      13. 4.13 Spectral Analysis with Nonuniform Frequency Spacing
      14. 4.14 Summary
    13. Chapter 5: Complements and Proofs on Spectrally Correlated Processes
      1. 5.1 Proofs for Section 4.2 “Characterization of SC Stochastic Processes”
      2. 5.2 Proofs for Section 4.4 “The Bifrequency Cross-Periodogram”
      3. 5.3 Proofs for Section 4.5 “Measurement of Spectral Correlation –Unknown Support Curves”
      4. 5.4 Proofs for Section 4.6 “The Frequency-Smoothed Cross-Periodogram”
      5. 5.5 Proofs for Section 4.7.1 “Mean-Square Consistency of the Frequency-Smoothed Cross-Periodogram”
      6. 5.6 Proofs for Section 4.7.2 “Asymptotic Normality of the Frequency-Smoothed Cross-Periodogram”
      7. 5.7 Alternative Bounds
      8. 5.8 Conjugate Covariance
      9. 5.9 Proofs for Section 4.8 “Discrete-Time SC Processes”
      10. 5.10 Proofs for Section 4.9 “Sampling of SC Processes”
      11. 5.11 Proofs for Section 4.10 “Multirate Processing of Discrete-Time Jointly SC Processes”
    14. Chapter 6: Functional Approach for Signal Analysis
      1. 6.1 Introduction
      2. 6.2 Relative Measurability
      3. 6.3 Almost-Periodically Time-Variant Model
      4. 6.4 Nonstationarity Classification in the Functional Approach
      5. 6.5 Proofs of FOT Counterparts of Some Results on ACS and GACS Signals
    15. Chapter 7: Applications to Mobile Communications and Radar/Sonar
      1. 7.1 Physical Model for the Wireless Channel
      2. 7.2 Constant Velocity Vector
      3. 7.3 Constant Relative Radial Speed
      4. 7.4 Constant Relative Radial Acceleration
      5. 7.5 Transmitted Signal: Narrow-Band Condition
      6. 7.6 Multipath Doppler Channel
      7. 7.7 Spectral Analysis of Doppler-Stretched Signals –Constant Radial Speed
      8. 7.8 Spectral Analysis of Doppler-Stretched Signals –Constant Relative Radial Acceleration
      9. 7.9 Other Models of Time-Varying Delays
      10. 7.10 Proofs
    16. Chapter 8: Bibliographic Notes
      1. 8.1 Almost-Periodic Functions
      2. 8.2 Cyclostationary Signals
      3. 8.3 Generalizations of Cyclostationarity
      4. 8.4 Other Nonstationary Signals
      5. 8.5 Functional Approach and Generalized Harmonic Analysis
      6. 8.6 Linear Time-Variant Processing
      7. 8.7 Sampling
      8. 8.8 Complex Random Variables, Signals, and Systems
      9. 8.9 Stochastic Processes
      10. 8.10 Mathematics
      11. 8.11 Signal Processing and Communications
    17. References
    18. Index