Telecommunications Topics : Applications of Functions and Probabilities in Electronic Communications

Telecommunications Topics : Applications of Functions and Probabilities in Electronic Communications

by E. Bryan Carne, Bryan E. Carne

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Product Details

ISBN-13: 9780136455653
Publisher: Simon & Schuster Adult Publishing Group
Publication date: 09/10/1998
Pages: 385
Product dimensions: 6.70(w) x 9.78(h) x 1.54(d)

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PREFACE: This book is written for those of us who came first to computer engineering and then discovered that digital communications were vital to the continuing expansion of the information age. As a result, we picked up bits and pieces of lore— enough to make a go of communicating, but not enough to fully appreciate so demanding a discipline. Also, it is for those who, through a better understanding of the applications of functions and probabilities to digital communications, wish to further their comprehension of what may be the most important technical development of the last quarter of the twentieth century. In many ways, Telecommunications Topics complements my previous book Telecommunications Primer (Prentice Hall; 1995), which provides an overview of modern, mostly digital communications without supporting analysis.

The 22 topics relate to one another, and progress from techniques for analysis to the analysis of operating techniques. Taken from the current telecommunications environment, they reflect some of the problems that have been investigated and solved over the last 30 years of intense development in predominantly digital communications. They are divided into three sections—Functions, Probabilities and Applications- which can be summarized as follows.

Functions. The notion of surrogate functions is fundamental to the analysis of communication systems. Chapter 1, Signals, describes the advantages and limitations of mathematical functions that mimic signals. With them, models are built to explore the behavior of systems. As a framework for future results, a chart is included that maps the relationships among time and frequencydomains and the techniques employed. In Chapter 2, Periodic Functions; Chapter 3, Transient Functions; Chapter 4, LTI Systems; and Chapter 5, Autocorrelation and Spectral Density; the techniques of deterministic analysis are reviewed and applied to periodic and transient signals. On a limited understanding of signal processing, the foundation is laid for the analysis of digital signals.

Probabilities. To come closer to real-world situations, ideas of randomness and measures of probabilities are introduced in Chapter 6, Probability. Chapter 7, Random Variables, develops the concepts of Binomial-, Poisson-, and Normal-distributions and introduces the properties of uniform-, exponential-, and Erlang-distributed random variables. The second section closes with Chapter 8, Random Processes. It provides a limited look at random processes and introduces the all-important Wiener-Khinchine connection between the autocorrelation function and the power spectral density of power-type functions.

Applications. Chapters 9 through 22 apply the results of the first eight chapters to the modern communications environment. In Chapter 9, Queues, steady-state results are developed for three basic queueing systems, and Erlang's formulas for telephone traffic are introduced. In Chapter 10, Noise, signal-to-noise ratio is defined, white noise is characterized, and the effect of noise on binary decisions is analyzed. Chapter 11, Information Theory, provides an elementary view of Shannon's theory including self-information and entropy, describes Shannon-Fano coding, and discusses Shannon's capacity theorem and the Hartley-Shannon law.

Chapter 12, Digital Voice Signals, describes the processes (sampling, quantizing, companding, and reconstruction) required to produce a digital signal from an analog voice signal. The effect of signal-to-noise ratio on the performance of PCM signals is discussed.

Chapters 13 through 17 are concerned with topics in data communication. In Chapter 13, Data Signals, several signal formats are described, and the frequency spectrums of random data signals are estimated. Coding and scrambling are discussed. In Chapter 14, Intersymbol Interference, pulse shaping, equalization, and regeneration of data signals are considered. Chapters 15 and 16 are devoted to error correction. In Chapter 15, Error Detection, parity checking, the use of checksums and cyclic redundancy checking are discussed. In Chapter 16, Error Correction, ARQ and forward error correction techniques are described. The throughput of various correction strategies is calculated for a range of data rates and other conditions. Chapter 17, Access to Shared Media, describes and analyzes popular techniques for providing shared access to common facilities.

Chapters 18 through 21 examine the characteristics of various types of radio signals. In Chapter 18, Amplitude Modulation, five methods of producing AM are analyzed. In Chapter 19, Angle Modulation, narrowband and wideband angle modulation is discussed, and the spectral characteristics of frequency modulation are developed. In Chapter 20, Digital Modulation, techniques for amplitude, phase, and frequency keying are discussed. Chapter 21, Spread Spectrum Modulation, describes direct spreading and frequency-hopping techniques and CDMA.

Finally, Chapter 22, Transmission Media, describes some of the properties of wire cables, optical fibers, cellular radio, and communication satellites.

Since very little happens in a vacuum, I would like to thank the many students, particularly those involved in continuing education, who asked questions of me and stimulated this work. The contents should be comfortable for those who have received courses in technical analysis. Hopefully, the result will be an increased understanding of some of the practices of digital communications.

E. Bryan Carne
Peterborough, NH

Table of Contents

Preface.
Functions.
1. SIGNALS.
Variation of Values with Time. Certainty with Which Behavior Is Known. Time for Which They Exist. Energy-Type or Power-Type. Signal Power. Signal Energy. Parameters for This Classification.

2. PERIODIC FUNCTIONS.
Fourier Series. Trigonometric Fourier Series. Fourier Cosine Series. Complex Periodic Function. Complex Quantities. Exponential Fourier Series. One-Sided and Two-Sided Spectrums. Rectangle Trains and Square Waves.

3. TRANSIENT FUNCTIONS.
Fourier Transform. Dirac's Improper Function. Fourier Transform of a Periodic Function. Additional Examples.

4. LTI SYSTEMS.
Laplace and Fourier Transforms. Impulse Response. Transfer Function. Bandwidth and Passband.

5. AUTOCORRELATION AND SPECTRAL DENSITY.
Correlation Functions. Energy-Type Functions. Power-Type Functions.

6. PROBABILITY.
Sets and Venn Diagrams. Probability. Probabilistic Functions.

7. RANDOM VARIABLES.
Binomial-Distributed Random Variable. Poisson-Distributed Random Variable. Normally-Distributed Random Variable. Uniformly-Distributed Random Variable. Exponentially-Distributed Random Variable. Erlang-Distributed Random Variable.

8. RANDOM PROCESSES.
Random or Stochastic Processes. Autocorrelation and Power Density of Random Processes.

9. QUEUES.
Queueing Theory. Queueing Models. Erlang's Formulas.

10. NOISE.
Sources of Noise. Signal-to-Noise Ratio. White Noise. Noise and Binary Decisions.

11. INFORMATION THEORY.
Self Information. Entropy and Information Rate. Entropy Coding. Channel Capacity.

12. DIGITAL VOICE SIGNALS.
Sampling an Analog Signal. Quantization. Companding. Reconstructing the Signal. PCM Voice.

13. DATA SIGNALS.
Operations. Binary Signal Formats. Scrambling. Estimating Spectral Densities.

14. INTERSYMBOL INTERFERENCE.
Pulse Shaping. Equalization. Regeneration.

15. ERROR DETECTION.
Parity Checking. Techniques That Employ Calculations. Coding.

16. ERROR CORRECTION.
ARQ Techniques. Forward Error Correction.

17. ACCESS TO SHARED MEDIA.
Pre-Assigned Access. Demand Assigned Access. Random Access.

18. AMPLITUDE MODULATION.
Message Signal. Large-Carrier AM (LCAM). Double-Sideband Suppressed-Carrier AM (DSBSC). Quadrature-Carrier Amplitude Modulation (QAM). Single-Sideband AM (SSB). Vestigial-Sideband AM (VSB). Signal-to-Noise Ratios. Frequency-Division Multiplexing.

19. ANGLE MODULATION.
Relationship between £M and FM. Narrowband Angle Modulation. Estimating the Bandwidth of Wideband Angle Modulation. Single-Tone Angle Modulation. SNR of Frequency Modulation with Discriminator Detection.

20. DIGITAL MODULATION.
Binary Keying. Quadrature Binary Modulation. M-ary Modulation.

21. SPREAD SPECTRUM MODULATION.
Channel Capacity. Process Gain and Jamming Margin. Pseudo-Noise Sequence. Spreading Techniques.

22. TRANSMISSION MEDIA.
Wire Cables. Optical Fiber. Cellular Radio. Communication Satellites.

List of Acronyms.
List of Symbols.
Appendix.

Preface

PREFACE: This book is written for those of us who came first to computer engineering and then discovered that digital communications were vital to the continuing expansion of the information age. As a result, we picked up bits and pieces of lore— enough to make a go of communicating, but not enough to fully appreciate so demanding a discipline. Also, it is for those who, through a better understanding of the applications of functions and probabilities to digital communications, wish to further their comprehension of what may be the most important technical development of the last quarter of the twentieth century. In many ways, Telecommunications Topics complements my previous book Telecommunications Primer (Prentice Hall; 1995), which provides an overview of modern, mostly digital communications without supporting analysis.

The 22 topics relate to one another, and progress from techniques for analysis to the analysis of operating techniques. Taken from the current telecommunications environment, they reflect some of the problems that have been investigated and solved over the last 30 years of intense development in predominantly digital communications. They are divided into three sections—Functions, Probabilities and Applications- which can be summarized as follows.

Functions. The notion of surrogate functions is fundamental to the analysis of communication systems. Chapter 1, Signals, describes the advantages and limitations of mathematical functions that mimic signals. With them, models are built to explore the behavior of systems. As a framework for future results, a chart is included that maps the relationships among time andfrequencydomains and the techniques employed. In Chapter 2, Periodic Functions; Chapter 3, Transient Functions; Chapter 4, LTI Systems; and Chapter 5, Autocorrelation and Spectral Density; the techniques of deterministic analysis are reviewed and applied to periodic and transient signals. On a limited understanding of signal processing, the foundation is laid for the analysis of digital signals.

Probabilities. To come closer to real-world situations, ideas of randomness and measures of probabilities are introduced in Chapter 6, Probability. Chapter 7, Random Variables, develops the concepts of Binomial-, Poisson-, and Normal-distributions and introduces the properties of uniform-, exponential-, and Erlang-distributed random variables. The second section closes with Chapter 8, Random Processes. It provides a limited look at random processes and introduces the all-important Wiener-Khinchine connection between the autocorrelation function and the power spectral density of power-type functions.

Applications. Chapters 9 through 22 apply the results of the first eight chapters to the modern communications environment. In Chapter 9, Queues, steady-state results are developed for three basic queueing systems, and Erlang's formulas for telephone traffic are introduced. In Chapter 10, Noise, signal-to-noise ratio is defined, white noise is characterized, and the effect of noise on binary decisions is analyzed. Chapter 11, Information Theory, provides an elementary view of Shannon's theory including self-information and entropy, describes Shannon-Fano coding, and discusses Shannon's capacity theorem and the Hartley-Shannon law.

Chapter 12, Digital Voice Signals, describes the processes (sampling, quantizing, companding, and reconstruction) required to produce a digital signal from an analog voice signal. The effect of signal-to-noise ratio on the performance of PCM signals is discussed.

Chapters 13 through 17 are concerned with topics in data communication. In Chapter 13, Data Signals, several signal formats are described, and the frequency spectrums of random data signals are estimated. Coding and scrambling are discussed. In Chapter 14, Intersymbol Interference, pulse shaping, equalization, and regeneration of data signals are considered. Chapters 15 and 16 are devoted to error correction. In Chapter 15, Error Detection, parity checking, the use of checksums and cyclic redundancy checking are discussed. In Chapter 16, Error Correction, ARQ and forward error correction techniques are described. The throughput of various correction strategies is calculated for a range of data rates and other conditions. Chapter 17, Access to Shared Media, describes and analyzes popular techniques for providing shared access to common facilities.

Chapters 18 through 21 examine the characteristics of various types of radio signals. In Chapter 18, Amplitude Modulation, five methods of producing AM are analyzed. In Chapter 19, Angle Modulation, narrowband and wideband angle modulation is discussed, and the spectral characteristics of frequency modulation are developed. In Chapter 20, Digital Modulation, techniques for amplitude, phase, and frequency keying are discussed. Chapter 21, Spread Spectrum Modulation, describes direct spreading and frequency-hopping techniques and CDMA.

Finally, Chapter 22, Transmission Media, describes some of the properties of wire cables, optical fibers, cellular radio, and communication satellites.

Since very little happens in a vacuum, I would like to thank the many students, particularly those involved in continuing education, who asked questions of me and stimulated this work. The contents should be comfortable for those who have received courses in technical analysis. Hopefully, the result will be an increased understanding of some of the practices of digital communications.

E. Bryan Carne
Peterborough, NH

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