Book contents
- Frontmatter
- Contents
- Preface
- List of Abbreviations
- List of Notation
- 1 Overview of Wireless Communications
- 2 Path Loss and Shadowing
- 3 Statistical Multipath Channel Models
- 4 Capacity of Wireless Channels
- 5 Digital Modulation and Detection
- 6 Performance of Digital Modulation over Wireless Channels
- 7 Diversity
- 8 Coding for Wireless Channels
- 9 Adaptive Modulation and Coding
- 10 Multiple Antennas and Space-Time Communications
- 11 Equalization
- 12 Multicarrier Modulation
- 13 Spread Spectrum
- 14 Multiuser Systems
- 15 Cellular Systems and Infrastructure-Based Wireless Networks
- 16 Ad Hoc Wireless Networks
- Appendix A Representation of Bandpass Signals and Channels
- Appendix B Probability Theory, Random Variables, and Random Processes
- Appendix C Matrix Definitions, Operations, and Properties
- Appendix D Summary of Wireless Standards
- Bibliography
- Index
Appendix A - Representation of Bandpass Signals and Channels
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- List of Abbreviations
- List of Notation
- 1 Overview of Wireless Communications
- 2 Path Loss and Shadowing
- 3 Statistical Multipath Channel Models
- 4 Capacity of Wireless Channels
- 5 Digital Modulation and Detection
- 6 Performance of Digital Modulation over Wireless Channels
- 7 Diversity
- 8 Coding for Wireless Channels
- 9 Adaptive Modulation and Coding
- 10 Multiple Antennas and Space-Time Communications
- 11 Equalization
- 12 Multicarrier Modulation
- 13 Spread Spectrum
- 14 Multiuser Systems
- 15 Cellular Systems and Infrastructure-Based Wireless Networks
- 16 Ad Hoc Wireless Networks
- Appendix A Representation of Bandpass Signals and Channels
- Appendix B Probability Theory, Random Variables, and Random Processes
- Appendix C Matrix Definitions, Operations, and Properties
- Appendix D Summary of Wireless Standards
- Bibliography
- Index
Summary
Many signals in communication systems are real bandpass signals with a frequency response that occupies a narrow bandwidth 2B centered around a carrier frequency fc with 2B « fc, as shown in Figure A.1. Since bandpass signals are real, their frequency response has conjugate symmetry: a bandpass signal s(t) has |S(f)| = |S(−f)| and ∠S(f) = −∠S(−f). However, bandpass signals are not necessarily conjugate symmetric within the signal bandwidth about the carrier frequency fc; that is, we may have |S(fc + f)| ≠ |S(fc − f)| or ∠S(fc + f) ≠ −∠S(fc − f) for some f : 0 < f ≤ B. This asymmetry in |S(f)| about fc (i.e., |S(fc + f)| ≠ |S(fc − f)| for some f < B) is illustrated in the figure. Bandpass signals result from modulation of a baseband signal by a carrier, or from filtering a deterministic or random signal with a bandpass filter. The bandwidth 2B of a bandpass signal is roughly equal to the range of frequencies around fc where the signal has nonnegligible amplitude. Bandpass signals are commonly used to model transmitted and received signals in communication systems. These are real signals because the transmitter circuitry can only generate real sinusoids (not complex exponentials), and the channel simply introduces an amplitude and phase change at each frequency of the real transmitted signal.
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- Wireless Communications , pp. 573 - 576Publisher: Cambridge University PressPrint publication year: 2005