Preface |
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xiii | |
Contributors |
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xv | |
List of Figures |
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xvii | |
List of Tables |
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xxi | |
Acronyms |
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xxiii | |
Acknowledgments |
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xxv | |
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Chapter 1 Fundamentals of Probability Theory |
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1 | (36) |
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1 | (1) |
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1.2 Basics of Probability |
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2 | (5) |
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1.2.1 Probability of an Event |
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4 | (2) |
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1.2.1.1 Axiomatic Definition |
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4 | (1) |
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1.2.1.2 Relative Frequency Definition |
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5 | (1) |
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1.2.1.3 Classical Definition |
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5 | (1) |
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1.2.2 Conditional Probability |
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6 | (1) |
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1.2.3 Independence of Events |
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7 | (1) |
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7 | (18) |
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1.3.1 Cumulative Distribution Function (CDF) |
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8 | (1) |
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1.3.1.1 Properties of Cumulative Distribution Function |
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8 | (1) |
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1.3.2 The Probability Density Function (PDF) |
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9 | (1) |
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1.3.2.1 Properties of Probability Density Functions |
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9 | (1) |
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1.3.3 Joint Distribution and Density Function |
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9 | (1) |
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1.3.4 Conditional Probability Density Function |
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10 | (1) |
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1.3.5 Statistical Independence |
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11 | (1) |
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1.3.6 Moments of a Random Variable |
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11 | (3) |
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1.3.7 Some Key Random Variables |
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14 | (8) |
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1.3.7.1 Discrete Random Variables |
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14 | (1) |
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1.3.7.2 Continuous Random Variables |
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15 | (7) |
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1.3.8 The Markov and Chebyschev Inequalities |
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22 | (1) |
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1.3.9 The Sample Mean and the Laws of Large Numbers |
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22 | (2) |
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1.3.9.1 Weak Law of Large Numbers |
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24 | (1) |
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1.3.9.2 Strong Law of Large Numbers |
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24 | (1) |
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1.3.10 Central Limit Theorem (CLT) |
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24 | (1) |
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25 | (12) |
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1.4.1 Definition of Stochastic Process |
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25 | (1) |
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1.4.2 Statistics of Stochastic Process |
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26 | (2) |
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28 | (2) |
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1.4.3.1 Properties of Autocorrelation Function |
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29 | (1) |
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1.4.4 Random Process through Linear System |
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30 | (2) |
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1.4.5 Power Spectral Density (PSD) |
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32 | (2) |
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1.4.5.1 Properties of Power Spectral Density |
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33 | (1) |
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1.4.5.2 Output Spectral Density of an LTI System |
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34 | (1) |
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1.4.6 Gaussian Random Process |
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34 | (1) |
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35 | (2) |
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37 | (18) |
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38 | (5) |
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43 | (9) |
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2.2.1 Narrowband Spectrum Sensing |
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43 | (4) |
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2.2.1.1 Matched Filter Detection |
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44 | (1) |
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2.2.1.2 Cyclostationary Detection |
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45 | (1) |
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2.2.1.3 Covariance-Based Detection |
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46 | (1) |
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2.2.1.4 Eigenvalue-Based Detection |
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46 | (1) |
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46 | (1) |
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2.2.2 Wideband Spectrum Sensing |
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47 | (2) |
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2.2.2.1 Nyquist Wideband Spectrum Sensing |
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48 | (1) |
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2.2.2.2 Sub-Nyquist Wideband Spectrum Sensing |
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48 | (1) |
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2.2.3 Cooperative Spectrum Sensing |
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49 | (2) |
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2.2.4 Machine-Learning-Based Spectrum Sensing |
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51 | (1) |
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52 | (1) |
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53 | (2) |
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Chapter 3 Literature Review |
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55 | (12) |
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3.1 Narrowband Spectrum Sensing |
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55 | (3) |
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3.2 Wideband Spectrum Sensing |
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58 | (2) |
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3.3 Cooperative Spectrum Sensing |
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60 | (2) |
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3.4 Machine-Learning-Based Spectrum Sensing |
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62 | (5) |
Part I Narrowband Spectrum Sensing |
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Chapter 4 Energy-Detection-Based Spectrum Sensing over Generalized Fading Model |
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67 | (16) |
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4.1 System and Channel Models |
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68 | (2) |
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4.1.1 Energy Detection (ED) |
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68 | (2) |
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70 | (1) |
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4.2 Average Probability of Detection over ηλμ Fading Channel |
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70 | (6) |
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70 | (2) |
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4.2.2 Square Law Selection (SLS) Diversity |
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72 | (2) |
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4.2.3 Cooperative Spectrum Sensing |
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74 | (2) |
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4.3 Average Probability of Detection over Channels with ηλμ Fading and Shadowing |
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76 | (1) |
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4.4 Results and Discussion |
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77 | (5) |
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82 | (1) |
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Chapter 5 Generalized Energy Detector in the Presence of Noise Uncertainty and Fading |
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83 | (38) |
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84 | (1) |
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5.2 Noise Uncertainty Model |
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85 | (1) |
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5.3 SNR Wall for AWGN Channel |
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86 | (17) |
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87 | (2) |
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89 | (7) |
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96 | (2) |
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5.3.4 CSS with Hard Combining |
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98 | (4) |
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99 | (1) |
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100 | (1) |
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5.3.4.3 k Out of M Combining Rule |
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101 | (1) |
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5.3.5 CSS with Soft Combining |
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102 | (1) |
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5.4 SNR Wall for Fading Channel |
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103 | (5) |
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103 | (2) |
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105 | (1) |
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106 | (1) |
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5.4.4 CSS with Hard Combining |
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106 | (2) |
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107 | (1) |
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107 | (1) |
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5.4.5 CSS with Soft Combining |
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108 | (1) |
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5.5 Results and Discussion |
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108 | (9) |
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5.5.1 SNR Wall for AWGN Case |
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109 | (3) |
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5.5.2 SNR Wall for Fading Case |
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112 | (2) |
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5.5.3 Effect of Noise Uncertainty and Fading on Detection Performance |
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114 | (2) |
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116 | (1) |
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117 | (4) |
Part 2 Wideband Spectrum Sensing |
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Chapter 6 Diversity for Wideband Spectrum Sensing under Fading |
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121 | (32) |
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6.1 System Model and Performance Metrics |
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122 | (2) |
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124 | (5) |
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6.2.1 Channel-by-Channel Square Law Combining (CC-SLC) |
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125 | (1) |
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6.2.2 Ranked Square Law Combining (R-SLC) Detection |
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126 | (1) |
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6.2.3 Ranked Square Law Selection (R-SLS) Detection |
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127 | (2) |
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6.3 Approximation of Decision Statistic |
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129 | (4) |
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6.3.1 PDF for SLC Diversity |
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130 | (2) |
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6.3.1.1 Without Using Approximation |
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130 | (1) |
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6.3.1.2 Using Approximation |
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130 | (2) |
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6.3.2 PDF for SLS Diversity |
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132 | (1) |
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6.3.2.1 Without Using Approximation |
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132 | (1) |
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6.3.2.2 Using Approximation |
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133 | (1) |
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6.4 Theoretical Analysis of Detection Algorithms |
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133 | (6) |
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6.4.1 Channel-by-Channel Square Law Combining (CC-SLC) |
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133 | (2) |
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6.4.2 Theoretical Analysis for R-SLC |
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135 | (3) |
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6.4.3 Theoretical Analysis of R-SLS |
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138 | (1) |
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6.5 Results and Discussion |
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139 | (12) |
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151 | (2) |
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Chapter 7 Cooperative Wideband Spectrum Sensing |
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153 | (26) |
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7.1 System Model and Performance Metrics |
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154 | (1) |
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7.2 Proposed CWSS Algorithms |
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155 | (4) |
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7.2.1 Proposed Algorithm Based on Hard Combining |
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155 | (2) |
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7.2.2 Proposed Algorithm Based on Soft Combining |
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157 | (2) |
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7.3 Approximation to pdf of Decision Statistic |
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159 | (3) |
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7.4 Theoretical Analysis of the Detection Algorithms |
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162 | (6) |
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7.4.1 Theoretical Analysis for Algorithm 4 |
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162 | (3) |
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7.4.1.1 Performance Using Any Value of M with Fixed L |
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164 | (1) |
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7.4.1.2 Performance Using Any Value of L with Fixed M |
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165 | (1) |
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7.4.2 Theoretical Analysis for Algorithm 5 |
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165 | (3) |
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7.5 Results and Discussion |
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168 | (10) |
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7.5.1 Experimentations Using Algorithm 4 |
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168 | (6) |
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7.5.2 Experimentations Using Algorithm 5 |
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174 | (4) |
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178 | (1) |
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Chapter 8 Conclusions and Future Research Directions |
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179 | (4) |
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179 | (1) |
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8.2 Future Research Directions |
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180 | (3) |
Appendix A Appendix for Chapter 1 |
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183 | (4) |
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A.1 Proof for Markov Inequality |
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183 | (1) |
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A.2 Proof Central Limit Theorem |
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184 | (1) |
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A.3 Characteristic Function of Gaussian Random Variable |
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185 | (2) |
Appendix B Appendix for Chapter 4 |
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187 | (2) |
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B.1 Derivation for PF (τ) in Eq. (4.3) |
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187 | (2) |
Appendix C Appendix for Chapter 5 |
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189 | (6) |
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C.1 Derivation for PD,plc in Eq. (5.27) |
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189 | (3) |
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C.2 Derivation for PDNak in Eq. (5.77) |
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192 | (1) |
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C.3 Derivation for PDNak,plc in Eq. (5.81) |
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193 | (2) |
Appendix D Appendix for Chapter 6 |
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195 | (8) |
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D.1 Proof for Convergence of PDF of SLC under Nakagami Fading Channel in Eq. (6.12) |
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195 | (1) |
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D.2 Derivation of PDF of SLS under Nakagami Fading in Eq. (6.17) |
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195 | (1) |
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D.3 Proof for Convergence of PDF of SLS under Nakagami Fading in Eq. (6.17) |
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196 | (1) |
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D.4 Derivation of PDF in Eq. (6.13) |
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197 | (1) |
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D.5 Derivation of Eq. (6.34) |
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198 | (1) |
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D.6 Derivation of PDF in Eq. (6.36) |
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199 | (1) |
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D.7 Theoretical Analysis of R-SLC for L = 3 |
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199 | (4) |
Appendix E Some Special Functions |
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203 | (6) |
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203 | (1) |
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E.2 Lower Incomplete Gamma Function |
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203 | (1) |
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E.3 Upper Incomplete Gamma Function |
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204 | (1) |
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E.4 Generalized Marcum Q-Function |
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204 | (1) |
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E.5 Bessel Function of the First Kind |
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204 | (1) |
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E.6 Modified Bessel Function of the First Kind |
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205 | (1) |
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E.7 Confluent Hypergeometric Function |
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205 | (1) |
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E.8 Confluent Hypergeometric Function of the Second Kind |
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206 | (1) |
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206 | (1) |
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206 | (1) |
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207 | (1) |
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207 | (2) |
Bibliography |
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209 | (18) |
Index |
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227 | |