Notation ....................................................... xi
Introduction .................................................... 1
§0.1 Motivation ................................................ 1
§0.2 Problem Statement ......................................... 1
§0.3 Research Objectives ....................................... 2
§0.4 Contributions ............................................. 2
§0.5 Dissertation Outline ...................................... 3
Chapter 1 Spread Spectrum and Location Systems ................. 5
§1 Introduction ................................................ 5
§2 Basic Principle of Spread Spectrum .......................... 6
§3 Spreading Signal ............................................ 7
§3.1 Correlation Measures .................................. 7
§3.2 Pseudo Random Signal .................................. 9
§4 Location using SS-CDMA ..................................... 18
§4.1 Ranging .............................................. 18
§4.2 Positioning .......................................... 20
§4 Summary ..................................................... 21
Chapter 2 Design of Ranging Signals ........................... 23
§1 System Structure ........................................... 23
§2 Estimation Precision ....................................... 24
§2.1 Maximum-Likelihood Estimators ........................ 24
§2.2 Estimation of ToF .................................... 25
§3 Theory of Ranging Signals .................................. 29
§3.1 Traditional Ranging Signals .......................... 29
§3.2 New Concept of Ranging Signals ....................... 32
§3.3 Decrease Effective Code Length ....................... 33
§3.4 Decrease Pulse Energy Efficiency ..................... 37
§3.5 Secondary Ranging Signals ............................ 38
§3.6 Initial State for Low Correlation Zone ............... 43
§4 Numerical Evaluations ...................................... 44
§4.1 Real Codes ........................................... 44
§4.2 Complex Codes ........................................ 46
§5 Summary .................................................... 48
Chapter 3 Sensing of Ranging Signals .......................... 51
§1 Introduction ............................................... 51
§1.1 General Representation ............................... 51
§1.2 Finding Representation ............................... 52
§1.3 Uniqueness of Underdetermined Problem ................ 53
§1.4 Sparse Condition using Correlation ................... 54
§2 Sparsity and Basic Recovery Approaches ..................... 56
§2.1 Sufficient Condition for BP and GA ................... 58
§2.2 General Recovery ..................................... 60
§3 RIP for Ranging Signals .................................... 63
§3.1 Recovery Algorithms .................................. 64
§3.2 RCoSaMP .............................................. 65
§3.3 Theoretic Model ..................................... 67
§4 PN-Chirp Sensing ........................................... 68
§5 Summary .................................................... 74
Chapter 4 Multi-Correlation Receiver .......................... 77
§1 Introduction ............................................... 77
§1.1 Delay-and-Multiply ................................... 77
§1.2 Multi-Correlation Function ........................... 79
§1.3 Modified DAM ......................................... 80
§2 Amplitude Scaling .......................................... 82
§2.1 Unipolar Pulse Codes ................................. 86
§2.2 Generalized DAM ...................................... 86
§3 Numerical Evaluations ...................................... 87
§3.1 Single-User Case ..................................... 89
§3.2 Multi-User Case ...................................... 90
§4 Summary .................................................... 91
Chapter 5 Conclusions and Future Work ......................... 93
§1 Synopsis ................................................... 93
§2 Future Work ................................................ 95
Appendix A Mathematical Tools ................................. 97
Appendix В Mathematical Derivations ........................... 99
§0.1 Derivation of Correlation Bound .......................... 99
§0.2 Derivation of Correlation Parameter ..................... 101
§0.3 Linear Chirp Ambiguity Function ......................... 102
§0.4 LCZ and ZCZ ............................................. 103
§0.5 Compressible Signals .................................... 105
§0.6 Gram Matrix ............................................. 106
§0.7 Routine Map of Gold Codes ............................... 107
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