INTRODUCTION ix CHAPTER 1. BACKGROUND AND SYSTEM MODEL 1 1.1. Channel model 1 1.1.1. The multipath channel 1 1.1.2. Statistics of the channe l2 1.2. Transmission of an OFDM signal 7 1.2.1. Continuous representation 7 1.2.2. Discrete representation 9 1.2.3. Discrete representation under synchronization mismatch 12 1.3. Pilot symbol aided channel and noise estimation 12 1.3.1. The pilot arrangements 12 1.3.2. Channel estimation 15 1.3.3. Noise variance estimation 19 1.4. Work motivations 22 CHAPTER 2. JOINT CHANNEL AND NOISE VARIANCE ESTIMATION IN THE PRESENCE OF THE OFDM SIGNAL 25 2.1. Presentation of the algorithm in an ideal approach 25 2.1.1. Channel covariance matrix 25 2.1.2. MMSE noise variance estimation 27 2.1.3. Proposed algorithm: ideal approach 27 2.1.4. Simulation results: ideal approach 41 2.2. Algorithm in a practical approach 48 2.2.1. Proposed algorithm: realistic approach 48 2.2.2. Convergence of the algorithm 51 2.2.3. Simulations results: realistic approach 60 2.3. Summary 65 CHAPTER 3. APPLICATION OF THE ALGORITHM AS A DETECTOR FOR COGNITIVE RADIO SYSTEMS 67 3.1. Spectrum sensing 67 3.1.1. Non-cooperative methods 69 3.1.2. Cooperative methods 71 3.2. Proposed detector 73 3.2.1. Detection hypothesis 73 3.2.2. Convergence of the MMSE-based algorithm under the hypothesis H0 74 3.2.3. Decision rule for the proposed detector 79 3.3. Analytical expressions of the detection and false alarm probabilities 82 3.3.1. Probability density function ofMunder H1 82 3.3.2. Probability density function ofMunder H0 85 3.3.3. Analytical expressions of Pd and Pfa 86 3.4. Simulations results 88 3.4.1. Choice of the threshold 88 3.4.2. Effect of the choice of e on the detector performance 89 3.4.3. Detector performance under non-WSS channel model and synchronization mismatch 92 3.4.4. Receiver operating characteristic of the detector 94 3.5. Summary 98 CONCLUSION 99 APPENDICES 101 BIBLIOGRAPHY 109 INDEX 119
