Cover Page -- Half-Title Page -- Title page -- Copyright page -- Contents -- Introduction -- 1: Background and System Model -- 1.1. Channel model -- 1.1.1. The multipath channel -- 1.1.2. Statistics of the channel -- 1.1.2.1. Rayleigh channel -- 1.1.2.2. WSSUS model -- 1.2. Transmission of an OFDM signal -- 1.2.1. Continuous representation -- 1.2.2. Discrete representation -- 1.2.3. Discrete representation under synchronization mismatch -- 1.3. Pilot symbol aided channel and noise estimation -- 1.3.1. The pilot arrangements -- 1.3.2. Channel estimation -- 1.3.2.1. LS estimation -- 1.3.2.2. LMMSE estimation -- 1.3.2.3. Other estimation techniques -- 1.3.3. Noise variance estimation -- 1.4. Work motivations -- 2: Joint Channel and Noise Variance Estimation in the Presence of the OFDM Signal -- 2.1. Presentation of the algorithm in an ideal approach -- 2.1.1. Channel covariance matrix -- 2.1.2. MMSE noise variance estimation -- 2.1.3. Proposed algorithm: ideal approach -- 2.1.3.1. Description of the algorithm -- 2.1.3.2. Convergence of the algorithm -- 2.1.3.2.1. Scalar expression of the sequence (σˆ2(i)) -- 2.1.3.2.2. Proof of convergence -- 2.1.3.3. Uniqueness of the solution: proof by contradiction -- 2.1.3.3.1. Polynomial expression of the problem to solve -- 2.1.3.3.2. Sign of the polynomial considering R_H -- 2.1.3.3.3. Sign of the polynomial considering R˘_H -- 2.1.3.4. Characterization of the channel and noise estimations -- 2.1.4. Simulation results: ideal approach -- 2.1.4.1. Convergence of the noise variance estimation -- 2.1.4.2. Speed of convergence of the algorithm -- 2.1.4.3. Bias of the noise variance estimation -- 2.1.4.4. Comparison of SNR estimation with other methods -- 2.1.4.5. Channel estimation -- 2.2. Algorithm in a practical approach -- 2.2.1. Proposed algorithm: realistic approach -- 2.2.2. Convergence of the algorithm.

2.2.2.1. Scalar expression of the sequence (σˆ2(i)) -- 2.2.2.2. Necessary condition for the convergence of the sequence (σˆ2(i)) -- 2.2.2.3. Sufficient condition for the convergence of the sequence (σˆ2(i)) -- 2.2.2.4. Optimal choice of the initialization σˆ2(i=0) -- 2.2.3. Simulations results: realistic approach -- 2.2.3.1. Convergence of the noise variance estimation -- 2.2.3.2. Characterization of the threshold eσ -- 2.2.3.3. Comparison of SNR estimation with other methods -- 2.2.3.4. Channel estimation -- 2.3. Summary -- 3: Application of the Algorithm as a Detector for Cognitive Radio Systems -- 3.1. Spectrum sensing -- 3.1.1. Non-cooperative methods -- 3.1.2. Cooperative methods -- 3.2. Proposed detector -- 3.2.1. Detection hypothesis -- 3.2.2. Convergence of the MMSE-based algorithm under the hypothesis H0 -- 3.2.2.1. Expression of the algorithm under H0 -- 3.2.2.2. Scalar expression of the sequence (σˆ2(i)) -- 3.2.2.3. Convergence of the sequence (σˆ2(i)) to a non-null solution -- 3.2.3. Decision rule for the proposed detector -- 3.3. Analytical expressions of the detection and false alarm probabilities -- 3.3.1. Probability density function of M under H1 -- 3.3.2. Probability density function of M under H0 -- 3.3.3. Analytical expressions of Pd and Pfa -- 3.4. Simulations results -- 3.4.1. Choice of the threshold ς -- 3.4.2. Effect of the choice of eσ on the detector performance -- 3.4.3. Detector performance under non-WSS channel model and synchronization mismatch -- 3.4.4. Receiver operating characteristic of the detector -- 3.5. Summary -- Conclusion -- Appendix 1: Appendix to Chapter 2 -- Appendix 2: Appendix to Chapter 3 -- Bibliography -- Index.