Behaviour of the eigenvalues of the empirical spatio-temporal covariance matrices of temporally and spatially complex Gaussian noise.

Get Complete Project Material File(s) Now! »

Behaviour of the largest eigenvalues and corresponding eigenvectors of §(L) N §(L)¤ N

Estimation of regularized spatio-temporalWiener filters

Performance analysis of spatial smoothing schemes in the context of large arrays

Table of contents :

Remerciements
1 Introduction
1.1 Introduction
1.2 Review of useful known results.
1.3 Behaviour of the eigenvalues of the empirical spatio-temporal covariance matrices of temporally and spatially complex Gaussian noise.
1.4 Contributions of the thesis.
2 Spatial-temporal Gaussian information plus noise spiked model
2.1 Introduction
2.2 Behaviour of the largest eigenvalues and corresponding eigenvectors of §(L) N §(L)¤ N
2.3 Detection of a wideband signal.
2.4 Estimation of regularized spatio-temporalWiener filters
2.5 Performance analysis of spatial smoothing schemes in the context of large arrays
3 Complex Gaussian information plus noise models: the deterministic equivalents
3.1 Notations and useful tools.
3.2 Random variables notations and tools.
3.3 Overview of the results of Chapter.
3.4 Poincaré-Nash variance evaluations
3.5 Expression of matrices E(Q) and E(˜Q) obtained using the integration by parts formula
3.6 Preliminary controls of the error terms ¨, ˜¨
3.7 The deterministic equivalents: existence and uniqueness
3.8 Convergence towards the deterministic equivalents: the normalized traces
3.9 Convergence towards the deterministic equivalents: the bilinear forms
3.A Proof of lemma
4 Convergence towards spiked model : the case of wideband array processingmodels
4.1 Introduction
4.2 Overview of the results.
4.3 Simplified behaviour of the bilinear forms of QN(z) and ˜QN(z).
4.4 Application to regularized estimated spatial-temporalWiener filters in large system case .
4.5 Asymptotic behaviour of the SINR
4.A Proof of lemma 4.3.1
4.B Proof of lemma 4.5.2 .