Data Driven Algorithms for the Estimation of Low Rank Signals in Structured Subspaces
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In this thesis, we focus on both the design and analysis of new singular value decomposition (SVD) based algorithms for problems arising in array processing.
We show that for a single source, in the presence of noise and randomly missing samples, the Multiple Signal Classification (MUSIC) estimate is consistent. We derive an analytical expression for its mean square error performance, valid in both sample rich and deficient regimes. We show the existence of a critical SNR and observed fraction of entries below which MUSIC algorithm breaks down.
We propose new algorithm for the estimation of single clutter source subspace, for STAP and MIMO STAP. These algorithms exploit the double (STAP) or triple (MIMO STAP) Kronecker product structure of the underlying singular vector. We quantify the relative estimation performance of the algorithms, and their breakdown points. We discover that first using SVD and then exploiting Kronecker structure yields the best estimation performance.
We derive optimal (rank one case) and approximate (higher rank case) shrinkage weights that improve the performance of SVD based beamformers, and approximate shrinkage weights that improve the estimation performance of low rank tensors. We propose data driven algorithms for their computation. Throughout, we validate our analyses with numerical simulations.