PROJECT TITLE :
Coupled Canonical Polyadic Decompositions and Multiple Shift Invariance in Array Processing - 2018
The canonical polyadic decomposition (CPD) plays an necessary role for signal separation in array processing. The CPD model needs arrays composed of many displaced but identical subarrays. Consequently, it's less appropriate for more advanced array geometries. In this Project, we have a tendency to make a case for that coupled CPD permits a much a lot of flexible modeling that can handle multiple shift-invariance structures, i.e., arrays which will be decomposed into multiple but not identical displaced subarrays. Each deterministic and generic identifiability conditions are presented. We conjointly purpose out that, underneath gentle conditions, the signal separation downside can in the exact case be solved by suggests that of an eigenvalue decomposition. This can be like ESPRIT, though the operating conditions are a lot of more relaxed. Borrowing tools from algebraic geometry, we derive generic uniqueness bounds for L-shaped, frame-shaped, and triangular-shaped arrays that return close to bounds that are necessary for uniqueness. Recognizing multiple shift invariance can be a bit of an art by itself. We have a tendency to justify that any centrosymmetric array processing drawback will be interpreted in terms of a coupled CPD. Additionally, we have a tendency to demonstrate that the coupled CPD model permits us to considerably relax the far-field assumption commonly employed in CPD-based array processing.
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