New Low-Rank Filters for MIMO-STAP Based on an Orthogonal Tensorial Decomposition

We develop in this paper a new adaptive low-rank (LR) filter for MIMO-space time adaptive processing (STAP) application based on a tensorial modeling of the data. This filter is based on an extension of the higher order singular value decomposition (HOSVD) (which is also one possible extension of singular value decomposition to the tensor case), called alternative unfolding HOSVD (AU-HOSVD), which allows us to consider the combinations of dimensions. This property is necessary to keep the advantages of the STAP and the MIMO characteristics of the data. We show that the choice of a good partition (as well as the tensorial modeling) is not heuristic but have to follow several features. Thanks to the derivation of the theoretical formulation of multimode ranks for all partitions, the tensorial LR filters are easy to compute. Results on simulated data show the good performance of the AU-HOSVD LR filters in terms of secondary data and clutter notch.