A Survey on PARATREE and SUSVD Decomposition Techniques and Their Use in Array Signal Processing

Abstract

The present manuscript is intended to review few applications of tensor decomposition model in array signal processing. Tensor decomposition models like HOSVD, SVD and PARAFAC are useful in signal processing. In this paper we shall use higher order tensor decomposition in signal processing. Also, a novel orthogonal non-iterative tensor decomposition technique (SUSVD), which is scalable to arbitrary high dimensional tensor, has been applied in MIMO channel estimation. The SUSVD provides a tensor model with hierarchical tree structure between the factors in different dimensions. We shall use a new model known as PARATREE, which is related to PARAFAC tensor models. The PARAFAC and PARATREE both describe a tensor as a sum of rank-1 tensors, but PARATREE has several advantages over PARAFAC, when it is applied as a lower rank approximation technique. PARATREE is orthogonal, fast and reliable to compute, and the order of the decomposition can be adaptively adjusted. The low rank PARATREE approximation has been applied to measure noise suppression for tensor valued MIMO channel sounding measurements.